THE USE OF COMMUNITY DIVERSITY
FOR MONITORING TRENDS
IN WATER POLLUTION IMPACTS
B. Dennis and G. P. Patil
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THE USE OF COMMUNITY DIVERSITY FOR MONITORING
TRENDS IN WATER POLLUTION IMPACTS
by
B. Dennis and G. P. PatII
1208 South Garner Street
State College, PA 16801
Draft of the Final Project Report on the Use of
Community Diversity for Monitoring Trends in Water
Pollution Impacts - Environmental Protection Agency,
Program Evaluation Division, Washington, D. C.
Project Officer: William V. Garetz
Contract No: WA-6-99-2448-A.
A WORKING DRAFT
December 3, 1976
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THE USE OF COMMUNITY DIVERSITY FOR MONITORING
TRENDS IN WATER POLLUTION IMPACTS
PART A
IS COMMUNITY DIVERSITY A USEFUL CONCEPT FOR
MONITORING TRENDS IN WATER POLLUTION IMPACTS?
PART B
LITERATURE REVIEW OF COMMUNITY DIVERSITY AND BIOMONITORING
by
B. Dennis and G. P. Patil
Draft of the Final Project Report on the Use of Conmunity Diversity
for Monitoring Trends in Water Pollution Impacts - Environmental
Protection Agency, Program Evaluation Division, Washington, D. C.
Project Officer: William V. Garetz
Contract No. WA-6-99-2448-A
A WORKING DRAFT
December 3, 1976
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CERTAIN QUOTABLE QUOTES
"For top management and general public policy development,
monitoring data must be shaped into easy-to-understand indices
that aggregate data into understandable forms. I am convinced
that much greater effort must be placed on the development of
better monitoring systems and indices than we have in the past.
Failure to do so will result in sub-optimum achievement of goals
at much greater expense" . . . Russell E. Train.
"Monitoring the environment requires a working knowledge of
all its parameters and regular sampling of at least the most
important ones. There are often insufficient funds or staff for
this to be done properly by human agencies, but the plants and
animals which spend their lives there necessarily carry out a
continuous monitoring program, reporting on conditions by their
presence or abundance" . . . D. Reish.
"It is only as a result of thorough and continuous study
of an environment and the species living in it that one can
venture to describe the quantitative changes in the natural
environment by changes in the quantitative abundance of specific
kinds of species" . . . R. Patrick.
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THE USE OF COMMUNITY DIVERSITY FOR MONITORING TRENDS
IN WATER POLLUTION IMPACTS
Table of Contents
PART A : IS COMMUNITY DIVERSITY A USEFUL CONCEPT FOR MONITORING TRENDS IN
WATER POLLUTION IMPACTS? 1
1. Introduction and summary 2
2. Mathematical formulations of community diversity 6
3. Ecological theory and community diversity 9
4. Empirical studies and community diversity
5. Selected group of organisms versus all taxonomic groups 19
6. Biomass versus numbers of individuals 24
7. Artificial substrates versus natural sampling 31
8. Sampling many habitats versus sampling few habitats 33
9. The importance of taxonomy 35
10. References 38
PART B : LITERATURL REVIEW AND BIOMONITORING OF COMMUNITY DIVERSITY 42
APPENDIX: PROCEEDINGS OF THE NINETH INTERNATIONAL BIOMETRIC CONFERENCE. HELD
AT BOSTON, AUGUST 22-27, 1976. AN INVITED PAPER ON: ECOLOGICAL
DIVERSITY: CONCEPTS, INDICES, AND APPLICATIONS by G. P. Patil and
C. Taillie. 104
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PART A
IS COMMUNITY DIVERSITY A USEFUL CONCEPT FOR MONITORING
TRENDS IN WATER POLLUTION IMPACTS?
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1. INTRODUCTION AND SUMMARY
Man's activities are having important and little understood impacts on
aquatic communities. There is great need for the development of an applied
science of ecology. Ecological systems analysi-s currently are constructing
complex mathematical models in efforts to predict the responses of population
sizes to environmental disturbances. But the efforts have had only limited
success so far, as the biological processes at work in a community are compli-
cated. The need for environmental action, though, is critical, and existing
technology should je put to work. The understanding of ecosystems that is
available at present is fragmented at best, but what understanding there is
must be assembled and put to use in coping with environmental problems. By
some ecologists (eg. Hurlbert, 1971) community diversity is considered an
empty concept and, an imperfect technology; but the use of diversity in
biomonitoring is state-of-the-art knowledge that will find valuable if stop-
gap, applications.
A collection of individuals of the same species is called a population;
a collection of populations is termed a community. Each species population
consists of organisms that have become adapted to their habitat over a long
evolutionary history. Typically each species has d^ts own range of tolerances
to environmental factors. The organisms in the population will thrive if
these factors, such as temperature, pH, and dissolved oxygen, never exceed
lethal extremes. Other species are also important environmental factors, as
the abundance of a population will be affected by interactions with other
species in the community. These interactions may take such forms as predation,
parasitism, competition, and grazing.
Pollutants as well as most other environmental factors, actually act at
the level of the individual organism. If an organism is not adapted to thrive
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in an environmental disturbance, that organism's ability to grow, reproduce,
or compete in the community will be affected. The cumulative effects of
environmental perturbations on many organisms will result in changes in popu-
lation sizes in the community. The impacts of pollutants on an aquatic commu-
nity are manifested as shifts in population sizes in that community. Some
species that are pollution intolerant may decline, perhaps to extinction, while
other pollution tolerant species, perhaps newcomers, may increase in abundance
in response to environmental disturbances.
If it were possible, a community would be best characterized at any given
time by a vector of population sizes. Monitoring water pollution impacts would
then amount to following the changes in population sizes as the organisms
responded to the various environmental factors. However, obtaining estimates
of all the population sizes in a community would be a massively difficult task,
and the cost and manpower necessary to obtain these estimates make this approach
prohibitive for biomonitoring.
The concept of community diversity is useful now in biomonitoring essentially
because of the limitations of current field sampling procedures. It is difficult
if not impossible to monitor absolute population sizes in a biological community.
But through a sampling of a portion of a community we may obtain good estimates
of the relative abundances of the populations in that community. We characterize
the community by a vector of percentages or fractions of the total community
abundance with one element for each species:
nl n2 ns
• •
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4
Measures of community diversity, at least the ones most important to
biomonitoring, are basically indexes which signal when changes in the vector tt
occur. Diversity measures are of greatest value to pollution impact assessment
when the measures indicate that shifts in relative abundances of the species
in the community are taking place, as these shifts are results of changes in
the absolute population sizes themselves.
The question of whether community diversity is a useful concept for
biomonitoring should be considered on both theoretical and empirical grounds.
Ecological theory is needed in order to interpret a diversity change in terms
of impact of environmental stress on a community. A diversity fluctuation it-
self is not a direct impact of pollution, but an indicator which can signal
that events are taking place in the community which should be studied more
carefully. It will be emphasized in this report that a diversity index is not
a substitute for skilled field biological work, but diversity can be a useful
warning to the investigators to examine the community in depth. The response
of diversity to water pollution must also be backed by empirical evidence if
the technique is to be meaningful. Preferrably, controlled tests should be
performed to answer specific hypotheses about the relationships of community
diversity and environmental pollutants. Investigators must also be able to
distinguish pollution-caused diversity changes from those of natural causes
through attention to sampling methods (see Energy Resources Company report
for a thorough review) and statistical methods. Usefullness of diversity will
depend furthermore on the practicality of gathering data in a routine fashion.
Finally, whether diversity is useful or not will depend on. whether the concept
is applicable to the vast assortment of organisms of many different phyla
that are typically present in aquatic communities.
The first section of this report contains some comments on the variety
of diversity indices chat are available, and calls attention to some recent
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work which shows how certain diversity indices are conceptually similar.
The second and third sections of this report are reviews of the theoretical
and empirical justification of using community diversity for monitoring
trends in water pollution impacts. Other sections consider the sampling of
different tara or trophic levels, the use of biomass versus the numbers of
individuals, artificial substrates, sampling different habitats, and the
importance of identification of species.
The broad conclusions of this report are based on a careful study of the
existing literature on ecological diversity and biomonitoring. These
conclusions are as follows:
1. Community diversity is a useful concept for monitoring the impacts
of water pollution on biological communities. The application of diversity
in a biomonitoring program is justified both theoretically and empirically.
2. Community diversity may not be taken as a direct index of water quality
as such, but can be used to study the impact of water quality on aquatic organisms.
3. Trained field ecologists will be needed to gather data and interpret
diversity changes in terms of environmental impact. Investigators should be
able to design simple experiments on-location, as some basic research will be
needed at many stations to familiarize the investigators with the local commun-
ity processes. Taxonomic work is unavoidable, but workers can become familiar
with the species at a specific locale in a few months time.
4. Diversity alone is not adequate for assessing the overall biological
impact of water pollution, but diversity can be invaluable in signalling when
or where further work is needed.
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2. MATHEMATICAL FORMULATIONS OF COMMUNITY DIVERSITY
There is no shortage of literature on the various mathematical formulations
and statistical methodology of diversity indices. Statisticians and ecologists
alike have proposed many diversity formulas for use in ecology, to the extent
that the concept of ecological diversity must be defined in terms of the
particular index in question. Indeed, the number of measures of community
diversity that have been proposed have outstripped the need for such measures
in ecological theory and practice.
The Energy Resources Company report gives an account of the properties of
several of these indices; Pielou (1975, 1974, 1969) has written extensively on the
subject and her works, along with the ERCO report should be consulted. We will
not duplicate that material here, but wish to point out that certain diversity
indices which are important to biomonitoring have a common conceptual basis.
One of these diversity indices is simply the number of species in the
community, S. This quantity, sometimes referred to as "species richness," is
equated conceptually with diversity by some field ecologists (Whittaker 1972).
The number works better as an index if the diversity is computed as S-l, so that
the diversity is 0 when the number of species in the community is only 1. If the
number of species in the community is large (above 50 or so) and the community has
a logrormal abundance distribution, then the Shannon diversity formula will be
almost totally dependent on this number of species (May^l975). Such large numbers
of species and lognormal distributions are common in diatom communities (Patrick
et al., 1954).
Another diversity index is Simpson's formula, where is the relative
(percentage) abundance of the ith species. This quantity is of particular importance
to biomonitoring as the quantity can be estimated with the sequential sampling method
of Cairns (1968), which involves little or no taxonomic training (see Patil and Taillie
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1976 and the ERCO report). Simpson's index has the disadvantage of "saturating"
at values very close to 1 as the number of species in the community increases
above 50 or so (ERCO report).
The index most often used by ecologists in field studies is the Shannon formula
-I ir log This function has many desirable properties which make it useful in
field research and biomonitoring (ERCO report, Pielou 1975). However, ecologists
have felt somewhat uncomfortable with the conceptual basis of this function; the
relevance of "information theory" to a living community has been questioned
(Pielou 1975).
Patil and Taillie (1976) have recently shown that these three diversity indices
have a common conceptual basis. A single species, say species i, will be rare in
a community to a greater or lesser extent compared with other species. The "rareness"
of species i could be thought of as some decreasing function, R(tt^) , of that species'
relative abundance, tt^. Here are some possible candidates for'the exact functional
form of R(tt^) (see figure ) :
y
y+i
Starting with species i, an investigator randomly encounters individual members of
the community (as in Cairns' sequential sampling method). Y is the number of
encounters needed to find another individual of species i and is a random variable.
Then R(iri) , the rareness of species i, might take these forms:
1.) R1(iTi) - E[Y/tt^] - (1-tt^/t^ ; or
2.) R2(tt1) - E[Y/tt1 ]/E[Y+1/tt1] - (1—tt±) ; or
3.) R3(tt±) - E[~-/TTi]E[Y/ir1] - -log
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According to Patil and Taillie, the diversity of a community is the
average rareness of that community, depending on how rareness is measured.
1.) E[R^(iT^) ] - ZjTT.jR^Ctt^) 31 S-l, the species count;
2.) E[R2] = EjTT - Z^Cl-T^) , Simpson's index;
3.) E[R^(iri)] = EjTTjR (ti^) = log 7^, Shannon's index.
Thus, these three diversity indices arise from the same concept of average
rareness. In particular, ecologists need not invoke "information theory" as a
conceptual basis for the Shannon formula.
Summary and Recommendations
1. Certain references, in particular Pielou (1975) and the ERCO report, have
thoroughly delineated the properties of many diversity indices.
2. Three indices are of particular importance to biomonitoring; they are the
species number, Simpson's index, and Shannon's formula. These indices are linked
by an underlying concept of average rareness.
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3. ECOLOGICAL THEORY AND COMMUNITY DIVERSITY
It is helpful to briefly examine the current state of ecological theory on
diversity. The critical task in the use of community diversity for biomonitoring
is ttat of Intorp re cation; fluctuations ii comnunity diversity may arise frc:i a
large number of ecological causes. The ups and downs of a diversity index plotted
on a chart will provide little information on the actual impact of water pollution
on the community. But those fluctuations will provide signals that events in the
community are taking place. If unexpected or long-term diversity shifts occur,
then the specific ecological factors which are causing the diversity change can be
determined.
Diversity indexes such as the Shannon and Simpson formulas will be sensitive
to those community changes which will alter the relative abundance vector IT, with
one or two exceptions. These diversity indexes will not be sensitive to these
possible, but unlikely, community changes:
1. The abundances of species change according to some constant proportion.
This would happen if for some reason a pollutant killed a constant fraction
of each species present; that is, if
ni n2 ns
J- *' • ' §.\ „ / _£.» • • •» 8\ _ _
11 kn kn kn n n n '
Such a change would not be detected with either the Shannon or Simpson
diversity formulas. However, it is very unlikely that a pollutant would
affect the different species in exactly the same amounts. Species for
the most part will differ in their pollution tolerance.
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2. The abundances of species change so as to permute the elements,
tt_£, of the relative abundance vector. For instance, if a community
had the abundance vector
_ ,50_, 3o_> = rk> A_. 2-)
~ ~ K100 100 100J 2 10 10}'
and species 1 declined by 20 iudivlduals and species 2 gained 20
individuals, then the resulting community vector would be
TT1 = r30_> 50_, 20_ = ,3_, 1, 2_
~ UOO 100 100'' v10 2 nr *
The Shannon or Simpson indexes would be the same for J and But
this event is also very unlikely in a community.
3. New species replace old species in such a fashion as to leave the
TT vector unaltered. If for some reason a new species had established
itself in the community in exactly the same abundance as a species that
had gone extinct. Again, such an event is unlikely.
4. The community alters such that change in species number offsets
change in "evenness." If this occurred the community vector u with s
elements would become a new vector, tt^" , with some different number of
elements; corresponding changes in the evenness of the elements make up
for any diversity difference. This has happened in at least one field
study. Logan and Mauer (1975) reported the diversities of stations
located above and below a thermal effluent; stations below the effluent
showed a slight (not significant) diversity increase. The species
numbers at the below-effluent stations were low, however, and the
diversity had been kept high by the increased evenness of the remaining
species.
Thus it is important for the investigator to be aware of the nature of the
community changes and how they are affecting the diversity index. Important changes
in the community conceivably could go undetected if diversity is the only Item being
looked at. And when a diversity shift does occur the specific community changes
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that are responsible for the shift should be examined.
What kinds of community events are picked up by a diversity index? Formulas
such as the Shannon or Simpson will be responsive to events such as these:
1. Irregular changes in the absolute abundance of species in the
community. The vast majority of such changes will affect the evenness
of the community vector, and hence affect the diversity index.
2. Net changes in the number of species in the community. This
would happen if the number of colonizing species did not equal the
number of extinctions in the community.
Are there any patterns to be expected in these community events? Whittaker
(1972) has given an extensive review of ecological diversity and the factors which
affect it in communities. According to Whittaker, the process of competition is
very important to the evolution of a given diversity level in an ecosystem. Resources
in communities are essentially scarce and species must compete for resources to
survive. Given a resource gradient, such as prey size, substrate type, or light
intensity, species gradually evolve to utilize different portions of this gradient,
that is, species become specialized enough to out-compete other jpecies for portions.
Species which are so adapted can establish themselves in a community by "fitting in"
between other species on the same resource gradients and commanding those portions
for themselves. This is known as "species packing" in the ecological literature.
As the resources are divided up among species, the portions or amounts that a
species can preempt for itself may be reflected in that species' absolute abundance
in the community. Thus the relative abundance distribution of a community may
reflect a mechanism by which the resources are being divided in the community. When
the elements in the it vector are ordered from largest to smallest, mathematical series
formulas can be used as models for relative abundance. Two models in particular have
been found to closely represent field data for a wide variety of communities (see
Whittaker 1972 and May 1975 for extended discussions) :
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1. The geometric series is often the form of the relative abundance
distribution for communities in harsh or marginal environments; it
occurs also when a perviously unexploited resource is being colonized.
This distribution arises when a first or dominant species preempts a
fraction k of a resource, the next species takes the same traction of
the remainder, and so on.
2. The broken stick series is the form of the relative abundance
distribution when a group of species apportion a resource essentially at
random. It is found most often only for closely related species.
Both the above patterns of relative abundance only occur for the most part in
communities with few numbers of species. A different pattern is found in communities
with large numbers of species that are not closely related in resource use. It is
the lognormal distribution (again see VThittaker 1972 and May 1975) and it is a
species abundance distribution. This pattern has been found in many communities in
nature (Preston 1948, 1962, Patrick et al 1954; Whittaker 1965). The distribution
reflects the fact that large numbers of relatively independent factors may be
governing the abundances of the species in the community (May 1975). In biomonitoring,
samples of large numbers of species of diatons will likely have this pattern (Patrick
et al 1954).
I:i the event of an environmental disturbance, shifts in abundance patterns may
be expected to occur in a community. Ruth Patrick has developed a method of bio-
monitoring for use with diatoms which involves fitting a lognormal curve to the
species abundance data, rather than (or in addition to) computing diversity (see
Patrick, et al, 1954).
According to current ecological theory, if pollution - intolerant species
decline in abundance, resources may be left unutilized. The pollution tolerant
organisms then find themselves with a lack of competition for space, nutrients, or
other resource, and they can rapidly increase in numbers. Also, new pollution
tolerant organisms may be able to colonize the community, but many more sensitive
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species generally go extinct altogether. The resulting community abundance pattern
of heavy dominance and fewer species gives the characteristic decline in diversity
observed so often in the field (see section ).
Disruptions in community food chains can cause shifts in relative abundance.
Paine (1966) has found that predation may allow high diversity levels to be
maintained if a predator eats a dominant competitor in the community. The predator
("keystone species") regulates the growth of the competitor by eating it, thus
making available resources for other species.
In contrast, Kushlan (1976) found that preditors could actually reduce the
diversity of species at lower trophic levels, simply by eating the prey species to
extinction.
Investigators in biomonitoring programs should look for community events such
as these when a change in diversity occurs. The information thus gathered will help
greatly in forming more detailed, applied theories of the impact of pollution on
aquatic communities.
SUMMARY AND RECOMMENDATIONS:
1. Investigators should be aware of the types of community fluctuations that can
occur, and should try to explain diversity change in terms of its component events.
Diversity is seen as an indicator that a biological community is experiencing
environmental impact; diversity itself is not seen as an impact.
2. Investigators should be aware that certain types of community events could go
undetected if only diversity is used for monitoring the community. Perhaps more
importantly, the investigators should become very familiar with the specific habitats
being monitored as each habitat will have its own peculiar ecological events.
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4. EMPIRICAL STUDIES AND COMMUNITY DIVERSITY
According to the ecologic theory in the pervious section, pollutants will
generally cause adjustments and alterations in species abundances and community species
composition. Furthermore, these adjustments should be detectable through use of an
appropriate diversity measure.
Is this assertion supported by field evidence? Investigators have reported
diversity index responses in a scattered but growing literature. The studies
indicate that diversity measures are indeed sensitive in general to the addition of
various pollutants to aquatic systems.
Howell and Gentry (1974) have shown that thermal effluents from a nuclear power
plant decreased the diversity of aquatic insects in the Savannah River in South
Carolina. Coutant (1962) reported a decline in diversity of macroinvertebrate riffle
organisms in the Delaware River due to heated-water effluents. Temperature shifts
in water are known to cause major alterations in the communities of algal flora in
streams (Patrick et al 1969) ; presumably these changes would be detectable if the
data were used to compute diversity. Johnson and Schneider (1976) have found that
slight long-term temperature alteration can cause significant changes in entire
communities; again such changes should likely show up in a diversity measure.
Wilhm (1967) concludes from a study that populations of benthic macroinvertebrates
can be used to assess pollution in a stream receiving organic wastes, and that a
diversity index is a clear and brief way to summarize the data.
Wilhm and Dorris (1966) studied the physicochemical conditions and benthic
macrionvertebrate diversity in a stream receiving domestic and oil refinery effluents.
They concluded that information theory diversity measures were more precise measures
of stream conditions as reflected by benthic macroinvertebrate populations than
traditional methods.
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Oil spills have been shown to reduce macroinvertebrate diversity in streams in
two field studies (Hoen et al 1974, 1975; Nauman and Kernodle 1975).
Williams (1964) reported the results of an extensive study that was conducted
at 103 stations scattered on the Great Lakes and the major rivers of the United States.
The numbers of species of diatoms at eutrophic stations were found to be generally
lower than the numbers at "clean" stations. Diversity measures were not used in this
report, but such community differences could probably be seen if the measures were
used.
Heavy metals find other toxic constituents of industrial and domestic waste
water significantly altered diversity of benthic organisms in a lake and stream in
Maine (Davidson 1974).
The species diversity of the benthic oligochaete fauna in a lake polluted by
acid mine drainage are significantly lower than the species diversity of a comparable
unpolluted lake (Orciari and Hummon 1975).
Swartz et al (1975) report the decreased diversity of marine macrobenthos as
an impact of sewage sludge.
The ERCO report cites several studies in the literature which appear to give
conflicting or contradictory evidence on the use of diversity in biomonitoring.
These papers merit closer attention here, for in reality no such conclusions should
be drawn from these studies about the use of diversity:
ERCO cites Ewing and Dorris (1970) as supportive of the usefulness of diversity
indexes, whereas this study was inconclusive. Ewings' and Dorris' study was
performed in artificial ponds, and they found that in general, algol species diversity
was not positively correlated with the nutrient concentrations in the ponds. But the
nutrient concentrations (dissolved nitrate, nitrite, phosphorous) were not significantly
different in the ponds and so no conclusions should be drawn about diversity indices
from this study.
The study by Winner (1972) was cited in the ERCO report as evidence against the
use of the diversity concept in biomonitoring. Winner was evaluating various indexes
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of eutrophy and maturity in lakes of different ages in effect testing various
assertions by E. Odum and Margalef that diversity, P/B ratio, pigment ratio, and
assimilation number will be affected as a lake undergoes its natural succession.
Margalef's and Odum's theories of ecological succession have not been supported
by field data through the years (Colinveaux, 1973) and seem to be less accepted now
among ecologists. Note that Winner was not investigating the response of the lake
biota to man-induced or sudden environmental stress. The aquatic community could
respond differently to a sudden or artificially higa nutrient load as compared to
the nutrient buildup of a gradual system aging process.
ERCO pointed out that Logan and Maurer (1975) found an increased diversity of
macroinvertebrates in a thermal effluent. But Logan and Maurer may have been dealing
with very different communities at each of their sampling sites. Their four sites
(one above, 3 below the thermal outflow) were located in an estuary along an increasing
salinity gradient. The species compositions at the sites were somewhat different from
each other. And the site locations varied from close to shore in a relatively
narrow river to out in the middle of a bay, which suggests that the investigators
were sampling different habitats. Finally, though diversity as measured by Shannon's
formula did not decrease significantly in the thermal effluent, the number of species
did decrease. This indicates that one aspect of diversity, the evenness or equitability,
actually increased while the species number aspect of diversity decreased. The study
is an example of one of the exceptional community events mentioned earlier which might
go undetected if the data aren't analyzed further than merely computing diversity.
We wish to point out that there is a fundamental distinction between two potential
uses of diversity in biomonitoring. The first use of diversity occurs when an
investigator is interested in this question: given that a known pollutant is present
in the system, are there consequences taking place in the natural community? Diversity
is used in this case to assess impact of pollution on aquatic communities. The other
question that might be of concern to an investigator is: "given that changes have
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taken place in the community, is there a pollutant present in the system?" Diversity
here is used as an indicator of water quality.
The field studies mentioned above generally support the use of community diversity
in the first sense. The investigators in these studies usually measured diversity above
and below pollution outflows, so that a pollutant was known to be present in the water
for these studies. In almost all cases clear community impacts could be demonstrated
with the use of diversity measures. We conclude that diversity measures are among the
best tools available for monitoring water pollution impacts on biological communities.
The validity of the use of diversity in the second sense, i.e., as a water quality
index, still remains an open question. Wilhm and Dorris (1968) go so far as to propose
the establishment of water quality criteria by the evaluation of biological conditions
in receiving streams. They claim that values of diversity less than 1 (Shannon
formula with logs taken to base 2) have been obtained in areas of heavy pollution,
values from 1 to 3 in areas of moderate pollution, and values exceeding 3 in clean
water areas. On the other hand, Swartz et al (1976) state that structure analysis
provides an exceptionally good method for assessing ecological alterations at specific
sites, but quantitative criteria s-ich as diversity indices should not be used as
universal regulatory standards.
On the basis of available data the position of Swartz et al seems preferrable to
that of Wilhm and Dorris. Aquatic habitats are extremely varied in their environmental
conditions from one area to another, and the natural communities present in each area
consist of organisms uniquely adapted to these local conditions. Thus what may be a
high diversity figure for one stream may be a low figure to another stream with different
conditions and organisms. The natural diversities of two completely different areas
are essentially uncomparable quantities; establishing water quality criteria on the
basis of diversity indices seems unwarranted at this time.
Additionally, the number of studies which use diversity to evaluate pollution
impacts is remarkably small to date. There are a vast number of chemical substances
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which pollute water at a great many concentrations, and quantitative field studies
using diversity have been performed for relatively few of these contaminants. In
this regard much of the data gathered in a biomonitoring program will be new infor-
mation for ecologists.
The ERCO report concludes, as a result of their own evaluation of the literature:
"Because of the contradictory nature of some of the diversity studies, it is highly
doubtful whether diversity indices in their present form will serve as useful indicators
of water quality." Perhaps this statement by ERCO is too pessimistic, for the field
work done to date on diversity measures seems to give fairly consistent results. It
is reasonable to think that an aquatic ecologist could very well monitor water quality
trends in a particular area after the investigator had become thoroughly familiar with
the local biota and natural conditions. To quote Ruth Patrick: "It is only as a
result of thorough and continuous study of an environment and the species living in it
that one can venture to describe the quantitative changes in the natural environment
by changes in the quantitative abundance of specific kinds of species." (Patrick 1963).
SUMMARY AND RECOMMENDATIONS
1. Empirical studies performed to date indicate that diversity measures are indeed
sensitive to the addition of various pollutants to aquatic systems.
2. Diversity measures are an excellent method of monitoring whole community impacts
of water pollution.
3. Diversity measures have not been studied enough to be used as indicators of water
quality.
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5. SELECTED GROUP OF ORGANISMS VERSUS ALL TAXONOMIC GROUPS
Should all taxonomic groups in a community be sampled, or may the
sampling effort be confined to a selected group of organisms? This
complex question is of obvious practical concern in a biomonitoring
program. Invariably, decisions at the present time on this question will
involve a conflict between biological concerns and costs. The reason for
this is the question has not been adequately researched.
The work done up to the present time indicates that as many taxonomic
groups should be sampled as are possible under the constraints of cost and
time. The investigations of Winner (1972) and Kushlan (1976) show that
the diversities of different taxonomic groups or different trophic levels
may behave in contradictory ways.
The diversity computations, however, should be confined to within
these groups, that is, diversity should be calculated separately for each
group. A diversity index calculated across a vast community of unrelated
organisms may not be sensitive to environomental impacts thai, affect some
groups but not others. The changes in numerical abundance that take place
in zooplankton are on a totally different scale from the changes in abun-
dance of, say, fish.
The work of Dickman (1968) illustrates the problems associated with
computing diversity across many different taxonomic groups. Dickman included
bacteria, phytoplankton, and zooplankton species in the diversity computations.
He used the Shannon formula H = - S TT^ log t.j as a diversity index: inter-
estingly he defined the values three separate ways. The first definition
used numbers of individuals to compute values, the second definition used
biomass, and the third used relative productivity.
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When biomass or numbers were used in the computations, the diversity
index failed to be sensitive to changes in the higher trophic levels in
the community. Dickman noted that over two thirds of the species encoun-
tered in a typical plankton sample had no significant effect on the diver-
sity of that sample when numbers of individuals were used. However, the
diversity index did respond to changes in the higher trophic levels when
the relative abundances Hi were defined in terms of productivity.
The way Dickman used productivity in this study is misleading and is
not recommended for biomonitoring purposes. Dickman failed to take into
account the important distinction between growth and reproduction in
computing the diversity of productivity: the relative abundance of the
ith species IT^ was defined as pr^/PR where pr^ was the productivity of
species i and PR was the total sample productivity. Productivity was
calculated by multiplying the mean sample density and biomass for species i
and then multiplying that product by the number of times that species i
reproduced in one year. This ignores the possibility that the mean mass
per individual in microbial proulations may undergo drastic fluctuations of
many orders of magnitude. Cell growth research has indicated that there is
only a loose connection between cell mass and cell division (Williams 1971).
Obtaining the true productivity values for many species in an aquatic system
would require techniques which are too costly and involved for use in
biomonitoring. In addition the use of true productivity values in diversity
indices is unresearched.
Dickman concluded that the Shannon-Weaver diversity formula fails to
reflect significant changes in a community's structure because it is only
sensitive to changes in relative abundance of a few of the trophic levels of
a community. This conclusion is somewhat incorrect; if the organisms at all
trophic levels happened to have comparable abundances then the diversity
index would be sensitive to changes in community structure. Most often,
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21
though, t^e organisms on the first level or two of the trophic pyramid
tent to vastly outnumber and outweigh the higher level carnivore popula-
tions. Obviously} if diversity is computed across a whole community of
many phyla and several trophic levels certain organisms will swamp the
diversity index with their relative abundance. This is what occurred
in the Dickman study when diversity was computed across a community of
bacteria, phytoplankton, and zooplankton.
Dickman's study indicates that the diversity calculations should
be confined to within single groups of organisms. Diversity as a concept
is most meaningful when applied to a "guild" of organisms. Guild refers
to a set of species which are utilizing a specific type of resource (Root 1967).
Generally the species in a guild are competing for the resource, or
partitioning the resource in some way such as along a gradiant. For the
purposes of biomonitoring groups which are naturally sampled as a unit such
as diatoms or benthic insects may be considered guilds. Each species out-
competes the others in the guild only along a certain portion of the resource
gradient; the resources are apportioned by competition. An environmental
perturbance such as a pollutant may kill intolerant species or may reduce
their ability to compete in the community. Pollution tolerant or unaffected
species would then increase in abundance because lack of competition would
allow them to broaden their resource utilization. A diversity index computed
for a single guild or group of taxonomically close species will likely reflect
these sort of changes in community structure.
But knowledge of diversity trends within one group of organisms may
not reflect the diversity trends within other groups in the same aquatic
system. Until difinitive research shows otherwise as many guilds should be
sampled and studied as are possible under cost constraints. Diversities of
phytoplankton, zooplankton, benthic insects, and fish should be computed
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22
separately and monitored. An investigator may wish to split these groups
further when cost and effort constraints permit as these broad groups contain
a large variety of organisms and are not strictly guilds as such.
Winner (1972) reported lack of correlations between phytoplankton and
zooplankton diversities in five Colorado lakes. The lakes were all different
in their relative degrees of eutrophication. Winner concluded that measure-
ment of diversity in one community of an ecosystem does not necessarily
indicate what diversities are in other communities of that ecosystem.
Further evidence that different groups of organisms should be monitored
separately is given by Kushlan (1976). Kushlan studied changes in fish
species diversity in the Everglades marshes and how such diversity was
affected by the degree of water level stability. The overall fish species
diversity increased during a prolonged period of high water and decreased
during regimes of fluctuating water levels. Kushlan looked further into
these trends by dividing the fish community into "functional groups." He
placed each species into one of three categories: small omnivores and
herbivores, small carnivores, and large carnivores. The separate diversities
of these groups responded differently to water level stability; combined as
one fish community the diversities summed to the overall results mentioned
above. The diversity of the small omnivores and herbivores decreased during
the stable high water period and increased during the fluctuating water
periods. The diversity of both carnivore groups increased during the stable
period and decreased during the fluctuating periods . Thus the diversities of
different guilds within the overall fish community responded differently to
environmental change.
More research is needed on this question of which taxonomic groups to
sample. Information on the effects of specific pollutants on specific groups
in aquatic communities will probably be available only after a national
monitoring effort has been underway for some time. In this sense field
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23
workers in a biomonitoring program should be capable of conducting on-site
research projects.
SUMMARY AND RECOMMENDATIONS
1. In a biological monitoring program, what little research there is
indicates that several guilds, taxonomic groups, or trophic levels
should be studied instead of just one group.
2. Diversity need not be computed across all these groups as the
abundances of different phyla are generally not comparable numerically
or conceptually.
3. Productivity - based measures of diversity are impractical in a
biomonitoring program.
4. Diversity should be computed separately within each of the groups;
each group diversity should be monitored and studied.
5. The information collected by field workers in a biomonitoring
program will be valuable for its research purposes as well as its
applied purposes.
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6. BIOMASS VERSUS NUMBERS OF INDIVIDUALS
In studying a biological community an investigator must decide whether to
use numbers of individuals or biomass in computing diversity. At first glance
ths problem s?c>bs a trivial one: if n: is thr number of individuals Jn species
i and m_^ is the total biomass of the species then these tvo quantities are
related to each other at any given time by the relation
where is the mean biomass per individual of species i. It would seem th<;n
that biomass-diversity and individuals-diversity would be closely related
measures in a community.
In fact, a biomass-diversity and individuals-diversity may behave very
differently from each other. Field studies by Wilhm (1968) and Kushlan (1976)
have shown that knowledge of trends in biomass-diversity is generally insufficient
to predict trends in individuals-diversity, and vice-versa. The two statistics
yield complimentary information about the aquatic life; an investigator may wish
to gather the data to compute both. In biological monitoring the critical task
is to interpret a diversity change in terms of an impact on the community.
Knowledge of both biomass- and individuals-diversity will aid an investigator in
this interpreting task.
One reason why these two diversity measures are different is the fact that
the mean biomass per individual of species i, m^, varies from one species to the
next. The relative abundance of the biomass of species i, therefore, may be
substantially greater than or less than the relative abundance of individuals of
species i:
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25
where Is relative abundance of biomass; 7T^ is relative abundance of
numbers; me is total community biomass; n is total numbers of Individuals
in the community. The when m^,n < m and > tt^ when m^n > m. Both
these cases are biologically meaningful; the B^ values for all species
i « 1,2,... , s will be greater than or less than the tt^ values depending on
the corresponding values. This means that the community biomass vector
3 = (B,, B„, ..., B ) may be practically unrelated to the individuals vector
12 s
TT = (ir1 ,tr0 ,.. . ,tt ), other than the fact that both contain the same number
^ J. z s
of elements and that all the elements in each sum to unity. Any diversity
Index for which evenness or equitability is important will likely be different
for both B and J.
Another important problem arises from the fact that the mean biomass per
individual, m^, may vary through time for any given species. To complicate
matters the changes seen in are often not related to the changes in numbers
of individuals n^. Individuals of a species could become larger in size but
less abundant; thus n^ would decrease when m^ was actually increasing. To
illustrate the effects of this process on ecological diversity consider a
community of n total individuals and m total biomass. The relative abundance
vector using numbers would be
TT - ( "1 "2 ... "s ) = (7^ 7T2 . . . .
n n n
Similarly, the relative abundance vector using biomass would be
g „ ( ®1 ®2 ,.. ) = (Bi B2 ...Bg).
mm m
We assume that both vectors have their elements arranged in order of relative
abundance, that is
n, > n„ >...> n , and m, > >...> m .
1—2— — s 1—2— — s
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26
Then suppose the biomass of species 1 decreases by an amount over a time
interval, while the biomass of species 2 increases by that same amount :
„ ^ , m -e m +e m m
B « ( 1 2 3 .. . s ) .
m m m m
This would mean that the diversity of B^ had become larger than that of B
according to the criteria of Patil and Taillie (1976) for diversity indexes.
But it is entirely possible that species 1 could increase in numbers during
the same interval, with the average mass per individual declining. The
diversity of the vector tt would then decline; that is, if
/ n,+k n« ri %
tt = ( 1 2 .. s ; ,
n+k n+k n+k
then the diversity of tt^ is less than that of tt if an evenness-sensitive
index is used. In general, if the diversity of one of the vectors g or J
changes, the other vector may not change in the same fashion.
Very little attention has been paid to this question of biomass versus
numbers by ecologists. The underlying problem is that growth and reproduction
are different processes in living things. These processes are affected
differently by the various environmental factors. In particular, there seem
to be no studies which have looked at specific pollutants and distinguished
their effects on biomass- and individuals-diversity.
Wilhm (1968) gives empirical evidence that biomass- and individuals-diversity
may change in different fashions. Wilhm studied a benthic macroinvertebrate
community in a small Tennessee spring. Essentially two habitats existed in the
spring for benthic organisms; one area of the spring was choked with vegetation
and the other area was open. Wilhm sampled each of the two habitats monthly;
the benthic organisms were sorted by species, counted, and weighed.
Wilhm stated that "differences were noted when biomass units were used
instead of numbers." In the open areas of the spring, one species tended to
increase its total biomass and decrease the biomass diversity. That same
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27
species also increased its mean weight per individual, so that its numbers
did not increase very much. As a consequence, individuals-diversity tended
to be higher in the open areas. In the vegetation-choked areas, the biomass-
and individuals-diversity changed in the same directions. However, individuals-
diversity showed much more pronounced fluctuations, while the blomass
diversity in the choked area remained relatively constant. Finally, Wilhm
noted that biomass per individual tended to vary monthly within many species.
Kushlan (1976) has recently reported more differences in individuals-
and biomass-diversjty trends, this time in the fish community of the Everglades
marshes. Kushlan's study suggests that both biomass- and individuals-diversity
should be obtained when possible, for they both contain important and compli-
mentary information about changes in a biological community. Kushlan found
that during a several year period of stable environmental conditions, individuals-
diversity tended to increase among the fish. However, biomass-diversity decreased,
and the mean weight per fish increased over the same period. These trends all
reflected a shift of the fish community to a large predator dominated system;
stable water levels allowed large carnivore fish to thrive in uhe community.
Kushlan states: "The different pattern of biomass diversity shows that the
changes were more complicated than the mere redistribution of relative abundances."
Kushlan paid particular attention to interpreting the diversity changes in
the Everglades fish community. He separated the fish into trophic groups (see
section ) and followed the diversity trends of each group separately. He
measured the changes in average fish size as well as kept track of the species
composition. Ir this way he was able to sort Out the ecological processes or
events that were taking place in the community which were causing the community
diversity to shift.
What ecological processes cause changes in m^? The mass of an organism
increases through uptake and assimilation of materials (nutrients) and decreases
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28
with processes such as respiration and excretion. Numbers of individuals in
a population are affected by births, deaths, immigration and emmigration. Any
environmental perturbation which affects these processes differentially will
probably cause discrepancies between the biomass- and the numbers-diversity in
the community.
Almost nothing is known about the relationships between numbers and mass
of organisms. What little is known comes from research on populations of
single cells. Williams (1971) proposes this concept of a cell:
The cell comprises two basic portions, a synthetic portion and a
structural/genetic portion.
1. The synthetic protion (s) increases by uptake
of externally available nutrient (c).
2. The structural/genetic portion increases in turn
from the materials in the synthetic portion.
3. Total cell mass M = S + N
4. The cell divides into d daughter cells only
when the N-portion of the cell has become d
times its initial size.
C
This means that the size of the S portion of the cell, and hence the overall
size of the cell at division, is not uniquely determined* Results of cell
growth experiments indicate that the N and S portions of cellp are only loosely
coupled. The implication is that growth and reproduction in populations are
loosely related processes. These statements hold true for single cell populations;
the statements may or may not be true for multi-celled organisms.
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29
Further research will be needed to delineate the effects of specific
environmental pollutants on biomass- and individuals-diversity, as well as to
delineate the relationships between growth and reproduction in communities.
Investigators will then be able to make decisions between use of biomass or
use of individuals on the basis of which index is the most sensitive to the
specific pollutant. For instance, in single cell populations the process of
reproduction is affected by changes in temperature far more than growth is
affected (Williams 1971). It is possible then that individuals-diversity may
be a more sensitive indicator of thermal pollution than biomass-diversity, but
this question will need testing. The data from a biomonitoring program in
which both biomass and numbers are used will be invaluable in addressing these
problems.
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3U
Summary and recommendations
1. Theory as well as field studies by Wilhm (1968) and Kushlan (1976)
indicates that biomass-diversity and individuals-diversity can often
behave in different fashions in a biological community.
2. The differences in response of these two diversity measures is largly
due to changes in m^, the average mass of an individual of species i. Shifts
in species composition of a community can also cause discrepancies between
biomass- and individuals-diversity.
3. The quantity 5u is affected by two fundamentally different processes:
growth and reproduction.
4. Growth and reporduction are probably loosely related, and are affected
differentially by various environmental factors.
5. An investigator in a biomonitoring program should compute both biomass
diversity and individuals diversity if possible. The investigator should
also keep track of m^ for each species as well as the community species
composition. These efforts will:
a) aid in the task of interpreting biological impact of pollutants, and
b) be invaluable in answering basic ecological questions on growth and
reproduction.
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7. ARTIFICIAL SUBSTRATES VERSUS NATURAL SAMPLING
Artificial substrates can only be used for those aquatic organisms that
will colonize various surfaces by attaching, rooting, or burrowing. This
rules out fish, ^ooplankton, and phytoplanktcn that do not attach themselves
to substrates. Various types of algae, such as diatoms, and bottom dwelling
organisms can be sampled with artificial substrates.
Several considerations must be weighed in deciding to use an artificial
substrate for biomonitoring:
1) The technique must be scientifically defensible, that is,
the effects of pollution on the substrate organisms should be
comparable with the effects on the natural community. The
investigators must determine that the artificial substrates
are not propagating "artificial communities."
2) The convenience or savings on cost must be substantial
enough to warrant using an artificial substrate instead of
some other sampling method. This consideration, however, must
be subservient to 1).
3) The colonization time will have to be taken into account.
An unutilized substrate will require a certain amount of time
before enough species have established themselves for a good
sample. This colonization period will cause delays in the
gathering of the data.
Diatoms can be sampled with ordinary glass microscope slides that are
placed in the water for two weeks. This method was developed by R. Patrick
and has been extensively tested (Patrick et al. 1954; Patrick 1963; Patrick
1968). The costs of this method are minimal and the colonization time (about
14 days) is reasonable for most purposes. J. Cairns has described a modifi-
cation of the sequential sampling technique for estimating diversity which
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32
can be used while scanning the diatom slides with a microscope (Cairns 1968).
Benthic organisms can be sampled with baskets or trays of bottom
materials such as rocks, mud, and sand (Cummins 1962, Cooke, 1956, Wene and
Wickliff 1940) , or with mats of artificial moss made out of string (Glime
and demons l'J?2). These artificial substrate techniques for benthic organ-
isms have several drawbacks. First, a long colonization time of up to 30
days may be necessary (Wene and Wickliff 1940). Second, the number of
individuals on the artificial substrates tends to be less than on the natural
substrate (Glime and demons 1972). Third, the techniques have not been
tested as biomonitoring tools. Finally, there are effective alternatives
in sampling methods available for the natural sampling of benthic organisms
(ERCO report, Cairns 1971).
Summary and Recommendations
1. Artificial substrate sampling methods are available for periphyton
(particularly diatoms) and benthic organisms.
2. The sampling of diatoms with glass slides is a technique that has been
well developed and should play a prominant role in a biomonitoring program.
3. Artificial substrates are not a recommended technique for use with
benthic organisms.
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8. SAMPLING MANY HABITATS VERSUS SAMPLING FEW HABITATS
The habitat of a species is the environment of that species, as
characterized primarily by physical and chemical qualities rather than
position vithin a community (Whittaker 1972). For instance, a lake might
have several habitats for benthic organisms such as rocky areas, sandy
areas, and muddy areas. Whittaker defines the diversity found within a
specific habitat as the alpha diversity; under natural conditions the alpha
diversity is essentially the "species packing level" for that habitat.
Beta diversity, iccording to Whittaker, is the between habitat diversity of
an area. Beta diversity will determine the rate that the community composition
will change as an observer travels from one habitat to the next.
A biomonitoring sample typically will be concerned with the alpha diversity
of a given habitat. Beta diversity is mostly a concept of ecological theory
and has been actually measured for very few communities (mostly terrestrial).
The effect of pollution on beta diversity in aquatic systems is virtually
uninvestigated at this time. If data is collected for many different habitats
in a biomonitoring program, the data will be a valuable contribution to basic
ecological research on beta diversity.
The question as to how many different habitats will be sufficient for
biomonitoring purposes will have to be determined with on-site studies. Each
lake or river has a particular set of environmental conditions, habitat combin-
ations, and pollution problems; the investigators should study many habitats
at first to get an idea of species compositions and to get an overall view of
the sort of changes to expect in the diversities. If it turns out that the
species compositions are similar for several habitats or that communities with-
in different habitats respond similarly to changes in water quality then sampling
only one of those habitats would probably be sufficient. If, however, the
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communities within habitats are quite different in their species composition
or responses to pollution then many habitats will have to be monitored.
Allan (1975) studied the distributional patterns and diversity of benthic
insects in a Colorado stream; this study contains some encouraging results for
biomonitoring. Allan found that most of the species diversity of these insects
was found within habitats rather than between habitats at the microhabitat
level. This may indicate that investigators in a biomonitoring program will
be able to be somewhat broad in their designations of habitats for sampling
purposes. However, more information such as this for many different bodies
of water is needed to form definite conclusions about habitat monitoring.
Summary and Recommendations
1. Investigators in a biomonitoring program should study many different
habitats at first to achieve an overall view of the environmental problems
peculiar to the specific body of water.
2. Data gathered for many habitats at once will constitute new knowledge
for both basic and applied ecology.
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9. THE IMPORTANCE OF TAXONOMY
Identification of species is perhaps the major technical problem in
sampling for community diversity. Two groups of organisms, the diatoms
and the benthic insects, are considered promising organisms for use in
diversity monitoring, because of their ease of collection, large numbers
of species, and sensitivity to water quality.
Both these groups, however, are notoriously hard to identify. Keying
out a single individual to species can be a time consuming challenge to a
PhD systematise The alternatives to species identification are of mixed
promise:
One idea is to simply not identify the organisms to species, but key
them out to a higher taxonomic level such as genus or family. The diversity
measure would then be computed using a vector of relative abundances of
genera or families. According to Resh and Unzicker (1975) this approach is
of dubious value. Resh and Unzicker point out that much of the variation in
pollution tolerance is within genera rather than between genera for benthic
insects. They found that out of 89 genera for which water quality tolerances
("tolerant", "facultative", or "intolerant") have been established for more
than a single species, the component species fell into different tolerance
categories in 61 of those genera.
Though Resh and Unzicker were specifically examining the "indicator species"
method of water quality monitoring, their conclusions about species identification
apply to diversity monitoring. Important community shifts in abundance at the
species level could take place and not be detected if only genera figures were
available for computing diversity.
The second alternative to species identification is to use the sequential
sampling method developed by J. Cairns (Cairns et al. 1968). In this method
individual specimens are taken sequentially and at random from a sample; each
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36
specimen is compared with the previous one as to whether it is the "same"
or "different." The more times the comparisons are "different" for a given
sample, the greater the biological diversity. Cairns proposed using #"runs"/
#specimens as a diversity index; the sampling technique is now known to yield
an estimate of the Simpson index (see Patil and Taillie 1976 and the ERGO
report). According to Cairns this method of assessing the biological conse-
quences of pollution would be useful for preliminary surveys or when results
of some sort must be made available without delay.
There are some drawbacks to this sampling method. One drawback is that
the data gathered in this fashion cannot be used for anything else. Another
drawback is that changes in community composition would not be evident.
Additionally, the investigator could not monitor changes in abundances of
"indicator species" with this method. Finally, the Simpson diversity index
has disadvantages when there are a large number of species (as is likely the
case with diatoms or benthic insects) , or when a few species are dominant in
the community (see ERCO report for discussion of this). Taxonomic effort will
be required if the investigator wishes to use another diversity index besides
Simpson's.
Nonetheless, this is an easy and rapid method of sampling for diversity,
and Cairns gives convincing data that indicate that the method can be used by
non-biologists. Cairns had a non-biologist and a biologist
both estimate the number of species of benthic organisms that were in several
collectionsjthe estimates of the two did not differ significantly. The
method was also employed to assess pollution impacts above and below an outflow;
Cairns' index showed the characteristic diversity decline for experiments of
this sort. More field testing will be needed, but this method should have a
significant role in a biomonitoring program.
Detailed community knowledge will be necessary many times, however, as the
task of interpreting pollution impacts requires more information than a diversity
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J/
figure . One possibility is that B.S.-level personnel could be trained to
identify the species found in a local area within a few month's time.
Another possibility lies in the perfection of optical identification devices
(Cairns 1972). Much work will be necessary to carry out these possibilities.
Summary and Recommendations
1. Identifying the organism only to family or genus is not a recommended
alternative to obtaining species diversity.
2. The sequential sampling method of J. Cairns is a rapid method of
estimating diversity that should prove especially useful for preliminary
surveys. Studies should be done on the effectiveness of this method for
routine monitoring and on the effectiveness of training non-biological
personnel to use this method.
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Kushlan, J. A., 1976. Environmental stability and fish community diversity.
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Patrick, R., B. Crum and J. Coles, 1969. Temperature and manganese as determining
factors in the presence of diatom or blue-green algal floras in streams.
Proc. Natn. Acad. Sci. U.S.A. 64, 472-478.
Patrick, R., M. H. Hohn, and J. H. Wallace, 1954. A new method for determining
the pattern of diatom flora. Notul. Nat. 259, 1-12.
Pielou, E. C. 1969. An introduction to mathematical ecology. Wiley, New York.
Pielou, E. C. 1974. Population and community ecology: Principles and Methods.
Gordon and Breach, New York.
Pielou, E. C. 1975. Ecological diversity. John Wiley and Sons, New York.
Preston, F. W. 1948. The commonness and rarity of species. Ecology, 29, 254-283.
Reish, D. 1973. The use of benthic animals in monitoring the marine environment.
Journal of Environmental Planning and Pollution Control, 1(3} , 32-38.
Resh, V. H. and J. D. Unzicker, 1975. Water quality monitoring and aquatic organisms:
the importance of species identification. J. Wat. Poll. Con. Fed. 47, 9-19.
Swartz, R. C., J. D. Walter, W. A. DeBen, and F. A. Cole, 1976. Structural analysis
of stressed marine communities. Water Quality Criteria Research of the U.S.
Environmental Protection Agency: Proceedings of an E.P.A.-Sponsered Symposium
(EPA-600/3-76-079), 3-12.
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40
Train, R. E. 197X. Address at the National Conference on Managing the Environment.
Environmental Protection Agency, Washington, D.C.
Wene, G. and E. L. Wickliff, 1940. Modification of a stream bottom and its effect
on the insect fauna. Can. Entomol. 72, 131-135.
Whittaker, R. H. 1972. Evolution and measurement of species diversity. Taxon,21,
213-251.
Wihlm, J. L. 1967. Comparison of some species diversity indices applied to
populations of benthic macroinvertebrates in a stream receiving organic
wastes. J. Water Pollution Control Fed., 39, 1673-1683.
Wihlm, J. L. 1968. Biomass units vs. numbers of individuals in species diversity
indices. Ecology, 49, 153-156.
Wihlm, J. L. and T. C. Dorris 1966. Species diversity of benthic macroinvertebrates
in a stream receiving domestic and oil refr.nery effluents. Am. Midland
Naturalist, 76, 427-449.
Williams, F. M. 1971. Dynamics of microbial populations. Systems Analysis and
Simulation in Ecology vol. 1., B.C. Patten, ed., New York: Academic Press 1971.
Williams, L. G. 1964. Possible relationships between plankton-diatom species numbers
and water quality estimates. Ecology, 45, 809-823.
Winner, R. W. 1972. An evaluation of certain indices of eutrophy and maturity in
lakes. Hydrobiologia 40, 223-245.
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PART B
LITERATURE REVIEW OF COMMUNITY DIVERSITY AND BIOMORITORING
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PART B
Section I
AN ANNOTATED BIBLIOGRAPHY OF COMMUNITY DIVERSITY AND ITS
APPLICATIONS TO BIOLOGICAL MONITORING OF WATER QUALITY
Section II
A SELECTED LIST OF PUBLICATIONS ON COMMUNITY DIVERSITY
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Section 1
AN ANNOTATED BIBLIOGRAPHY OF COMMUNITY DIVERSITY AND ITS
APPLICATIONS TO BIOLOGICAL MONITORING OF WATER QUALITY
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45
LITERATURE REVIEW OF COMMUNITY DIVERSITY AND BIOMONITORING
I. INTROPUCTIO"?
Human use of aquatic ecosystems invariably creates impacts on those
environments, if even only slight impacts. Though such human use must
continue, careful management of the use is necessary as water is a finite
resource and a limiting factor in many parts of the globe. Much attention
has been given recently to the question of assessment of impact on water
quality, and also the assessment of impact on water as a habitat for living
things.
The diversity of an aquatic community is a measure of the variety of
the types of organisms which thrive there. The species which characterize
a lake or a stream are found there due to a vast assortment of ecological
forces, including nutrient availability, colonizing ability, co-evolution,
competition, environmental stability or predictability, and predation. In
general, a community, if left undisturbed, will become more complex, that is,
acquire a greater variety of species over an evolutionary time period.
Human use of acquatic systems often perturbs the environment of these
organisms. The resulting extinctions and changes in abundance of species
will be reflected in a change in the diversities of the communities.
Use of ecological diversity in biomonitoring then will require an
integration cf i wide spectrum of scientific literature. Some of the topics
of relevance to the use of diversity are niche theory and species packing,
evolution, mathematical formulations, statistical methods, field sampling
methods, and the field biology of aquatic systems. To aid in locating
publications of relevance to diversity, this bibliography has been compiled
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46
from a variety of sources in different fields.
The bibliography is presented in two parts. The first part provides
an annotated bibliography of ecological diversity and its applications to
biological monitoring. Approximately fifty publications are listed in this
first part. For each, a summary has been given of the results, methods, or
discussions that will be of interest for biomonitoring applications. The
publications have been selected for inclusion in this part on the basis of
whether they will b<2 of primary importance to the current project.
The entries in the annotated bibliography can be categorized into three
basic topics. First, approximately ten publications have been included
which delineate the current state of ecological theory in community diversity.
They cover the time-stability-diversity hypotheses, species packing, and
species abundance modeling among other topics. This basic research should
be examined carefully by investigators interested in applying diversity
measures to their problems. This theoretical work is needed to draw conclu-
sions about what a diversity index can or cannot reveal about an ecological
community.
The second topic is applied ecological diversity, which includes papers
directly concerned with biomonitoring. These publications often report
studies in which a community is sampled, data are gathered, a diversity
index computed, and conclusions are drawn from the results. Such work is
valuable to biomonitoring for reasons of data, field sampling methods, or
basic field biology of aquatic organisms of interest.
The third t jpic in the annotated bibl iot,r:..phy concerns the stat" st.ica ¦
treatment of data. This category includes mathematical formulations,
properties and implications of different diversity indices, and problems of
sampling and estimation.
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The publications in the annotated bibliography have been numbered, and
at the end of this first part, they are listed by number under the topic(s)
to which they are relevant. The three topics are identified as: (I) eco-
logical theory and concepts; (II) ecological applications including bio-
monitoring; and (11T ) statistical methodology.
The second part, which comes after the annotated bibliography, consists
of a selected list of publications on ecological diversity. Over three
hundred entries appear here. These have been included on the basis of their
general interest to the broad subject of comi\ui.ity diversity. It is hoped
that this collection of titles will aid present investigators and others
who are attempting to cope with the vast array of different journals in
which diversity information is published.
The authors wish to note in passing that the number of papers directly
concerned with biological monitoring is small compared with the numbers in
other diversity areas. This list calls attention to the paucity of data
and field studies, which directly test water quality monitoring hypotheses
(with notable exceptions in the work of R. Patrick and J. Cairns). The
authors would welcome any additional information, unpublished or otherwise,
which would relate to monitoring problems.
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ANNOTATED BIBLIOGRAPHY
ALLAN, J. D. 1975.
The distributional ecology and diversity of benthic insects in Cement
Creek, Colorado.
Ecology, 56:1040-1053.
A brief review: Distributional patterns and species diversity of
benthic insects in an alpine stream in Colorado were investigated on
several levels of spatial scale, from faunal replacement over 1000
vertical m to microdistribution within the stony substratum. Most
Most of species diversity as measured by H* was found within habitats
rather than between habitats at the microhabitat level.
A comment: This material will be useful for biomonitoring purposes,
as it gives general information on the ecology of benthic insects and
sampling methodology. The within-and-between-habitat concept is a
specific case of a heirarcliial classification system.
BALL, R. C. and J. G. BAHR. 1975.
Intensive survey: Red Cedar River, Michigan.
In River Ecology.
A brief review: This is an integrated study of a Michigan watershed,
including abiotic ecosystem components such as water chemistry, climate,
discharge, and biotic components such as periphvton, aquatic macro-
phytes, macroinvertebrates, and fish. The study includes data on
benthic diversity; the authors conclude that information theory indices
of species diversity appear to be one of the more sensitive measures of
changes in community structure caused by human perturbation.
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A comment: The ERCO report cites a handful of contradictory studies on
the usefulness of diversity indices, concluding that it is highly
doubtful whether diversity indices in their present form will serve as
useful indicators of water quality. This is a drastic conclusion on the
basis of such a small sample of the literature. Revised conclusions
will have to take into consideration research such as this of Ball and
Bahr.
BARBOUR, C. C. and J. H. BROWN. 1974.
Fish specie;; diversity in lakes.
Amer. Nat., 108:473-489.
A brief review: Barbour and Brown use stepwise multiple regression to
obtain preliminary insights into the environmental parameters which
influence the number of fish species occurring in lakes. Among their
results: for a sample of 70 lakes and inland seas from throughout
the world, surface area and latitude account for about one third of
the variability in fish species diversity.
A comment: This is an investigation of fish species diversity on a
global scale, with a view toward confirming a prediction of MacArthur
and Wilson's island biogeography model. There may be useful material
here for biomonitoring purposes in terms of methodology: a problem
with using diversity in biomonitoring is to statistically "filter"
the naturally-caused diversity fluctuation from the human caused
fluctuation.
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4. CAIRNS, J. et al. 1968.
The sequential comparison index—a simplified method for non-biologists
to estimate relative differences in biological diversity in stream
pollution studies.
J. Water Pollution Control Fed., 40:1607-1613.
A brief review: A simple and rapid method is reported by which a non-
biologist can estimate species diversity of benthic invertebrates or
diatoms for the purpose of water quality monitoring. Individual
specimens are taken sequentially and at random from a sample; each
specimen is compared with the previous one. The more "runs" for a
given number of specimens, the greater the biological diversity.
Examples of use of this technique are reported for diatoms and inverte-
brates collected at varying distances from a sewage outfall.
A comment: The problem of taxonomic training is one of the most critical
in using diversity indices in water quality monitoring. The organisms
considered most suitable for biomonitoring use are diatoms and benthic
invertebrates, as large samples are easily collected and these organisms
are sensitive to changes in water quality. However, keying these
organisms to species can be a taxonomic challenge to a trained Ph.D.
biologist. Dr. Cairns' sequential sampling technique is a major alter-
native to laborious and difficult keying work that should be considered
when time, cost, or personnel limit a water monitoring effort. Cairns
proposes using if runs/it specimens as a diversity index; the sampling
technique has been subsequently shown to be an estimate of the Simpson's
diversity index (see Patil & Taillie, 1976, and ERCO report). The
drawback of this method is that the data so gathered cannot be used for
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anything else. A diversity index presented without any other informa-
tion may conceal changes in species composition of the community when
it is compared to a value computed for the community at an earlier
time. To monitor changes in species composition, changes in abun-
dances of "indicator species," or changes in diversity indices other
than Simpson's same taxonomic effort will be required.
5. DeBENEDICTIS, P. A. 1973.
On the correlations between certain diversity indices.
Amer. Nat., 107:295-302.
A brief review: DeBenedictis points out that positive correlations are
to be expected between a number of different diversity indices due to
the ways in which the indices are defined. He notes that obtaining the
expected values of the correlation coefficients would be impossible
without postulating probability distributions to describe the indices.
In a mathematical appendix, he derives an expected correlation coeffi-
cient between S (species number) and H' (Shannon-Weiner).
A comment: The main argument is rather self-evident; however, this
paper should be examined along with the work on correlations between
indices which was done by ERCO. (ERCO used data.)
6. EWING, M. S. and T. C. DAVIS. 1970.
Algal community structure in artificial ponds subjected to continuous
organic enrichment.
Amer. Mid. Nat., 83:565-582.
A brief review: Nine artificial ponds, each subjected to one of three
experimental treatments of organic enrichment, exhibited no significant
differences in mean concentration of dissolved nitrate, nitrite,
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52
amonia, or phosphate. In general, algal species diversity was not
positively correlated with nutrient concentrations.
A comment: This study was cited by ERCO as providing little support
for the use of diversity in water quaijry monitoring.
7. GLIME, J. M. and R. M. CLEMONS. 1972.
Species diversity of stream insects on fontinalis spp. compared to
diversity on artificial substrates.
Ecology, 5?:*58-464.
A brief review: Two types of artificial mosses (string and plastic)
were compared with Fontinalis spp. for their insect inhabitants. These
communities were sampled on six dates at eight stream sites and com-
pared by community coefficients, information theory analysis, and rank
correlations. The number of individuals found on artificial substrates
was substantially less compared with Fontinalis, leading the investi-
gators to conclude that these substrates provide a poor substitute for
Fontinalis. However, there was a high degree of correlation of insect
species among the substrates, and species diversities of the individual
samples were not significantly different when comparing string and moss.
A comment: The moss sampling method was: "pulling a handful from the
stream and putting it in a jar." This sampling method seems reliable
according to previous work done by J. M. Glime. For the purposes of
biononitoi there would be no information or cost benefit in substi-
tuting one of these artificial substrates for sampling purposes.
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LLOYD, M., R. F. INGER, and F. W. KING. 1968.
On the diversity of reptile and amphibian species in a bornean rain
fores t.
Amer. Nat , 102:497-515.
A brief review: The diversity of a tropical reptile and amphibian
community is investigated with an intensive collecting effort carried
out over an entire year. "Equitability" of species is lower than
expected for the tropics, which leads Lloyd £lt jil. to re-examine the
assumption that the rain forest floor environment is relatively con-
stant and predictable. Conceivably, intense rains which cause raging
floods in breeding streams might often result in catastrophic mortali
to the herptiles.
A comment: This massive survey uses Pielou's recommendations for
estimating the Shannon index of diversity. The investigators also
partition the data heirarchially into families, genera, and species.
It would have been interesting if they had published computations of
diversity on the basis of biomass in addition to the number of
individuals.
LLOYD, M., J. H. ZAR, and J. R. KARR. 1968.
On the calculation of information—theoretical measures of diversity.
Amer. Mid. Nat., 79:257-272.
A brief review: Computing formulae are given, along with an example,
to show that the Shannon and Brillouin indices of diversity can be
calculated with equal ease. A table is presented for rapid calcula-
tion of both indices, as well as Basharin's standard error.
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A comment: Pocket scientific calculators and computers have eliminated
computing difficulties in information-type diversity indices. Nonethe-
less, this paper is interesting for its discussion of the use of the
indices themselves. The paper additionally gives examples of use with
field data from Sander's (1936) Quaker Run Valley bird censuses.
10. L0NGUET-HIGG1NS, M. S. 1971.
On the Shannon-Weaver index of diversity, in relation to the distribu-
tion of species in bird censuses.
Theor. pop. Biol., 2:271-289.
A brief review: Longuet-Higgins investigates the relationship of
relative abundance distributions (Dirichlet series, broken-stick,
gamma) to the Shannon information measure of diversity. The log-normal
distribution is also studied; it is shown that if the distribution is
not truncated that the diversity H is given by:
H = log S - y a2,
2
where S is the number of srecies in the community and O is the variance
of the distribution.
A comment: Use of log-normal curve for large assemblages of species
such as are found in diatom studies is an alternative to using a
diversity index. This paper helps clarify the relationship between
the two methods of representing the data.
11. MacARTHUR, R. 1972.
Geographical Ecology.
New York: Harper and Row. 269 pp.
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A brief review: This is a book on patterns of distribution and abun-
dance of species. There are chapters on climates on a rotating earth,
competition and predation, economics of consumer choice (optimal
feeding, geography of species classification, island patterns, species
distributions, patterns of species diversity, comparisons of temperate
and tropics, the role of history.
12' MacARTHUR, R- 1970.
Species packing and competitive equilibrium for many species.
Theoretical. Population Biology, 1:1-11.
A brief review: This is an expanded version of MacArthur (1969) with
added insights and easier readability.
13. MacARTHUR, R. 1969.
Species packing, and what interspecies competition minimizes.
Proc. Nat. Acad. Sci., 64:1369-1371.
A brief review: MacArthur proposes a model of many species competing
for a gradient of renewing resources. Near equilibrium the model is
essentially the same as the Volterra competition model. MacArthur
shows that a quadratic expression of the species abundances, X^'s, is
minimized at competitive equilibrium. With certain restrictions the
quadratic expression can be shown to be a weighted squared deviation
of available production of resources from species harvesting abilities.
An environment of renewable resources wit1, hold an additional species
if by adding that species the quadratic expression is minimized further.
A comment: The concept of diversity will be of no use to ecologists
interested in basic research unless it can be "explained" or
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"predicted" in terms of fundamental biological laws. The very defini-
tion of 'ecology' specifies this unification of life and natural laws:
the definition is that ecology is the study of organisms in relation
to their environment. Diversity will be unimportant to ecologists
unless its dependence on environment is clarified. MacArthur's work
on species packing is an important step in that direction, even though
the assumptions in his models are very restrictive.
14. MAY, R. M. 1974.
Stability and complexity in model ecosyf.t'ims.
Princeton: Princeton University Press.
A brief review: The relationship between complexity of interconnections
in a food web and stability is examined using mathematical models of
multispecies communities. The statement that increased diversity in
an ecological system leads to increased stability does not appear to
be a mathematical consequence in community models. Environmental
fluctuations theoretically are apt to put a limit to niche overlap
among competing species.
15. MAY, R. M. 1975.
Patterns of species abundance and diversity. In Diamond, J. M., and
M. L. Cody (eds.) 1975.
Ecology and evolution of communities, Harvard Univ. Press, Cambridge,
Mass.
A brief review: With a theoretical argument May shows that for large
assemblies of species, a lognormal pattern of relative abundance may
be expected, and that Preston's canonical hypothesis is an approximate
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_/ /
but general mathematical property of the lognormal distribution.
Ecological mechanisms which would lead to the broken stick and log
series distributions are also examined. It is shown that many common
measures of species diversity tend not to distinguish these relative
abundance distributions if the total number of species in the community
is small.
A comment: R. Patrick fits lognormal curves to her diatom data; other
investigators use diversity indices in biomonitoring work. This paper
sheds light on the relation between diversity indices and relative
abundance distributions.
16. PATRICK, R. 1963.
The structure of diatom communities under varying ecological conditions.
Ann. New York Acad. Sci., 108(2):359.
A brief review: Patrick uses the technique of fitting a truncated
log-normal curve to species-abundance data to compare different diatom
communities.
A comment: One of her quotes from this paper is enlightening: "It is
only as a result of thorough and continuous study of an environment and
the species living in it that one can venture to describe the quantita-
tive changes in the natural environment by changes in the quantitative
abundance of specific kinds of species."
1/. PATRICK, R. 1968.
The structure of diatom communities in similar ecological conditions.
Amer. Nat., 102:173-183.
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58
A brief review: Patrick reports results of experiments which were
designed to determine the degree and kind of variability in the
structure of diatom communities that one might expect under very
similar ecological conditions. Species composition, Shannon diversity
measure, and the structure of the truncated log-normal curves were very
similar in all the communities.
A comment: This surprising lack of variability of diversity in several
slide-colonizing experiments would support the use of her diatom methods
in a biolo^i:al monitoring program.
PATRICK, R., J. CAIRNS, and S. S. ROBACK. 1967.
An ecosystematic study of the fauna and flora of the Savannah River.
Proc. Acad. Nat. Sci. Phila., 118:109-407.
A brief review: This is a report of a program which was designed to
determine the communities of aquatic organisms living in the Savannah
River in the vicinity of the Savannah River Plant of the Atomic Energy
Commission, and the ecological characteristics of the environment in
which they are found.
A comment: This massive study contains much information on the basic
ecology of the flora and fauna of a large river. The studies were
designed to monitor river changes due to plant operation, but the
results of value to the monitoring program were not reported in this
paper.
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19• PATRICK, R., B. CRUM, and J. COLES. 1969.
Temperature and manganese as determining factors in the presence of
diatom or blue-green algal floras in streams.
Proc. Natn. Acad. Sci., 64:472-478.
A brief review: An average temperature of 34° to 38°C results in a
shift of dominance in the algal flora from diatoms to blue-green algae.
Furthermore, a blue-green and green algal flora of species typically
found in organically polluted water is favored if the manganese content
is a few parts per billion.
A comment: This paper contains useful information for applied workers
who are studying algae in rivers or streams.
20. PIELOU, E. C. 1975.
Ecological diversity.
New York: John Wiley & Sons.
A brief review: This is a textbook on concepts and methods in eco-
logical diversity. There are chapters on indices of diversity and
evenness, species abundance distributions, testing hypotheses about
species abundance, diversity and spatial pattern, diversity on
environmental gradients, local and global determinants of diversity.
A comment: This is an indespensable reference for applied diversity
work.
21. PIELOU, E. C. 1966.
Shannon's formula as a measure of specific diversity: Its use and
misuse.
Amer. Nat., 100:463-465.
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A brief review: Pielou explains the difference between the uses of
Brillouin's diversity formula and Shannon's formula. Brillouin's
formula gives the true diversity per individual in a finite collection;
there is no sampling error. Shannon's formula is used when the
community is too large for all its members to be counted. The formula
must be estimated and there is a sampling variance. Pielou points out
that there are pitfalls to simply plugging N^/N values into Shannon's
formula from a field sample.
A comment: It is important that field workers understand the statisti-
cal methodology of use of information diversity measures if these
measures are to be a part of a biological monitoring program.
PIELOU, E. C. 1966.
The measurement of diversity in different types of biological collections.
J. Theoret. Biol., 13:131-144.
A brief review: Information content may be used as a measure of the
diversity of a many-species biological collection. The diversity of
small collections all of whose members can be identified and counted,
is defined by Brillouin's measure of information. With larger collec-
tions, it becomes necessary to estimate Shannon's measure of diversity.
Different methods of estimation are appropriate for different types of
collections.
A comment" This paper contains i-'portair statistical prjcedurp-3 with
examples for those who use information—theoretic measures of diversity.
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23. SAGER, P. E. and A. D. HASLER. 1969.
Species diversity in lacustrine phytoplankton. I. The components of
the index of diversity from Shannon's formula.
Araer. Nat,, 103:51-59.
A brief review: Seasonal observations on the diversity of phytoplankton
communities were made in three lakes in Wisconsin. Extremes in nutrient
availability and morphometry in the lakes yielded a range in diversity
indices calculated from Shannon's formula. Examination of the relative
importance of the two components in the index indicated that the vari-
ability of the index can in large part be attributed to the component
of equitability as expressed in the 10 to 15 most abundant species.
A comment: It would seem good news to an investigator who is monitoring
water quality that if many rare species are missed in. a sample the
computed diversity index (Shannon's) will not change much. Costs of
sampling and taxonomic costs perhaps could be reduced if only the 15
most abundant species of phytoplankton need be sampled. However, this
paper raises an important question about use of diversity in water
quality monitoring: Do we lose too much information about the eco-
logical community by packaging the data all up in a sing!e number?
"Species of low abundance appear to have a minor effect on the
(Shannon) index of diversity" (Sager and Hasler). Yet, environmental
stress of pollution is likely to have major effects on those species
of low abundance.
24, WENE, G. and E. L. WICKLIFF. 1940.
Modification of a stream bottom and its effect on the insect fauna.
Can. Entomol., 72:131-135.
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OA
A brief review: This is a report on the use of the "basket method"
for studying the effects of contrasting types of stream bottoms on
the insect fauna. Wire baskets were constructed and filled with
various types of stream bottom materials which had been previously
cleaned. The insect populations reached maximum in about a month's
time.
A comment: One disadvantage of artificial substrates is the coloniza-
tion time. This is the time that is needed to allow the species number
on the substrate to reach a maximum equilibrium value; this colonization
time can be a week or two for diatoms on glass slides and a month for
benthic insects in rock baskets. Such time intervals will produce
delays in a monitoring program. We would also like to see any arti-
ficial substrate method tested on-location in a biomonitoring program.
This paper shows the relative ease of comparing an artificial substrate
with the natural stream bottom as a habitat for benthic insects.
25. WHITTAKER, R. H. 1972.
Evolution and measurement of species diversity.
A brief review: Given a resource gradient (e.g., light intensity,
prey size) in a community, species evolve to use different parts of
this gradient; competition between them is thereby reduced. Using this
theme, niche theory and species packing is discussed. Also, several
relative abundance distributions (geometric, broken stick, log normal)
are discussed in terms of the way they represent manners in which
resources are divided among species. Ecological and evolutionary
factors which contribute to alpha, beta, and gamma diversity are
discussed.
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0 J
A comment: This massive paper is poorly summed up here. It is a full-
scale presentation of the ecological factors behind community diversity,
and an important review of the current state of diversity-related
theory.
26. WILHM, J. L. 1975.
Biological indicators of pollution.
In River Ecology, B. A. Whitton, ed.
Berkeley: Univ. of Cal. Press.
A brief review: This is a thorough review of the various types of
biological indicators that have been used in water quality monitoring
studies. Wilhm covers biochemical indicators, cell and tissue indi-
cators, species toxicity tests, behavior tests, species lists and
species as ecological indicators, stream zones, graphic methods of
view species—abundance data, and mathematical expressions including
species diversity. He concludes that until biologists agree on
concentrating on a thorougn analysis and development of a few standard
biological techniques of analyzing water quality, biological methods
will not be as widely accepted in most monitoring programs as
physicochemical methods.
A comment: Wilhm's conclusion serves to emphasize the importance of
diversity-related work in biomonitoring.
27. WILHM, J. T.. ]968.
Use of biomass units in Shannon's formula.
Ecology, 49:153-156.
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A brief review: Half of the paper is a review of previous work
regarding use of the Shannon-Weiner index of diversity. Wilhm then
proposes use of biomass instead of numbers based on Odutn's (1959)
statement that the pyramid of numbers is not very fundamental or
instructive as an illustrative device because of the geometrical fact
that a great many small units are required to equal the mass of one
large unit. Wilhm then gives data from a benthic macroinvertebrate
study. Differences were noted when biomass units were used instead of
numbers of individuals in computing diversities.
A comment: Seems that very little attention has been given to the
question of biomass vs. number of individuals in the ecological
literature. Our initial opinion is that biomass should be used more
often. Ecosystems are bound by physical laws as is the rest of
nature. One of the most significant physical constraints on living
things is the supply of materials. Altering an organism's environment
(i.e., adding nutrient, changing temperature, adding toxins or heavy
metals) affects that organism's ability to uptake and assemble
materials, i.e., that organism's ability to grow. In microbial organ-
isms, a species may have exhausted the nutrient supply and maintain a
constant mass through time, but continue to divide and thus vastly
increase in numbers. This is possible for larger organisms also.
WILHM, J. L., and T. C. DORRIS. 1968.
Biulogicc;! parameters for water quality criteria.
Bioscience, 18:477-481.
A brief review: Wilhm and Dorris propose the establishment of water
quality criteria by the evaluation of biological conditions existing
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65
in receiving streams. Effluents produce striking changes in the
structure of the benthic macroinvertebrate community. The structure
of a benthic community can be summarized clearly and briefly in diver-
sity indexes derived from information theory. Values less than 1 have
been obtained in areas of heavy pollution, values from 1 to 3 in areas
of moderate pollution, and values exceeding 3 in clean water areas.
A comment: The paper cites several field studies in support of using
benthic macroinvertebrate diversity in a water monitoring program. It
is very readable.
29. WILHM, J. L. and T. C. DORRIS. 1966.
Species diversity of benthic macroinvertebrates in a stream receiving
domestic and oil refinery effluents.
Amer. Mid. Nat., 76:427-449.
A brief review: A study was made of physicochemical conditions and
benthic macroinvertebrate community structure in a stream receiving
domestic and oil refinery effluents. Measures derived from information
theory, diversity per individual and redundancy, were found to be more
precise measures of stream conditions as reflected by benthic macro-
invertebrate populations than traditional methods.
A comment: This study could serve as a model stream monitoring project.
The paper contains informative discussions on the use of diversity,
invertebrate sampling techniques, snd physicochemical monitoring.
30. WILLIAMS, L. G. 1964.
Possible relationships between plankton-diatom species numbers and
water-quality estimates.
Ecology, 45:809-823.
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A brief review: Semimonthly samples from 103 scattered stations on
the major rivers and Great Lakes of the United States revealed differ-
ences in kinds and numbers of dominating planktonic organisms. Diatoms
dominated at these stations. Eutrophic stations generally were repre-
sented by a few species composing a large portion of the diatom popu-
lation, and the density level was usually high. "Clean" stations, on
the other hand, had more species composing a small portion of the
total live diatom population, and the overall density was low.
A comment: This is the reporting of one of the most extensive algae
monitoring efforts ever undertaken in the United States, and the results
generally support using diversity of diatoms in water quality monitoring.
However, the familiar diversity indices were not used in this study and
the data not reported to compute the indices. The paper was written
before computing "diversity" came into vogue. This investigation,
along with the work of R. Patrick, would indicate that diatom diversity
should play a fundamental role in a biomonitoring program.
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ADDENDUM
ALLAN, J. D. 1975.
Components of diversity.
Oecologia, 18:359-367.
A brief review: The information theory measure H' = - E Pi log Pi is
partitioned into components to allow evaluation of various contribu-
tions to total diversity. If a species collection is sampled at
several mLcrohabitats within each of several sites, we may ask whether
the niche breadth of a particular species, and the diversity of the
entire collection, are greater with respect to microhabitats or sites.
The usefulness of these measures is discussed in the context of within
habitat and between-habitat contributions to diversity.
A comment: This paper contains much of interest to the study of heir-
archial classification and diversity. Of interest to monitoring:
perhaps the niche-breadth of "indicator" species could be followed in
addition to following trends in community diversity. In this fashion,
field workers would be better able to make conclusions about what is
happening in a community being exposed to pollution.
BUZAS, M. A. 1972.
Patterns of species diversity and their explanation.
Taxon, 21:275-286.
A brief review: Patterns of species diversity and equitability, and
the hypotheses suggested to explain them are examined in the terres-
trial and marine environments, and the fossil record. Although all
the hypotheses are important in explaining diversity, none of them
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singularly or in various combinations are sufficient to explain the
observed patterns.
A comment: Diversity is such a complicated function of environmental
history that most ecological theories obout diversity have be.^n ir£.ie~
quate so far. We would caution against use of diversity in monitoring
simply on theoretical grounds, and would stress that much basic research
on the effects of many aquatic environmental parameters on community
diversity is needed.
33. COOKE, W. B. 1956.
Colonization of artificial bare areas by microorganisms.
Bot. Rev., 22:613-638.
A brief review: This is a review (1956) of artificial substrate tech-
niques for a variety of terrestrial or aquatic microorganisms.
34. CORNELL, H., L. E. UURD, and V. A. LOTRICH. 1976.
A measure of response to perturbation used to assess structural change
in some polluted and unpolluted stream fish communities.
Oecologia, 23:335-342.
A brief review: A new method for measuring structural change in sets
of species which have been subjected to natural or experimental
perturbation is developed and is shown to be superior to static
diversity and evenness measures for this purpose. Three parameters,
HA', JA1, and XA are shown to provide necessary and sufficient infor-
mation on the severity of a perturbation as well as the uniformity of
its effect on all species in the set. When positive and negative
changes in species abundance are considered separately, the method
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69
sensitive to compensatory changes which are not detected by static
measures. The parameters are then calculated for some data sets on
polluted and unpolluted fish communities in streams in Kentucky. The
notion of these three parameters as the "vital signs" of a healthy
ecosystem is presented.
A comment: We are studying this paper closely.
35. CUMMINS, K. W. 1962.
An evaluation of some techniques for the collection and analysis of
benthic samples with special emphasis on lotic waters.
Amer. Mid. Nat., 67:477-504.
A brief review: A consideration of a large number of procedures for
the collection and analysis of benthic samples, with particular
emphasis on stream investigations and the importance of substrate
particle size as a common denominator in benthic ecology, reveals
that only certain techniq-ies are suitable.
A comment: This is a thorough study of lotic benthic sampling tech-
niques which will be invaluable for field workers. The paper has many
references.
36. CUMMINS, K. W. 1973.
Trophic relations of aquatic insects.
Ann. R$v. Entomol., 18:183-206.
A brief review: Freshwater ecosystems of the temperate zone might be
generalized as having a reasonably constant bioroass of macrobenthic
animals, dominated by aquatic insects, which is turning over at a
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70
rate contro;;ed primarily by temperature. Food resources are par-
titioned on the basis of particle size and whether active, stationary,
or in suspension.
A comment: This is a detailed review ot the role of aquatic insects
in freshwater ecosystems.
DICKMAN, M. 1968.
Some indices of diversity.
Ecology, W>:1191-1193.
A brief review: The Shannon-Weaver diversity formula fails to reflect
significant changes in a community's structure because it is only
sensitive to changes in relative abundance of a few of the trophic
levels of a community. Over two-thirds of the species encountered in
a typical plankton sample had no significant effect on the index of
diversity (H) calculated for that sample. To overcome this, the.
Shannon-Weaver formula was twice altered by redefining P^ in order to
give a new index of community diversity which was sensitive to changes
in community structure. defined in terms of relative biomass 0^)
failed to improve the index substantially and P^ was then successfully
defined in terms of relative productivity (Hp). An index of community
diversity sensitive to changes in relative abundance of all the trophic
levels, such as the index Hp, appears to be a necessary prerequisite
to comparative community studies.
A comment: This study used diversity calculated for a whole community
of many phyla and several trophic levels including bacteria, phyto-
plankton, and zooplankton species. Obviously, when this is done, the
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71
organisms on the lower and of the "trophic pyramid" will swamp the
diversity index with their relative abundance.
Diversity seems to be most effective when applied to a community
of organisms that are competing along a resource gradient (or several
resource gradients). When one species in such a community is elimin-
ated, the other species may expand their resource utilization ("niche")
and increase in abundance. Such changes would be reflected in a
diversity index; example communities of this type would be phyto-
plankton (could restrict to diatoms), looplankton, aquatic benthic
insects, or fish.
This paper does not take into account the important difference
between growth and reproduction in computing the diversity of produc-
tivity: was defined as pr/PR where pr was the productivity of a
particular species in the sample and PR the total sample productivity;
productivity was calculated by multiplying a species mean sample density
and biomass times the number of times a species reproduced per year.
But cell growth research has indicated that there is only a loose
connection between cell mass and cell division (Williams, 1971).
HAMILTON, M. A. 1975.
Indexes of diversity and redundancy.
J. Water Poll. Control Fed., 47:630-632.
A brief review: This is a comment on some incorrect descriptions of
the Shannon formula and l.he "redundancy1' formula that have occurred
in the literature on the structure of aquatic invertebrate communities.
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39. HOWELL, F. G., and J. B. GENTRY. 1974.
Effect of thermal effluents from nuclear reactors on species diversity
of aquatic insects.
In Gibbons, J. W. and R. R. Sharitz (eds.). 1974. Thermal ecology.
Oak Ridge: U. S. Atomic Energy Commission Technical Informaticn
Center.
A brief review: Aquatic insect populations of thermal post-thermal,
and natural streams on the Savannah River Plant site were compared
according to species composition and diversity. Insect communities
in the natural stream had the highest diversity indexes; communities
in the post-thermal stream had intermediate diversity estimates;
communities in the thermal stream had the lowest diversity estimates.
In the aquatic habitats sampled, species-diversity and evenness esti-
mates were reliable indicators of thermal stress.
40. KOCHSIEK, K. A., J. L. WILHM, and R. MORRISON. 1971.
Species diversity of net zooplankton and physiochemical conditions in
Keystone Reservoir, Oklahoma.
Ecology, 52:1119-1125.
A brief review: Net zooplankton collections and physiochemical measure-
ments were made monthly in four stations at various locations in the
Keystone Reservoir, Oklahoma. Shannon's formula was used to evaluate
species diversity of zooplankton. Variance values of diversity indi-
cated only a slight gain in precision by increasing the sample size to
above 400 individuals. Coefficients of correlation between physico-
chemical parameters and species diversity unadjusted for month and
station effect were compared with adjusted coefficients.
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73
A comment: The feasibility of using zooplankton in biological moni-
toring has been little studied; diatoms and benthic invertebrates have
received most of the attention. This paper is a useful reference on
the ecology of zooplankton.
41• MacKAY, R. J., and J. KALFF. 1969.
Seasonal variation in standing crop and species diversity of insect
communities in a small Quebec stream.
Ecology, 50:101-108.
A brief review: This paper contains some information on the basic
ecology of benthic insects, including the importance of substrate type
to insect populations. As ERCO has pointed out in its report, a
stream (or other freshwater body) should be studied year-round in a
monitoring program in order to gain information on natural diversity
fluctuations such as those reported in this paper.
42. MUNDIE, J. H. 1971.
Sampling benthos and substrate materials, down to 50 microns in size,
in shallow streams.
J. Fish. Res. Bd. Canada, 28:849-860.
A brief review: Stream bed materials, both biotic and abiotic, in
the size range 50 microns - 200 millimeters can be sampled unselec-
tively, in shallow streams, with a simple inexpensive apparatus
consisting of a box provided with an adjustable upstream inlet:, md,
downstream, two nets, one within the other.
A comment: The paper cites quite a few other works on benthic sampling
techniques.
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74
43. PEET, R. K. 1975.
Relative diversity indices.
Ecology, 56:496-498.
A brief review: Diversi :y indi :es ar? frequently applied in the f itt.
of ratios of absolute diversity to the maximum diversity possible.
Regardless of whether the maximum diversity is defined to be limited
by the number of species or by the number of individuals present, the
resultant indices can be shown to possess mathematically undesirable
qualities. All such indices are inappropriate for most ecological
applications.
44. WILHM, J. L. 1967.
Comparison of some diversity indices applied to populations of benthic
macroinvertebrates in a stream receiving organic wastes.
J. Water Poll. Control Fed., 39:1673-1683.
A brief review: Populations of benthic macroinvertebrates can be used
to assess pollution in a stream receiving organic enrichment. Sampling
stations should be established at various distances below the pollution
outfall. For comparative purposes, samples should be collected in
clean areas either above the outfall or at a sufficient distance
downstream. Sampling methods should be the same at each station.
Data can be summarized clearly and briefly with a diversity index.
The index selected for use must be independent of sample size.
45. WINNER, R. W. 1972.
An evaluation of certain indices of entrophy and naturity in lakes.
Hydrobiologia, 40:223-245.
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75
A brief review: Data from five Colorado Lakes were utilized to test
the usefulness of net primary productivity, seston, chlorophyll _a and
Secchi disc transparancy as indices of eutrophy. The Four were in
essential agreement as to the relative degree of eutrophication in
each of the five lakes. The concept of maturity is also considered
by ranking the Colorado lakes according to several maturity indices:
phytoplankton diversity, zooplankton diversity, Margalef1s pigment
ratio, P/B ratio, and assimilation number. The relative maturity of
the lakes shifts considerably, according to which maturity index one
utilizes.
A comment: The paper is interesting for its report of lack of correl-
ations between phytoplankton and zooplankton diversities. Winner
concludes "... that measurement of diversity in one community of
an ecosystem does not necessarily indicate what diversities are in
other communities of that ecosystem." This indicates that several
aquatic "trophic levels" should be studied instead of just one in a
biological monitoring program.
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CLASSIFICATION OF THE ANNOTATED BIBLIOGRAPHY
ACCORDING TO THE TOPICS OF PUBLICATIONS
I. Ecological theory and concepts.
10, 11, 12, 13, 14, 15, 20, 25, 32
II. Ecological applications including biomonitoring.
1, 2, 3, 4, 6, 7, 8, 16, 17, 18, 19, 20, 23, 24, 27,
28, 29, 30, 33, 35, 36, 37, 39, 40, 41, 42, 44, 45
III. Statistical methodology.
5, 9, 10, 15, 20, 21, 22, 31, 34, 38, 43
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77
Section II
A SELECTED LIST OF PUBLICATIONS ON COMMUNITY DIVERSITY
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78
2. AN ALPHABETICAL LIST
Abele, L. G. (1974). Species diversity of decapod crustaceans in marine
habitats. Ecology, 55, 156-161.
Allan, J. D. (1975). The distributional ecology and diversity of benthic
insects in Cement Creek, Colorado. Ecology, 56, 1040-1053.
Almeida, S. P.; et al. (1972). Holographic microscopy of diatoms. Trans.
Kansas Acad. Sci., 74, 257-260.
Anscombe, F. J. (1949). The statistical analysis of insect counts based
on the negative binomial distribution. Biometrics, 5, 165-173.
Anscombe, F. J. (1950). Sampling theory of the negative binomial and
logarithmic series distributions. Biometrika, 37, 358-382.
Arnold, S. J. (1972). Species diversity of predators and their prey. Am.
Naturalist, 106, 220-236.
Auclair, A. N.; and Geoff, F. G. (1971). Diversity relationships of
upland forests in the Western Great Lakes area. Aisier. Nat., 105,
499-528.
Bailey, R. C. (172). A montage of diversity. Ph.D. thesis, Emory Univ.,
1-183.
Barbour, C. D. ; and Brown, J. H. (1974). Fish species diversity in lakes.
Amer. Natur., 108, 473-489.
Bartlett, M. S.; and Hiorns, R. W. (1973). The mathematical theory of the
dynamics of biological populations. Academic Press, New York.
Bazzaz, F. A. (1975). Plant species diversity in old-field successional
ecosystems in Southern Illinois. Ecology, 56, 485-488.
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79
Beerbower, J. R.; and Jordan, D. (1969). Application of information theory
to paleontologic problems: Taxonomic diversity. J. Paleontology, 43,
1184-1198.
Berger, W. H.; and Arker, F. H. (1970). Diversity of planktonic forminifera
in deep sea sediments. Biol. J. Linn. Soc., 3, 1-21.
Bhargava, T. N.; and Doyle, P. H. (1974). A geometric study of diversity.
J. Theo. Biol., 43, 241-251.
Bhargava, T. N.; and Doyle, P. H. Reclassification, diversity and elementary
number theory. In stock.
Bhargava, T. N.; and Uppuluri, V. R. R. On diversity in human ecology.
In. stock.
Bhargava, T. N.; and Uppuluri, V. R. R. Sampling distribution of Gini's
index of diversity. Typescript.
Bhargava, T. N.; and Uppuluri, V. R. R. (1975). An axiomatic derivation
of Gini's index of diversity with applications. Metron.
Black, G. A. Dobzhansky, T.; and Pavan, C. (1950). Some attempts to estimate
species diversity of trees in Amazonian forests. Bot. Gazette, 111,
413-425.
Bliss, C. I. (1958). Analysis of insect counts as NBD. Prox x Int. Cong.
Entolmol., 2, 1015-1032.
Bliss, C. I. (1965). An analysis of some insect trap records Classical
and contagious discrete distributions, G. P. Patil, Ed., Statistical
Publishing Society, Calcutta.
Eliss, C. I.; and Fisher, R. A. (1953). Fitting the negative binomial
distribution to biological data, note on the efficient fitting of the
negative binomial. Biometrics, 9, 176-200.
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80
Bowman, K. 0.; Hutcheson, K.; Odum, E. P.; and Shenton, L. R. (1971).
Comments on the distribution of indices of diversity. Statist. Ecology.
Vol. 3. Populations, Ecosystems, and Systems Analysis, pp. 315-366.
Bratton, S. (1975). Comparison of the beta diversity functions of the
overstory and herbaceous understory of a deciduous forest. Bull. Torrey
Bot. Club., 102, 55-60.
Brillouin, L. (1962). Science and information theory, 2nd ed. Academic
Press, New York.
Brisbin, I. L. (1973). Abundance and diversity of waterfowl inhabiting
heated and unheated portions of a reactor cooling reservoir. In
Thermal Ecology, U. S. Atomic Energy Commission.
Bulmer, M. G. (1974). On fitting the Poisson lognormal distribution to
species-abundance data. Biometrics, 30, 101-110.
Buzas, M. A. (1972). Patterns of species diversity and their explanation.
Taxon, 21, 275-286.
Buzas, M. A.; and Gibson, T. G. (1969). Species diversity: Benthonic
foraminifera in Western North Atlantic. Science, 163, 72-75.
Cairns, J. (1968). The sequential comparison index—a simplified method
for non-biologists to estimate relative differences in biological
diversity in stream pollution studies. J. Water Poll. Cont. Fed., 40,
1607-1613.
Cairns, J.; and Dickson, K. L. (1971). A simple method for the biological
assessment of the effects of wastes discharges on aquatic bottom-
dwelling organisms. J. Water Poll. Cont. Fed., 43, 753-772.
Cairns, J.; et al. (1972). Coherent optical spatial filtering of diatoms
in water pollution monitoring. Arch. Mikrobiol., 83, 141-146.
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81
Cassie, R. M. (1962). Frequency d Istribution models in the ecology of
plankton arid other organisms, J. Anim. Ecol., 31, 65-92.
Chatfield, C. (1969). On estimating the parameters of the LSD and NBD.
Bioraetrika, 56, 410-414.
Church, V. (1974). Bird species diversity in patagonia: A critique.
Amer. Natur., 108, 235-236.
Cody, M. L. (1966). The consistency of intra- and inter-continental grass-
land bird species counts. Amer. Naturalist, 100, 371-376.
Cody. M. L. (1968). On the methods of resource division in grassland bird
communities. Amer. Natur., 102, 107-147.
Cody, M, L. (1969). Chilean bird distribution. Ecology, 51, 455-463.
Cody, M. L. (1973). Competition and community structure. Princeton Univ.
Press, Princeton, New Jersey.
Cohen, J. E. (1968). Alternative derivations of a species-abundance
relation. Amer. Natur., 102, 165-172.
Connell, J. H.; and Orias, E. (1964). The ecological regulation of species
diversity. Amer. Natur., 98, 399-414.
Conrad, M. (1972). Stability of food-webs and its relation to species
diversity. J. Theor. Biol., 34, 325-335.
Cramer, N. F. ; and May, R. M. (1972). Interspecific competition, predation
and species diversity: A comment. J. Thenr. Biol., 34, 289-293.
Dahlberg, M. D.; and Odum. E. P. (1969). Annual cycles of species occurrence
and diversity in Georgia estuarine fish populations. Amer. Midland
Naturalist, 83, 382-392.
David, F. N. (1970). Measurement of diversity. Proc. Sixth Berkeley
Symp. Math. Statist. Probability, 1, 631-648.
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82
David, F. N. (1971). Measurement of diversity. Multiple cell contents.
Proc. Sixth Berkeley Symp. Math. Statist. Probability, 4, 109-136.
Dayton, P. K.; and Hessler, R. R. (1972). Role of biological disturbance
in maintaining diversity in the deep sea. Deep Sea Res., 19, 199-208.
De Angelis, D. L. (1975). Stability and connectance in food web models.
Ecology, 56, 238.
De Loach, C. J. (1971). The effect of habitat diversity on predation.
Proc. Tall Timbers Conf. Ecol. Anim. Contr. Habitat Manage., 2, 223-241.
Deevey, E. S. (1969). Specific diversity in fossil assemblages. Brook-
haven Symp. Biol., 22, 224-241.
Debenedictis, P. A. (1973). On the correlations between certain diversity
indices. Amer. Natur., 107, 295-302.
Diamond, J. M.; and Cody, M. L. (eds.) (1975). Ecology of communities.
Harvard Univ. Press, Cambridge, Mass.
Dickman, M. (1968). Some indices of diversity. Ecology, 49, 1191-1193.
Dobzhansky, T. (1967). Genetic diversity and diversity of environments.
Proc. Fifth Berkeley Symp. Math. Statist. Probability, 4, 295-304.
Eberhardt, L. L. (1969). Some aspects of species diversity models.
Ecology, 50, 503-505.
Ebringer, A. (1975). Information theory and limitations in antibody
diversity. J. Theor. Biol., 51, 293-302.
Edden, A. C. (1971). A measure of species diversity related to the log-
normal distribution of individuals among species. J. Exp. Mar. Biol.
Ecol., 6, 199-209.
Engen, S. (1975). A note on the geometric series of a species frequency
model. Biometrika, 62, 697-699.
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83
Engen, S. (1974). On species frequency models. Biometrika, 61, 263-270.
Engen, S. (1975). The coverage of a random sample from a biological
community. Biometrics. In stock.
Fager, E. W. (1972). Diversity: A sampling study. Amer. Nat., 106, 293-
310.
Findley, J. S. (1973). Phenetic packing as a measure of faunal diversity.
Amer. Naturalist, 107, 580-584.
Fisher, R. A.; Corbet, A. S.; and Williams, C. B. (1943). The relation
between the number of species and the njmber of individuals in a random
sample of an animal population. J. Anim. Ecol., 12, 42-58.
Flessa, K. W.; and Irobrie, J. (1971). Phanerozoic fossil record: Quanti-
tative analysis of diversity levels. Geol. Soc. Amer. Abs., 3, 566-567.
Gage, J. (1972). Community structure of the Benthos in Scottish sea-lochs.
I. Introduction and species diversity. Marine Biology, 14, 281-297.
Ghent, A. W.; and Hanna, B. P. (1968). Application of the "broken stick"
formula to the prediction of random time intervals. Amer. Midland
Nat., 79, 273-288.
Gibson, L. B. (1966), Some unifying characteristics of species diversity.
Cushman Foundation Foram. Res., 17, 117-124.
Gibson, T. G.; and Buzas, M. A. (1973). Species diversity: Patterns in
modern and miocene forarainifera of the eastern margin of North America.
Geol. Soc. Amer. Bull., 84, 217-238.
Glenn-Lewin, D. (1975). Plant species diversity in ravines of the Southern
Fingerlakes Region, New York. Can. J. Eot., 53, 1465-1472.
Glime, J. M.; and Clemons, R. M. (1972). Species diversity of stream
insects on fontinalis spp. compared to diversity on artificial sub-
strates. Ecology, 53, 458-464.
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7
Goldman, S. (1953). Some fundamentals of Information theory. Information
theory in biology, H. Quastler, ed., Univ. of Illinois Press, Urbana.
Goodman, D. (1975). The theory of: diversity - Stability relationships in
Ecology. Quart. Rev. Biol., 50, 237-266.
Goulden, C. E. (1969). Temporal changes in diversity. Diversity a;id
stability in ecological systems, Brookhaven Symp. Biol., 22, 96-102.
Grundy, P. M. (1951). The expected frequencies in a sample of an animal
population in which the abundances of species are log-normally distrib-
uted. Part I. Biometrika, 38, 427-434.
Haas,- P. H. (1975). Some comments on the use of the species-area curve.
Amer. Natur., 109, 371-373.
Hairston, N. G. (1959). Species abundance and community organization.
Ecology, 40, 404-416.
Hairston, N. G. (1969). On relative abundance of species. Ecology, 50,
1091-1094.
Hairston, N. G. et al. (1968). Relationship between species diversity and
stability. Ecology, 49, 1091-1101.
Hamblen, L. T. (1974). Number of moves; an index of species diversity.
In stock.
Hammon, W. D. (1974). S sub H': A similarity index based on shared
species diversity, used to assess temporal and spatial relations among
intertidal marine gastrotricha. Oecologia, 17, 203-220.
Harger, J. et al. (1973). Experimental investigation into effects of pulp
mill efflucmt on structure of biological communities in Alber^ni
Inlet, British Columbia: I. Subtidal communities. Int. J. Environ.
Stud., 4, 269-282.
Hendrickson, J, A.; and Ehrlich, P. R. (1971). An expanded concept of
"species diversity". Notulae Naturae, No. 439, 1-6.
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85
Heyer, W. R.; and Berven, K. A. (1973). Species diversities of herpeto-
faunal samples from similar microhabitats at two tropical sites.
Ecology, 54, 642-645.
Hill, M. 0. (1973). Diversity and evenness: A unifying notation and its
consequences. Ecology, 54, 427-432.
Hohn, M. H. (1961). The relationship between species diversity and density
in diatom populations from Silver Springs, Florida. Trans. Amer.
Microscop. Soc., 80, 140-165.
Hohn, M. H.; and Helelrman, J. (1963). The taxonomy and structure of
diatom populations from three Eastern North American rivers using three
sampling methods. Trans. Amer. Microsc. Soc., 82, 250-329.
Holgate, P. (1969). Species frequency distributions. Biometrika, 56, 651-
660.
Holling, C. S. (1973). Resilience and stability of ecological systems.
Ann. Rev. Ecol. Syst., 4, 1-23.
Horn, H. S. (1975). Markovian properties of forest succession. Ecology of
communities, J. M. Diamond and M. L. Cody (eds.), Harvard Univ. Press,
Cambridge, Mass.
Howell, F. G.; and Gentry, J. B. (1973). Effects of thermal effluents from
nuclear reactors on species diversity of acquatic insects. In Thermal
Ecology, U. S. Atomic Energy Commission.
Hulburt, E. M. (1963). The diversity of phytoplanktonic populations in
oceanic, coastal, and esturine regions. J. Marine Res., 21, 81-93.
Kurd, L. E.; hcllinger, M. V.; Wolf, L. L.; and McNaughton, 3. J. (1971).
Stability and diversity at three trophic levels in terrestrial succes-
sional ecosystems. Science, 173, 1134-1136.
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Hurlbert. S. H. (1971). The nonconcept of species diversity: A critique
and alternative parameters. Ecology, 52, 577-586.
Hutcheson, K. (1969). The moments and distribution for an estimate of the
Shannon information measure and its application to ecology. Ph.D.
thesis, Va. Polytechnic Inst., 1-142.
Hutcheson, K. (1971), A test for comparing diversities based on the Shannon
formula. J. Theore. Biol.
Hutcheson, K. et al. (1972). Diversity: What is it? Presented at
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effluents. Am. Midland Naturalist, 76, 427-449.
Williams, F. M. (1973). Mathematical modelling of microbial populations.
Bull. Ecol. Res. Comm., 17, 417-426.
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103
Williams, L. G. (1964). Possible relationships between plankton-diatom
species numbers and water quality estimates. Ecology, 45, 809-823.
Williamson, M. (1973). Species diversity in ecological communities. In
the Mathematical Theory of the Dynamics of Biological Populations, ed.
by M. S. Bartlett and R. W. Hiorns.
Woodwell, G. M. (1970). Effects of pollution on the structure and
physiology of ecosystems. Science, 168, 429-433.
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APPENDIX
PROCEEDINGS OF THE NINETH INTERNA!ION.\L BIOMETRIC CONFERENCE
HELD AT BOSTON, AUGUST 22-27, 1976.
AN INVITED PAPER ON:
Ecological Diversity: Concepts, Indices, and Applications
By
G. P. Patil and C. Taillie
-------
105
PROCEEDINGS OF THE
International
Biometric
Conference
Invited Papers
Volume II
BOSTON
AUGUST 22-27,1976
THE BIOMETRIC SCCETY
-------
106
ECOLOGICAL DIVERSITY: CONCEPTS, INDICES AND APPLICATIONS
G. P. Patil and C. Tailli".
Department of Statistics and Graduate Ecology Program
The Pennsylvania State University
University Park., Pa.
SUMMARY
This paper puts forth the view that diversity is an average property of
a community and attempts to identify that property. A few intuitive
cases of one community being more diverse than another are formalized
into a relation, "leads to". This relation generates a diversity ordering
of ecological communities which is shown to be equivalent to stochastic
ordering. Indices based on species rankini? are discussed. Also are
ctiaraccerize.., the indices which satisfy a weighted AIIOVA formula.
Application of diversity to environmental monitoring requires rapid and
reliable procedures. The statistical properties of one such biomonitoring
procedure are developed. Finally, certain methods for estimating the
number of species are discussed.
0. BACKGROUND AND INTRODUCTION
0*1 Background. "When several or many-species-populations occur
together and interact with one another in a small region of space, they
Jointly constitute an ecological community ... The ultimate objective
in studying the ecology of a community is to determine the nature and
the relative importance of the factors controlling its composition;
also whether, to what extent, and why, the community is changing with
time. To pursue this objective it is necessary to define some measurable
properties of the community as a whole. If this can be done, making
it possible to write down a short list of measurements that constitute)
a summary description of a particular community at n partlculnr tli»»»,
it then becomes possible to make quantitativa comparisons anion k novuml
communities. This is a necessary first step toward an understand lit}'
of how communities function ... The diversity of natural ecological
communities his never been more highly valued than they are now, as
they become increasingly threatened by the environmental crisis. The
purpose of measuring a community's diversity is usually to Judge
its relationship either to other community properties such as productivity
and stability, or to the environmental conditions that the community
is exposed." — E. C. Plelou [ 20, 21] ~
"Numbers alone do not make science; it is relations between numbers
that are needed. Applying a formula and calculating a species fivers ty
from a census does not reveal very much; only by relating this divers y
to something else something about the environment perhaps «oes
it become science. Hence there is no intrinsic virtue y P ^
diversity neasure except insofar as it leads to clear relations.
R. E. MacArthur [ 16].
383
-------
. 107
"For top management and tenca'. public policy development, eon 1 cor Inr
data cust be shaped Into easy-to-understand Indices that ajinroRite
data into understandable forms. I am convinced that much greater effort
must be placed on the development o£ better monitoring systt?n>s and
indices than we have in the past. Failure to do ao will result In
8ub-optitnum achievement of goals at much greater expense," — Ru3sell
E. Train [27].
"Biological monitoring plays an important role in a pollution monitoring
program providing information not available through conventional physical
and chemical monitoring. The structural and functional changes in
aquatic communities have been used, for example, in assessing the effects
of pollutants on aquatic cormr.unities. Most forms of environmental stress
cause a reduction In the CLuplexity of the system, or in other words,
a simplification. From a biolugical point of view, this is expressed
by a marked reduction in species diversity ... The most suitable means
of analyzing community structure for the purposes of pollution assessment
appears to be the diversity index [29]. By comparing the diversity
indices between sampling stations, it is possible CO determine the
relative biological conditio., of these stations.
Healthy Station
200
150 >
100 I
50 5
0
LL
Semi-Healthy Station
Ll
Polluted Station
200
150
100
50
0
I
J L
Very Polluted Station
1
1. Pollution Algae 2. Tolerant Worms, etc. 3. Protozoa 4. Algae
(non-pollution) 5. Clams, etc. 6. Insects, Crustacea 7, Pish
Bar graphs showing population structure of aquatic communities
under different degrees of pollution. •* Cairns et al [ 5, 7,10].
Figure 0.1
384
-------
108
0,2 Introduction. What is diversity? Can it be measured? If so, how?
and why? This paper represents a preliminary attempt on out part to
come to grips with some of these Issues. Section 1 puts forth the view
that diversity is an average property of a community and attempts to
identify that property. Even so, diversity, like any other concept,
remains elusive until it can be quantified, and so, section 2 provides
some biologically realistic examples of the construction of diversity
Indices. Section 3 identifies the altogether too few cases In which It
can be argued on intuitive grounds that one community Is more diverse
than another. These cases are formalized Into a relation, "leads to", which
in turn generates a diversity ordering of ecological communities. The
ordering is shown, in section 4, to be equivalent to what Is known in
the statistical literature as stochastic ordering. Section 5 discusses
a class of Indices based on species ranking. The sampling theory for
these indices poses a number of challenging and unsolved problems.
For hierarchial classifications, an index which satisfies an ANOVA
formula may be convenient. Section 6 characterizes the class of diversity
indices which satisfy a weighted ANOVA formula. Application of diversity
to environmental monitoring requires rapid -vnd reliable procedures for
estimating diversity from a sample. The statistical properties of one
such procedure (Cairns sequential comparison index) are developed in
section 7 with a central lial: theorem of Hoether aa the main analytical
tool. The final section 8 describes five methods for estimating the
number of species in a community, the methods are applied to several
data eats.
385
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109
1. diversity as an average property of a community
Ke view diversity as an average, property of an ecological cosmwnity.
But the average of what? To an outside observer, variety is a moat
striking feature of a diverse community. Alfred Russell Wallace's [28 ]
description of a tropical forest is a vivid illustration:
If the traveller notices a particular species and wishes
to find more like it, he may turn his eyes in vain in
any direction. Treec of varied forms, dimensions and
colours are around him, but he rarely sees any one of them
rejeated. Time after time he goes towards a tree which,
looks like the one he ueeks, but a closer examination
proves it to be distinct. He may at length, perhaps, meet
with a second specimen 'ialf a mile off, or may fail
altogether, till on another occasion he stumbles on one
by accident. (Quotation from Uulbert [13 ].)
In a diverse community, such as that described by Wallace, the typical
species is relatively rare and, consequently, diversity may appropriately
be defined as the average rarity vithin. the covvsiunity.' • To make this idea
precise, the concepts of "community" and "rarity" must be formalized.
For our purposes, a community may be defined as a collection of
individuals grouped into species which, in turn, are ranked in order of
decreasing abundance. The parameters of a community are denoted by
C - (s;tt) where s is the nvwher of species (finite or countably Infinite)
and 7T - (ir^.ir^,...,1^) so that ir^ > tt^ > .., j> tt# > 0 are the ranked relative
abundances. Necessarily £ir^ - 1. Given the community, a numerical
measure of rarity is to be associated with each species. Denote the
rarity of the 1th ranked species by R(i;n). With these notations,
Definition 1.1: The diversity of tha cosmualty C * (i Is Its average
•t
rarity and la given by
s
A(t> - Z if. R(ljir)
1-1 1 ~
386
-------
110
where A is the diversity index associated with the measure of rarity R.
The concepts most fruitful for deciding upon the functional form
of RCi;ij) include:
(I) Dichotomy: R(I;ir) depends only on the numerical value of and
not explicitly upon either 1 or the other components of ir. For
notatlonal simplicity write R(l;ir) as ROr^).
(II) Ranking: R(i;ir) depends only on tha rank. 1 and not explicitly upon
the numerical values of the components of. ir. Vrlte R(l;ir) as R(i).
Before proceeding with the formal devalopment, It may be useful
to Indicate how various measures of rarity can be constructed In a
meaningful and interpretable way.
2. THE CONSTRUCTION AND INTERPRETATION OF DIVERSITY INDICES t EXAMPLES
Three of the more widely used indices of ecological diversity are
the "species count", the Shannon-Wiener Index and Simpson's (complementary
index. These will be denoted as followsj
Species count: - s-1
Shannon-Wiener: A^ - -I ir^ log rr^
, 2
Simpson: A^ - 1 - £ .
All three assign diversity zero to a single-species community.
Aa Simpson [ 25] himself has observed, Ax nay be Interpreted as the
probability that two randomly selected members of the community belong
to different species. However, there Is an alternative Interpretation
which, can be fruitfully generalised. When rewritten in the form
A1 " £ *1 Z W1 R^irl^» Simpson's Index expressea the average
cowunlty rarity, with the understanding Chut species rarity it measured
387
-------
Ill
by RC.tr) - l-ir. Now comtetnplate Wallace's traveler who first cornea upon.
a member of, say, clta itK species. As his journey continues, the traveler
til
encounters other organisms, sometimes of the i species and sometimes
not. The rarer species 1, the. more likely are interspecific encounters.
- l~ir1 precisely the probability that a giv«> encounter is
interspecific. In what follows, this concept of inter- vereus intra-
specific encounters is exploited. Three different schemes are examined.
2.1 Waiting time for an ititr.ispeci-fic encounter; Again consider the
traveler in* search o£ the ltl> upecies.
. Figure 2.1
With t+1 equal to the number of encounter* upto and including the first
lntraspeclfic one, we have,
EttjiTj] • Cl-TTj,) ElT+lj-rr^ « 1/*^
Etl/Ct+l)!^] - -nt logGr^/U-i^).
when ¦ Cl-ir^)^ r^, y *¦ 0,1,...
Since large Y are associated with, rare species, both Y and Y/Ct+1)
389
-------
112
are reasonable measures of rarity. But these are random variables and
should be replaced by- average quantities. There are several ways to
interpret the. "average.' of a ratio: each, gives rise to a different index.
1. Species Count:
ROr£) - EIyIitJ - S ff1 RC^) - E Cl-^) - a-1.
2. Simpson"s Index:
RCiTj) - EtYlirJ/ElY+lJir^ - 1-ff^ Z 7^ RClfj) - (1-lTj) .
Shannon-Wiener Index:
R(ir^) ¦ E[ —• lir^J • E[Y|ir^J - -log ir^, £ R(irt> ¦"-£ log :
4. An Unfamiliar Index:
R(if±) - E[Y/(Y+1)|tt1] - 1 + logdt^/Cl-^)
E ir4 Rfc^) - 1 + I irj logCTr^/Cl-T^) .
2.2 Waiting time for an interspecific encounter. Hers we suppose the
traveler to be in search of a new species tvnd put Z+l equal to the number
of encounters up to and Including the first interspecific one.
Figure 2.2
389
-------
113
Ve have. Elzl^] - 1^/(1-^), ElZ+lluJ -
-Cl-T } logCl-TT.)
EU/CZ+i)|ir ] — .
1 t
Small Z are associated with rare species and the variables of Interest
are 1/Z and l/(Z+l).
1. Species Count: R(tt^) » l/Elz|ir^J " (I-WjJ/tt^ .
2. Simpson's Index; R(iTj> ~ l/E[Z+l|ir^] ~ 1—ir^ .
3. A Second Unfamiliar Index:
ROTj) - E[l/(z+l) |ir^] ' — CI—rrlogCl-ir^).
The index itself is £ RCtfj) - -£ (1-TTj) logCl-1^) .
Note that E[l/z|ir^] • » ,
2.3 Fixed nuiaber of encounters. Here we let 1 be the'number of inter-
specific and Z the number of intraspecific encounters out of a fixed
total of N encounters.
1. Species Count: RO^) ¦ E[TCJir^J / E£Z¦ (l-tr^/i^ .
2. Simpson's Index: Rfir^) - E[Y|ir^] / E[Y+Z|7r^J » 1-ir^ .
Note that EfY/zl^] - », while E[Y/(Y+Z) I^J - 1-1^ .
Remarks: 1. It is curious that the Shannon>-Wiener index arises in
only the first scheme.
2. For a given measure, R(tt) , of species rarity, R(Q+)
may be finite or infinite. When it Is finite, the.:* is a dual measure,
defined by R(ir) " R(P } » RCl) - R(l-ir). Three facta are easily verified,
a. R • R.
390
-------
114
b. The two unfamiliar Indices constructed above are duals of one
another.
c. Simpson's index 1b self dual.
Some biological motivations for considering Interspecific encounters
have been discussed by Kulbcrt [13], who concluded that, if an index
Is to be used, Simpson's is conceptually preferable to Shannon's.
His negative assessment of the Shannon-Wiener index would appear to be
unduly pessimistic. In fact, additional arguments can be put forth in
support of the Shannon-Wiener index. Motivated, in part, by the fact
that biological grovtH processes are often multiplicative, Preston [ 22 ]
suggests that logarithmic abundances are more useful than absolute
4.L
abundances. With as the abundance of the i species, log (1/X^)
becomes an Intuitively reasonable measure of species rarity. Since
. constant, the average community rarity Is
Z ir^ logd/X^) ¦ -Z logO^) + constant.
We also note that it is frequently useful (in the study of contingency
tables, for example) to express probabilities in the fozs " exp(-ci^),
> 0. Since rare species (small correspond to l*rge a^, the at^
may be taken as a measure of species rarity And this leads, once again,
to the Shannon-Wiener index.
3. TWO CRITERIA FOR DIVERSITY INDICES
»
Recalling the definition of dichotomous indices, A{C) ¦ E it. R(tt.),
i-1 1 L
observe that R(0) la inherently undefined while the value R(l) is germane
only to a single-species community and, in fact, equals the diversity
of such a community. R(l) ¦ 0 is a natural normalizing requirement.
fch&S else might be required of R? Ot intuitive grounds, R(tt) should
391
-------
Hi
be a decreasing function of it (.species J is rarer than species i if
TTt > TTj).
First Criterion CI; R is a decreasing function defined on (0,1]. If
the normalizing condition BC1) - 0 is also imposed, R will as a consequence,
be nonnegative.
This monotonicity requirement on ft, simple and intuitive though
it is, has a striking implication. Consider two communities,
where h > 0 is sufficiently small that the species, ranking is left
undisturbed. (Ties are not a problem. Take i to be the highest rank
within the tied set.) We say that C leads to C' by introducing a species.
A possible biological interpretation is that species i shares its
resources with a newly arrived competing species. Note that the relative
abundances of all other species are unchanged.
Theorem 3.1; Assume R(ir) is decreasing in tt. Then Introducing a species
increases the diversity of a community. More precisely, if C leads
to C' by introducing a species, then A(C) < A(C') .
Proof: By assumption 7r( > ffj-h > h > 0 and so R(h) >_ RO^-h) > R0r^).
Figure 3.1
Bqt ACC') - A.CC) - OTj-h} R0rt-h) + h.R(h) - irt RC^)
- h[R(h) - R0rt-h)3 .+ - RC*,)] >0,
392
-------
116
Any community C - (a,rr) with, finitely many species can be construct*
r®5~i ,
' i"
^ si'
I * 3
Figure 3.2
from a single-species community hy successively
Introducing new species Csee Figure 3.2). theorem
3.1 asserts that the diversity increases at each,
step. None the less, indices satisfying Criterion
CI may have undesirable properties, as illustrated
by the next example.
'2 *
Example 3.1: Let R(n) '» 1/tt - 1 and A » Z 1/tt, - 1. This index
1-1 1
satisfies Criterion CI and assigns diversity zero to a single-species
community. Figure 3.3 includes a plot of the values of A for communities
with ranked abundance vector (1-tt ,tt) , 0 <_ ir < 1/2. The point A represent
a single-species community, while B, C and D represent successively
more even two-species communities. In accord with Theorem 3.1, B,
C and D are more diverse than A. But among thte three two-species communl
ties, the diversity as measured by & decreases as the evenness increases.
V
0
If
A
B
I i
Figure 3.3
( 2
In going from B to C to D in Example 3.1, the change In community
composition may be described as a transfer of. abundance from one species
to anftthpr JLess abundant species. The next definition formalizes this
concept for many—species comaunitiei.
393
-------
117
Definition 3.1: Let C - (s.J) and C' - (s'.jr') be two conmualties.
C leads to C' bv a transfer of abundance if s " 8* and if J and j' have
the. form
tt - Cir^ ,irit iTj ,irg)
7T 0 small. In particular ir^ ¦ ir£ for It # i,J. We
write C « C' when C leads Co C' by either introducing a species or by
transfering abundance.
Second Criterion C2: C « C' -> A(C) <_ A(C') .
The Index of example 3.1 does not satisfy Criterion C2. In fact,
for this example, A(C) <: A(C') when C leads to C' by introducing a
species while A(C) > A(C') when C leads to C' by transfering abundance.
To state conditions under which the two criteria will be satisfied,
it is convenient to define an auxiliary function V by
( hR(it) it e (0,1]
V(tj) -
¦ V. 0 IT - 0 .
For the index s-l, V(ir) ¦ 1-ir for positive ir, which shorn that V may b*
discontinuous at the origin.
Theorem 3.2: Criterion C2 is satiofled <¦>
VCir.-HO-VCirJ VCu,)-VU,-h)
—1 1 >—i i— <3.i)
h I h
Assuming differentiability of V, condition (3.1) may be replaced by
V' (iTj) > V' CiTj) whenever > ir^ > 0 and ir^ + ± 1.
394
-------
118
Proof: Straightforward.
Exfraple 3,2: The condition (3.1) has i simpi •. geometric interpretation
as illustrated hy figure 3.4 for communities with, abundance vectors
CVVir3}. The convention ir^ >_ 21.^3
requires that the diversity increase as a point
moves toward the center of the triangle along any line segment parallel
to an edge. The arrows in the figure Indicate the direction of increasing
diversity.
Theorem 3.3: Criterion CI and Criterion C2 are both satisfied if V
is concave on the closed unit interval [0,1].
Proof: Criterion CI: Let 0 < x < y < 1. Observe that V(x)/x is the
slope of the line from the origin to the point V(y)/y and hence that R(x) > R(y).
Criterion C2: Condition (3.1) requires that L should have greater
•lope than t' (Figure 3.6). But this is a well-known consequence of
of the triangle represents the completely
Is dropped for this example-. Points on the vertlc
edges, and interior of the triangle represent
respectively single-species, two-species,
and three—species communities. The centrold
even three-species community. Condition (3.1)
Figure 3.A
concavity
I I 1
Tfi-a n I
-I 1—
1Tj f$+k
Figure 3.5
Figure 3.6
395
-------
119
Remark: Because of the constraint < 1, the converse of Theorem
3.3 is not quite true. For example, let R00 ¦ 3/4 - tt for it £ (0,3/4)
and RCO - 0 for it e [3/4,lj.
Corollary 3.1: The three indices considered in section 2
saticfy both Criterion CI and Criterion C2.
The two criteria are invariant to positive affine transformations
of form R* - OR + g. A* - otA + 0 , a,£5 constants, o > 0 .
It is not hard to show that R'(1) is strictly negative If RCl) • 0
and V Is concave. (R = 0 is a trivial exception.) Where available the
conditions R(l) - 0 and R'(1) - 0 are convenient normalizing requirements.
A ^>Aq, and A^ are normalized in this sense.
For concreteness, the criteria of this section were developed In
terms of dichotoinous indices. For the general index with rarity measure
R(1;tt), Criterion C2 requires no change and Crlterioa CI Is replaced byt
CI': For fixed ir» R(i;j) Is an increasing function of 1.
4. STOCHASTIC ORDERING
Solomon [ 26] has proposed that diversity indices be required to
preserve stochastic ordering and has stated a necessary and sufficient
condition (finitely many species) which is closely related to the second
condition of Theorem 3.2. Solomon actually considers the dual but
equivalent notion of majorization. He would like to briefly Indicate
how the more primitive and intuitive concepts of the previous section
relate to stochastic ordering. The main result -la that stochastic
order Is the partial order generated by- the relation C «C'.
396
-------
120
Definition 4.1: Let F(x) and GCx) be two cumulative distribution functions
s
on the real line. F is stochastically leas than G (F G) provided
1 - F / i|iG0 dF(x) <_ / t|;(x) dG(x) for all Increasing
functions i|>.
For a community C - (s,j), the ranked abundance vector jr may be
thought of as a probability- distribution on the set of positive Integers.
8
With, such an Interpretation, it < tt* <-> Z ir. < Z tt* for k " 1,2,3
~ ~ " j>k 3 ~ j>V. J
Notice that this says that jj' has uniformly greater tail weight (rarity)
than ff and it becomes plausible that diversity Indices should preserve
stochastic ordering.
Theorem 4.2: Let C - (s,rr) and C' - (s'.ir') be two communities.
"a
a) If C « C' then it < ir'.
b) Conversely if ir < ir* and if s' Is finite, then there la a finite
sequence of communities satisfying
C - CQ « Cj « ... « cn ¦ C' .
Proof; By Induction on
Corollary 4.1: Any diversity Index satisfying Criterioa C2 preserves
stochastic ordering on the claaa of communities having finitely many
species. Any- diversity index which, preserves atuchaatie ordering
satisfies tha Criterion C2.
397
-------
LZl
5. INDICES BASED ON RANKING
The Indices considered thus far have been of the dichotomous type.
A measure of species rarity, with, a more detailed dependence upon
community composition, Is the number of more abundant species. For the
ith species, this number is i-1 (recall that ; is ranked) and average
community rarity becomes Z (i—1) ir^ ¦ £i TTj~l ™ average rank — 1.
Solomon [26], from a quite different point of view, has introduced the
average rank as a diversity Index. (The —1 has the effect of assigning
diversity zero to a single-species community and appears to be a
generally useful convention.)
A related index is Fager's [ 12] "Number of Moves" which is, in
effect, the average rank rescaled to range between zero and one.
However, Feet [ 19] has given persuasive arguments against rescaling
diversity indices. Fager\s basic idea is attractive, though. As an
alternative to Fager's number of moves needed to convert a sample to an
even distribution, one may cor.sider the "work (* mass x distance)"
required to construct a given community from a single species community.
T}i^ s "work" is seen to be average rank -1.
Tor the general measure of rarity base4 on ranks, the analogue of
ic CI la the requirement that R(i) be an increasing function of i.
-ht. comments at- the end of section 3). Interestingly, this
monotonicity turns out to be sufficient for Criterion C2.
Theorem 5.1: A(C) • Z R(i) • ir^ preserves stochastic ordering
<-> R(i) is increasing in i.
Proof i ~> trivial.
Theorem 4.1.
398
-------
122
Remark: For finitely many species, a straight-forward proof may also
be based on either Theorem 4.2 or, equlvalently, on Solomon's I 26]
condition of "S-coacavity".
6. PTELOU'S AXIOMS AND HIERARCHIAL CLASSIFICATION
Plelou [ 21,p.7] has given three axioms for a diversity Index:
PI. For given a, the index should have its greatest value for a
completely even community, i.e. when ir^ - 1/s, i - 1,2,...,* .
P2. Given two completely even communities, the one with nore species
should have the greater diversity.
P3. For hlerarchial classifications, Che ANOVA formula should hold.
Theorem 6.1: Any diversity index &(C) which satifies Che Criterion C2 -
also satisfies PI and P2.
Proof: For finitely many species, if A satisfies C2 it slso preserves
stochastic order.
As has been shown by Khinchin [14], the three axioms PI, P2 and
P3 characterize the Shannon-Wiener Index up to a constant multiple.
However, weighted ANOVA formulas can be associated with more general
indices. Wfc restrict attention to those indices of form A ¦ £
and impose the following regularity assumptions (Criteria CI and C2
are not needed).
Al. R Is continuous and not identically zero on (0,1].
A2. R(l) - 0.
A3. R'CI) exists and is finite Cone-aided derivative).
399
-------
123
Examples: (.a clarified below).
a
-1
0
1
-(1-n*1)
-log if
1-TT
Index
8-1
Shannon-Wiener
Simpson
CI" istfy the community into g categores and further
classify each A^ into subcategories. Let be the probability of
th
A. and i, , the conditional probability, given A., of tha J subcategory
i j*i 1
of A^.
*i Ai:
"Li
Vi
• t f
* 4
V1
g
Then A(A) - £
i-1
R(7rt)
, A("B"|At) -
Bi
Z rt ± R
J-1 3 1
E
A (total) - £ z rr. ir. . Rftr, tt. .) and
i-1 j-1 1 I'1 1 J*1
g
A (total) - a(A) + E it. t Z 1T. , there exists a-real number a such that
W(7r) - tt® , and R(n) - constaut • (1-Tr°) for a V 0 and R(ir) -
constant • logCir) for a - 0. -
400
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124
Proof: The proof is lengthy and will appear elsewhere.
Remark; At first glance, the theorem appears to characterize the
Shannon-Wiener index using only P3 and mild regularity. But, in accord
with our view that diversity Is an average property of the community,
there is the additional assumption that the index has form ROr^)*
If the normalizing conditions R(l) "0, R*CD " —1 ere imposed,
the rarity mc-asures given, by the theorem a.iaume the standardized fora
RGr) ¦ (l-rra)/a with diversity Index - (1 - Z ir®+^)/a . (The
usual Uniting convention Is understood when a » 0.)
Theorem 6.3: Criterion CI la satisfied for all a while Criterion C2
Is satisfied <-> a >,-1.
Proof: Apply Theorem 3.2 end Theorem 3.3.
It is worth noting that
-log (1-aAJ log Eit?+1
¦ " " ^iW
a -a
where Is Renyl's [ 23] entropy of order o+l. Since -log Cl-oit)/a
is an increasing function of t, it follows that Ha+^ preserves acochaatic
ordering when a > -1., The sets ja >,-1/ , :o >, -l) constitute
two pencils of Indices having the Shaanon-Wlenec Index aa_ common intersectio
Figure 6.1
-------
125
Advocates of the Shannon-Wiener index may feel equally comfortable with.
either family of indices Ccorapare with Plelou [21 ,p.9]). We prefer
L since it can be interpreted aa an average quantity,
a
7. ESTIMATION OF SIMPSON1 S INDEX
A prohlem associated with the use of diversity indices as Indicators
of environmental quality is the time and level of professional expertise
required for a taxonomic classification of the sample. Cairns et al
[6,8,9] have developed an ingenious technique to overcome this
difficulty. Their approach is a nice illustration of the concept of
inter- and intra-specific encounters discussed in section 2. Given- a
random sample Aj^Ag,...»Au»Au+i specimens, define a run to be a maximal
sequence of consecutive specimens of the same species. Cairns suggests
the ratio, # runs/(N+l), as a measure of the diversity of the sample.
In implementing the technique, the investigator need only make the
successive comparisons A^ vsAj, vs A3> A3 vs A^, etc. so that the
method is rapid and does not <;all for sophisticated taxonomic skill.
It i be possible to adapt Calms technique to the measurement of
foregp diversity along a line transect. (See figures 2.1 and 2,2) .
r——— 1 I
£,)** CKT* O** n^/+> C-T**
Tfl o o o x o X 1 o
Figure-7.1
what follows, it is shown that, with « minor bias correction,
Calv ; diversity measure become aa unbiased estimator of Simpson's
lndejr Asymptotic normality is also established. The unbiased
402
-------
J.ZO
version is obtained as
CL - 0 runs - 1)/N
and vlll be called Cairna linked estimate?. The statistical analysis
is facilitated by Introducing Indicator random variables with the
property that each occurence of « 1 signals the start of a new run.
The are defined by
(l if and belong to different species
Ti - '
0 otherwise.
\
Then, Ti»T2''"'TN "e identical 0-1 variables, but adjacent T^ need
not be independent (since the comparisons are linked). Let p be
the correlation between and .
Theorem 7.1; a) S[T^J - ^ b) Var(Tj) - ^(1-^)
c) Cov(T^,T2) - s irj - (£ ttJ)2
. d) 0iP< 1/2 .
The lower bound p ¦ 0 is achieved only for a completely even community:
ir^ - Tij " ••• "'*8* The uPPer bpund p - 1/2 is approached as ¦* 1.
(p is undefined when « 1).
proof: a) and b) are obvl>us a^ncp T^ ;.t a 0-1 random . arial e with
•
c) Cov(TltT2) « Cov ^-T^l-Tjj-j n PCT^O.r -O) -(P^-'O))2
- Z nj - (Z w*>? .
2 ~ 9
d) The covariance has the fori# pf a variance, Iir^ (£ it - ^ .
Hence p > 0 with, equality <"> tha art all equal. Ve eaplc,. a standard
Inequality to show that p <_1/2|
«03
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127
£ tt^ < (X (Bechkenbach. and Bellman [ l,p.l8]
<. E tt2 (l-TTt)2 + a 1T*)2
< E IT* - 2 E + E ir£ + (Z ir^)2
2En J - 2(E tt*)2 < E ffj - (E irj)2 - ^ Cl-^i
Remark.; The bounds 0 < p < 1/2 can be improved if the value of ^
Is known. For given A.^, we have obtained sharp upper and lower bounds
on p. \'h«jse are complicated and vill not be given. The upper bound
confirms the Intuition that p tends to be small for highly diverse
communities.
N
Theorem 7.2: a) CL "¦ E T,,/N , b) E[CL] ¦ .
x x i
c) Var[CL] - [l+2p-2p/N] ^(1-A^/N
- ll+2p] Ax(l-A^/N for large N
< 2AX (1-a'1) /N .
d) CL is asymptotically normal as N •* «• .
Proofi a) and b) are obvious and c) Is a routine calculation oace it
is noted that nonadjacent X4 are independent. The asymptotic normality
follows from Noether's central limit theorem vhlch Is stated below.
¦Theorem 7.3; (Noether [18 ]). Let Z^.Zj.Z^,,,. be Independent random
variables, a) Let TitT^/In,... be uniformly bounded random variables
. N
with a function of Z± and Z1+1 only. Then ¦ E ^ la asymptotically
normal provided Var [S^] is of exact order N.
b) Let T ., l,j - 1,2,... be uniformly bounded random variables with
N
T a function of Z and Z only. Then S - I T t i* asymptotically
. l.J-1 13
normal provided Var [S„] is of exact order .
n
404
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128
Remark: Noether presents a proof of b). The proof of a) requires only
slight modifications in hia argument.
Remarki Theorem 7.2 is related to a result of Mood [17] who examined
the distribution of the number of runs when a fixed sample is subjected
to random permutations.
Use of the exact formula for Var [CL] requires estimation of the
correlation p . The pairs (T^T^, (^y»Tg) ... constitute
approximately N/3 Independent observations on the blvarlate distribution
of (T^.Tj) from which an estimate may be obtained.
The nonnegativlty of p indicates unat linking the consecutive
comparisons reduces the efficiency of the estimate and suggests an
estimate based upon independent pairs of specimens. For N such pairs¦
(2N specimens), define Cairns unlinked estimator as
CU « 1/N • (# of unlike pairs).
Then, trivially,
Theorem 7.4: a) E^CU] - b) Var[CU] - (1-A^ Aj/N,
c) CU Is asymptotically normal as N
Efficiency comparisons of the linked and unlinked estimators
require a common yarstick. The number of specimens in the sample Is a
natural yardstick If specimens are difficult to obtain. For n specimens,
Var[CL] „ n . . _n_ n-7.1 VarfCL] .
VarECU] s(n-l) p n-1 n-i 2 - Var[CU] -
Thus CL is at least as efficient as CU in these circumstances and may
be twice as efficient.
In the event that specimens are easily obtained, the number of
comparisons, N, seems to be a reasonable statistical yardstick. Here the
405
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129
situation Is reveraed.
|2ligi- 1 + 2p Cl-l/N) : 1 + 2P and 1 < < 2 .
Operational considerations may give preference to the linked estimator,
however, This is especially true for a highly diverse community where
p may be expected to be small.
We now turn our attention to the case of a complete taxonomlc
classification of the sample, which, la taken to consist of t species
and n specimens with as the species counts. Simpson I 25]
C x TWX
has shown that D - E i , i v is an unbiased estimator of .
1 ~ k 5=T~ ; 1
On the basis of the asymptotic behavior of the third and fourth moments,
he also concluded that D was likely to be asymptotically normal (provided
P l1 0) , Bowman et al [ 3 ] have also examined the moments of D. We
show how Noether's central limit theorem can be used to establish the
asymptotic normality without the need for laborious moment calculations.
2A,(1-A )
Theorem 7.5: a) E[D] - A^» b) VarlD] - a(n_xj— [1 + 2(n-2)p] ,
c) If p 0, 0 is asymptotically normal,
n
Proof; Let S » £ T vhcre
i,j-l 13
(1 if i < j and specimens 1 and j are of different species
TU j
(0 otherwise.
It may be seen that S * 2Sn/n(n-l) . Being Theorem 7.1, the calculation
of E[D] and Var{D] is routine after It Is noted that T.. and T. are
1] ICitt
independent whenever {i,j> O {k,o} • a , Part t>) implies that Var[S ]
II
3
is of exact order n when p j* 0. The asymptotic normality of D now
follows from No ether's theorem.
406
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130
8. ESTIMATION OF SPECIES RICHNESS
Estimation of the number of species In the community Is one of the
more interesting and Intriguing problems facing the ecologlst. Usually,
he la not In a position to establish, sharp boundaries for the community
and finds it Impossible to describe his sampling scheme with any degree
of statistical precision. Likewise we will not be precise about the
sampling method, but shall suppose that the species are represented
in the sample independently of one another and in accord with their
own individual probability distributions. As usual, e is the number of
species in the community and tt is the ranked abundance vector.
Let p^Cx), x " 0,1,2,..., i ~ l,2,...,s, be the probability that
the ith ranked species in the community is represented in the sample by
x individuals. The probability distributions p,(x),p-(x).,p (x)
xt s
depend in an unknown way upon the vector tt, the sampling intensity and
the response of the various species to the sampling effort (catchability).
The number of species actually present in the sample (i.e. represented
by a positive number of individuals) is itself a random variable.
This random variable, and 3ometimes its observed value, is denoted by t.
We have
E[t] - I [l-p.(0)] - s[l - J I p.(0)] - s[l-?(0)],
i-1 1 8 1-1 1
1 8
where p(0) - — E p.(0) is the average species absence probability.
B i-1
IC an estimate, p(0), of p(0) is available, then s may be estimated as
5 - t/(l-pC0».
Estimation Method 1: Assume that the probability distributions
p^Cx),...,PgG0 are members of a known parametric family p(sj0) with
possibly different values of 8: p^Cx) - p(x;6g), 1 - l,...,s .
407
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131
Further assume that e is. a scalar parameter and can be estimated from
a single observation. Let ^,^,...,1,. be the. Gmknovn) ranks of the
syeclss actually present in t"ie sample For J • 1^, i^ > • • • »iti estimate
6 hy, say, 0 and pCO;0 ) by p(a;0 )• Take t pCO;0,j)/t as the
j J J J j„l _
estimate of pC°)- Tfl® method may be expected to underestimate pCO)
and hence to underestimate a.
Estimation Method 2; Assume that the probability distributions
p (x) (x) are all identical and equal to p(x;0) where p(x;0)
Is * -
is a known parametric family and 0 is a vecto.: of parameters. Let
X1,X2••,Xt be the observed (nonzero) species counts in the sample,
listed in some random order. It may be shown that, conditional on t,
Xi,X2,...,Xt are independent and identically distributed with common
distribution p(x;0)/(l-p(x;0)), which gives an estimate, 0, of 8 .
*• * • % «
Estimate p(0) - p(O;0) by p(0;8).
The nbovo methods are standard in the literature. We suggest a
third method that seems to be new and which leads to modified versions
of Method 1 and Method 2.
Estimation Method 3: Let the sample consist of n individuals of which
n^ are singletons. Assume the sample is representative of the community
In the sense that the 'rare'species (i.e. singletons) In the sample
correspond to the 'rare' (i.e. unobserved) species In the community.
The singletons taken together comprise a fraction n^/n of the sample and
they divide this fraction among themselves Into equal parts. Extrapol-
ating (not Interpolating!) to the'community, conclude that the unobserved
species comprise a fraction u. /'a of the community and that they divide
this fraction among themselves Into n^ equal pares. In particular,
408
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132
estimate the number of unobserved species as and the total number of
species as t+n,. To correct for any bias of this estimator, note that
_ a _
- s[l-p(0)], E£n.] - Z p.(lj - ap(l),
1 i-i t
Eft-h^l - s[i-pC0) + iCD] .
Under the assumptions of either Method 1 or Method 2, both. £(0) and p(l)
may be estimated by, say, p(0) and p(l)« "7ake 5 - Ct+n^J/Cl-pCO) + pCD)
As a modified estimate of s.
Example 8.1; The five methods were applied to the Rothaosted light
trap data reported by Bliss [ 2 ]. The underlying distribution for
Method 1 and Method 2 was assumed to be Polsson. The last column of the
table gives the estimate of s which Bliss obtained by fitting the
lognormal distribution (Method 2). All figures are rounded to the
nearest integer. Standard errors are being computed.
Modified Modified
Year
t
»1
Method 1 Method 1
Method 2
Method 2
Method 3
Lognormal
1933
183
32
232 250
133
215
215
208
1934
176
34
226 251
176
210
210
199*
1935
202
39
260 289
202
7A1
241
239
1936
157
51
243 295
157
208
208
222
*Bulmer [ 4 ] has obtained the estimate s ¦ 226 by fitting Che
Polsson-Lognormal distribution.
pymart• in a different context and with, a different viewpoint, Robbins [ 24 ]
has suggested an estimator similar to n-j/n for estimating the proportion
of unobserved outcomes.
Our are due to M. T« Boswell and B. C. Dennis for lively
discussions during an ecological diversity seminar at the university.
409
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133
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