UNITED STATES ENVIRONMENTAL PROTECTION AGENCY
WASHINGTON, D.C. Z0460
CCT17 1983
OFFICE OF
RESEARCH AND DEVELOPMENT
SUBJECT: Transmittal of ORD Final Report "Prediction of Ecological Effects
of Toxic Chemicals: Overall Strategy and Theoretical Basis for
the Ecosystem Model"
FROM: Erich Bretthauer, Directorial—J-J
Office of Environmental Processes
and Effects Research (RD-682)
TO: John Melone, Director
Hazard Evaluation Division (TS-769C)
THRU: Marcia Williams, Acting Director
Office of Toxic Substances (TS-92)
The attached ORD research report (EPA-660/3-83-084) which was
recently released is being transmitted to you for your use. The
report responds to the Agency's need for predictive models of toxic
chemical effects in natural waters.
The objective of this research was to develop the rationale for a
prognostic model for ecological effects of toxic chemicals. Included
were efforts to more clearly define the scope of "ecological effects,"
to define the level of resolution needed to permit application of existing
toxicological measures, to analyze avarRa^U/toxicity data statistically,
and to initiate development of a *«y?King model.
In this research project, performed under EPA's Innovative Research
Program, a strategy was developed for modeling ecosystems to permit
assessment of effects of toxic chemicals on element cycling and other
cosystem processes. Progress also was made in defining ecological
effects, establishing model resolution requirements, and providing stat-
Tstical analysis of data on the LC50 toxicity measure. The research
provides a basis for continuing work toward a prognostic evaluation model
for new chemicals or those without extensive field data.
cc: Greg Grinder, OEPER
Calvin Lawrence, CERI
EJBD
ARCHIVE
EPA
600-
3-
83-
084
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EPA-600/3-83-084
t-"" Repository Material
Permanent Collection
Prediction of Ecological Effects of Toxic Chemicals: Overall
Strategy and Theoretical Basis for the Ecosystem Model
by
Ray R. Lassiter
Environmental Systems Branch
Environmental Research Laboratory
Athens, Georgia 30613
Innovative Research Project
Cooperative Agreement No. CR808629
Principal Investigator
James L. Cooley
Institute of Ecology
University of Georgia
Athens, Georgia 30602
US EfA
Headquarters &,id Chemical Libraries
EPA West Bldg HOS^.T 3340
Mailcode3^04T
1301 Constitution Ave NW
Washington DC 20004
202-563-0556
ENVIRONMENTAL RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
ATHENS, GEORGIA 30613
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DISCLAIMER
The information in this document has been funded wholly or in part by
the United States Environmental Protection Agency under Cooperative Agreement
No. CR808629 with the University of Georgia. It has been subject to the Agency's
peer and administrative review, and it has been approved for publication as an
EPA document.
ii
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FOREWORD
Environmental protection efforts are increasingly directed toward
preventing adverse health and ecological effects associated with
specific compounds of natural or human origin. As part of this
laboratory's research on the occurrence, movement,
transformation, impact, and control of environmental
contaminants, the Environmental Systems Branch studies complexes
of environmental processes that control the transport,
transformation, degradation, fate, and impact of pollutants or
other materials in soil and water and develops models for
assessing exposures to chemical contaminants.
Concern about adverse environmental effects of synthetic organic
compounds has increased the need for techniques to predict the
ecological effects of chemicals entering the environment as a
result of the manufacture, use, and disposal of commercial
products. Th is research is directed toward a new approach to
predicting the probable effects of toxic chemicals expressly for
environmental assessment. The research was done under one of the
USEPA's Innovative Research Projects. The research is continuing
toward providing the capacity to assess the ecological effects of
chemicals particularly on element cycling processes. Upon
completion it is anticipated that it will comprise one of the
components in a risk analysis system.
William T. Donaldson
Ac t ing Director
Environmental Research Laboratory
Athens, Georgi a
111
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PREFACE
It is very difficult conceptually to design a means by which
effects of toxic chemicals in natural waters can be predicted.
Part of the difficulty lies in identifying exactly what those
effects are. Determining the scale of the effect of interest is
a particularly difficult aspect of the identification problem.
In particular, it must be determined whether the effect of
interest is expressed at the chemical, biochemical,
physiological, individual, population, community or even larger
scale. Most experimental studies are carried out at the finer
scales of resolution, whereas most of our ultimate interest with
respect to environmental risk is at the coarser and more
integrated scales. Experimental studies have been done at the
finer scales partly because they are the scales that can be
readily handled experimentally, but also, I believe, because
there is an implicit assumption that there are comprehensible
connections between behavior at the finer scales and that at the
coarser. That is, it seems to me that there is a general
expectation that inferences can be drawn about the ecological
scale behavior and results obtained at the finer scales of
resolution. The aim of this study is to provide a mechanism for
making such inferences. Specifically, my aim is to predict
behavior at the ecological level of organization based upon
considerations at the lower levels. This report details my
efforts toward that end.
The project began as a result of a proposal to EPA's Innovative
Research Program. Under this program I carried out two years of
research at the University of Georgia in the Institute of
Ecology. Th e subject partitioned naturally into two major
subareas, one on the specific representation of the aquatic
ecosystem and the other on the specific representation of the
direct effects of toxicants. Approximately equal time was spent
on the two subprojects. The subproject on representing the
direct effects did not progress as well, however, as the
subproject on ecosystem representation. For this reason the
direct effects subproject is not reported in detail. Only the
rationale for interfacing the representation of direct effects
with the ecosystem representation is discussed.
This report is intended to convey two major sets of ideas and to
give the specifics of one of them. The first idea is the overall
approach and its rationale. The second is the idea on which the
ecosystem representation is based. This idea is that ecosystem
processes can be described functionally as material and energy
transduction, and that the embodiment of these functions by
discrete species is an essential feature of ecosystems that must
be represented if ecosystem- 1 ike behavior is to be achieved by
the model. Relative stability of processes in the presence of
fluctuations of species carrying them out is an example.
Specific equations describing most of the functional ecological
processes occupy most of the volume of the report. The level of
detail used in the presentation is intended to indicate the level
iv
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of resolution to be used and to document the specifics of the
ecosystem model as it will be translated into computer code.
The overall goal of developing the capability to predict the
ecological effects of toxic chemicals has not yet been achieved.
On the contrary the difficulty and magnitude of the project are
realized to be greater than was at first appreciated.
Nevertheless, the potential to achieve that goal still appears to
be good. Work has begun toward a computer code for the mu1ti-
species ecosystem model, and work is continuing on a sound
representation of direct effects to include the simultaneous
action of multiple chemicals. One major area of the ecosystem
representation that still needs further work is that of
fermentation, probably of great importance in the cycling of
elements.
The opportunity to work for two years, relatively unencumbered,
on this project is greatly appreciated. I extend thanks to the
numerous individuals associated with the U. S. Environmental
Protection Agency's Innovative Research Program and the Athens
Environmental Research Laboratory who made it possible for me to
do this research. Among those individuals, I am especially
appreciative of the efforts of the project officer, Dr. Morris
Levin, of the support of the formez laboratory director, Dr.
David Duttweiler, and of the innovative and untiring effort of
Ms. Connie Shoemaker to work out the institutional arrangements
between the EPA and the University of Georgia. I thank Ronnie
Moon and Bruce Bartell for drafting the figures.
The Institute of Ecology at the University of Georgia graciously
made their facilities available to me for the term of the
project. Dr. James Cooley, Director of that institute served as
the official principal investigator for the project and was
helpful in numerous ways. To him and other individuals at The
Institute I am appreciative. Of all individuals who contributed
ideas and constructive criticism, no one was more helpful than
Mr. Robert Hermann, graduate student in ecology. Providing
continuity, coherence, and logical completeness to the
theoretical basis for this modeling approach was the most
important, difficult, and time consuming part of this project.
In these efforts Bob Hermann was of inestimable help with his
willing assistance and input through many protracted, and
undoubtedly sometimes disjointed, discussions. Discussions of
these and many related ideas in a weekly seminar led by Dr.
Bernard Patten and myself provided continual stimulation and
difficult to assess, but certainly positive, benefit.
It is traditional for authors to make a statement of explicit
assumption of errors of omission, logic, or other sorts. Such a
statement is more necessary here than usual, because of the stage
of the research on which I report. It is probable that there are
errors, and, in spite of all the invaluable assistance generously
given me, the errors are definitely my own.
Finally, this report officially is the final report at the end of
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the term of the Innovative Research project, but I intend that it
be considered to function more as a progress report. My
admittedly biased assessment of the potential for results of this
project when successfully completed are that it is of a high
magnitude. It is my hope and intent to add to this report on the
theoretical basis for the ecosystem model, additional reports on
the basis for the ecotoxico1ogy model, on the design,
implementation, and initial results from the working computer
model, and on results of experiments to test predictions of the
mode 1 .
VI
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ABSTRACT
A strategy for predicting the ecological effects of toxic
chemicals in aquatic systems is developed. The strategy for
obtaining the predictions is to carry out a process of several
steps. The ecosystem is obtained first by specifying
characteristics of the abiotic and biotic systems. The biotic
system is initially represented by a large set of state variables
representing potential species that initially exist in the
environment. The operating ecosystem is obtained by selecting
via computer simulation the smaller set of state variables that
persist for an arbitrary period. The resulting system is a
synthetic system. Any one synthetic system represents real
systems only in a general way. Monte Carlo techniques are to be
used to obtain a distribution of synthetic systems that persist
for the arbitrary period in the given environment.
Characteristics of a real system that could occupy a real
environment similar to the one described are expected to be
included in the distribution. Ecological effects are obtained by
comparing computer simulations that differ only in the presence
or absence of a toxic chemical along with its direct effects.
The ecosystem is to be described in the computer simulation as a
set of differential equations representing the biotic and
chemical species. Processes that occur in ecosystems are
described fundamentally as energy transductions. Organisms are
represented as reaction systems carrying out kinetically hindered
redox reactions and using part of the released energy for
metabolism, activity, and growth. Elements are cycled between
their oxidized and reduced states via these biotically catalyzed
redox reactions. The fundamental distinction between autotrophy
and heterotrophy is recognized and their complementary roles in
element cycles are represented. Distinction between the modes of
ecological coupling of micro- and macroorganisms is recognized.
Mathematical models of growth of autotrophs and heterotrophs are
assimilated or developed. The level of resolution used in these
models is selected to permit coupling of toxic effects by mode of
action of the toxicant. It is argued that the relevance of the
synthetic approach to modeling the ecological effects of toxic
chemicals depends upon the fidelity with which the model
processes represent real processes; not on an inherent limitation
of the approach.
This report covers the period from November 1980 to June 1983,
and the work reported was completed as of February 1983.
vii
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CONTENTS
Foreword
Preface ................................. 1V
Abstract ................................. V11
Figures. ..... ......... ............ « ....... x
Tables ....... . ........................... x
Introduction ............................... 1
Nature of Element Cycles and Importance of Considering
Their Response to Toxicants ..................... 2
Basic Aspects of a Model for Predicting Ecosystem Effects ....... 3
Aquatic Ecosystem. ... ....................... 4
Theory of Ecosystem Structure and Function .............. 4
Integration of Ecosystem Theory and Toxicity Theory ....... ... 5
Motivational Basis .......................... 7
Theoretical Basis ........... ................ 8
Ecology as the Environmental Pattern of Biochemical Energetics .... 8
An Ecosystem Model for Element Cycling .................. 1°
A Model for Uptake and Feeding Rate with Potential Limitation
by Simple Saturation Mechanisms ................... 11
Transport-Limited Chemical Uptake Rate ................ 13
Autotrophy .............................. 1 5
Heterotrophy ............................. 20
Model Summary. .................. .......... 39
Concluding Comments
Macroscopic Metaview and Microscopic Apologia ............. 39
Scale of Resolution, Reductionism, Holism, and Predicted
Ecosystem Behavior ......................... 41
References
53
IX
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FIGURES
1 Schematic for redox processes that yield energy useful for 43
biotic processes
2 Relationships among chemical and biotic forms of elements 44
in biosynthesis
3 Variation in terminal electron acceptor as function of depth 45
4 Diagram of cell in aquatic medium indicating the concentration 46
gradient surrounding the cell
5 Major components and relationships of autotroph biosynthesis 47
6 Major components and pathways (energy and mass) of heterotrophy 48
7 Categories of organic chemicals 49
8 Relationships characteristics of a filter feeding predator 50
and its potential prey
9 Relationships between characteristics of a pursuing predator 51
and its potential prey
Tables
Some reactions used by chemoautotrophs for energy 52
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INTRODUCTION
When analyzing the risks associated with the presence of toxic
chemicals in the environment, one can be concerned with a variety
of potential effects. Effects that are manifested not as a
result of direct toxicity but as alterations of the
interrelationships among organisms and with their chemical and
physical environment are most difficult to evaluate. Many
possible effects of this sort are recognized. Alterations in
element cycles, for example, are one set of such effects worth
considering for their potential to change environmental levels of
natural chemicals. An ecosystem model representing the processes
important in element cycling, if based on fundamental theory, in
principle could be used to predict effects on element cycling.
There is a practical difficulty, however, in basing an operating
model on fundamental considerations. Element cycle
transformation rates are rather stable, relative to fluctuations
typical of individual populations. It is nearly compelling to
visualize that this stability arises from the presence of
populations of several species able to carry out a single
process. In this view loss or diminution of a population is
followed by compensating increases in one or more others, so that
the function (element cycle transformation) is carried out rather
smoothly even in the presence of extreme fluctuations of the
individual populations involved. The difficulty lies in finding
an appropriate representation for a system, so that the model
will exhibit whatever functional stability that results from
compensation by competing species. In addition the
representation must permit the coupling of toxico1ogica 1 and
other effects to system components (species, chemicals, chemical
pools, etc.) in such a manner that destabi1ization of system
functions will be predicted when appropriate. No simple solution
to this problem is apparent. My approach is to describe the
ecosystem using a system of differential equations for which the
associated state variables represent population densities or
chemical concentrations. System functions are fluxes of
materials and energy and are represented by terms that couple
these equations. Several equations representing biotic species
will each contain a term representing a single function so that
both compensation and toxico1ogica 1 effects can be represented.
Such a model will be very large, potentially with a few hundred
state variables. There are associated methodological
difficulties, and these have not been ignored. For this report,
however, I shall not discuss them, so that I may focus on the
model and its theoretical derivation. Because of my intent for
the model to be comprised, in part, of the explicit
representation of many species, all derivations of the
descriptions of interactions will be made with the assumption of
the existence of an arbitrary number of species in the system.
One potential difficulty in using a model comprised of many state
variables to represent a community comprised of a large number of
species is design of the mechanism for achieving the coupling
structure for trophic interactions. The approach that makes the
least demand on the underlying theory is to use a set of
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predation lates assigned to species pairs (the per capita rate at
which one species feeds on another). I have chosen to use a
different approach, however, in which feeding rates aie
calculated from morphological and behavioial characteristics and
swimming velocities of predator and prey. It is presumed that
these characteristics could be determined for individual species.
The rationale is that any quantity that can be measured for
individuals of a species is much more accessible than are
quantities requiting observation of the interactions of
individuals of two or more species. Th e latter kind of
measurements will seldom be available.
THE NATURE OF ELEMENT CYCLES AND IMPORTANCE OF CONSIDERING THEIR
RESPONSE TO TOXICANTS
All processes occur as changes from disequilibrium toward
equilibrium conditions. Biotic processes predominantly occur as
a result of redoz disequi1ibria. Plant photosynthesis creates
the highest degree of disequi1ibci um by producing both reduced
carbon and the strong oxidant, molecular oxygen. Aerobic
respiration is the converse process. In this same sense
anaerobic respiration, in which oxidants other than oxygen are
reduced, and chemosynthesis are converse processes.
Chemosynthesis is driven by energy released upon oxidation of
reduced forms of N, S, and C. Because light drives
photosynthesis and is available in aerobic environments,
photosynthesis and its converse process, aerobic respiration, can
proceed in the same environments. Respiration using oxidized
forms of N, S, and C, however, proceeds only in anaerobic
environments, whereas the converse processes (chemosynthetic
processes utilizing the same elements) proceed only in aerobic
environments. Thus for these components of element cycles,
reduced forms of elements must be transported into aerobic
environments for chemosynthesis and accompanying oxidation of the
elements to occur. Completion of element cycles does not
necessarily depend on transport between environments, however.
Reduction of oxidized forms also occurs during biosynthesis
regardless of the environment. Most organisms that live in
aerobic environments can incorporate ami no and thiol groups into
biomass by obtaining oxidized forms of N and S from the
environment and reducing them internally. This is assimilatory
reduction (to distinguish from dissimi1 atory reduction, the
comparable term corresponding to respiration using electron
acceptors other than oxygen). Upon death and decomposition in
aerobic environments, these reduced forms are either assimilated
directly or oxidized via chemosynthesis. By these mechanisms
element cycles are complete in aerobic environments.
The relative importance of assimilatory and dissimilatory
pathways in maintaining local and global pool sizes of elemental
forms is not clear, nor is the importance of the role of abiotic
processes or boundary conditions imposed by geological and
meteorological factors relative to biotic factors. If, in
principle, these factors are included, however, it is fair to
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say that element cycling is responsible for pool sizes of
geochemica 1s. These include the atmospheric gases, the
composition of the oceans, and the earth's soils. The remarkable
stability of these characteristics over geological time scales
(1) probably is indicative of the robustness of the component
processes (perhaps due largely to functional compensation arising
from species diversity). No comparative analysis of the role of
biotic versus abiotic processes in element cycling has been made,
but the number and importance of processes known to be carried
out by organisms leaves no doubt that the characteristics of the
earth depend on the continuation of biotic processes at about the
level that they are presently occurring. Large scale
introduction of new xenobiotic chemicals into the biosphere is a
practice that has been occurring for only a short time. Whether
the robustness that apparently has been exhibited over geological
time will continue in the presence of these chemicals is not
known. It is prudent,therefore, to make the effort to consider
potential changes in element cycling, to make it possible to
identify conditions that might lead to serious results, and,
equally importantly, to provide an estimate of the probability
that the change will occur.
BASIC ASPECTS OF A MODEL FOR PREDICTING ECOSYSTEM EFFECTS
The importance of the ecosystem concept is to account for
phenomena that result from the interaction of smaller scale
entities, such as physical factors, chemicals, species
populations, and functional groups of populations. Examples are
concentrations of chemical nutrients, population densities of
component living species, various rate related measures such as
productivities, and less easily quantitated concepts such as
community structure. When these phenomena are viewed in the
context of the whole ecosystem, i. e., not in an experimentally
controlled situation, they are often referred to as whole system
phenomena. Predicted ecosystem effects, as I shall refer to
them, are standardized differences in whole system phenomena
between a system in its undisturbed state and its state in the
presence of a quantity of a particular toxic chemical. Effect
can be quantified only against normal functioning; thus predicted
ecosystem effect can be made only by contrasting the predicted
affected state to the predicted normal state.
In predicting an effect, the same conditions are assumed for the
normal as for the affected state, except that for the affected
state the added presence of a toxicant is assumed. Predicted
ecosystem effect is, therefore, conditional. Utility will depend
both on the theoretical basis of the model and on the relevance
of the conditions selected for the conditional mode analysis.
The theoretical basis in the underlying disciplines of physics,
chemistry, and biology, and the less structured discipline of
hierarchial organization of the system representation is quite
obviously a scientific question. Discussion of the theoretical
basis occupies the bulk of this report. That the manner in which
questions are asked of the model is also a problem for science is
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less obvious. The problem of identifying, at least to my own
satisfaction, the kinds of questions that one can logically
expect to answer was a necessity for carrying out this research.
I shall discuss this question also later in this report.
AQUATIC ECOSYSTEM
To predict effects of toxic chemicals in aquatic ecosystems
several items are required. The most fundamental item is a clear
definition of what effects are to be predicted. The term
"aquatic ecosystem" must be defined specifically for the present
purposes. As used in the assessment of ecological effects, the
term can have one of two possible meanings. It can mean a
particularly defined aquatic ecosystem (a single instance), or it
can mean a range of defined aquatic ecosystems so that the
effects of the toxicant over the range of systems can be referred
more generically to "the aquatic ecosystem." In either case the
term is used in conjunction with predicted ecosystem effects and,
when so used, refers to the set of attributes that represent the
aquatic ecosystem in the theoretical model. That is, one needs
to realize that use of "the aquatic ecosystem" in conjunction
with this model refers not to a physically identifiable
environment, but to a set of attributes that relate abstractly to
a set of attributes of real systems. The more substantial
problem, however, is the provision of theory of ecosystem
structure and function at a level of resolution to permit
observation of the effects. Integration of information on
toxicity of chemicals to aquatic organisms to the same level of
resolution is a necessity. Finally, not only must both ecosystem
theory and toxicity theory be organized at the level of
resolution to permit observation of the effects, but each must be
organized to interface with the other in a model to make the
predictions of effects.
THEORY OF ECOSYSTEM STRUCTURE AND FUNCTION
Structure and function are inseparable in ecology. Structures
enable functions. It is my assumption that there is parsimony of
structure and behavior in biotic systems (an assumption in
keeping with the principle of Ockam's razor): structures do not
exist without function. Generally, this is a reasonable
assumption, because power is required to maintain structures, and
the competitive advantage is held by organisms without the added
burden of useless structures. In the theory of ecosystem
function proposed here the power demand is calculated as the net
cost of carrying out the functions. It is assumed that there are
no overhead costs for maintaining structure, except structure
that is used in obtaining energy, survival, or reproduction.
These assumptions are in keeping with the overall assumption of
pars imony .
Much theory exists in ecology, in the generic sense of theory.
This theory is diffuse, and it has not been assimilated at the
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level of resolution that is useful for a theoretical model for
predicting ecosystem effects of toxic chemicals, at least not in
the vein of the model discussed here. The major effort in this
research, therefore, has been to assimilate a theoretical basis
for the model. In doing so I have held to the parsimony
hypothesis. The level of resolution is such as to permit
information on mode of action to be used when it is available.as
well as to permit more general statistical measures of toxicity
to be used. The ecosystem theory that is the basis of this
theoretical model uses concepts from chemical thermodynamics (in
much the same way as they are used in biochemistry),
biochemistry, physiology, population dynamics, and limnology. A
biophysical approach is used to derive relationships so that the
resulting model equations are written primarily at the population
level, with terms of the equations calculated using expressions
reflecting underlying physiology, biochemistry, etc., all
constrained by mass and energy accounting. Because reference is
made to these finer levels in the describing equations, system
effects at these levels also can be explored.
INTEGRATION OF ECOSYSTEM THEORY AND TOXICITY THEORY
Theory developed or assimilated in this research is primarily
ecosystem theory. As noted, however, the ecosystem theory has
been expressed so as to permit the application of various
toxicity measures. Translation of LC50 values to effects on
death rates in this model has the usual accompanying difficulties
of interpreting LD5Q values as rates and the additional
difficulty of extrapolation to very low concentrations. Whatever
the assumed interpretation and extrapolation mechanisms, the
method of application of toxicity measures will be influenced by
the approach taken in the model to represent ecosystem processes.
This approach is to represent processes or functions as being
carried out by a group of populations differing from each other
in various ways, one of which is their susceptibility to a toxic
chemical. The model does not represent particular existing
species, but instead the model parameters are in the range of
analogous values expected for existing species that carry out the
process that is represented.
A fundamental assumption that amounts to a principle for this
modeling approach is the basis for this non-specificity of
representation. Simply stated, I assume that element cycling and
most other macroscopic properties of ecosystems derive from
interactions of organisms as they obtain useful energy via modes
of metabolism suited to the energy sources. These modes of
metabolism, unlike species, are common to diverse environments
(see ECOLOGY AS THE ENVIRONMENTAL PATTERN OF BIOCHEMICAL
ENERGETICS). I view a particular biotic community simply as a
complement of species populations that are able to exploit the
energy sources, grow and reproduce in a particular environment.
This-is not, I think, an extreme view. However, in a similar
sense, for the model to be operational, computer algorithms are
required to select coexisting species as represented in the
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model. These ace selected in the context of a given environment
representation. It will be impossible foe this environment to
tepcesent precisely any real environment, and by virtue of
selection of species representations as a function of the
environment descriptors, the species representations will not
represent specific real organisms. For that matter, no one teal
environment can be said to represent precisely any other one, yet
many organisms are common to widely different environments. Over
time intervals relevant to selection processes, environments are
not isolated and selection occurs over all communicating
env iionments.
Derivation of the species representations, while not representing
particular species, to maintain a credible level of reality, will
use available information on appropriate existing organisms.
Discussion of these matters, however, is very premature, because
the working program is far from complete. The main ideas to
derive from the comments are that this model is not directed
toward any specific system representation, that on the contrary,
a fundamental assumption is that the macroscopic system
properties such as element cycling do not depend on any such
specificity, and that perturbations (as by a toxic chemical) on a
biotic community in a particular environment will result in
characteristic alterations to the unperturbed behavior (see also
CONCLUDING COMMENTS).
From a preliminary analysis on several compounds, considering all
species together, toxicity can be represented by an asymmetric
frequency distribution in which no taxonomic relationships above
the species level are apparent. That is, if the frequency of
occurrence of LC50 values (Criteria Documents Data Base 2,3) are
plotted, the distribution is unimodal and skewed such that there
is a low frequency tail at relatively highLC5Q values. If one
then identifies the species occurrence in this distribution, no
pattern associated with taxa higher than the species level is
apparent. These analyses are highly tentative, however, and
another analysis with a much larger data base is beginning.
Assignment of toxicities to the model populations with
probability reflecting the frequency distribution appears to be a
reasonable approach. In any case there is no basis to expe'ct a
close match between measured toxicities and the explicit needs of
any ecosystem model, and therefore, no specific parameterization
of a model can be expected. Use of toxicity information,
therefore, will require that some rationale be employed; that
employed here is to assign toxicities to the model as nearly as
possible to match the measured fzequency distribution. Use of
this rationale, in general, will be limited by data availability,
particularly for assignment of behavioral effects such as
variation in hunting or escaping efforts.
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MOTIVATIONAL BASIS
The motivation for this research project was the perceived need
to be able to assess probable ecosystem effects, particularly
effects on the cycling of major elements, resulting from the
introduction of a toxic chemical. Such a capability would be
most useful if it were prognostic and able to be used in an
exploratory mode in search of generalizations about expected
effects. Planning research to develop such a capability is an
exercise in matching the possible forms of theoretical prediction
with potentially useful questions. As a result of indulging in
such an exercise I drew the following conclusions about some
reasonable forms of useful questions, and what basis exists to
support research toward providing answers to such questions using
predictive models.
Questions relating to effects on identifiable existing
species in specific environments cannot be answered by a
synthetic, predictive ecosystem model.
It is feasible to answer questions relating to probable
effects on ecosystem functions, given the following
conclusions that a basis exists for a model of ecosystem
functioning and effects of toxic chemicals on the
funct ioning.
Enough is known of physical, chemical, biochemical,
microbial, macro-organism biology, etc., to support
virtually any level of underlying process description.
Enough is known of ecological relationships to provide a
basis for structural relationships in addition to those
implied by the underlying process descriptions.
It is hypothesized (rathex than concluded) that there is no
dependency of system function on presence of particular species
(as already discussed) nor on species diversity. Capacity of a
system to carry out a process smoothly while populations involved
in the process are stressed by a toxicant, however, depends
entirely upon species diversity. The additional hypothesis is
made that capacity for compensation increases at a decreasing
rate as diversity increases. There is, therefore, dependency on
the presence of species to carry out each function, and there is
dependency on a minimal degree of diversity within each function
to permit compensation by non-susceptib1e populations for
reduction in population levels of species susceptible to toxic
chemicals. The importance of this latter hypothesis to modeling
the functional behavior of ecosystems using a multispecies
representation, is that it is possible to represent ecological
processes using a limited number of species, if it is true.
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THEORETICAL BASIS
Following these ideas, a theory of ecosystem function was
assimilated and wotk towatd a functioning model based on the
theory is in progress. The theory is not new in its entirety,
but it does contain original elements. Perhaps mote
significantly, it departs from both holistic and reductionistic
views. It departs from the traditional holistic view by
attempting to synthesize system properties using a biophysical
integration of finer scale components to the level required to
represent the system. It departs from the reductionist view by
concentrating on the ecosystem as the object to be represented
and by virtue of interest in processes whose behavior cannot be
considered to be a function of any single system component.
This theory like every theory of macroscopic phenomena, is based
upon phenomenologica 1 models of its fundamental components. In
an attempt to give the theory a greater predictive capability, I
have selected as fundamental components, models representing
energy transduction at the biochemical level. In these models
organisms are considered as reaction systems that catalyze
energy-rich, kinetically hindered redox reactions and, in the
process, use part of the reaction energy for biosynthesis and
mechanical work. Ultimately, population rates of change result
from the biochemical models based upon redox chemistry.
Ecological interactions result from dependencies among organisms
for elements from which to form biomass and for compounds to
serve as oxidation and reduction reactants to provide energy. To
maintain the identity of all organic compounds that could serve
as chemical nutrients or as energy substrates in the working
model would be an impossible computing problem.
To overcome this problem, organic chemicals are aggregated into
classes that are ecologically relevant. The underlying theory is
worked out elsewhere (4) and does not depend on this aggregation.
Toxic chemicals interfere with the processes by which organisms
obtain or use energy or elements. Thus this theory of ecosystem
function is based upon fundamental conceptual components that are
models of real components that respond to toxic chemicals.
Integration of toxicology at lower resolution, such as altered
probability of death as obtained from reported LC5fl values, can
also be used directly without reference to the fine scale
phenomeno1ogical models.
ECOLOGY AS THE ENVIRONMENTAL PATTERN OF BIOCHEMICAL ENERGETICS
ECOLOGICAL MODES OF METABOLISM. Disequilibria that drive biotic
processes are in two forms: light and chemical. Organisms that
use light induced disequi1ibria are phototrophs, and those that
utilize chemical are chemotrophs (5,6) Phototrophy and
chemotrophy refer to the source of energy, i. e., whether the
free energy is derived from photochemical or biochemical
reactions. In either case the electron donor (reducing agent)
can be either inorganic or organic (lithotrophy or organotrophy
-------
with the prefix photo- or chemo-) making a total of four major
classes of energy metabolism.
Figure 1 is a schematic of the processing of energy. For
biosynthesis the source of carbon can be either CO2 or organic
compound (autotrophy or heterotrophy). Combining the modes of
energy metabolism with the modes of biosynthesis, eight
categories are formed, all eight of which exist in nature along
with variations on these major categories. For the initial
theoretical development, it will suffice to consider only three
of the major categories: photo1ithoautotrophy, chemo1ithoauto-
trophy, and chemoorganoheterotrophy. Because there will be no
risk of confusion, I shall refer to these categories by the
shortened terms, photoautotrophy, chemoautotr ophy , and hetero-
trophy. I shall further subdivide the latter category into
macroheterotrophy and microheterotrophy, and microheterotrophy
further into categories reflecting the electron acceptor used. I
shall refer to these latter categories occasionally by the
coarser terms, oxymicroheterotrophy and anoxymicroheterotrophy.
Figure 2 is a schematic of biosynthesis at the ecological scale.
Figure 3 indicates the spatial and energetic relationships of
microheterotrophy as a function of presence of potential terminal
electron acceptors. Although too complex to represent
graphically, a composite of Figures 1, 2, and 3 provides a rather
complete, but abstract, scheme for element cycling.
ECOLOGICAL ENERGETICS. Energetics is simply a term for
thermodynamics as applied to the analysis of biological
processes. Biological processes, like all processes,proceed
only when conditions of disequilibrium exist. More specifically,
biochemical mechanisms proceed by transfer of electrons and
associated energy to form, primarily, ATP and NADPH (or NADH).
ATP is the universal mediator of biochemical reactions;
NADPH and NADH are the major biochemical reductants. Processes
in which these compounds participate are subcellular, yet
processes by which they are formed and in which they are used are
of utmost relevance at the ecological level of organization and
of great utility in theoretical ecology. This is so because the
macroscopic patterns in which they occur are interpretable, not
at the cellular, individual, or population level -- but only at
the ecological level of organization. That is, the existence of
a particular mode of metabolism, for example -- chemoautotrophy,
is a phenomenon that can be explained only with reference to
ecological processes.
These processes are interactions of biotic and abiotic components
that create and maintain environments suitable for particular
modes of energy metabolism. Organisms can sustain a mode of
energy metabolism in an environment only if the reaction on which
this metabolism depends is thermodynamically favored (exergonic)
in that environment. Specifically, organisms cannot maintain
physiological conditions that permit a net derivation of energy
from biochemical processes unless the net of those processes is
-------
exeigonic in their environment. This fact can be used as a major
organizing principle for theoretical ecology. It provides the
basis for calculation of potential modes of energy metabolism for
given environmental conditions without reference to organisms.
The Gibbs free energy function is the appropriate measure for
such calculations because it is a measure of the useful work that
can be extracted from the energy of a reaction, and it refers to
conditions of constant temperature and pressure, but allows
volume to vary (as, for example, occurs in a biotic process that
results in the evolution of a gas). These are conditions most
appropriate to biological systems. Such calculations are not of
energy budgets as such. Calculations for energy budgets usually
consider that energy is conserved (in keeping with the first law
of thermodynamics) and accountable when all system gains and
losses are considered. Conservation of energy,thus, refers to
conservation of the sum of all forms of energy. Energy that can
be used by biotic systems is the Gibbs free energy for the
specific energy yielding reactions, such as the oxidation of
organic compounds with sulfate as the terminal electron acceptor.
The useful energy that can be extracted from these processes is a
function of the concentrations of the reactants and products.
Hence, ecologically relevant calculations for the amount of
useful energy that can be derived from chemical reactions are
functions of the conditions of the environments in which the
reactions occur, and, hence, very definitely not subject to
conservation laws. In contrast, however, mass conservation is a
principle that is useful for theoretical ecological computations.
In fact in the ecosystem model mass conservation is the
fundamental principle for accounting that permits the
calculation of the Gibbs free energy. This comes about because
mass conservation is used directly as the accounting principle
for calculating chemical quantities including concentrations, and
the Gibbs free energy function for chemical reactions is
dependent on concentrations of reactants and products.
AN ECOSYSTEM MODEL FOR ELEMENT CYCLING
An ecosystem model for element cycling is necessary for
predicting effects of toxic chemicals on cycling processes.
Morowitz (7) has shown that flow of energy through a system from
a source to a sink will necessarily result in cycling in steady
state systems. Ecosystems approximate steady state systems that
are far from equilibrium, a condition that is associated
necessarily with structure (8). The model presented here
represents ecosystems as open systems that are far from
thermodynamic equilibrium. The degree of approximation to steady
state, however, is not explicitly assumed, but rather, the
ecosystem is represented as a dynamic system. This is done
because interest is in alterations in the rate of cycling, not
10
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just in whether elements cycle. The fundamental basis for this
model can be stated rather simply, but the details of these
fundaments will occupy the next several pages.
The organisms that carry out the ecological modes of metabolism
comprise the structures that are necessary for element cycle
transformations. For each mode of metabolism, stability is
maintained in part by diversity among the populations in their
response to external factors. As a consequence of diversity,
compensatory changes occur, resisting fluctuations in the fluxes
of materials and energy that result from element cycle
transformations. There is a high degree of similarity at the
biochemical level within each mode of metabolism. Diversity
exists in morphological variation and is expressed in
physiological and behavioral differences. The development that
follows is based on the foregoing assumptions of biochemical
similarity and morphological diversity within metabolic modes.
The derivations and equations that follow, while comprising the
greatest part of this report, should not be considered to be the
most important part. They constitute my rationale for the way to
express, ultimately in a computer model, the hypotheses and
working assumptions already discussed. In attempting to develop
a predictive model for aquatic systems without relying on the
specifics of any one system, it has become apparent that
traditional views of ecology present a barrier to the development
of ecological theory. These traditional views, utilizing natural
history and taxanomic approaches, have overemphasized, I believe,
differences among ecosystems to the exclusion of theoretical
approaches that do not assume from the outset the primacy of
importance of specific taxa. This is not to claim that the
approach put forth here has, indeed, overcome these barriers to
the extent that a general ecological theory will result. Indeed,
the approach that I present is also highly complex, dependent
upon as yet unsupported hypotheses, and upon computational
capabilities that could be very difficult to achieve. What I do
claim, however, is that the viewpoint taken, which is more akin
to that of microbial ecologists, is a valid one, and I should
hope that if it does not lead directly to the goal of a model
capable of predicting ecological effects, perhaps indirectly it
will contribute to another approach that will.
A MODEL FOR UPTAKE AND FEEDING RATE WITH POTENTIAL LIMITATION BY
SIMPLE SATURATION MECHANISMS
Every organism must cope with two problems, obtaining energy and
obtaining elements from which to form biomass. Photoautotrophs
potentially are limited in their energy supply rate by light
availability because of light attenuation by various agents in
water. For all microorganisms, obtaining chemicals from the
environment is a process of molecular uptake of chemicals
dissolved in water. There is a concentration gradient from the
bulk water concentration to the concentration localized at the
cell boundary. The gradient is generated when the cell removes
dissolved material from the water at a rate that is competitive
11
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with diffusional replenishment of the matetial at the external
cell bound a c y .
These localized concentrations can limit the energy supply rate
as well as the rate of supply of elements for biosynthesis.
Mac r ohe t e r ot r ophs either move through the water or move water
past themselves to obtain food. Mobile organisms use energy for
evasion of predators. In these activities the power to overcome
drag can account for a considerable fraction of the total power
expenditure. For large aquatic animals food supply for energy
and biosynthesis must be maintained in an environment that is
fluctuating with respect to food supply and pressure from
predators. In the following the supply rate of energy and
materials will be considered for each of the metabolic modes, and
a resultant expression for population rate of change will be
ob t ained .
It is usually assumed that the uptake rate of dissolved chemicals
by microorganisms is best described by a rectangular hyperbola as
first proposed for microbial processes by Monod (9). Such a
description can be rationalized by any one of several specific
mechanisms. All such processes appear to have a common
characteristic, however, y_Lz^., a saturable component. In this
respect many such processes exist, not all associated with
microorganisms, and not all of which are biotic processes.
Molecular sorption to particles is frequently described by the
Langmuir isotherm, which, although not a rate description, is a
rectangular hyperbola. In this instance the saturable component
is the surface of the particle, or at least the capacity of the
surface for the sorbate. The feeding of fishes was described in
much the same way by Rashevsky (10) and the feeding of insect
predators by Holling (11), the saturable component being the gut
capacity in Rashevsky's analysis and available time in Rolling's.
Specifics of such processes will be discussed in the appropriate
sections. The model is so generally applicable that it will be
useful to indicate its derivation prior to specific uses.
The model consists of a description of each of two simultaneous
processes: obtaining material (filling the saturable component)
and removing material (restoring or emptying the saturable
component). The rate of obtaining is proportional to the degree
of unsaturation (S-x) and to the concentration of the material
being ob t ained (s) :
The rate of change of material associated with the saturable
component is the difference between the rate of obtaining and the
12
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rate of emptying, the latter being proportional to the quantity
of material associated with the saturable component:
at - a
In the above, y is the material being obtained, x is the same
mateiial in the saturable component, S is the capacity of the
saturable component, and kQ and k£ are rate constants for
obtaining and emptying, respectively.
For large populations over time intervals long with respect to
characteristic times for the two processes, the degree of
saturation will reach a stable value, implying that the rate of
emptying is equal to the rate of obtaining. Thus
f rom which
X =•
(4)
Substituting into equation 3 gives the expression for the rate of
obtaining material when the processes are at a steady state:
TRANSPORT LIMITED CHEMICAL UPTAKE RATE
Even though microorganisms move, it is not clear what stimuli
result in the movement, what terminates movement, whether
movement ceases upon reception of other stimuli, etc.. There is
difficulty, therefore, in representing activity of microorganisms
as a function of their energetic needs. It is more convenient to
consider activity as part of the fundamental metabolism of
microorganisms. As noted one aspect of microorganism physiology
that is a result of size and the related absence o f mo r pho 1 o g i c a 1
features for feeding is the uptake of dissolved chemicals from
the environment. For very small organisms viscosity of water is
high enough that movement results in little advantage in terms of
increased food availability. Diffusion and other mixing
processes, threrefore, are important in bringing food to the
organ i sm (12, 13).
The rectangular hyperbola is assumed to be the appropriate
description of uptake of dissolved chemicals from the
13
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environment. Depending upon char ac t ei i s t i cs of the environment
and the organisms, depletion of the chemical in the immediate
vicinity of the cell surface can reduce the uptake rate below
that expected when depletion is not considered. Pasciak and
Gavis (14, 15) and Gavis and Ferguson (16) analyzed this problem.
Their model for the influence of local depletion of dissolved
chemicals on uptake rate accounts for the effects of cell size
and shape. If s is replaced by Cu , the concentration of the
chemical at the cell boundary, ana S by M, the capacity of the
cell membrane for the chemical in moles cm , then equation 6
represents a flux onto the cell membrane (Figure 4). This flux
can also be described in terms of Fick's first law:
Jb = -
where J ^ is the flux at the cell membrane. D is the diffusivity
of the chemical in water (cm2 sec ), C is the bulk
concentration, R is the cell radius, and conversion to moles cm
hr requires the conversion factor, 3.6. The flux to a
spherical cell is equation 6 multiplied by 4 R :
When the two expressions for the flux into the cell (equations 5
and 7) are equated, a quadratic in Cu is obtained. Pasciak and
Gavis (14) write this equation in non dimensional form as
c;
where Cu = kuCu/k|, C = kuC/kj, and P = 14.4 RD/ku. Cb is
available via the quadratic formula and r e s ub s t i tu t i on of the
above .
To account for cell geometries other than spheres, Pasciak and
Gavis (15) modified the above results to represent oblate and
prolate spheroids (disks and spindles). This is accomplished by
multiplying P by a shape factor that is a function of the
eccentricity of the cells (eccentricity is a measure of the
relationship of the major and minor axes). For a complete
description and derivation see Pasciak and Gavis (15) and their
refer ence s .
This description of the uptake process is rather general,
permitting uptake to be represented for any micr roor gani sm that
uses dissolved substances. It does not provide, however, a
description of uptake by aufwuchs or benthic communities. This
is easily accomplished by a development similar to the one
described above, but using a rectangular coordinate system. In
this solution the concentration at the surface of the community
depends upon the thickness of the unstirred layer adjacent to the
14
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surface. Accuracy of uptake calculations depends strongly upon
knowledge of the thickness of this layer.
AUTOTROPHY
Phot osynthe t i c production of biomass and G>2 coupled with aerobic
respiration form a complete element cycle. Respiration in light
and diffusion limited environments depletes O^, , and consequently
other oxidizing agents are used. These conditions are usual in
deep waters, organically rich waters, wetlands and soils. Each
oxidizing agent, like O2 , participates in a cycle that is
complete. These redox cycles, mediated biologically for the
elements of interest here (C, O, N, P, and S) , form the basic
structures of the biogeochemical or element cycles.
Chemoaut o t r ophs obtain energy from oxidation of reduced inorganic
compounds, usually with G>2 as the oxidizing agent (terminal
electron acceptor, TEA). Elements that are reduced during
anaerobic respiration are oxidized during chemo au t o t r ophy ,
thereby completing the cycle. These processes occur in different
environments, however, and therefore transport is a key process
in the cycles and potentially is the limiting step.
Most chemoautot r ophs are gram negative bacteria of pseudomonad
related genera (17) and are, therefore, prokaryotes.
Photoautot rophy is carried out predominantly by green algae and
cy anoba c t e r i a. Green algae are eukaryotes and cy anob ac t e r i a ,
prokaryotes. It might be expected that extreme diversity of
biochemical function exists among such diverse kinds of
organisms. In regard to energy metabolism and biosynthesis
(Figure 5), however, there is little diversity. The Calvin cycle
is the mechanism for fixation of CO2 and production of hexoses
(17) Lehninger (18) gives the following reaction for
biosynthesis in photoautot r ophs :
Here (CH2O) refers to 1/6 of a hexose. The degree to which the
reaction is favored thermodynami c al ly can be seen by decomposing
it into its three component reactions.
+P
= -7-3
* /l4'8
15
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When the standard free energies are used the net free energy for
the reaction is -12.12. Under physiological conditions, however,
the reaction is probably even more favorable. An indication of
this can be obtained by introducing only the free energy of ATP
hydrolysis (-12.5 kcal M"1) reported by Burton (19). This
increases the tendency of the reaction to proceed (AG(v»)= -27.72).
The analogous reaction for chetnoautot r ophi c bacteria differs only
in the use of NAD+ and NADH rather than NADP+ and NADPH (17).
The energetics are approximately the same.
Diversity of autotrophy lies neither in energy metabolism nor
biosynthesis but in the sources of energy: light for the
phot oauto t r ophs and a very large variety of redox reactions for
the chemoautot r ophs. Table 1 gives several of the reactions used
by chemoau t o t r ophs as energy sources.
MODELING AUTOTROPHIC ENERGY METABOLISM AND BIOSYNTHESIS. The
strategy that I have adopted for representing autotroph growth is
similar for both pho t o au t o t r ophs and chemoau t o t r ophs . Energy,
whether light or chemical, and chemicals for biosynthesis have to
be obtained separately. Therefore, energy or any element can
limit the growth rate at a given time. My strategy is to
calculate the growth rate that could be sustained on the supply
rate of each required factor (element or energy), if no other
factor were limiting. That is, given the concentration or
density of a resource, the rate at which it can be obtained and
used assuming that nothing else limits the use rate is
calculated. This produces a set of potential resource limited
growth rates. The actual growth rate is then taken to be the
minimum of this set.
LIGHT LIMITED GROWTH OF PHOTOAUTOTROPHS IN AQUATIC SYSTEMS.
Suspended substances reduce light by shading and dissolved
substances by frequency selective sorption. The Bee r -Lambe r t 1 aw
expresses the reduction in intensity with depth (or mean optical
path) as a function of a situation specific attenuation
coefficient, £ :
= -el
Units of the rate are E absorbed m ~ 2 of surface area m" depth
day'1, the units of I are E m~2 day"1, and of the characteristic
attenuation coefficient, £, are m'1. Steele (20) proposed an
equation for the rate of photosynthesis as a function of light
intensity:
(i)
(12)
16
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where pm is the maximal rate of photosynthesis, ceached when the
light intensity is Im. Equations 11 and 12 can be combined for
the tate expected at any depth, etc., when the parameters aie
known .
Bannister (21) developed production equations in terms of a
parameter that is mote closely related to the biochemical
processes of energy gathering and utilization, 0k> the maximal
quantum yield. Bannister's analysis was carried out in terms of
productivity, M(C) m'^day"1. It perhaps would be a purer
analysis to express the quantum yield in terms of electron moles
E~ , and to work in terms of electron equivalents throughout the
model. At this point, however, it would introduce an extra and
apparently unnecessary step, and so I shall use Bannister's
analysis including his units. He used three separate light curve
equations. Because it includes the pho t o i nh ib i t i on effect, I
shall use Steele's equation (20, 21) as equation 12 above. The
derivation is given here in abbreviated form.
Reduction of light with depth can be partitioned into reduction
by each of the causal components. Reduction rate by suspended
algae is caused primarily by the absorption of light by the
cellular pigments. The molar adsorption rate is
(13)
with units of E absorbed m~3day~1 (actually to be in keeping with
the units of the derivative with respe
better be expressed as E m~* of su
the units of the derivative with respect to depth the units might
rface day m"1 of depth).
'"
Normally productivity is measured in g(C) m'^day"1 or equivalent.
Division by 12 converts to moles. Th e quantum yield is
expressible as the ratio of the molar productivity to the molar
adsorption rate, with units of M(C) E" , and an explicit
expression for the quantum yield can be obtained by substituting
from equations 12 and 13.
' C$ =- f*>e 7-
? ^ 12 r ix A
•X. J-W Kft. f*
As light intensity approaches zero, saturation effects on the
photopigments disappear and the quantum yield approaches a
max imum:
pme
This quantity theoretically is a constant, its value in natural
waters being approximately 0.06 (21) or 0.07 (22) in units of
M(C) E'1 absorbed. Substituting for I in equation 12 and
integrating with respect to depth gives the total photosynthesis
rate per unit surface area. Further substitution for pm (from
17
-------
equation 15) and foe £ in terms of the light attenuation factors
provides the total photosynthesis rate in terms of parameters and
the chlorophyll concentration, A. If this rate is integrated
over time, production is obtained. To do so requires that IQ be
written as a time dependent light flux. This can be approximated
in several ways, but is not represented here.
The quantity that is needed for the simulation approach taken
here is the dep t h- i nt eg r a t ed photosynthesis rate of carbon
assimilation, considering no limiting factors besides light. Two
depths are of interest: either a given depth as, for example, is
of interest when a volume element of particular dimensions is
considered, or the compensation depth given by the depth at which
the light compensation point is reached. In either instance the
applicable equation for photosynthesis rate is
in which L is the fraction of the incident light that is
transmitted through the element, and is given by
r
If z' is a fixed depth, equation 17 can be used, but if z*
represents the compensation depth, then the light level, I1, at
the compensation depth must be specified, and L is calculated
directly as L = I'/Im.
Equation 13 is the primary equation for calculating 1 i ght- 1 imi t ed
rate of growth of pho t oauto t r ophs . In simulation calculations it
may prove convenient to express the rate as a quantity per
volume, rather than per surface area. This is a simple
multiplication of the quantity , p-p, by the applicable surface
area to which the total applies.
ENERGY LIMITED GROWTH OF CHEMOAUTOTROPHS IN AQUATIC SYSTEMS.
Energy is obtained for chemo au t o t r ophy by uptake of reduced
inorganic chemical species and of oxygen as an oxidizing agent,
and by carrying out the redox reaction. Both the chemicals that
are used for the energy reaction and those that are used in
biosynthesis are obtained by uptake through a gradient.
Therefore the concentration at the cell membrane can be the
limiting factor (equation 8). The chemical that is used as the
electron donor in the energy reaction can also be used as a
18
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substrate for biosynthesis. Foe example in nitrifying bacteria
the following reaction is used for energy:
Ammonia is also used for synthesis. It must be supplied at a
rate that is commensurate with the other needs of growth, and
therefore, the rates at which it is required for energy and for
synthesis each need to be calculated and compared to the other
needs. Equations 9 and 10 apply equally well to all autotrophs.
From these equations it can be seen that three moles of ATP and
two of NADPH are required to synthesize one mole of carbon.
Using standard free energy values, this requires that at least
126.9 kcal be supplied via the above reaction (equation 18).
Assuming 38% efficiency (the same as is often calculated for
photoauto t r ophs (23) and heterotrophs (18), 334 kcal from about 5
moles of NH4+ must be released (a quantum yield of 0.2 M carbon
synthesized M"1 NH^+ utilized for energy). A quantum yield of
0.2 was observed by Gunderson and Mountain (24). It can be seen
that for energy to be a non limiting commodity, ammonia must be
obtained at five times the rate of obtaining CO, and at 3 1/3 the
rate of obtaining O 2 . Th e same kinds of calculations apply to
each of the energy reactions indicated in Table 1.
THE ACHIEVED GROWTH RATE OF AUTOTROPHS. The above kinds of
comparisons are valid if autotroph growth is resource limited, a
situation that is expected in all but unusual transient
conditions. Energy and all chemicals can be present transiently
in abundant supply. Under these conditions growth is limited by
some inherent i n t r a c e 1 1 ul a r property. Growth rate is then
maximal, and the condition is transitory because the populations
that are growing maximally increase rapidly until some resource
again becomes limiting. I shall assume that the minimum of the
maximum uptake rates, as limited by membrane transport, is the
growth limiting factor for autotrophs. That is, the maximal
growth rate that is achieved under these conditions is the
minimum of the growth rate that would be achieved maximally for
each of the required resources. By this assumption it is not
necessary to provide a separate growth model for this special
case, because it is calculated naturally as the limit of the
general case.
The general case of growth is the minimum of the growth rates
that would be achieved on each of the required resources.
Elemental composition of the organisms has to be considered when
calculating these minima, however. One way to accomplish this is
to reference each of the rates to the carbon assimilation rate.
If the organism's elemental composition is C£NnP S$l then the
ratio of nitrogen to carbon is n/c, nitrogen is required at only
n/c dC/dt, and thus the minimum of dC/dt and c/n dN/dt would be
the expected growth rate if either carbon or nitrogen were
limiting (here and in the following equation dC/dt and dN/dt are
19
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used to indicate the uptake rates of C and N). In general the
growth rate is given by
(19)
irJ
Each of the rates of assimilation is described by an equation
like equation 5.
HETEROTROPHY
Heterotrophs derive both energy and biomass from a complex
mixture of chemicals. Some fraction of this mixture is
essentially indigestible. The remainder is hydrolyzed to small
compounds and further broken down to small monomers (7) Some of
the monomers are used as reactants for energy production and some
for biosynthesis. Essentially any of the monomers can be used
for energy, but in biosynthesis discrimination among monomers
must occur so that biomass specific to the particular heterotroph
can be synthesized. This general scheme characterizes the
metabolism of both m i croheterotrophs and macroheterotrophs .
Microheterotrophs, of course, deal with the complex organic
mixture extracellularly first, then after it is broken down into
soluble compounds, absorb it and use it for energy and synthesis.
Excretion of products that cannot be used for energy or synthesis
is an important process for microheterotrophs. Macroheterotrophs
consume complex organic mixtures either as other organisms or as
detritus, and the whole process of digestion and metabolism is
carried out internally. Elimination of indigestible material and
breakdown products that cannot be used for energy or synthesis
are both important processes for macroheterotrophs.
A MODEL FOR CALCULATING GROWTH RATE OF HETEROTROPHS. The above
description of the growth and energy metabolism of heterotrophs
is a simplification, whose purpose is to establish the categories
of organic chemicals that I shall employ to represent growth of
heterotrophs. In keeping with the overall objective of
representing ecological processes that are important in element
cycling, the growth model will be a function of the supply rate
of each of the important elements. As already discussed these
processes are driven by redox disequilibria, created by
photoautotrophy and providing continual input to the respiratory
(redox) processes carried out by heterotrophs in obtaining
energy. The model for calculating growth rate consists of three
parts. One is the component for partitioning of food into power
supply and biomass synthesis. A second is the ca 1culation of
power demand. The other is the calculation of food consumption
rate in terms that permit calculation of power supply as well as
the supply rate of food components whose composition is similar
to that of the consumer.
20
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PARTITIONING OF FOOD INTO POWER SUPPLY AND BIOSYNTHESIS. Food
consumption, power consumption, power production, and
biosynthesis are rates. The problem faced by heterotrophs is to
obtain food at a rate so that the power produced from it
satisfies the power demand of obtaining food and escaping
predators plus the basic power demand of life processes and
repair with enough remaining power and materials to support
growth. Figure 6 gives the scheme for accounting the energy and
materials in partitioning the food intake rate into power output
and biosynthesis. The scheme refers most directly to
macroheterotrophs, but it is applicable to microheterotrophs if
food is considered to consist of dissolved organic chemicals and
elimination of the indigestible fraction is ignored. Figure 7
shows the assumed relationships of the categories of organic
chemicals in the aquatic system. Processes and states inside the
dashed line occur inside microbial cells.
The object of the model is to calculate growth rate of a
heterotroph population. This is accomplished in several steps.
Composition of the food is compared to the composition of the
heterotroph so that the rate of consumption of two food
components can be calculated. The two components are biomass-
1 ike (referenced as pool 1 in the following) and non biomass-like
(pool 2). (The term "pool" should be interpreted to indicate a
dynamic quantity characterized by varying elemental composition
as the composition of food varies.) In the overall model, the
free energy content of total food at any time is known via an
accounting chain. The free energy content of each pool is
calculated as part of the function of this model as is discussed
below. This provides the power supply via each of the two pools.
The disposition of the pools is determined by comparison to the
power demand, and growth rate is immediately available as a
result of this comparison. The specifics of the process are
given below in the sequence of the descriptive overview presented
in this paragraph.
The process of partitioning food into power supply and
biosynthesis is developed in the following in terms of
macroheterotrophs. The situation for microheterotrophs is
simpler in one aspect because of the representation as lumped
categories of the organic chemicals on which they feed. The
development for macroheterotrophs can be applied to
microheterotrophs by considering the categories of organic in
place of the species of prey. But in another aspect it is more
complex. Macroheterotrophs use a single electron acceptor,
oxygen, whereas microheterotrophs use a whole series of them.
Use of the term "energy content" is to be interpreted as the free
energy of the reaction between a chemical serving as an electron
donor and another chemical serving as an electron acceptor. In
much of the following the electron acceptor is assumed to be
oxygen and no single chemical will serve as electron donor, but
rather electrons will derive from a mixture of chemicals,
comprised of the biomass of higher organisms. In this situation
21
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also, I shall use the term "energy content." A discussion of
energetics with electron acceptors other than oxygen will follow
the section on food partitioning.
The food intake rate (Mass t'1
consumer' )
i s
(20)
where i indicates a source of food (prey population or
environmental pool of chemical), and j identifies the predator.
The overall elemental composition of an organism (or of a
chemical pool can be represented for the elements of concern as
where the upper case letters symbolize the elements as usual, and
the lower case letters represent the mole numbers of the elements
with which they are associated. Let nik represent the mole
number of element k, species i, and w^ represent the gram atomic
weight of element k. Then the fraction of food mass obtained
from prey species i comprised of element m is
I. - 0»
1 mi W"
that the rate of consumption of element m in the mixed food is
Th e average
i s the set
molar rate
of
(23)
consumption of elements by consumer j
J
EJLL
0_ , .
16
F*
14
,-H*.
3 1
Division of each of the elements of this set by the mole number
of the consumer for the corresponding element gives another set,
the least value of which corresponds to the element of the food
which is in least supply relative to the composition of the
consumer. A set of mole numbers for the composition of the food
normalized to the element in least supply can be obtained by
dividing the elements of the set of molar consumption rates
(equation 24) by the rate for the element in least supply. A
similar set can be obtained for the consumer by dividing the mole
numbers of the consumer empirical formula by the mole number of
22
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the element in least supply. Then the food
into the two pools. The noimalized empirical
be t ept esent ed as
can be partitioned
formula of food can
and, because pool
r epr es ent ed as
1 is like consumer biomass, it can be
CON PS
«j •* "a P
(26)
In the above formulae, the subindez F indicates that the mole
numbers are for the food, and the subindez j indicates that those
mole numbers are for pool 1 which is like consumer j. Pool 2
component constitutes the remainder of food. Its mole numbers
are the difference between the mole numbers of the food and of
pool 1 :
0
^
(27)
Now the rate of consumption of the two pools can be calculated.
First let n^; represent the mole number of element j in pool k.
Conservation requires that
The fraction
of
food that is pool k is
4 «*
and the rate of consumption of pool k (k = 1 or 2) is
ir ' _
1 -
f
(30)
If the free energy content of food is known, then it too can be
partitioned. Morowitz (7) discussed some of the problems of
using free energies of biological materials and concluded that
enthalpy (heat content) values are useful approximations. There
are other approaches to this problem that could yield better
approximations, but that problem will be left, and I shall merely
assume at this time that free energy values are available.
23
-------
The free eneigy content of food can be obtained if the free
energy content of individual food items is known:
GC ^ is the free energy content of species i.
During the process of digestion of the food to monomers, a small
loss of free energy occurs, the polymer bond energy, AG^. The
free energy of pool 1 is the same as the free energy of the
consumer less the free energy loss of depo 1 ymer i za t i on, 4Gm* =
AG • - AGj. Pool 2 free energy is the remainder less the energy
loss of depolymer izat ion: AGm2 = (SFjj AGp - FI AG,:)/F, - AGd.
The power supply from the two pools can now be calculated. From
pool 1 it is
where B- indicates the mass of an individual of species j, and
f r om pool 2 it is
Describing the way that this free energy is used to produce ATP
and NADPH requires a model of cellular biochemistry. I assume
that discrimination between the two pools occurs, so that pool 2
is used preferentially for energy and pool 1 as material for
biosynthesis. Power demand, Pfl is taken to be the sum of the
energy expense rates for maintenance, repair, motility of hunting
and escaping, and other activities associated with feeding. If
the power demand is greater than power production from pool 2,
then pool 1 is used as needed. If the power demand is less than
power production from pool 2, then pool 2 remainder is converted
into new biomass at at rate determined by the uptake of the
necessary inorganics to achieve the consumer's elemental
composition or it is converted into storage compounds. The
remainder, in excess of the rate of conversion by these
processes, is eliminated. Four distinct cases arise as a result
of the comparison of the power supply and demand:
Case 1: pool 2 power supply > power demand for activity
plus synthesis of pool 1 into consumer biomass:
-I
< (34)
24
-------
Case 2: pool 2 power supply > power demand foe activity
but < power demand for activity plus synthesis
of pool 1 into consumer biomass:
Case 3: pool 2 power supply < power demand for activity,
but pool 1 + pool 2 power supply > power demand
for activity:
P
-------
Case 2: pool 2 supplies the power demand of activity plus
patt of the power demand of synthesis. The growth
rate on pool 1 monomers sustained by power derived
f r om pool 2 is
Power to synthesize the remainder of pool 1 must
derive from pool 1, itself. The remainder of
powe r in pool 1 is
Thus, the growth rate sustained by the remainder
of pool 1 is
"
jx »&&?-,.- P.)
The net growth rate is the sum of the two, which
after simplification is
(43)
Case 3: pool 2 is insufficient to supply the power demand
of activity, so pool 1 is diverted at the
necessary rate. The power available from pool 1
remainder is
-I
: (44)
The growth rate that is sustained on pool 1
remainder is
Case 4: the power obtainable from the total food is less
than the activity power demand. It is assumed
that the consumer continues to attempt
to carry out normal activities of feeding,
escaping, etc., at the expense of body mass. The
26
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net effect to the whole population is a loss
of biomass, expressible as a negative growth rate:
' (46)
The growth rates calculated above (equations 38, 43, 45, and 46)
use values for power production rate and power utilization rate,
in addition to the patterns of physiological processes and
biomass composition. Power is used at the cellular level, but it
can be accounted most easily at higher levels of organization.
Power is required for biosynthesis, hence the accounting point is
in the model for biosynthesis, i^. £_^, in the above equations
describing growth. There are two other major categories of power
demand. One is the basic metabolic demand. The other is the
demand due to motile activity. This latter demand is more
readily accounted at a higher hierarchial level, the power
required to move a body through a liquid medium. Power production
rate is a function of the composition of the food, and of the
rate at which it is obtained. Hence, a description of the
feeding process is an important part of the model, because in its
development the basis will be obtained for calculating power
supply, supply of materials for biosynthesis, motile activity for
obtaining food, and motile activity for escaping predators. In
addition loss rates caused by predation are obtained by simple
rearrangement of the equations for feeding.
FEEDING BY MACROHETEROTROPHS. Macroheterotrophs capture discrete
food particles by one of two general means. Either they feed
upon all particles encountered that are within the size range
that they can handle, or they select and capture individual food
particles by explicit overt action. I shall refer to organisms
characterized by the former behavior as filter feeders and to
those by the latter as pursuit feeders.
The derivation for uptake and feeding given in equations 1-5
follow the general pattern of Rashevsky's (10) derivation of
stationary state feeding rate for fishes. His work was motivated
by Ivlev's (25) studies on the feeding of fishes. Ivlev's model
for fish feeding is widely used in mathematical models of systems
that include feeding by large consumers. It was derived as a
formal mathematical expression that fitted his data. Rashevsky
derived his model from assumptions about the way that fishes
feed. Part of his purpose was to present a stationary state
analysis based on Ivlev's model, which described the feeding of
of fishes as a function of the density of food. Ivlev's equation
was of the form
(47)
where R is the food eaten per experiment (a fixed time), Rm is
the maximum feeding rate for the fixed time, BW is the biomass
27
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density of prey (mass per volume), and z is a fitted constant.
Rashevsky's derivation of an equation comparable to Ivlev's began
with the statement that the feeding rate (F) equals the encounter
rate (E) times the probability that the prey is eaten if
encount er ed (P):
F = E P (48)
The encounter rate is derived by assuming that the predator
sweeps out a right circular cylindrical volume as it swims in
search of food. The encounter rate is then the product of this
volume per time and the density of prey in the volume, r vB,
where r is the radius of the cylinder, v is the swimming
velocity, and B is the mass of the prey per volume of water.
Rashevsky took the probability of consumption given an encounter
to be proportional to the unfilled gut capacity, an assumption
exactly equivalent to that made in equation 1.
The latter assumption is credible for situations in which the
saturable component is filled via mechanisms that operate
passively, such as the adsorption of dissolved chemicals onto a
microbial cell membrane. Where the component is filled by active
processes, however, such as the filling of a fish's stomach by
active feeding, it is not clear that the rate of filling is
necessarily proportional to the unfilled capacity. If the
probability that an individual consumes a prey increases as
unfilled stomach capacity increases, but not linearly, then this
model better approximates the feeding of a population where there
is a distribution of the extent of filling than it does an
individual's feeding. Ivlev's fits of the model to data
indicated no discrepancy from the model of direct
proportionality, however, and therefore, the point is more
cautionary than substantial. The point should simply be borne in
mind that it is not necessary for a higher organism to reduce its
feeding rate to the fraction of its maximum that corresponds
exactly to the fraction of unfilled stomach capacity. In this
particular regard the model of Rashevsky and the models that are
developed here are not necessarily based upon an unassailable
as sump t i on.
The encounter rate is
(49)
•^ i _*^~
* TT
28
-------
where r is the encounter radius, v is the swimming velocity, and
M is the biomass density as in Ivlev's model. The probability
of consumption of prey given an encounter is
P -
(50)
where M$ is the capacity of the stomach, M is the quantity of
food in the stomach, and c is a constant of proportionality. If
the probability of consumption is 1 when the gut is empty (M
= 0) then the proportionality constant, c, is MS-I. Thus the
feeding rate is
r-
F =
.
"
Trr"vC>, <, 'M ') (Ji>
Feeding rate, F, is the same as the rate of change of stomach
content, dM /dt if the experiment is done over a short enough
time interval that stomach emptying can be ignored (there is no
loss term). Integrating and putting M = 0 when t = 0, the
stomach content is
Mfl = M, (l -
(52)
For Ivlev's experiment, t = tf, the fixed experimental length, so
that the constant, z, of Ivlev's model is equivalent to TIT vt£/M
of Rashevsky's. As noted by Rashevsky (10), Ivlev's model
applies only to the phenomenon of feeding as a function of
concentration of food. That is, it does not take into account
other factors that affect feeding, such as stomach emptying rate.
It is not suitable, therefore, for use in a model in which time
intervals are long enough that the other factors become
impor t ant .
For a population considered over a time interval that is long
compared to the characteristic times for stomach filling and
emptying, the mean food intake rate equals the mean stomach
emptying rate, i. e. T steady state feeding is achieved:
where k is the stomach emptying rate constant. The feeding rate
is obtained by rearranging Equation 53 so that kM is expressed
29
-------
in terms that do not include the stomach content, M , and
recalling that at steady state feeding, feeding rate equals the
stomach emptying rate, or
_ kMsB,,
F -T*T7^
•t- L->^
Note that this equation is of the same form as Equation 5, and
that its equivalent components are int er pr e t abl e similarly.
To the extent that this model represents the main features of
pr edat or -p r ey interactions in aquatic systems it has a property
that is very useful, it permits complete specification of
predator-prey interactions as a function of the characteristics
of the individual predator and of the population densities of
predator and prey. That is, no species specific, pairwise
interaction coefficients are needed. Immediately, however, one
rejects that pr edat or -prey interactions involve characteristics
of the predator and not the prey. In the following a more
detailed derivation of predator-prey models is made for two major
ecological modes of feeding by aquatic organisms, filter feeding
and pursuit feeding. In these models characteristics of both
predator and prey are incorporated while retaining the
characteristic that no interaction coefficients are required.
FILTER FEEDING. Consumers that feed i nd i s c r imi nan t 1 y upon all
organisms that they encounter that are within the size range
possible for them to feed upon are grouped here under filter
feeders. It is assumed that they move through the water creating
a disturbance front detectable by prey with suitable sensory
organs. Some of these prey are able to escape and some are
captured. The scheme for this type of feeding is given in Figure
8. If a prey organism swimming at velocity v swims normal to
the path of the oncoming predator, reaching the edge of the
encounter cross section, the distance P- r, before the predator
swimming at velocity v swims the encounter distance s^, then the
prey escapes; else it is captured. All distances, T , such that
are escape distances. All prey inside the radius, (, at the
point of encounter with the disturbance front preceding the
predator are captured. The feeding rate of an individual
predator feeding on a single prey of population density, M, is
<56>
The first of the two forms of F, although somewhat more
cumbersome, is preferable, because it groups quantities together
30
-------
that are properties of the predator alone. Hence, in dealing
with several prey populations and one predator these quantities
are constants. They are the factor, kM , and the whole first
term in the denominator. The second of the two forms indicates
that the effective rate that the predator hunts is dependent upon
both predator and prey. That is in the first the volumetric
search rate is fT/*2 vc, but in the second the comparable term is
fCt*vc, a smaller quantity that is a function of both predator and
prey because *P is a function of the swimming velocities of both.
The expression for feeding by predator j on n prey populations is
FL- = _, • <">
•4; * />>lrVBl-
PURSUIT FEEDING. Consumers that swim at one velocity while
searching for prey, then pursue the prey at another velocity are
referenced here as pursuit predators. Figure 9 gives the
schematic for this mode of food gathering. The searching
velocity of the predator is v •. The distance at which the
predator can detect prey is taken here to be a constant that is
characteristic of the predator, sdj. It can be made a function
of water clarity or even a function of prey size or other
characteristic without major change in the form of the
derivation. Upon detection both predator and prey begin swimming
at the pursuit velocity, vpj. and flight velocity, V£if
respectively. The duration of the pursuit, t •:, is given by
v,.
The prey's distance of the flight, «£—, is given by
< (59)
S*-'J = V*; V^3
It is arbitrarily assumed that prey that escape swim the same
distance as prey that are captured, and similarly for predators.
Another arbitrary (but necessary for simulation) function was
developed (but not discussed in detail here) to calculate the
probability of escaping pursuit predators. Essentially it is
assumed that the probability of escape is greater, the closer is
vf • to v •. That is if the prey can swim nearly as fast as can
the predator, there is a high probability of escape.
As with filter feeders the effective rate that the pursuit
predator hunts is a function of both predator and prey.
Gerritsen and Strickler (26) developed a model for predation that
depends on both predator and prey cruising velocities. This
31
-------
model is equivalent to the effective hunting rate, the rate of
encounters while hunting:
Aij ~ " *dj ^ ' 3^ J (60)
where u = min(v -, v •), w = max(vc£,v •), and vcj and v • are
the cruising velocities of prey i and predator j, respectively.
The rate of encounters while hunting is greater than the feeding
rate, because pursuit feeders spend their time in two ways,
searching and pursuing. (In general I shall aggregate all
activities involved in feeding into pursuing, i. e., pursuit,
capture, handling, ingestion. First, however, it is less
cumbersome to develop the model in terms of overall rate of
encounter, then later to introduce the probabilities of pursuit
given encounter and of capture given pursuit.)
In parallel to the phenomenon of partitioning a saturable
component into filled and unfilled portions, a pursuit predator
partitions time into searching and capturing:
F*; = (Tc + T,,)"1 (61)
j s p'
where F j is the encounter rate, TS is the mean time spent
searching per encounter, and T is the mean time spent pursuing
per encounter. More specifically the mean search time per
encounter and the mean pursuit time per encounter are
T3=
where R— is the relative frequency of the ijtn encounter:
V
(63)
After rearrangement the encounter rate can be written as
l;J^'' (64)
Unlike the expression (Equation 57) for filter feeders, the
components of Equation 64 are not as simple dimensionally as is
desirable for ease of interpretation. The terms of the
denominator each represent an encounter rate, the first relating
to pursuits and the second to detections of prey while the
32
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pcedatot is searching. If the equation is rewritten by dividing
both numerator and denominator by the sum of the velocity
differences, the "half saturation" term becomes simply the
detection distance for an encounter, a form that is perhaps more
easily interpreted. Without exhausting the possible ways that
the equation could be rewritten in search of a form that is most
readily int erpr e t abl e , it is apparent that the components of the
expression are functions of characteristics of both predator and
prey to a greater extent than are the comparable components of
Equation 57. It is therefore comparably more difficult to
separate the components of the equation in such a manner that it
is as easily interpreted.
To complete the model for pursuit predation, the effect of
stomach filling must be incorporated. In the general expression
for the limitation of feeding rate by stomach filling (Equation
51), the probability of feeding was taken to be proportional to
remaining stomach capacity. A similar assumption is made here.
The encounter rate times the probability of encounter for pursuit
feeders is the encounter rate, F , as developed above times the
probability of feeding given an encounter, (Ms= - Mgj)/Msi- At
steady state feeding this rate equals the stomach emptying rate,
Rewriting to remove terms involving the variable, M •
6 J
<66>
*
Equations 57 and 66 are expressions for feeding rate of the two
major ecological modes of feeding by mac r ohe t e r ot r ophs . By
parameter variation they can be made to describe a wide variety
of behavior by these types of organisms. For example, Equation
66 can be made to describe the feeding of an ambush predator by
noting that the cruising velocity of such a predator is zero,
which reduces the expression for the volumetric search rate to
aii = frsdi ci' ^n additional consideration is the feeding of
ma c r ohe t er o t r ophs in communities in which there is a wide
disparity in sizes of the organisms present. Introduction of a
factor in the numerator of both equations to account for the size
window within which feeding occurs overcomes the potential
problem for an operating model. The function that I have used
expresses the probability of ingestion as a function of prey
size. I shall not describe it in detail in this report.
Expressions can be obtained for mortality occurring in a
population as a result of consumption by populations of filter
and pursuit feeding predators, and for power used in moving about
in the activities of feeding and escaping being fed upon.
33
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MORTALITY CAUSED BY PREDATION. The mortality rate experienced by
a population is the sum of the mortalities caused by all the
predators. The quantity, therefore, is obtained by summing the
rates over all predators. One approach is to consider that the
mortality caused by a predator population, j, on a prey
population, i, is the total feeding rate of the predator
multiplied by the fraction that the specific prey population
comprises of the total prey encountered by the predator. The
appropriate fraction, however, is not simply the prey population
mass divided by total prey mass of all species. The appropriate
expression is obtained by using the encounter radii, T;
-------
Fot pursuit feeders essentially the same approach is used, except
that encounter rate constants (equation 60) are used as weighting
factors. The resulting expression is
(70)
where ni- is the mortality rate to population i caused by
pursuit feeders.
POWER DEMAND RESULTING FROM MOTILE ACTIVITY. The power required
to move around in a viscous fluid nominally is porportional to
the third power of the velocity of movement:
where GJ is the drag coefficient, O is the density of water, A is
the appropriate area of the moving organism, and V is velocity.
The drag coefficient, Cj, is not a constant, however, but is a
complex function of velocity. In practice Cj has to be measured
as a function of the velocity (or the Reynolds number) for each
shape (13). This difficulty of operation will not be discussed
further here. Instead, it is assumed that equation 71 is
sufficient to develop the ideas for the model, thereby deferring
this operational difficulty until the time when parameter values
are sought for the model.
A heterotroph does not swim at constant speed, so its power
demand is a variable. I assume that a he t er o t roph1 s time can be
partitioned into four kinds of activities: searching, pursuing,
escaping, and inactivity. (Filter feeders do not pursue, so for
them this fraction is zero.) If every individual in the
population behaves in this way, and the behavior is not
synchronous, nor correlated time-wise, then an alternate view is
that the fractions refer to the fractions of the population
engaged in the four activities at any time. I have not taken
into account a time fraction spent in reproductive activities as
would be appropriate for higher organisms. There is, however,
allowance for energy of reproduction in the cost of biosynthesis
(see PARTITIONING OF FOOD INTO POWER SUPPLY AND BIOSYNTHESIS). A
rationale for accounting power expenditure for reproductive
activities could possibly begin by partitioning the power that
now is allotted to growth into a portion for activities associated
with reproduction (nesting, migrations, etc.) and a portion for
population growth. Unfortunately, no means is apparent to me at
this time by which to rationalize this partitioning, and a great
deal of research would necessarily precede such a model. It
35
-------
would be necessary to determine whether any relationships
for example, between power availability and the elaborateness of
reproductive behavior. As represented in the present model, any
unaccounted activity will result in calculation of growth rates
greater than could be attained in reality.
To obtain the fractions, I have assumed that an organism's first
priority is self preservation. Therefore the fraction of time
spent escaping predators can be calculated independently of all
the other fractions, and the other fractions simply partition the
remaining time. A given organism can be subject to predation by
both filter feeders and pursuit feeders. The fraction of time
spent escaping predators, in general, will be a function of both
types of predation. The fraction of time remaining for feeding
after escaping predators, in general, will alter feeding
behavior, and equations 57 and 66 must be correspondingly
corrected to account for this effect.
Calculations of these fractions of time make use of the
relationships already developed. When all ramifications are
considered, however, they are more tedious than is worthwhile for
presentation in this report. Therefore they will not be
presented in detail. Instead the general approach taken in
obtaining the derivations will suffice.
The fraction of time spent in an activity is the time per unit
(or event) of that activity times the zate of occurrence of that
activity. Thus the fraction of time spent escaping predators is
the time per escape times the encounter rate. (Naturally, the
actual calculation is far more involved. For example, one
complication is that the fraction of time spent fleeing is
calculated as the difference between the fraction of time spent
being pursued and the fraction of time spent being captured,
because the power used by those that are captured is irrelevant
to the surviving population.) After the fraction of .time spent
escaping, f£, is accounted, the remaining time, ft, is
partitioned into feeding and inactivity. The expressions for
feeding are corrected for reduction in available time by escaping
predators by noting that stomach emptying occurs at the same rate
regardless of the predation pressure, while feeding itself is
limited to the remaining time. The power required for the
activity is obtained by multiplying the velocity of swimming in
each activity by the fraction of time spent in each activity and
using equation 71 for organism j in the following form
where f^j is the fraction of time spent in the kth activity by
organism j, and v^- is its velocity in that activity.
At this point power supply via feeding, power demand as a
function of activity, and disposition of the elements comprising
the food are all calculable for heterotrophs using the
36
-------
relationships developed. One additional aspect of metabolism
needs to be considered foi theoretical completeness, so that a
closed system of equations can be developed to represent element
cycling. That aspect is the use of different oxidizing agents as
terminal electron acceptors in the energy metabolism carried out
by all heterotrophs.
ENERGY METABOLISM AS A FUNCTION OF TERMINAL ELECTRON ACCEPTOR. To
represent organic chemicals in a general way as sources of
materials for energy and synthesis, it is necessary to group them
into categories. Criteria for establishing these categories
include similarity of elemental composition, energy content, and
the way in which organisms use them. These criteria do not
specify the level of resolution, however, and in the final
analysis the categories will be selected through experience with
attempts to match several possible categorization schemes with
the other model components to achieve the results with reasonable
economy. An initial scheme is presented in Figure 7. In this
scheme the categories are particulate organic matter (POM),
refractory organic matter (ROM), digestible organic matter (DOM),
soluble organic matter (SOM), itself consisting of two
components: biomass-like monomers (BOM) and non-biomass-1 ike
monomers (NOM). POM receives input from organism deaths, molts,
egesta, etc. The distinction between ROM and DOM is purely
categorical, i. e. f no process separates ROM from DOM. DOM,
however, is readily hydrolyzed by exoenzymes of microorganisms
into SOM, whereas ROM is only very slowly solubilized. SOM is
absorbed by the organisms, and separation into BOM and NOM
occurs. (This is also a categorical distinction as discussed in
the section on partitioning of food into power supply and
biosynthesis.) This categorization scheme reflects the mode of
biological utilization more explicitly than similarity of
composition or energy content. It is possible that for the
latter criteria additional categories will be required. It might
become necessary, for example, to represent CH4 , acetate, or
other specific categories of chemicals that are important in
microbial systems for the model to reflect certain aspects of
their dynami c s.
As organisms oxidize organic chemicals for energy, there is a
sequence of utilization of electron acceptors that corresponds to
the variation in redox potential for the reactions (4, 27). That
is, a preferred electron acceptor is used until it is depleted,
then the next preferred form is used, and so on. O2 is used
first, followed by NO,"1 and NO2"1, SO4"2, and CO,. Other
oxidants are also usea, such as other forms of sulfur. The
interesting point of this sequence is that the preferred sequence
is in the order of the energy released in the reactions.
Oxidations of organic compounds using the more preferred electron
acceptors result in greater energy yield than reactions using the
less preferred. It is unlikely that this reflects any chemical
necessity (4), but more likely reflects the competitive advantage
accruing to organisms that use the more highly productive energy
sources. This sequence of reactions will be expressed wherever
37
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transport or regeneration of electron acceptors is slower than
their use by organic decomposition. In natural systems, it is
expressed temporally in highly eutrophic systems and spatially as
vertical stratification in systems with highly organic sediments,
such as wetlands and many water bodies.
The use of ozidants in sequence can be represented by the
assumption that the strongest oxidant present is used. The
problem that then remains is that of calculating the energy yield
appropriate to the oxidant that is being used. One direct
approach to this problem is that suggested as appropriate by
McCarty (4), the use of half reactions and equivalent weights as
described in elementary chemistry texts, and as is commonly used
in biochemical calculations (28, ch. 17). If this approach is
taken the standard free energies of the half reaction of their
reduction (at pH 7, and unit activity for the other reactants),
per equivalent weight of the oxidants is in the order
corresponding to the sequence of their utilization. An exception
to this is nitrite, whose value for AG°(w) is higher than that of
O,. It is not clear whether this apparent reversal in tendency is
a consequence of adaptation of the organisms that use nitrite as
an electron acceptor or of the peculiar relationship of nitrite
to nitrate. That is, nitrite is formed as a product of nitrate
reduction and is available as a reactant, therefore, only after
nitrate is reduced.
For the scheme for representing organic matter to be used
effectively, an accounting algorithm must be applied to enforce
the conservation of mass. The algorithm that is applied here is
in outline the following. Each of the categories of OM are
treated as state variables, except that POM is not represented as
a separate state variable, but rather as a sum of DOM and ROM.
Fractions of the various sources of detritus are refractory to
hydrolysis and are therefore ROM. The remainder is DOM. DOM is
lost through hydrolysis to soluble compounds, SOM, which in turn
is lost via uptake by microorganisms. As discussed above, the
subsequent processes are as represented for macroheterotroph
metabolism. Conservation of mass in this model, however, has a
more specific meaning. The elements of concern must be
individually conserved. This is accomplished by accounting the
concentration of the elements in each of the pools. The rules
given above then apply to the individual elements. The pools are
treated in many respects as a single type of molecule with mole
numbers proportional to the concentrations of the elements.
(Except that for computations using the Gibbs free energy, it is
not assumed that the concentration of the molecule as a reactant
is that of the whole pool. See Energetics above.)
The above procedures will guarantee conservation of mass, but to
calculate the energy yield from reaction with the various
oxidizing agents requires an additional algorithm. The oxidants
are represented as half reactions in which an electron equivalent
of the oxidant plus an electron (hence electron acceptor) yields
a reduced form of the element. A complementary half reaction is
required for the electron donor, a molecule from one of the
38
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categories of organic matter. This can easily be done (but is
not discussed here). Of more difficulty is the problem of
obtaining the appropriate free energy for this half reaction.
The approach to be taken initially is to use a conservation rule
for heat of combustion with oxygen so that the energy of the
pools is accounted dynamically. When calculating the energy
yield for reaction with another oxidizing agent, the reaction
with oxygen will be replaced by an equation for the appropriate
reaction by first removing the half reaction for oxygen and then
substituting the half reaction for the oxidizing agent of
interest.
MODEL SUMMARY
The above several sections summarize a complete and theoretically
rationalized basis for a multi-species, yet functionally
oriented, ecosystem model. It yet remains for this theory to be
implemented into a working computer model. Further work is
needed to provide a basis for describing physiological,
behavioral, population level, and other specific effects with a
comparable degree of theoretical rationale. It is quite possible
that this work will require yet additional work on the model as
pr esent ed.
CONCLUDING COMMENTS
MACROSCOPIC METAVIEW AND MICROSCOPIC APOLOGIA
The futility of the reductionist method for studying systems has
often been argued convincingly. Early in this report I noted
that I have departed from both the holistic and reductionistic
approach. Yet it has not surprised me to find that many with
whom I have discussed these ideas have gained the impression that
this research is extremely reductionistic. They have noted that
it is reductionistic to attempt to understand a natural system by
studying its parts in detail, and that this approach to ecology,
historically has failed. They have further noted that my work
bears a strong resemblance to that approach. There is a great
philosophical and operational difference, however, between this
model and the reductionistic approach.
This model is indeed constructed of fine scale components. But
in contrast to the failures to comprehend natural systems through
comprehensive study of their parts, I expect to obtain
predictions at the ecological scale. The reason for optimism can
be explained by contrasting the comprehensibi1ity of natural and
engineered systems. Engineered systems are understood
essentially as well as their component parts are understood,
because they have been explicitly designed and constructed.
Oftentimes models are constructed of mathematical analogs of the
component parts and coupled in a way considered to be analogous
to the way that the engineered system is built. The model is
itself an engineered system, built in strict analogy to the
physical engineered system. It is intended that the model output
39
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represent the system level behavior of the engineered system.
The degree to which the model behavior actually represents that
of the physical system depends upon the closeness of the
analogies between the systems, which in turn depends upon the
skill of the modeler. There is no question of whether any
failure of the model to describe the physical system's behavior
is due to inherent impossibility of obtaining system level
behavior from a model constructed of mathematical analogs to fine
scale physical components.
All coupled models, including the one discussed in this report,
are engineered systems. At issue is whether this model's
behavior will represent, to any useful extent, behavior of
natural systems. Specifically not at issue, as argued above, is
whether system behavior can result from a model constructed of
fine scale components. As with models of engineered system, the
extent to which model behavior will represent natural system
behavior will depend upon the closeness of the analogies between
model components and physical couplings.
Physical ecosystems are comprised of a virtual infinitude of
components. It is patently obvious that it is impossible to
study or represent all of them. But even if it could be done,
one would have a representation of only a single ecosystem.
Patterns of ecosystem behavior for broad categories of systems
are recognizably similar, even if not predictably so. There is
structural and functional similarity that apparently emerges, in
the presence of significant diversity of system components.
Analogously, a system model, if constructed of components that
well represent the processes that occur in a type of ecosystem,
can be expected to exhibit functional behavior similar to that of
the system type whose components are represented, despite the
unavoidable misrepresentations of the greatest majority of
species present in physical ecosystems.
The manner in which I anticipate that this model's system
behavior will represent real system behavior is best explained in
terms of three macroscopic, testable hypotheses about this model
and its relationship to natural system behavior. It is my
hypothesis that it will be possible to find comp1ements of
species representations (sets of attributes) that will coexist
for very long times (not necessarily asymptotic coexistence), and
further that among such coexisting complements that there will be
a high degree of similarity of process rates. That is, I
hypothesize that there may be many nearly stable model
communities that could occupy a model environment, but that one
will not be able to discriminate among them merely by considering
differences in process rates. Further, I hypothesize that the
predicted ensemble average ecological effect of a specific
toxicant will not differ distinguishab1y among such coexisting
complements. A connection with reality is needed for these
results to be considered predictions, and the final hypothesis
provides this connection. I hypothesize that one will not be
able to discriminate between measurements on processes occurring
in a real system and analogous values of processes as calculated
40
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by this model, including the ecological effects of toxic
chemicals, provided that the teal system's boundary conditions
can be well represented in the model. This latter provision
recognizes that uncertainty in boundary conditions can limit the
capability to discriminate between the predictions and
observations. Laboratory ecosystems hold some promise of
overcoming this potential limitation by permitting control over
boundary conditions so that they can be represented in the model.
If these hypotheses are borne out, and calculational difficulties
can be overcome, then this model will provide a synthetic means
of predicting ecosystem effects. If they are refuted, the
results will suggest other hypotheses.
SCALE OF RESOLUTION, REDUCTIONISM, HOLISM, AND PREDICTED
ECOSYSTEM BEHAVIOR
The third hypothesis is the critical one. Underlying this
hypothesis is the premise that interactions of the equations will
be analogous to interactions among real ecosystem components. In
fact the results of any ecosystem model must depend upon the same
premise, regardless of whether they are considered reductionistic
or holistic. The equations of any model must bear some
relationship to the system components that they represent. The
degree of resemblance is dependent on the correspondence of the
level of resolution to the resolution of the components of the
natural system components of interest, and on the skill with
which these components have been selected and described. If a
fine scale of resolution is selected, a model is apt to be called
reductionistic, or conversely, if coarse, then holistic. But is
the difference between reductionism and holism merely a
quantitative difference in scale of resolution? I would argue
that scale of resolution is not even relevant to the distinction
between the two views. If one is interested in studying the
response of processes or entities as a function of the level or
intensity of various influences, where the uncontrolled
fluctuations of the system have been "reduced" to an acceptable
level, then the view is r educ t i on i s t i c . If, on the other hand,
one is interested in processes or entities that take on their
special characteristics as a result of the direct and indirect
influences of other system components, then the view is holistic.
Moreover, taking a holistic viewpoint does not necessarily admit
a coarse scale of resolution. The scale of resolution dictated
by the processes and entities of interest, whether the viewpoint
is reductionistic or holistic.
There is no intent for this model to reproduce the detailed
behavior of a real physical system in such a manner that one
could identify the behaviors of real living species in the
results. What is intended is that this model be an analog of
aquatic systems, in the sense that system behaviors that cannot
be attributed to individual biotic species, i. e^., whole system
properties, are indistinguishable from results of the same
kinds of behaviors of natural systems with similar boundary
41
-------
conditions. The possibility that such results can be obtained
depends on the choice of processes to represent, the adequacy of
the description of those processes over the operating range, and
the application of constraints (conservation laws, thermodynamic
and kinetic principles) in a manner that is analogous to
constraints on natural systems.
All results of a system model must necessarily be viewed as
system level results. There are two categories of system level
results, however. One is the sort that could also be measured in
a reductionistic way in a controlled experiment, for example -- a
chemical reaction, but whose peculiar characteristic in the
system context results from system interactions. The other is
the sort that cannot be observed in a reductionistic way, because
it does not exist apart from the system. An element cycle is an
example of such a result, and measurement of the flow of material
around an element cycle loop is an example of a system level
measur ement.
The distinction is not as great as it might at first appear,
however, because of the possibility of interpreting the former
sort of result as indicative of the latter. Patterns of
interactions are new macroscale phenomena that arise via the
existence of the system, but they can be observed only at the
scale of observation possible for the observer. Thus
measurements of chemical reaction rates in the system can be
observed and used to infer behavior of the whole pattern of the
element cycle in which it participates. It is not inconceivable
that some sort of observation could be made at the scale of the
pattern itself. It is characteristically human to perceive and
discriminate among patterns, but it is quite another level of
difficulty to quantify objectively patterns of behavior in a
manner to permit discrimination among behaviors of ecosystems.
If the capacity for this sort of perception and discrimination
among ecosystem behaviors is to be developed, it would appear
that models of about the complexity of that described here would
be valuable in the endeavor.
42
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Energy Processing Cycle
Photo-
Reduced
Forms
A Chemolitho- w
Oxychemo—
\ 9
Oxidized
Forms
urgano—
Oxic
electron
Transport
Transport
flow
Anoxic
Reduced
Forms
^ Anoxychemo— k
Organo-
Oxidized
Forms
Figure 1. Schematic for redox processes that yield energy useful
for biotic processes. Elements cycle between reduced
and oxidized forms.
-------
Biosynthesis
Saprophagy
1
? f
Reduced Chem.
Forms in Biomass
Predation
Production of
Meath.moltine.ee
O.M. fc
estion.
r
Reduced Chem.
Forms in O.M.
t
excretion, etc.)
Assimilatory
reduction
Oxidized
Inorganic Forms
OXIC
ANOXIC
Reduced Chem.
Forms in Biomass
Production of O.M.
decomposition
p
Reduced
Inorganic Forms
o
a.
n
a
a
Reduced
Inorganic Forms
Reduced Chem.
Forms in O.M.
Figure 2. Relationships among chemical and biotic forms of
elements in biosynthesis.
-------
A
-4->
a,
o
light
aerobic, C02 + H20 > Org
Higher Organisms, Food Web, Microorganisms
Org + 02 > C02 + H20, AG° = -25.5
Org
Org
anaerobic, N03 present,
- > N02 + C02 + H20, AG°
N02 - > N2 + C02 + H20, AG°
-16.3
-29.1
Org + S0|
2-
anaerobic, no N03 present,
S0|~ present
H2S + C02 + H20,
= -1.7
Org
anaerobic, no N03 present,
A
no SOf" present, C02 present
(C02) + H20 - > C02 + H20, AG°
= -1.1
Figure 3. Variation in terminal electron acceptor as function
of depth.
45
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\ C (in bulk fluid)
7* Cb (at cell surface)
Figure 4. Diagram of Cell in aquatic medium indicating the concentration
gradient surrounding the cell.
46
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Autotroph Biosynthesis
Maintenance
Expenditure
ADP + P > ATP
NADP > NADPH
(CHgO),
CHONPS
N.P.S
Biomass
Figure 5. Major components and relationship of autotroph biosynthesis.
47
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Indigestible
Components
(macroconsumers)
Heterotrophy
Food
Power Output
o AGd(loss)
Monomers
(AGp - AGd)
glycolysis
Biomass
ATP
AGD (cost)
Monomers
(AGC - AGd)
•C02 + H20
TCA cycle
Pyruvate
etc.
N & S input, function
of pool Z synthesis
Figure 6. Major components and pathways (.energy and mass) of heterotrophy.
-------
Organic Matter
Dead organisms,
molts, egesta
uptake
excretion
monomerization
BOM
NOM
Figure 7. Categories of organic chemicals (P=particulate,
R=refractory, D=digestible, S=soluble, B=biomass-
like, N=non-biomass-like)
49
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Filter Feeding Schematic
disturbance
front
predator
prey
Figure 8. Relationships characteristics of a filter feeding
predator and its potential prey that determine
probability of capture.
50
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Pursuit Feeding Schematic
'cj
vc] s predator search velocity
s
-------
Table 1
Some reactions used by chemoautotrophs for energy
Reaction Free Energy
kcal/M( substrate) kcal/eq.wt. (substrate)
-.*•
N02~
HS~ +
S° +
S2°3
so32~
HS~ +
S° +
•2 +
H2 +
H2 +
CH4 +
CHA +
+ 1 .5 O, = NO.," + 2 H+ + H-,0
^ A &
+ .5 O2 = NO3~
2 02 = S042~ + H+
5/2 O2 + H2O = S042~ + H+
+ 2 02 + H20 = 2 S042~ + 2 H+
+ 1/2 02 = S042-
8/5 N03~ + 3/5 H+ = S042~ 4- 4/5 N2 + 4/5 H2O
6/5 NO3~ + 2/5 H2O = S042" + 3/5 N2 + 4/5 H+
2/5 N03 + 2/5 H+ = 1/5 N2 + 6/5 H2O
1/4 SO42~ + 1/4 H+ = HS~ + H2O
1/2 CO2 = CH3COOH + 1/2 H2O
2 O2 = CO2 + 2 H2O
S0.2~ + H+ = CO, + HS~ + H-.O
-64.92
-18.50
-190.30
-139.98
-190.16
-29.54
-177.92
-130.74
-53.60
-9.10
-4.30
-195.50
-5.20
-10.82
-9.25
-23.79
-23.33
-23.77
-29.27
-22.24
-21 .79
-26.80
-4.55
-2.15
-24.44
-0.65
52
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REFERENCES
1. Ehhalt, P. H. The Atmospheric Cycle of Methane. Tellus
26:58 - 70 (1974).
2. Skucnick, J. Risk/Concentration Estimates for Aquatic Life
by Species Within Pollutant. Appendix: Acute Criteria
Documents Data Base. SRI International, Menlo Park
California, 307 p (1980).
3. JRB Associates, Inc. User Documentation for Criteria
Documents Data Base. JRB Associates, Inc., McLean, Virginia
(1980) .
4. McCarty, P. L. Energetics and Bacterial Growth. J.n: Organic
Compounds in Aquatic Environments, S. J. Faust and ]. W.
Hunter, Eds., Marcel Dekker, Inc., New York, p 495 - 529
(1971) .
5. Docile, H. W. Bacterial Metabolism, 2nd Ed. Academic Press,
New York, 738 p (1975).
6. Fenchel, T. and T. H. Blackburn. Bacteria and Mineral
Cycling. Academic Press, London, 225 p (1979).
7. Morowitz, H. J. Energy Flow in Biology, Biological
Organization as a Problem in Thermal Physics. Academic
Press, New York, 179 p (1968).
8. Nicolis, G. and I. Prigogine. Se 1 f-Organization in
Nonequi1ibrium Systems. From Dissipative Structure to Order
through Fluctuations. John Wiley and Sons, New York, 491 p
(1977).
9. Monod, Jacques. Recherches sur la Croissance des Cultures
Bacteriennes. Hermann et Cie, Paris (1942).
10. Rashevsky, NF. Some Remarks on the Mathematical Theory of
Nutrition of Fishes. Bull. Math. Biophys. 21:161 - 183
(1959) .
11. Holling, C. S. The Functional Response of Predators to Prey
Density and Its Role in Mimicry and Population Regulation.
Mem. Entomol. Soc. Can. 45:1 - 60 (1965).
12. Purcell, B. M. Life at Low Reynolds Numbers. Am. J. Phys.
45:3 - 11 (1977).
13. Vogel, S. Life in Moving Fluids. The Physical Biology of
Flow. Willard Grant Press, Boston, 352 p (1981).
14. Pasciak, W. J. and J. Gavis. Transport Limitation of
Nutrient Uptake in Phytoplankton. Limnol. Oceanogr. 19:881
- 888 (1974).
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IS. Pasciak, W. J. and J. Gavis. Transport Limited Nutrient
Uptake Rates in Di.t_y_lum br_i£ht_we.ll.jLi_. Limnol. Oceanogr.
20:604 - 617 (1975).
16. Gavis, J. and J. T. Ferguson. Kinetics of Carbon Dioxide
Uptake by Phytop 1ankton at High pH. Limnol. Oceanogr.
20:211 - 221 (1975).
17. Schlegel, H. G. Mechanisms of Chemo-autotrophy. in: Marine
Ecology. A Comprehensive, Integrated Treatise on Life in
Oceans and Coastal Waters. O. Kinne, Ed., John Wiley and
Sons, New York, p 9 - 60 (1975).
18. Lehninger, A. L. Biochemistry. The Molecular Basis of Cell
Structure and Function, 2nd. Ed. Worth Publishers, Inc. New
York, 1104 p (1975).
19. Burton, K. Energy of Adenosine Triphosphate. Nature
181:1594 - 1595 (1958) .
20. Steelc, J. H. Environmental Control of Photosynthesis in the
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21. Bannister, T. T. Production Equations in Terms of
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Production. Limnol. Oceanogr. 19:1 - 12 (1974).
22. Dubinsky, Z. and T. Herman. Light Utilization Efficiencies
of Phytopiankton in Lake Kinneret (Sea of Galilee). Limnol.
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23. Clayton, R. K. Photosynthesis: Physical Mechanisms and
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(1980) .
24. Gunderson, K. and C. W. Mountain. Oxygen Utilization and pH
change in the Ocean Resulting from Biological Nitrate
Formation. Deep Sea Res. 20:1083 - 1091 (1976).
25. Ivlev, V. S. Experimental Ecology of the Feeding of Fishes.
English Trans, by D. Scott. Yale Univ. Press, New Haven,
302 p (1961).
26. Gerritsen, J. and J. R. Strickler. Encounter Probabilities
and Community Structure in Zooplankton: a Mathematical Model.
J. Fish. Res. Board Can. 34:73 - 82 (1977).
27. Stumm, W. and J. J. Morgan. Aquatic Chemistry. An
Introduction Emphasizing Chemical Equilibria in Natural
Waters. John Wiley and Sons, New York, 780 p (1981).
28. Lehninger, A. L. Principles of Biochemistry. Worth
Publishers, Inc., New York, 1011 p (1982).
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TECHNICAL REPORT DATA
(Please read laarucnons on the reverse before completing)
1 REPORT NO
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3 RECIPIENT'S ACCESSION NO.
4 TITLE ANOSUBTITLE
S REPORT DATE
Prediction of Ecological Effects of Toxic Chemicals:
Overall Strategy and Theoretical Basis for the
6 PERFORMING ORGANIZATION CODE
lS)
8 PERFORMING ORGANIZATION REPORT NO
Ray R. Lassiter
9 PERFORMING ORGANIZATION NAME AND ADDRESS
Environmental Research Laboratory
U.S. Environmental Protection Agency
College Station Road
Athens GA 30613
10. PROGRAM ELEMENT NO.
ACBE1A
11 CONTRACT/GRANT NO.
CR808629
12 SPONSORING AGENCY NAME AND ADDRESS
Environmental Research Laboratory—Athens GA
Office of Research and Development
U.S. Environmental Protection Agency
Athens GA 30613
13
•RIOO COVERED
14. SPONSORING AGENCY CODE
EPA/600/01
IS. SUPPLEMENTARY NOTES
6. ABSTRACT
A strategy is developed for modeling ecosystems to permit assessment of effects
of toxic chemicals on element cycling and other ecosystem processes. The strategy
includes use of multi-species representations of biotic communities and mathematical
descriptions of the processes that are important in aquatic ecosystems. Direct
effects of toxicants are assigned to the species comprising the biotic community
in a manner suggested by available toxicological information. Effects are calculated
as the difference between selected measures of processes from unaffected systems and
systems affected by the presence of a toxic chemical. Ecological effects calculated
in this manner are considered to be heuristically useful.
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RELEASE TO PUBLIC
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UNCLASSIFIED
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63
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UNCLASSIFIED
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EPA Form 2220-1 (9-73)
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