EPA/600/P-04/116F
March 2006
Estimation and Application of
Macroinvertebrate Tolerance Values
National Center for Environmental Assessment
Office of Research and Development
U.S. Environmental Protection Agency
Washington, DC 20460
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DISCLAIMER
This report has been reviewed in accordance with U.S. Environmental Protection Agency
policy and approved for publication. Mention of trade names or commercial products does not
constitute endorsement or recommendation for use.
ABSTRACT
Tolerance values provide a measure of the sensitivity of aquatic organisms to
anthropogenic disturbance and have historically provided a useful tool for assessing the
biological condition of streams and rivers. However, the tolerance values that are currently
available are limited by the geographical areas in which they can be applied, and do not provide
diagnostic information as to the causes of the impairment in streams. This report reviews and
compares methods for estimating tolerance values from field data and for applying them to assess
the biological condition of streams and to diagnose the causes of impairment. The intent of this
report is to provide a resource of state, tribal, and regional biologists who wish to use tolerance
values to help interpret biological data.
Methods for estimating tolerance values first model (either explicitly or implicitly) the
relationship between a given taxon and an anthropogenic stressor gradient (the taxon-
environment relationship). Then, a single representative value is extracted from this relationship,
which is designated as the tolerance value. Three types of tolerance values are expressed on a
continuous scale: (1) the weighted average, (2) cumulative percentiles, and (3) the maximum
point of the taxon-environment relationship. A fourth type is categorical and classifies the shape
of the taxon-environment relationship. All types of tolerance values provide fairly comparable
rankings of tolerance among different taxa.
After tolerance values are estimated, metrics can be computed that summarize the
tolerance information of all the taxa observed at a test site. Two types of metrics can be
computed: compositional metrics and the mean of observed tolerance values. Compositional
metrics apply categorical tolerance values and summarize characteristics of different groups of
taxa (e.g., the relative abundance of tolerant taxa). The mean of observed tolerance values can be
computed for any continuously valued tolerance value. Virtually all metrics are found to be
strongly associated with observed stressor levels. The means of weighted average tolerance
values are consistently and strongly associated with observed stressor levels in the data analyzed
for this report. Ultimately, metrics values at test sites must be compared with reference
distributions to determine whether conditions at test sites differ significantly from expectations.
The main areas of uncertainty with the tolerance value methodology are discussed. Some
of these uncertainties and additional implementation issues must be addressed to more fully
facilitate the use of tolerance values for the management of the nation's waters.
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CONTENTS
LIST OF TABLES v
LIST OF FIGURES vi
PREFACE viii
AUTHOR AND REVIEWERS ix
1. INTRODUCTION 1
2. THEORETICAL UNDERPINNINGS 2
2.1. UNIMODAL NICHE MODELS 2
2.2. NON-UNIMODAL MODELS 5
2.3. DEFINITIONS 6
2.4. TYPES OF TOLERANCE VALUES 7
3. ESTIMATING TOLERANCE VALUES FROM FIELD DATA 8
3.1. DIRECT METHODS 8
3.1.1. Central Tendencies (Weighted Averages) 8
3.1.2. Environmental Limits (Cumulative Percentiles) 9
3.2. INDIRECT METHODS 11
3.2.1. Regression Estimates of Taxon-Environment Relationships 11
3.2.1.1. Parametric Regressions 11
3.2.1.2. Nonparametric Regressions 14
3.2.1.3. Model Performance and Overfitting 16
3.2.2. Optima 18
3.2.3. Curve Classification 19
3.3. COMPARING DIFFERENT TOLERANCE VALUES 19
3.3.1. Continuous Tolerance Values 19
3.3.2. Tolerance Classifications 22
3.3.3. Comparisons Between Continuous and Categorical Tolerance Values 23
3.3.4. Effects of Regional Characteristics 25
4. APPLYING TOLERANCE VALUES IN ASSESSMENT 27
4.1. BIOLOGICAL METRICS 27
4.1.1. Metrics Based on Categorical Tolerance Values 27
4.1.2. Metrics Based on Continuous Tolerance Values 31
4.1.3. Performance of Tolerance Value Metrics 32
4.1.3.1. Characteristics of the Stressor Gradient 32
4.1.3.2. Acceptance Criteria for Tolerance Values 33
4.1.3.3. Specificity of Response 34
4.1.3.4. Effects of Taxonomic Resolution of Tolerance Values 37
4.2. REFERENCE CONDITIONS 38
in
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CONTENTS (continued)
5. AREAS OF UNCERTAINTY AND RESEARCH PRIORITIES 39
5.1. CAUSAL RELATIONSHIPS 41
5.2. DEFINING STRESSOR GRADIENTS 44
5.2.1. General-disturbance Gradients 44
5.2.2. Indirect Stressor Gradients 45
5.2.3. Sampling Issues 46
5.3. FUNDAMENTAL ECOLOGY 47
5.3.1. Biological Interactions 47
5.3.2. Temporal Characteristics of Stream Communities 48
6. IMPLEMENTATION 48
6.1. INFORMATION MANAGEMENT 48
6.2. TAXONOMIC QUALITY ASSURANCE 49
7. CONCLUSIONS AND RECOMMENDATIONS 49
REFERENCES 51
APPENDIX A: ATTENDEES AT THE WESTERN TOLERANCE VALUES WORKSHOP,
CORVALLIS, OREGON 54
APPENDIX B: DATA DESCRIPTION 56
APPENDIX C: TOLERANCE VALUES 58
APPENDIX D: EXAMPLE STATISTICAL SCRIPTS 68
D.I. R: BASIC SYNTAX 68
D.2. LOADING DATA 69
D.3. ESTIMATING TOLERANCE VALUES FROM FIELD DATA 70
D.3.1. Weighted Averages 70
D.3.2. Cumulative Percentiles 71
D.3.3. Parametric Regressions 72
D.3.4. Nonparametric Regressions 73
D.3.5. Assessing Model Fit 74
D.3.6. Optima 75
D.3.7. Curve Shape 76
D.4. APPLYING TOLERANCE VALUES IN ASSESSMENT 77
D.4.1. Richness 78
D.4.2. Proportion Total Taxa 78
D.4.3. Relative Abundance 79
D.4.4. Mean Tolerance Value 79
IV
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LIST OF TABLES
Table 1. Observed versus predicted occurrences for Heterlimnius 17
Table 2. Correlation coefficients for temperature tolerance values 20
Table 3. Correlation coefficients for sediment tolerance values 21
Table 4. Confusion matrix for temperature tolerance classifications 22
Table 5. Confusion matrix for sediment tolerance classifications 22
Table 6. R2 values for spline fits between metric and stressor level 30
Table 7. R2 values for spline fits between mean tolerance values and observed temperature
and sediment in Oregon 32
Table 8. R2 values for models with ROC > 0.65 criteria imposed 34
Table 9. R2 values for family-level tolerance values 38
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LIST OF FIGURES
Figure 1. Theoretical unimodal distribution of species occurrence 3
Figure 2. Different unimodal relationships within a species pool 4
Figure 3. Monotonic responses to an environmental gradient 5
Figure 4. Examples of ecological tolerance and biological assessment tolerance 6
Figure 5. Empirical cumulative distribution method for defining tolerance values 10
Figure 6. Relationships between probability of occurrence and temperature for Heterlimnius
and Malenka 13
Figure 7. Relationship between relative abundance and temperature for Heterlimnius and
Malenka 14
Figure 8. Relationship between probability of occurrence and temperature for Heterlimnius
and Malenka 16
Figure 9. Receiver operator characteristic (ROC) curve for Heterlimnius 18
Figure 10. Graphical approach for classifying curve shapes for Heterlimnius, Malenka, and
Hydropsyche 20
Figure 11. Comparison of optima tolerance values determined by parametric logistic
regression model (GLMMAX) and weighted average tolerance values (WA) for
temperature 21
Figure 12. Histogram of weighted average tolerance values for temperature and fine
sediment 24
Figure 13. Histogram of weighted average tolerance values for temperature and fine
sediment classified by curve shape 25
Figure 14. Illustrations of effect of gradient length 26
Figure 15. Relationship between temperature tolerance metrics and observed temperature
in Oregon 29
Figure 16. Relationship between sediment tolerance metric and observed sediment
in Oregon 30
VI
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LIST OF FIGURES (continued)
Figure 17. Temperature tolerance metrics plotted versus percent sands and fines 35
Figure 18. Sediment tolerance metrics plotted versus temperature 36
Figure 19. Mean weighted average (WA) tolerance values for sediment plotted against
observed temperature, and mean WA tolerance value for temperature plotted
against observed sediment 37
Figure 20. Comparison of temperature and sediment tolerance metrics at a single test site
with reference distributions 40
Figure 21. Comparison of taxon-environment relationships for Glossosoma andMalenka ... 42
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PREFACE
This document, Estimation and Application of Macroinvertebrate Tolerance Values, was
prepared by the National Center for Environmental Assessment. The document is a technical
review of statistical methods for estimating macroinvertebrate tolerance values from field data. It
also reviews different methods for applying tolerance values for assessing biological conditions
of streams and rivers and for diagnosing the causes of impairment. The purpose of this document
is to provide a technical resource for states, tribes, and regions that wish to use tolerance values
to interpret stream biological data.
This final document reflects a consideration of all comments received on an External
Review Draft dated September 2004 (EPA/600/P-04/116A).
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AUTHOR AND REVIEWERS
This document was prepared by the National Center for Environmental Assessment.
AUTHOR
Lester L. Yuan
National Center for Environmental Assessment
U.S. Environmental Protection Agency
Washington, DC 20460
REVIEWERS
Susan B. Norton
National Center for Environmental
Assessment
U.S. Environmental Protection Agency
Washington, DC 20460
Amina I. Pollard
National Center for Environmental
Assessment
U.S. Environmental Protection Agency
Washington, DC 20460
John Van Sickle
Western Ecology Division
National Health and Environmental Effects
Research Laboratory
U.S. Environmental Protection Agency
200 S.W. 35th Street
Corvallis, OR 97333-4902
Charles A. Menzie
Menzie-Cura & Associates Inc.
2 West Lane
Severna Park, MD 21146
Mark T. Southerland
Versar ESM Operations
9200 Rumsey Road
Columbia, MD 21045-1934
Jon H. Volstad
Versar ESM Operations
9200 Rumsey Road
Columbia, MD 21045-1934
N. Scott Urquhart
Department of Statistics
Colorado State University
Fort Collins, CO 80523-1877
IX
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1. INTRODUCTION
Benthic macroinvertebrates are widely collected and used to assess the condition of
streams and rivers. One approach for interpreting biological assessment data is to group taxa
according to their perceived tolerance or sensitivity to anthropogenic disturbances. After these
groups, or tolerance values, are established, the condition of new sites can be assessed on the
basis of whether taxa from tolerant or sensitive groups are predominantly collected. Tolerance
values have historically played an integral role in biological assessment. One set of tolerance
values (the saprobrien system) was derived in the early 1900s in central Europe by documenting
differences in microorganism assemblages collected at progressively larger distances downstream
from sewage outfalls. Other early examples of assigning tolerance values to macroinvertebrates
include those of Chutter (1972), who assigned tolerance values to South African
macroinvertebrates using best professional judgement, and the Biological Monitoring Working
Party (BMWP) (Armitage et al., 1983), which assigned tolerance values to macroinvertebrate
families observed in Great Britain. In North America, Hilsenhoff (1987) developed tolerance
values with respect to a gradient of organic pollution, and these values are still widely used
today. Lenat (1993) refined Hilsenhoff s approach, defining tolerance values with respect to a
more comprehensive list of anthropogenic disturbances.
Tolerance values have been used successfully to assess the condition of running waters,
but in recent years two issues have arisen regarding the widespread application of these values.
First, the application of tolerance values in regions that differ from where they were originally
derived has been questioned. For example, most tolerance values (e.g., Hilsenhoff, 1987; Lenat,
1993) have been estimated using data collected in the midwestern and eastern United States, and
these tolerance values have then been modified for use elsewhere in the country. However,
regional species pools differ substantially in different areas of the United States, and as a result,
many of the taxa collected outside of the midwestern and eastern U.S. have not been assigned
tolerance values. Furthermore, the stressor gradients commonly observed in other regions can
differ from the organic pollution gradients for which the Hilsenhoff tolerance values were
originally designed. A more comprehensive examination of the estimation of tolerance values
and their general applicability to other regions is required.
The second issue is a growing interest in extending the use of tolerance values from
simple assessments of stream condition to diagnoses of the causes of impairment. Over a
thousand streams are currently listed on the U.S. Environmental Protection Agency's (EPA's)
303(d) list as being biologically impaired, but the causes of the impairment are unknown, which
severely hinders effective management actions. If organisms that are sensitive or tolerant to
particular anthropogenic stressors can be identified, the presence or absence of different
1
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organisms in impaired streams can potentially help identify possible sources of impairment.
Although most current organism tolerance values have been defined with respect to a single
gradient of anthropogenic disturbance (e.g., Hilsenhoff, 1987), the potential for estimating
tolerance values with respect to particular stressors has been described in a few studies: Slooff
(1983) showed that aquatic macroinvertebrates differ in their sensitivity to different stressors, and
in more recent work, Chessman and McEvoy (1998) attempted to estimate tolerance values that
discriminated between different types of anthropogenic disturbance. The tolerance values
developed by Chessman and McEvoy had limited discriminatory powers, but they did illustrate
the potential power of the method.
To address these issues, EPA and the Council of State Governments convened a
workshop in February 2004 in Corvallis, OR. Workshop attendees were selected for their
experience in deriving and applying tolerance values and included biologists from environmental
protection agencies in western states, EPA staff, academics, and industry representatives
(Appendix A). The program consisted of a day of presentations of current methods for deriving
tolerance values, followed by a day of discussion within smaller breakout groups and half a day
of discussion that included the full group.
This report continues the effort initiated by the workshop by synthesizing and expanding
on the deliberations of the attendees. In particular, this report (1) reviews the ecological theory
that underlies the concept of tolerance values, (2) reviews methods for computing tolerance
values from field data, (3) reviews methods for applying tolerance values in stream assessments,
(4) identifies uncertainties and research priorities in the derivation and application of tolerance
values, and (5) identifies practical issues hindering the broader use of tolerance values in
monitoring and assessment programs. The methods discussed in this report can be used to
estimate both general disturbance tolerance values (for assessing biological condition) and
stressor-specific tolerance values (for diagnosing the causes of impairment). However, the
examples provided in the report focus more specifically on the issues pertaining to diagnosis of
cause. The intent of this report is to provide a resource for state, tribal, and regional biologists
who wish to use tolerance values to help interpret biological data for evaluating biological
condition and for diagnosing the causes of stream impairment.
2. THEORETICAL UNDERPINNINGS
2.1. UNIMODAL NICHE MODELS
Ecological niche theory suggests that individual species are often unimodally distributed
along environmental gradients. This distribution dictates that the probability of a species'
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occurrence or abundance has a maximum value at some point along an environmental gradient
(e.g., with regard to temperature, Figure 1). This point is known as the species optimum.
Probabilities of finding a species and the expected abundance of a species decrease as conditions
depart from the species optimum. Unimodal distributions are thought to arise over evolutionary
time scales as species specialize to optimally exploit certain habitat conditions or resources
through the process of adaptive radiation (niche diversification) (Odum, 1971). Each species is
simultaneously affected by a variety of factors, but for simplicity, discussion is restricted here to
a single environmental gradient.
Species differ in their optima and in the range of conditions about their optima in which
they can persist, so unimodal response functions vary in their location along a particular gradient
and in the width of the curves. Furthermore, the frequency of occurrence and abundance of
different species can vary greatly, so the maximum values of the response functions will differ
among species (Figure 2). Thus, for a given species pool, a diverse set of species-environment
relationships are expected along a particular gradient, and if we sample streams at different
points along that gradient, we would expect to find a different assemblage of species. Based on
the responses shown in Figure 2, we would expect to find species B, C, and D in a 7°C stream,
whereas we would expect to find species C and E in a 25°C stream. This shift in
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Figure 1. Theoretical unimodal distribution of species
occurrence.
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Figure 2. Different unimodal relationships within a
species pool. Letters indicated different species.
assemblage composition across environmental gradients is the basic theory that underlies the
notion of tolerance values. That is, if we can construct species-environment relationships for
environmental gradients that are influenced by human activities, we can potentially predict
assemblage changes that are likely to occur as human activity alters conditions at a site. We can
also identify those species that are likely to disappear with increased human stress (i.e., sensitive
species) and those species that should thrive in anthropogenically stressed sites (i.e., tolerant
species).
Many environmental factors vary not only in response to human activities, but also
exhibit considerable variability due to natural factors. For example, stream temperature changes
naturally with the elevation of the stream, but it also can be changed by the removal of riparian
vegetation that shades the stream. Species-environment relationships can be estimated
regardless of whether the changes in the environment are due to natural or anthropogenic causes.
However, when strong natural and anthropogenic factors influence a particular environmental
variable, additional care must be exercised when interpreting the observed changes in species
assemblage (see Section 4.2).
The range of conditions in which a species is observed in the field is an estimate of its
realized niche. The realized niche is a function of the effects of both environmental gradients
and biological interactions. In contrast, the fundamental niche defines the range of conditions in
which an organism could persist, excluding the effects of any biological interactions. In theory,
the fundamental niche is an inherent characteristic of a species and is therefore invariant across
all geographical regions. However, species pools change across different regions, so the realized
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niche of a particular species may shift as different biological interactions affect its ability to
persist. Because many stream ecosystems are structured by disturbance rather than by biological
interactions, the realized niches for many species may provide reasonable approximations to the
fundamental niches (Allan, 1995). Differences between fundamental and realized niches are
discussed further in Section 5.3.1.
2.2. NON-UNIMODAL MODELS
The unimodal model may not be applicable to all types of environmental gradients. For
certain anthropogenic stressors (e.g., pesticides), a more appropriate model may be one in which
the abundance or the probability of observing a particular species decreases monotonically with
increasing levels of the stressor. As levels of such stressors increase, the rate at which expected
abundances or capture probabilities change may differ among species, but the optimum for all
species would be identical, where the stressor level is zero (Figure 3). Therefore, these
differences are more subtle than those that would be observed between unimodally distributed
species at opposite ends of a gradient (e.g., species B and E in Figure 2).
Non-unimodal relationships also appear when environmental gradients are incompletely
sampled. For example, if observations were collected only up to 16°C, then the probability of
occurrence for species A in Figure 1 would be observed to be monotonically increasing with
respect to temperature.
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Figure 3. Monotonic responses to an environmental
gradient. Letters indicate different species.
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2.3. DEFINITIONS
The use of the term "tolerance" in biological assessments differs from the ecological use
of the word. The ecological definition of tolerance refers to the niche breadth, or the range of
conditions that an organism can withstand (Odum, 1971). Based on this definition, more tolerant
organisms can withstand a broader range of conditions, regardless of the location of their species
optimum. To quantify niche breadth, we would measure the range of conditions over which a
particular taxon can persist.
In biological assessment, the term tolerance is generally used with respect to a gradient of
anthropogenic stress. That is, a tolerant organism is one that is likely to be found in a site that
has been highly altered or degraded by human activities. Many species would be considered
tolerant by both ecological and biological assessment definitions. For example, species A in
Figure 4 would likely be observed in a degraded site, and is therefore tolerant in terms of
biological assessment. It is also found in conditions that span the entire observed gradient, and is
therefore ecologically tolerant. However, some species thrive in degraded sites but have a
narrow niche breadth. These species are tolerant in the context of biological assessment even
though they are not tolerant in the ecological sense (species B in Figure 4). For this report we
use tolerance strictly in the sense of biological assessment and use niche breadth when referring
to the range of conditions within which an organism can persist. Similarly, we define a sensitive
taxon as one that tends to decline in abundance or occurrence probability as anthropogenic stress
increases. We further define a tolerance value as a single value that represents the tolerance of a
taxon to a particular stressor gradient. This value can have the units and range of the sampled
gradient, or it can be rescaled to an arbitrary range (e.g., 1-10).
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Figure 4. Examples of ecological tolerance (A) and
biological assessment tolerance (B). Magnitude of human
disturbance increases from left to right.
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Both single and composite stressor gradients are applicable when considering tolerance
values. A single-stressor gradient is defined by a single environmental attribute (e.g.,
temperature) that changes with the intensity of human activity. Composite-stressor gradients
represent simultaneous changes in many different environmental attributes (e.g., temperature,
toxicant concentrations, physical habitat quality) that occur with increased human activity. For
example, an aggregate gradient of human disturbance would be considered a composite-stressor
gradient. In general, the methods for estimating tolerance values described in this report can be
applied to both composite-stressor and single-stressor gradients, although defining an appropriate
gradient becomes more difficult with multiple stressors. These issues are explored in greater
detail in Section 5.2.1.
2.4. TYPES OF TOLERANCE VALUES
A tolerance value can be thought of as any single number that represents the
characteristics of a species' relationship with an environmental gradient. Ideally, tolerance
values should capture the critical aspects of the entire species-environment relationship, provide
a consistent ranking of different species in terms of their tolerance for a particular stressor, and
provide the means for analyzing data on species occurrences to derive inferences regarding the
environmental conditions at a site. Because species-environment relationships vary greatly in
their functional forms, it is difficult to completely characterize the relationship with one value.
However, single tolerance values have proven to be a useful tool for biological assessment,
where more complete representations of the species-environment relationship are usually too
cumbersome to use regularly.
In general, given species-environment relationships for different species, four approaches
can be used to derive tolerance values: (1) central tendencies, (2) environmental limits, (3)
optima, and (4) curve shapes. Tolerance values expressed in terms of central tendencies attempt
to describe the average environmental conditions under which a species is likely to occur;
tolerance values expressed in terms of environmental limits attempt to capture the maximum or
the minimum level of an environmental variable under which a species can persist; and tolerance
values expressed in terms of optima define the environmental conditions that are most preferred
by a given species. These three types of tolerance values are expressed in terms of locations on a
continuous numerical scale that represents the environmental gradient of interest.
The fourth type of tolerance value relies on a classification of curve shape to group
species. Species are first classified by the shape of their species-environment relationship into
three groups: (1) monotonically increasing, (2) monotonically decreasing, and (3) unimodal
(Yuan, 2004). Then, when an increasing value of the environmental variable can be attributed to
human activities, those species with monotonically increasing species-environment relationships
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are designated as tolerant and those with monotonically decreasing relationships are designated
as sensitive. Species with unimodal species-environment relationships are designated as
intermediately tolerant. These classifications differ from previously discussed tolerance values
because they yield categorical rather than continuous values.
3. ESTIMATING TOLERANCE VALUES FROM FIELD DATA
Given the different types of tolerance values defined in the previous section, how does
one estimate these values from field data? Analytical approaches for estimating tolerance values
can be divided into two main groups: (1) methods that directly estimate tolerance values from
field data (direct methods) and (2) methods that first require estimations of species-environment
relationships using regression techniques, and then estimate tolerance values from the regression
relationship (indirect methods). Central tendencies and environmental limits can be estimated
using methods from the first group, whereas optima and curve shape require methods from the
second group. In the following section we describe in more detail the methods for estimating
each type of tolerance value.
Until now, discussion has focused on distinct species and their relationship with
environmental gradients, because ecological theory hypothesizes that the fundamental niche of a
given species is invariant. However, species level identifications are not always available, so as
we turn to field data, the focus of the discussion is broadened to consider any level of taxonomic
resolution (i.e., taxon-environment relationships). The ramifications of defining tolerance values
for higher levels of taxonomy are discussed in Section 4.1.3.4.
Throughout this section methods are illustrated using macroinvertebrate data collected by
the EPA's Environmental Monitoring and Assessment Program-Western Pilot Project (EMAP-
West) (see Appendix B). Two representative environmental gradients are considered in
particular: stream temperature and the amount of bedded fine sediment. Both stream temperature
and the amount of bedded fine sediment vary naturally (e.g., with changes in elevation) and can
vary due to human activities (e.g., from logging). These two stressors have been identified as
particularly relevant to western streams.
3.1. DIRECT METHODS
3.1.1. Central Tendencies (Weighted Averages)
Weighted averaging (WA) has long been used in ecology as a simple, robust approach for
estimating the central tendencies of different taxa, or in our case, tolerance values (ter Braak and
Looman, 1986). WA and all its variants (e.g., partial least-square WA, ter Braak and Juggins,
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1993) operate on the same basic principle. The tolerance value, uwa, for speciesy is estimated by
computing the mean of the environmental variable of interest at the sites in which the species is
observed:
If !N
where TV is the total number of sites and xt is the value of the environmental variable of interest at
site /. For presence/absence data, Ytj is equal to 1 when speciesy is present and 0 when speciesy
is absent, and for abundance data, Ytj is the abundance of speciesy at site /.
When using weighted averages, a uniform distribution of samples across the
environmental gradient is preferred because each location on the gradient will then receive an
equal weight. Because environmental gradients are rarely uniformly sampled, weighted average
tolerance values are often biased away from the "true" central tendency of the taxon-environment
relationship. One solution to this problem is to average samples along the gradient that fall
within equal width bins and then to use these binned data to compute the weighted average.
However, this procedure is not generally recommended because the true central tendency is
rarely of interest. Instead, we are usually interested in the tolerance values of different taxa
relative to one another. Within a given data set, all weighted average tolerance values are
computed using the same set of environmental data, and therefore, any bias arising from a
nonuniform distribution of data will be the same for all taxa and their relative placement along
the axis will generally be preserved. Comparisons of weighted average tolerance values across
different data sets are more problematic and are discussed in much greater detail in Section 3.3.4.
Weighted average tolerance values can be further refined if information regarding the
strength of the association between taxon occurrence or abundance and the environmental
gradient of interest is available. Then, tolerance values for taxa that are not strongly associated
with the gradient can be omitted from future inferences. We return to this topic in Section
4.1.3.2.
3.1.2. Environmental Limits (Cumulative Percentiles)
Environmental limits can be estimated by computing cumulative percentiles (CPs) from
field data. An empirical CP is estimated for a given value of the environmental variable (jc0) as
follows:
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2-1
(2)
where 7=1 if xt < x0 and 7=0 if xt > x0 and other variables are as defined in eq 1. For presence/
absence data, the numerator is the number of occurrences of taxony at sites in which the value of
the environmental variable is less than the cutoff value, and the denominator is the total number
of occurrences of taxony. Plots of CP as a function of x0 are shown in Figure 5 for three genera.
A CP tolerance value would be estimated by fixing CP at a prescribed value and computing the
x0 that corresponds to that value of CP for all taxa. Then, x0 is an estimate of the tolerance value.
To estimate the maximum level of a stress under which a taxon could persist, CP would be fixed
at a relatively high value (e.g., 0.75).
HETERLIMNIUS
HYDROPSYCHE
J5
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) 15 20
Temperaflie
Figure 5. Empirical cumulative distribution method for defining
tolerance values. Cumulative percentile value shown is 0.75. The point
at which the dashed line intersects the horizontal axis is the tolerance
value for that taxon.
Different practitioners have used different CP values to define tolerance values. Lenat
(1993) tried different threshold probabilities and found that a value of 0.75 was most effective.
Relyea et al. (2000) used a value that ranged from 0.97 to 0.99, depending on the taxon. The
uncertainty in defining x0 for a given cumulative percentile increases as the percentile value
increases, so the selection of the CP value requires that one balance competing factors: higher
percentiles may more accurately express the environmental limit of an organism, but the error in
empirically defining tolerance values using higher percentiles also increases. In Figure 5, a CP
value of 0.75 is shown, which yields a temperature tolerance value of approximately 13°C, 16°C,
10
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and 19°C, respectively, for the three taxa. This same CP value is used in all example
computations.
3.2. INDIRECT METHODS
3.2.1. Regression Estimates of Taxon-Environment Relationships
To estimate tolerance values on the basis of taxon optima or curve shape, one first must
estimate a taxon-environment relationship for each combination of taxon and environmental
variable. In addition to providing a means of computing these additional tolerance values,
regression estimates of the taxon-environment relationship provide the additional benefit of
allowing one to quantify the strength of the association between a given environmental gradient
and changes in the occurrence probability or abundance of a taxon. Combinations of taxon and
environmental gradients that are not strongly associated can then be excluded from future
inference.
To estimate taxon-environment relationships one usually must apply constraints on the
form of the relationship. Two main types of constraints are possible. First, one can assume that
the taxon-environment relationship follows a pre-specified functional form. After the functional
form is specified, differences in taxon-environment relationships can be summarized by
comparing the parameters of the regression relationships. We refer to these methods as
parametric regressions. Second, one can require only that the taxon-environment relationship
vary slowly and smoothly over the range of observations. In this case, the relationship cannot be
described using a few simple parameters. We refer to these methods as nonparametric
regressions.
Ordinary linear regression methods cannot be applied in either of these cases because
both taxon presence/absence data and taxon abundance data are not normally distributed.
Instead, "generalized" regression methods are used, which adapt linear regression approaches to
non-normal distributions (Hastie and Pregibon, 1992). In the case of presence/absence data, the
response variable is modeled as a binomial distribution; in the case of abundance data, a negative
binomial distribution is often assumed.
3.2.1.1. Parametric Regressions
A common assumption for taxon-environment relationships is that the distribution of a
particular taxon is unimodal with respect to environmental gradients (see Section 2.1). Then, in
the case of presence/absence data, a convenient model for the probability of observing a
particular taxon, following ter Braak and Looman (1986), is as follows:
11
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lu^-
2 1 (X - li)
2
=a-—-—--— (3)
where/? is the probability of observing the tax on, and the left side of the equation is the logit
transformation of this probability. Additionally, x is the value of the environmental variable, u is
the species optimum (the point along the environmental gradient where the probability of
observing the species is maximized), Hs a measure of the niche breadth, and a is related to the
maximum probability of observation. The constants b0, b^, and b2 can be determined using
standard maximum likelihood estimation methods for fitting a curve to observed data and a
generalization of linear regression methods (i.e., generalized linear models, GLMs). Then the
parameters u, t, and a can be determined as follows: u = - b^ f2b2 , t: = \/^- 2&2 , and
a = b0 - b'i J2b-2 . Examples of taxon-environment relationships estimated using eq 3 for two
genera, Heterlimnius andMalenka, with respect to stream temperature are shown in Figure 6.
The computed curves closely track the observed capture probabilities for both genera.
Confidence limits broaden for Heterlimnius as temperatures decrease to the minimum values,
because data were sparse in that region.
A similar model can be specified for abundance data as follows:
r
(4)
where A is the observed abundance in a sample and the other variables are defined as above.
Abundance, A, is assumed to follow a negative binomial distribution, with a log-mean value
equal to the right hand side of eq 4. With negative binomial distributions, the residual variance
of A is a function of the mean value and one additional parameter that quantifies the degree to
which the variance differs from a simple Poisson distribution (White and Bennetts, 1996).
Abundance is loosely defined here because this modeling approach can be applied to both
absolute and relative abundances. Solving the regression is somewhat more complicated because
of the additional parameter, although GLMs can again be used.
12
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Figure 7. Relationship between relative abundance and
temperature for Heterlimnius (left) andMalenka (right). Solid line
is mean relationship determined between relative abundance and
temperature determined by a negative binomial regression. Dotted
lines are estimated 90% confidence limits about the location of the
mean relationship. Open circles represent observations. Thirteen
observations with abundances greater than 50 are not shown for
Heterlimnius and three observations with abundances greater than 50
are not shown for Malenka.
single-variable models in this report. The use of multiple variables is discussed further in
Section 5.1.
The use of parametric functions to describe the taxon-environment relationship is both a
strength and a weakness of the parametric approach. On the one hand, these functions provide
the means to summarize the taxon-environment relationship using a short list of pre-defined
parameters. On the other hand, the a priori assumption of a functional form may restrict the
taxon-environment relationship to a shape that is not fully supported by field observations.
Inspection of plots of observed data and modeled functional fits can help establish whether the
assumed functional forms are appropriate.
3.2.1.2. Nonparametric Regressions
Many researchers have noted that unimodal relationships cannot be expected for all taxa
across all gradients (Austin and Meyers, 1996; Oksanen and Minchin, 2002). To address this
issue, a modeling approach is often used that requires only that the modeled function vary
smoothly and slowly over the modeled range. Here, the distribution of a given taxon is modeled
as follows:
14
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f i
In -?— =s0+s(x) (5)
\1 - J
where/? is defined as before, s0 is a constant, and s represents a nonparametric smooth curve that
is fit through the data.
The locations of the mean responses for each point along a nonparametric curve, s, are
determined through an iterative procedure that uses data in a local neighborhood around each
point. The "local" nature of the fit differs fundamentally from that of a parametric model, which
computes a best fit based on the entire set of data. Thus, nonparametric responses have the
potential to capture smaller scale variations in response. Near the edges of the domain, though,
sufficient data do not exist on both sides of the point of interest, and increasing amounts of data
must be drawn from within the sampled range; therefore, the width of the neighborhood
broadens, and the fit is less local than in the center of the domain (Hastie and Tibshirani, 1999).
This boundary effect is evident in Figure 8, where the response determined by
nonparametric regression for Heterlimnius at low temperatures differs substantially from the
response found by parametric regression (Figure 6). The probability of occurrence, as
determined by nonparametric regression, continues to increase all the way to the lowest
temperature, whereas the parametric-derived response decreases at the lowest temperature.
Because the neighborhood used by the nonparametric curve increases as it approaches low
temperatures, it incorporates more of the high-occurrence probabilities at slightly higher
temperatures, which may have the effect of maintaining a high-occurrence probability all the way
to the boundary of the data. In contrast, the parametric model forces a fit to a unimodal curve
and decreases.
In both cases, the confidence limits are very broad at the lower boundary of the data, so
the "true" response is impossible to determine from this data set. However, the observed
frequency of occurrence at the lowest temperature (the left-most point in Figure 6) suggests that
occurrence probabilities for Heterlimnius may decrease at the lowest temperature, a feature that
is missed by the mean nonparametric response. In general, responses near the edges of the
sampled gradient must be interpreted with caution.
A commonly used approach to fitting nonparametric curves is known as the generalized
additive model (GAM) (Hastie and Tibshirani, 1999), which allows for more than one
explanatory variable, each associated with its own nonparametric smooth curve. For now,
though, we consider only a single explanatory variable and again defer discussion of multiple
variables to Section 5.1. The flexibility of nonparametric regressions also complicates its use
15
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Figure 8. Relationship between probability of occurrence and
temperature for Heterlimnius (left) and Malenka (right). Solid line
is mean relationship between probability of occurrence and
temperature determined by logistic regression. Dotted lines are
estimated 90% confidence limits about the location of the regression
curve. Each open circle represents the average occurrence probability
in approximately 10 samples surrounding the indicated temperature.
because there are no parameters with which the modeled relationship can be represented.
Instead, a numerical representation of the entire curve must be stored for further analysis (e.g., to
extract tolerance values).
3.2.1.3. Model Performance and Overfitting
Different species will vary in the degree to which their occurrence can be predicted by a
particular environmental gradient, and quantifying these differences can be useful for
characterizing the performance of different models of taxon-environment relationships. One
useful way to quantify the performance of a model is to examine the relationship between the
false positive rate and the true positive rate. The true positive rate is the proportion of sites at
which a taxon was predicted to be present and sites where it was actually observed. The false
positive rate is the proportion of sites at which the taxon was predicted to be present and sites
where it was not observed. At a set of test sites, given the values of the environmental gradient
and given a model for the taxon-environment relationship, we first compute the predicted
probability of occurrence for that taxon. To compare predicted probabilities with actual
observations of presence and absence, we then specify a threshold probability above which the
16
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taxon is predicted to be present and below which the taxon is predicted to be absent. An example
of this comparison is shown in Table 1 for Heterlimnius and a threshold probability of 0.5. The
true positive rate in this case is 717(49+71), or 0.59, and the false positive rate is 547(195+54), or
0.22.
Table 1. Observed versus predicted occurrences for Heterlimnius
Taxon
Absent
Present
Predicted absent
195
49
Predicted present
54
71
As the threshold value ofp is increased, both false and true positive rates increase. We
can quantify the trade-off by computing false and true positive rates over a range of threshold
values and plotting them against one another (Figure 9). The resulting curve is known as the
receiver operating characteristic (ROC) curve, and the area under this curve provides a measure
of the classification strength of the model (Manel et al, 2001). The 1:1 line indicates the
position of the ROC curve for a model in which the false positive rate is the same as the true
positive rate, regardless of the choice of threshold value. Such a model has no classification
power, and therefore this area (0.5) is the lowest possible ROC value. The area under the ROC
curve approaches 1 as classification strength increases. In the example shown in Figure 9, the
area under the ROC curve is 0.8. The minimum ROC value for an "acceptable" model varies
with different studies. For this report, we selected a value of 0.55 as a provisional cut-off value.
This cut-off value is relatively low compared to the more commonly-used value of 0.7 (Hosmer
and Lemeshow, 2000). However, the use of the model here differs from conventional regression
models in that we are interested only in characterizing the taxon-environment relationships and
not interested in actually predicting the presence or absence of different taxa. The effects of
using other cut-off values are explored in Section 4.1.3.2.
Overfitting the data can be an issue when developing taxon-environment relationships.
To avoid overfitting regression models, it is generally recommended that at least 10 to 15
observations of the response variable being modeled occur in the data set for each degree of
freedom in the explanatory variables. For example, to model the presence or absence of a taxon
with an overall frequency of occurrence of 20%, we would require 50-75 samples for each
degree of freedom that is contemplated. (Note that for a very common taxon that occurs at a
majority of sites, the appropriate definition of an "observation" for this purpose is the absence of
17
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op
ci
ca
ci
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ci
0.0 0.2 0.4 0.6 0.8 1.0
False positive rate
Figure 9. Receiver operator characteristic
(ROC) curve for Heterlimnius. Dashed line
shows 1:1 line. Area under the ROC curve is
0.8.
the taxon at a site.) Because most unimodal relationships require at least two degrees of freedom
to specify (e.g., the quadratic relationship shown in eq 3), we would require 100-150 samples for
each variable. Species-abundance relationships suggest that many taxa are observed infrequently
and only a few are relatively common. Thus, the number of taxa for which regression models
can be developed may be limited.
3.2.2. Optima
After a taxon-environment relationship is modeled by regression, defining the optimum
tolerance value is fairly straightforward. The optimum value in parametric regressions is
explicitly defined (eqs 3 and 4). For nonparametric regressions, one numerically locates the
point of maximum modeled occurrence probability along the regression relationship. Optima for
species-environment relationships that increase or decrease monotonically are necessarily
located at the edges of the environmental gradient. Thus, all species with monotonically
increasing relationships would have the same maximum point, as would all species with
monotonically decreasing relationships. In a region containing many such species, it can be
difficult to distinguish between their relative tolerances for a given stressor gradient.
Furthermore, the edges of the environmental gradient are usually defined only by the range of
conditions sampled and can therefore vary between data sets.
18
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3.2.3. Curve Classification
The process of curve classification can be accomplished analytically or graphically,
depending on whether parametric (GLM) or nonparametric (GAM) regressions are used to define
the taxon-environment relationship. In a parametric regression as defined by eq 3, the curve can
be classified according to the statistical significance of different coefficients in the regression.
More specifically, if the quadratic term in eq 3 reduces the model deviance by a statistically
significant amount, then the relationship is unimodal. Otherwise, the model equation reduces to
a linear relationship, and the relationship can be classified as increasing or decreasing, depending
upon the sign of linear coefficient (bl in eq 3). In rare cases, the quadratic term is statistically
significant but the sign of the coefficient (b2 in eq 3) is positive, indicating that the relationship is
concave up. In these cases, the data and the estimated taxon-environment relationship should be
examined more carefully to identify reasons for the anomalous behavior.
A graphical approach to curve classification is required for nonparametric regressions, in
which the maximum modeled occurrence probability is compared with the confidence limits on
either side of the taxon optima. If a horizontal line drawn through the maximum mean
occurrence probability deviates from the upper confidence limits on both sides of the taxon
optima (e.g., Malenka in Figure 10), then the taxon is designated as unimodal. If the line
deviates from the upper confidence limit only on the right-hand side of the taxon optimum (e.g.,
Heterlimnius in Figure 10), then the taxon is designated as a decreaser; if it deviates only on the
left-hand side (e.g., Hydropsyche in Figure 10), then the taxon is designated as an increaser. A
parallel set of conditions can be specified with regard to the lower confidence limit. Assuming
that human activities cause an increase in the value of the environmental gradient, increasers
would be identified as tolerant taxa, decreasers would be identified as intolerant taxa, and
unimodal taxa would be designated as intermediately tolerant.
3.3. COMPARING DIFFERENT TOLERANCE VALUES
3.3.1. Continuous Tolerance Values
We computed tolerance values for sediment and temperature using six different methods:
(1) weighted averages (WA), (2) cumulative 75th percentile (CP75), (3) parametric regressions
combined with the point of maximum occurrence probability (GLMMAX) , (4) parametric
regressions combined with curve shape classification (GLMCL), (5) nonparametric regressions
combined with the point of maximum occurrence probability (GAMMAX), and (6)
nonparametric regressions combined with curve shape classification (GAMCL). In both GLM
19
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10 15 20 25 3D
Temperature
10 15 20 25 30
Temperature
10 15 20 25 30
Temperature
Figure 10. Graphical approach for classifying curve shape for Heterlimnius,
Malenka, and Hydropsyche. Solid line is mean response, dotted lines are estimated
90% confidence limits about mean response, dashed line is location of maximum mean
response for comparison with confidence limits.
and GAM models, only a single explanatory variable was specified, and it was modeled with two
degrees of freedom. Tolerance values were derived only for taxa that occurred in at least 20
sites. Additionally, GLMMAX, GAMMAX, and curve classification tolerance values were
computed only for models for which ROC > 0.55. All tolerance values are tabulated in
Appendix C.
All sets of tolerance values except those determined by curve shape classification were
compared by computing correlation tables and examining scatter plots. Overall, tolerance values
derived by different methods were highly correlated. All types of continuous temperature
tolerance values (GLMMAX, GAMMAX, WA, and CD75) were strongly correlated with r,
ranging from 0.88 to 0.97 (Table 2). Correlation coefficients between different types of sediment
tolerance values were also high, varying from 0.84 to 0.98 (Table 3). The weakest correlation
Table 2. Correlation coefficients for temperature tolerance values
Method
GLMMAX
GAMMAX
WA
GAMMAX
0.96
WA
0.89
0.93
CD75
0.88
0.91
0.97
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Table 3. Correlation coefficients for sediment tolerance values
Method
GLMMAX
GAMMAX
WA
GAMMAX
0.98
WA
0.84
0.88
CD75
0.87
0.90
0.97
found was between GLMMAX and WA, primarily because taxon-environment relationships
were often monotonic and GLMMAX tolerance values were pinned at either edge of the sampled
domain (Figure 11). This same phenomenon was observed for temperature, but a smaller
proportion of taxon-environment relationships for temperature were monotonic and the
correlation coefficients were not as strongly affected.
o
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O 0
0 0
"o
o
0 20 40 60 80 100
GLMMAX
Figure 11. Comparison of optima tolerance value determined by
parametric logistic regression model (GLMMAX) and weighted
average tolerance values (WA) for temperature. Each point represents a
different taxon. Axis scales are nominally in units of °C. Points have been
jittered to more clearly show overlapping points.
The close relationships between different types of tolerance values is not surprising, given
that they were estimated from the same set of data. The main reasons for differences likely stem
from uncertainties in estimating the point of maximum occurrence probability for gradients that
21
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were only partially sampled. The distribution of samples across the gradient also influences
differences between WA and GLMMAX or GAMMAX tolerance values (ter Braak and Looman,
1986).
3.3.2. Tolerance Classifications
We compared curve classification tolerance values estimated by different methods using a
confusion matrix, in which each position in the matrix corresponds to a combination of GLMCL
and GAMCL categories and the number in that position is the number of taxa for which a
particular combination of tolerance classifications was found. For example, 35 taxa were
identified as sensitive to elevated temperature by both GAMCL and GLMCL and 33 taxa were
classified as intermediately tolerant by GLMCL and as sensitive by GAMCL (Table 4).
Comparisons of curve classification tolerance values for fine sediment are shown in Table 5.
Table 4. Confusion matrix for temperature tolerance classifications
^^^^^^GAM
GLM ^^^^^
Sensitive
Intermediate
Tolerant
Sensitive
35
33
0
Intermediate
0
16
0
Tolerant
0
21
30
Table 5. Confusion matrix for sediment tolerance classifications
^^^^^^ GLM
GAM ^^^^^
Sensitive
Intermediate
Tolerant
Sensitive
69
16
0
Intermediate
0
1
0
Tolerant
0
9
27
In general, the GLMCL reliance on the statistical significance of the quadratic term
yielded many more intermediately tolerant classifications (i.e., unimodal) than did the graphical
classification of GAMCL. That is, the quadratic term was often statistically significant, but the
confidence intervals surrounding the relationship were too broad to permit a graphical
classification of the relationship as unimodal. The taxon-environment relationship for
Heterlimnius (Figure 6) provides a good illustration of this effect. Here, the unimodal response
22
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was statistically significant, but the confidence intervals at the lowest temperatures were so broad
that the graphical method classified this relationship as monotonically decreasing. For our
purposes, classifications into tolerant and sensitive categories are more directly useful.
Furthermore, the graphical classification method can be applied to both parametric and
nonparametric regression results, so we focus only on GAMCL categories for the remainder of
this report.
3.3.3. Comparisons Between Continuous and Categorical Tolerance Values
Curve classifications provide a broad characterization of taxa into tolerant or sensitive
categories that complement continuous tolerant values (e.g., CP75, WA). In previous analyses,
taxa have been classified as tolerant or sensitive on the basis of an existing continuous tolerance
value. For example, Klemm et al. (2002) categorized taxa that had already been assigned
tolerance values ranging from 0 to 10. In their scheme, taxa with tolerance values less than or
equal to 4 were classified as sensitive and taxa with tolerance values greater than or equal to 6
were classified as tolerant. One concern with this approach is that the threshold value used to
discriminate between tolerant and sensitive taxa is determined through best professional
judgement and may not accurately capture the point at which taxon-environment relationships
actually exhibit a substantive change (e.g., a shift from a decreasing relationship to an increasing
relationship).
To further explore this issue, consider the distribution of WA optima values for sediment
computed from EMAP-West data (Figure 12). We can probably assume that taxa that have low
sediment optima are sensitive to excess fine sediment and taxa that have high sediment optima
are tolerant. In the middle of the range, though, it is difficult to identify a single WA optimum
value below which we are confident that all taxa are sensitive or above which we are confident
that all taxa are tolerant. Similarly, taxa that have low temperature optima are likely to be
sensitive to elevated temperature and taxa that have high temperature optima are likely to be
tolerant to elevated temperature, but taxa with moderate optima are difficult to categorize (Figure
12). A potential solution to this dilemma is to designate taxa with tolerance values falling in the
middle of the range as indifferent, following Klemm et al. (2002). However, this approach is
conservative, and it is likely that some taxa that are truly sensitive or tolerant will be classified as
indifferent.
23
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14 18
Temperature
10 20 30 40 50 60
Percent sands/fines
Figure 12. Histogram of weighted average tolerance values for temperature (left) and fine
sediment (right).
Tolerance values based on curve shape classifications provide a good alternative to
continuously ranked tolerance values. Curve shape classification provides a direct measure of
whether a taxon increases or decreases in response to anthropogenic stress, a more definitive
classification than can be achieved with continuous tolerance values. We look again at the
distribution of WA optima for temperature and sediment, this time color-coded for tolerance
classification in terms of curve shape (Figure 13). As expected, taxa classified by curve shape as
tolerant are clustered to the right-hand side of the histogram, with high WA optima, and those
classified as sensitive are clustered to the left-hand side of the histogram. At moderate WA
optima values, though, the correspondence between the value of the optima and the tolerance
classification is much weaker.
24
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10
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Temperature
10 20 30 40 50 60
Percent sands/fines
Figure 13. Histogram of weighted average tolerance values for temperature
(left) and fine sediment (right) classified by curve shape. Shading in bars
indicate numbers of taxa within each group classified as sensitive (open),
intermediately tolerant (hatched), and tolerant (gray). Black bars indicate taxa for
which classifications were not assigned.
3.3.4. Effects of Regional Characteristics
All tolerance values discussed above depend on the range of conditions under which they
are derived. This dependence stems from the fact that the range of sampled conditions imposes
arbitrary limits on the functions used to compute tolerance values. A simple example of this
effect can be seen in Figure 14, in which we consider a taxon-environment relationship that
increases linearly with temperature. In the left plot, samples are collected across a range of
temperatures from 5 to 30°C, whereas in the right plot, samples are collected across half the
range. In the first case the weighted average is 22°C and in the second case the weighted average
is 13°C. Similar changes in tolerance values would be observed for values derived by
cumulative percentile methods.
Optima and curve classification tolerance values are somewhat less susceptible to this
effect, but none are immune. For example, optima tolerance values for monotonically increasing
or decreasing taxon-environment relationships are located onthe edge of the sampled gradient.
These values therefore vary with the range of conditions sampled. Curve classification, on the
other hand, can be sensitive to the sampled range because species identified as monotonically
increasing could be identified as unimodal in a data set that samples a broader range of
25
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conditions. Thus, regardless of the derivation method, very different tolerance values could be
derived for a given species, depending on the range of data that are collected.
CO
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10
15 20
Temperature
25
30
10 12
Temperature
14
16
Figure 14. Illustrations of effect of gradient length. Solid circle indicates
location of the weighted average tolerance value.
We must consider the effects of regional characteristics when comparing tolerance values
across regions or when using tolerance values derived from different study areas in the same
assessment. When comparing tolerance values, the absolute values derived in different study
areas will always require that the range of conditions sampled in each of the study areas be
considered. Alternatively, the relative rankings of sensitivity should be relatively insensitive to
the range of sampled conditions, so comparisons of relative rankings across study areas should be
fairly straightforward. Furthermore, direct comparisons of species-environment relationships are
also possible.
One of the potential strengths of using tolerance values for assessment is that once a
tolerance value is derived for a species, it can be used wherever that species is observed.
However, as discussed above, the generality of a tolerance value across different regions is
influenced by the data set from which it was derived and the range of conditions sampled in that
data set. In certain cases, it may be necessary to use tolerance values derived from different data
sets within the same assessment. In such cases, tolerance values must be examined to ensure that
they are based on the same ranges of environmental conditions.
26
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4. APPLYING TOLERANCE VALUES IN ASSESSMENT
On their own, tolerance values provide valuable information about the relative sensitivity
of different taxa to different types of anthropogenic stressors. For example, taxa lists at impaired
and reference sites can be compared in terms of the presence or absence of taxa with different
tolerance values to infer possible sources of stress. The loss of particularly sensitive taxa could
also provide an early indication of impairment. However, to most effectively apply tolerance
values for biological assessment, biological metrics that summarize the observations of many
different tolerant and sensitive taxa at a given test site are required. These summaries must then
be compared with baseline conditions to ascertain whether observed changes are statistically or
biologically significant. Therefore, evaluating the efficacy of different tolerance value derivation
methods requires that we consider them in conjunction with biological metrics and baseline
conditions.
4.1. BIOLOGICAL METRICS
Biological metrics provide the means of summarizing the tolerance values of all of the
different taxa observed at a test site. The available types of metrics differ for categorical and
continuous tolerance values, so we discuss them in two separate sections.
We assess the performance of different metrics by comparing their values at independent
test sites with observations of stressor levels at those same sites. Ideally, metric values should be
strongly associated with the observed stressor level, and the variability about this mean response
should be low. These characteristics would suggest that small changes in the stressor level could
be detected with the biological metric. We compare the performance of biological metric values
computed at different sites using data collected in Oregon by the Oregon Department of
Environmental Quality (DEQ) (Appendix B). To compute metrics values, taxon abundance data
from Oregon streams were combined with tolerance values estimated previously from EMAP-
West data (Appendix C). Observations of stream temperature and fine bedded sediment were
also available at each of the sites. The Oregon data were collected from a small area within the
larger EMAP-West region and constitute a completely independent set of data.
4.1.1. Metrics Based on Categorical Tolerance Values
Compositional metrics summarize compositional characteristics of a sampled
assemblage, and metrics that incorporate aspects of tolerance values (i.e., tolerance value
metrics) have frequently been shown to distinguish between degraded and reference streams
(Barbour et al., 1999). Examples of tolerance metrics include the relative abundance of tolerant
27
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or sensitive taxa, the proportion of total taxa that are tolerant or sensitive, and the richness of
tolerant or sensitive taxa.
We used GAMCL classifications estimated from EMAP-West data to group taxa
collected in Oregon into sensitive and tolerance categories. Then, we computed values at the
Oregon sites for relative abundance of tolerant (RABN.TOL) and sensitive taxa (RABN.SEN),
richness of tolerant (RICH.TOL) and sensitive (RICH. SEN) taxa, and proportion of total taxa of
tolerant (PTAX.TOL) and sensitive (PTAX.SEN) taxa. Computed metric values were then
plotted against observed values of stream temperature and fine sediment. All of the temperature-
specific metrics exhibited strong relationships with the observed temperature (Figure 15). The
proportion of total taxa that were sensitive appeared particularly strongly related to stream
temperature. Many sediment-specific metrics also exhibited reasonably strong relationships with
the sediment gradient (Figure 16). As with temperature, the proportion of total taxa that were
sensitive exhibited the least variability in its relationship with observed sediment levels.
Metrics quantifying characteristics of tolerant taxa were more weakly associated with
observed stressor levels, and the magnitude of variability about the mean values was substantially
greater. This higher variability can likely be explained by the relatively low richness of tolerant
taxa observed (temperature-tolerant taxon richness increased to only about four taxa at the
warmest sites in the study area, and sediment-tolerant taxon richness increased to only about two
taxa at sites with high percentages of sands and fines). Low richness, then, contributed to high
variability in relative abundance values and proportions of total taxa because the presence or
absence of a single taxon could cause large changes in the values of these metrics.
But why is tolerant taxon richness so much lower than sensitive taxon richness?
Definitive answers to this question are elusive. One reason maybe that fewer taxa were
identified as tolerant than as sensitive. For example, a total of 71 of the taxa found in Oregon
were classified as sensitive to elevated temperature, whereas only 44 were classified as tolerant.
However, the difference in the number of sensitive versus tolerant taxa does not seem large
enough to explain the strong differences observed in richness. Another contributing factor may
be that sites with elevated temperature and increased fine sediment sites may also be affected by
other stressors, the aggregate effect of which is to strongly depress taxon richness. The potential
effects of such co-occurring stressors require further study.
To quantify the variability in the association between each metric and the stressor
gradient of interest, a nonparametric smoothing spline (as seen in eq 5) was fit to each
combination of tolerance value metric and stressor gradient (shown as solid lines in the Figures
15 and 16). Nonparametric curves were chosen because there was no a priori reason to expect
that the relationships between metrics and stressor gradient would be linear. An R2 statistic
28
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10 15 20
Temperature
10 15 20
Temperature
y
LC
10 15 20
Temperature
10 15
Temperature
z
s
IT
20
10 15
Temperature
20
o
cc
10 15
Temperature
20
Figure 15. Relationship between temperature tolerance metrics and observed
temperature in Oregon. PTAX.SEN: proportion of total number of taxa classified as
sensitive; RABN.SEN: relative abundance of sensitive taxa; RICH.SEN: taxon richness
of sensitive taxa; PTAX.TOL: proportion total taxa classified as tolerant; RABN.TOL:
relative abundance of tolerant taxa; RICH.TOL: taxon richness of tolerant taxa. Solid
line shows position of a smoothing spline fit through the data.
expressing the proportion of variability in the biological metric that was associated with changes
in the stressor level was then computed (Table 6). In general, changes in temperature accounted
for more variability in the temperature tolerance metrics than did sediment in the sediment
tolerance metrics. Also, environmental observations accounted for more variability in metrics
related to sensitive taxa than metrics related to tolerant taxa.
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t 2
0 20 40 60 80 100
Percent sandsffines
UJ
w
i
y
0 20 40 60 80 100
Percent sandsrtines
0 20 40 60 80 100
Percent sands/jnes
20 40 60 80 100
Percent sandsffines
o
t-
z
o
cc
20 40 60 80 100
Percent sandsfines
20 40 60 80 100
Percent sands/fnes
Figure 16. Relationship between sediment tolerance metric and observed
sediment in Oregon. Vertical axis abbreviations and symbols as in Figure 15.
Table 6. R2 values for spline fits between metric and stressor level
Metric
PTAX.SEN
RABN.SEN
RICH.SEN
PTAX.TOL
RABN.TOL
RICH.TOL
Temperature
0.53
0.50
0.35
0.30
0.12
0.23
Sediment
0.39
0.19
0.23
0.09
0.02
0.05
30
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4.1.2. Metrics Based on Continuous Tolerance Values
All of the metrics defined in the previous section can be computed using continuous
tolerance values, as long as the continuous tolerance value are first converted to categories (see
Section 3.3.3). However, a more natural metric to compute—one that makes use of the full range
of values—is the mean tolerance value of taxa observed at a site. If abundance data are
available, the tolerance values of each taxon can be weighted by the observed abundance. The
computation of these mean tolerance values can be expressed as follows:
N IN
where um is the mean tolerance value, TV is the number of taxa, and Uj is the tolerance value for
taxony. Ytj is defined as previously: for presence/absence data, Ytj = 1 when a taxony is present,
and Ytj = 0 when taxony is absent from site/; for abundance data Ytj is the abundance of taxony at
site /. This formula was used by Hilsenhoff (19 87) and Lenat (1993) and in weighted average
inferences of environmental conditions (e.g., Birks et al., 1990). The only differences between
various analyses are the tolerance value that is used and whether abundance or presence/absence
data are applied.
To compare the performance of different tolerance values, continuous tolerance values
(WA, CP75, GLMMAX, and GAMMAX) were computed from EMAP-West data for
temperature and fine sediment. Then, the mean of the tolerance values for taxa observed in each
test site in Oregon were computed. A nonparametric smoothing spline was then fit to the
relationships between the mean sediment and temperature tolerance values and observed
sediment and temperature, and an R2 statistic computed for each fit. The results are summarized
in Table 7.
Overall, the mean sediment and temperature tolerance values were strongly associated
with observed sediment levels and temperature. All types of temperature tolerance values
accounted for comparable proportions of the variability in the observations, with R2 ranging from
0.49 to 0.56. For sediment, GAMMAX and GLMMAX performed particularly poorly, with R2 =
0.31 and 0.28, respectively. For any given type of tolerance value, temperature was more
strongly associated with the mean temperature tolerance value than was sediment with the mean
sediment tolerance value. WA and CD75 consistently exhibited less variance in their
relationships with each environmental variable than did GLMMAX and GAMMAX.
31
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Table 7. R2 values for spline fits between mean tolerance values and
observed temperature and sediment in Oregon (One outlier dropped from
sediment data.)
Method
WA
CD75
GLMMAX
GAMMAX
Temperature
0.56
0.56
0.49
0.49
Sediment
0.45
0.42
0.28
0.31
Overall, compared with the compositional metrics computed from categorical tolerance
values (Table 6), the mean tolerance values exhibited less variable relationships with the
observed levels of temperature and sediment. These higher R2 values likely are a result of two
factors. First, the compositional metrics used only two categories to represent tolerance values,
whereas the mean tolerance values captured the full range of tolerance values. Second, each
mean tolerance value depended on changes in both tolerant and sensitive organisms, so both
increasing and decreasing taxa influenced the final mean value. Compositional metrics
disaggregate increasing and decreasing responses into distinct groups, which may lessen their
ability to represent the overall variability in the system.
4.1.3. Performance of Tolerance Value Metrics
We observed systematic differences in the performance of tolerance value metrics across
different stressors and across different types of tolerance values. In this section we discuss some
of the reasons for these differences.
4.1.3.1. Characteristics of the Stressor Gradient
We observed a consistent difference in the performance of the tolerance value metrics for
the two stressors considered as examples in this section: temperature tolerance metrics were
always more strongly correlated with temperature observations than were the corresponding
comparisons computed for sediment. This performance difference across stressors may reflect
(1) differences in the distribution of the sampled values for the two gradients, (2) differences in
the mechanisms by which temperature and sediment affect biota, and (3) differences in our
ability to measure these gradients.
First of all, a relatively uniform distribution of stream temperatures was sampled in the
EMAP-West. In contrast, the percentage of fine sediment in sampled streams was generally low,
32
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and the distribution of fine sediment levels was strongly skewed. A skewed distribution of the
underlying environmental gradient has been shown to degrade the accuracy of weighted average
optima (ter Braak and Looman, 1986) and would similarly degrade the accuracy of all other types
of tolerance values. One way to mitigate the effects of a skewed distribution is to stratify and
resample the existing data such that all locations on the environmental gradient are equally
represented, but this procedure can introduce errors.
Second, the mechanisms by which stream temperature can influence stream
macroinvertebrates are direct and relatively well understood. For cold-blooded organisms such
as stream macroinvertebrates, virtually all metabolic processes are linked to environmental
temperature, so stream temperature is necessarily a strong determinant of assemblage
composition (Allan, 1995). Conversely, the mechanisms by which fine sediment affect stream
invertebrates are less well understood and in many cases, less direct. Some proposed
mechanisms by which fine sediment can affect aquatic insects include reducing habitat by filling
interstitial spaces on stream bottoms and increasing the scour of the stream bottom in high-flow
events (Wood and Armitage, 1997). Because of these mechanistic uncertainties, taxon-
environment relationships for fine sediment are likely to be less precise than those for
temperature.
The final difference between the two stressors is in the precision with which
measurements can be collected. Quantifying the composition of a heterogeneous stream bottom
is accomplished by measuring a relatively small number of individual particles collected at
prescribed locations. Stream temperature is relatively homogeneous throughout the stream.
Measurements of substrate composition are therefore likely to be somewhat more variable than
measurements of temperature. Note, however, that both temperature and sediment exhibit a high
degree of temporal variability, which is measured poorly by one-time samples.
All of the factors discussed above may influence the predictive performance of the
tolerance values. Determining the relative contribution of each factor to the observed difference
in predictive accuracy requires further study.
4.1.3.2. Acceptance Criteria for Tolerance Values
Inherent in the GAM and GLM approaches was a model acceptance criterion whereby
models with classification accuracy below a certain limit (ROC < 0.55) were rejected and no
tolerance value was computed. No model acceptance criteria are typically imposed on WA or
CD computations, although in our case we did limit WA and CD optima computations to those
taxa that occurred in at least 20 sites. In additional tests (Table 8), we explored the effects of
tightening the acceptance
33
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Table 8. R2 values for models with ROC > 0.65 criteria imposed
Method
WA
CD75
GLMMAX
GAMMAX
Temperature
0.60
0.60
0.55
0.60
Sediment
0.40
0.38
0.29
0.28
criteria to ROC > 0.65, which omitted additional taxa from the computation of the metric values.
We then recomputed average tolerance values for GLMMAX and GAMMAX using this reduced
set of taxa. For comparison, we also recomputed average tolerance values for WA and CD75
using this same reduced set of taxa. The effects of the change in acceptance criteria differed for
temperature and sediment. For temperature, tightening the ROC criteria slightly increased R2
values. The R2 for GAMMAX, WA, and CD75 were all 0.60, while the R2 for GLMMAX was
slightly less. In contrast, for sediment, tightening the criteria actually decreased R2 values for
WA and CD75, while R2 values for GAMMAX and GLMMAX were essentially unchanged.
As noted, the distribution of sediment observations in the EMAP-West data set were
strongly skewed to the right, which created difficulties for statistical modeling. Many taxa that
exhibited strong relationships with the sediment gradient may have failed to meet the acceptance
criteria because of this distribution. Thus, for skewed distributions, it seems likely that the ROC
> 0.65 criterion was too stringent. On the other hand, for gradients that are sufficiently and
evenly sampled (such as temperature), a more restrictive ROC criterion may improve
performance.
4.1.3.3. Specificity of Response
We can test for the specificity of response for different tolerance value metrics by
examining their relationship with other environmental gradients. Ideally, a tolerance value
metric would exhibit a strong relationship with the stressor for which it was designed and would
show no relationship with other gradients. Examples of these comparisons are shown in Figures
17 and 18, where temperature compositional metrics are plotted against the sediment gradient
and sediment compositional metrics are plotted against the temperature gradient. Most
temperature metrics did not exhibit strong relationships with the sediment gradient. The relative
abundance, richness, and proportion of total taxa of temperature-sensitive taxa decreased with
increasing fine sediment, but these relationship were less strong and more variable than those
34
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observed between the same metric and stream temperature (Figure 15). Metrics derived from
temperature-tolerant taxa all showed no response to the sediment gradient.
Sediment tolerance metrics were less specific to the sediment gradient, as all metrics
exhibited a relationship with the temperature gradient. Sediment-sensitive metrics all initially
decreased gradually with increasing temperature but then decreased at a faster rate at higher
temperatures. Sediment-tolerant metrics all increased with increasing temperature, and R2 values
for these relationships were even higher than those observed for fine sediment.
20 40 60 80 100
Percent sandsrtines
o
DC
20 40 60 80 100
Percent sands/fines
0 20 40 60 80 100
Percent sands/ines
0 20 40 60 80 100
Percent sandsrtines
o
ce
0 20 40 60 80 100
Percent sandsAines
0 20 40 60 80 100
Percent sandsflnes
Figure 17. Temperature tolerance metrics plotted versus percent sands and fines.
Vertical axis abbreviations and symbols as in Figure 15.
35
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LU Q
if, IN
O
o:
10 16
Temperature
20
10 15
Temperature
10 15 20
Temperature
o
cc
10 16
Temperature
20
10 15 20
Temperature
5 10 15 20
Temperature
Figure 18. Sediment tolerance metrics plotted versus temperature. Vertical axis
abbreviations and symbols as in Figure 15.
We can perform the same type of comparison using mean tolerance values. In Figure 19,
mean WA tolerance values for fine sediment are plotted versus observed stream temperature, and
mean WA tolerance values for temperature are plotted versus observed fine sediment. Here,
mean sediment tolerance values showed a fairly strong relationship with temperature, whereas
mean temperature tolerance values were specific to stream temperature and were not associated
with fine sediment.
Results from this exercise suggest that the sediment tolerance classifications are less
specific to sediment than the temperature tolerance classifications are to temperature. However,
both performed reasonably well, as most metrics and inference indices explained more variability
in the stressor of interest than in the covarying stressor. The notable exception to this trend was
the sediment-tolerant taxa metrics, and their poor performance can likely be attributed to the
distribution of observed sediment values and perhaps to the low richness of sediment-tolerant
taxa observed at any given site (see Section 4.1.1).
36
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CD
(N
ID
O
C
O
(N
6 8 10 12 14 16 18 20
Temperature
c
03
(O .
*
0 20 40 60 80
P ercent sands/fines
Figure 19. Mean weighted average (WA) tolerance values for sediment
plotted against observed temperature (left), and mean WA tolerance value
for temperature plotted against observed sediment (right).
Generalizing the present findings to a broader array of stressors is challenging.
Covariance in stressors is common, however, and in many cases tolerance values will provide
only one line of evidence toward a diagnosis of the most likely cause of impairment. Other lines
of evidence will often be needed to supplement the information provided by tolerance values.
4.1.3.4. Effects of Taxonomic Resolution of Tolerance Values
Tolerance values for the examples considered thus far have been computed at the genus
level. In some monitoring programs, taxa are identified only to the family level. For certain
applications, this level of identification may be sufficient; however, as taxonomic resolution
coarsens, we can less confidently assume that an invariant fundamental niche is associated with
each taxon. A single family may contain numerous genera, each of which may contain numerous
species and all of which may have slightly different niches. Conversely, for certain families, we
may expect to find only one or two species, and in these cases family-level identification may be
sufficient. Furthermore, aggregation to genus or even family is often necessary because of
limitations on taxonomic identification accuracy.
To explore the effects of taxonomic resolution, we computed tolerance values in EMAP-
West at the family level and used these values to compute average tolerance values in Oregon.
The R2 values for comparisons between average tolerance values and environmental observations
are shown in Table 9.
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Table 9. R2 values for family-level tolerance values
Method
WA
CD75
GLMMAX
GAMMAX
Temperature
0.44
0.42
0.28
0.29
Sediment
0.34
0.34
0.30
0.31
As expected, a substantial deterioration in predicted accuracy is observed, as R2 decreased
for virtually all methods (compare with values in Table 7). A similar deterioration in
performance was observed when tolerance values compositional metrics were computed using
family-level identification. These results suggest that for the stressors considered here,
taxonomic identification to genus level provides indicators that are more closely associated with
observed stressor levels.
4.2. REFERENCE CONDITIONS
Reference conditions refer to streams or sites that are in their natural condition,
unaffected by human activities. These conditions establish the basis of comparison from which
we can evaluate the biotic condition of other streams (Bailey et al., 1998). Reference conditions
are often approximated within a study area using the "best" sites that are available, that is, sites
that are the least disturbed by human activities. Biological characteristics of assemblages in
these least-disturbed streams provide baseline expectations, and departures from these
expectations are often associated with human activities. With tolerance values, we can infer
stressor-specific characteristics of streams; however, we still need to know expected values for
these characteristics at the least-disturbed sites within the study area to determine whether
changes have occurred. The values of tolerance metrics and inference indices computed at least-
impacted sites determine this baseline distribution. Departures from this distribution then can
provide evidence for the existence of a particular stressor.
To demonstrate one approach for applying baseline conditions, we used 31 reference sites
in western Oregon, supplied by the Oregon DEQ (ODEQ, 2004). These sites were used to
compute reference distributions for all of the metrics that we have considered (RABN.TOL,
RABN.SEN, PTAX.TOL, PTAX.SEN) for temperature and fine sediment. We also used mean
WA tolerance values for sediment and temperature at reference sites. We then examined data
from a single, randomly selected site at which biological data had been collected but for which
other environmental data were not available. At this test site, we computed metric values for
38
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temperature and sediment and compared them with reference distributions (Figure 20). Test site
observations of temperature metric values were all located close to the median value observed
within reference sites. In contrast, test site observations of metric values for sediment departed
from reference distributions. More specifically, we observed that PTAX.SEN and RABN.SEN
were less than reference expectations, whereas PTAX.TOL, RABN.TOL, and WA were all
greater than reference expectations.
All of these indicators consistently suggest that sediment levels at the test site are
elevated and are influencing the macroinvertebrate assemblage. Sediment metrics also can
indicate an increase in temperature (as seen in Section 4.1.3.3), but in this case, the complete
absence of a change in the temperature-specific metrics seems to suggest that no change in
temperature has occurred. A follow-up visit to this site would be necessary to confirm whether
these inferences are accurate.
The results are somewhat surprising, given that the method was relatively crude. Note
though that this test involved only a single sample, and more samples are required to draw
substantive conclusions. Refining the descriptions of least-disturbed sites by grouping
biologically similar sites (Clarke et al., 2002) may further reduce the variability of the reference
distributions and improve the discriminatory power of tolerance metrics and indices. Also, in
cases where the presence of more than one stressor is indicated, we may have to examine the
magnitude of the effect of each stressor to identify the stressor that is responsible for the greatest
proportion of degradation.
39
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Temperature metrics
1.0 1
tn
CD
o
"CD 0.6
CT5
o 0.4
o
Q.
O
O
0.2 '
0.0 '
T
T
PTAX.SEN RABN.SEN PTAX.TOL RABN.TOL
Sediment metrics
WA
15
14
CD
_2
05
CD
O
c
05
13 -§
a) 0.6 '
15
.1 0-4 '
en
o
F 0.2 -
o
O
0.0 '
T
1
~i
j
r
L
;
A
= i
A
T
1
PTAX.SEN RABN.SEN PTAX.TOL RABN.TOL WA
30
27
23 -§
20
17
O5
(D
Figure 20. Comparison of temperature (top) and sediment (bottom)
tolerance metrics at a single test site (shown as a solid triangle) with
reference distributions (shown as box and whisker plots). Horizontal lines in
the boxes correspond to the 25th, 50th, and 75th percentiles of the reference
distribution. Whiskers extend away from the boxes a distance equal to two times
the distance between the 25th and 75th percentiles. Open circles represent samples
falling outside the range defined by the whiskers.
40
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5. AREAS OF UNCERTAINTY AND RESEARCH PRIORITIES
On the basis of the results shown in the previous section, stressor-specific tolerance
values appear to be a promising tool for monitoring the condition of streams and informing
diagnoses of the causes of impairment in streams. Broader application of this approach requires
the resolution of a few key areas of uncertainty: causal links between taxon occurrences and
environmental gradients must be established for tolerance values, stressor gradients of interest
must be clearly defined and measured, and basic ecological questions regarding the response of
stream communities to anthropogenic stress must be addressed.
5.1. CAUSAL RELATIONSHIPS
The tolerance values described in this report were all estimated from field data and
therefore are subject to the limitations imposed by such data. That is, the analysis of field data
provides only correlative relationships and does not necessarily provide any evidence of
causation. Thus, a tolerance value defined in terms of one stressor may, in fact, be an indicator
for a different, covarying stressor or natural gradient. Covariation among stressors is common.
The two stressors discussed extensively in this report—elevated stream temperature and
increased fine bedded sediment—can be strongly correlated when they originate from the same
human activity. For example, logging removes vegetative cover, which increases sediment
loading and also reduces shading to the stream (thus increasing stream temperature).
Furthermore, both temperature and fine sediment fraction increase naturally as high-gradient
mountain streams transition to low-gradient valley-bottom streams. Tolerance values can be
applied most effectively if they are specific to the stressor of interest; therefore, the effects of
covariation of variables must be controlled to whatever extent possible.
We briefly addressed the issue of correlated stressors in the previous section by
examining the specificity of the derived relationships and plotting relationships between
temperature tolerance metrics and observed fine sediment and between sediment tolerance
metrics and observed stream temperature. Results were mixed, but both sediment and
temperature tolerance metrics exhibited some strong relationships with the correlated stressor
gradient. Uncertainties regarding the causal relationships underlying some of the temperature
and sediment tolerance values do exist. Furthermore, these tests were limited in scope. It is very
possible that other, unsampled environmental gradients also could be correlated with the derived
tolerance metrics.
How then do we increase our confidence in the relationship between tolerance values and
the stressors for which they were derived? One approach is to compare taxon-environment
relationships across different data sets and different regions. We would expect environmental
41
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gradients in different regions to covary in different ways. Furthermore, if a particular taxon-
environment relationship truly represented the fundamental niche for a given taxon, then we
would expect it to remain similar regardless of location. Thus, if a given taxon-environment
relationship remained similar across different regions, we could be more confident that the
estimated taxon-environment relationship reflected an actual causal relationship. An example of
such a comparison is shown in Figure 21, where the relationship between probability of
occurrence of two genera, Glossosoma andMalenka, and stream temperature are plotted. Two
relationships for each genera are shown, one derived using EMAP-West data and one derived
using Oregon data. The shapes of the relationships for Glossosoma appear different: probability
of occurrence reached a maximum in Oregon at about 14°C, whereas it plateaued in EMAP-West
at 10°C and remained high for lower temperatures. However, occurrence probabilities in both
regions decreased as temperatures increased above 14°C. Taxon-environment relationships for
Malenha were very similar. Both peaked at approximately 15°C and decreased on either side of
the peak.
to
o
5
(C
p
CD
\
\
5 co
c: CD
(D
CO
d
.
S rN
0- CD
CD
CD
10 15 20 25
30
10 15 20 25
30
Temperature Temperature
Figure 21. Comparison of taxon-environment relationships for Glossosoma
and Malenha. Dashed line is relationship computed using Oregon data. Solid
line computed using date from EMAP-West.
These two examples highlight some of the difficulties inherent in comparing taxon-
environment relationships. First, the maximum probability of occurrence of a given taxon is
likely to be different across different regions, so taxon-environment relationships will be shifted
up or down on the plot relative to one another. Second, the range and distribution of
observations differ across regions, so we must attribute different levels of confidence to the
different parts of each curve. Further work is required to develop methods for more quantitative
comparisons. For now though, qualitative comparisons can provide some evidence of a common
42
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and causal response to a given gradient. For the cases shown in Figure 21, we would probably
attribute more confidence to a causal relationship between Malenka and temperature than
between Glossosoma and temperature.
As discussed in Section 3.3.4, the absolute values of tolerance values depend on the data
set from which they were derived, and comparing tolerance values across regions probably will
not yield insights into the strength of causal relationships. However, if tolerance values are
summarized using biological metrics and the relationships of these metrics with gradients in a
different region are examined (as with the examples shown in Section 4), these analyses can
provide further evidence of causality. Again, the reasoning here is that the covariance structure
of stressors differs across regions, and if tolerance metrics and inference indices derived using
data from one region are strongly correlated with the stressor of interest in a second region, then
it is more likely that the tolerance values reflect a true causal relationship.
Another approach for increasing the confidence assigned to correlative relationships is to
attempt to control for other possible sources of covariance by including additional variables in
regression models. The main weakness of this approach is that we cannot be sure that all
appropriate gradients are included or even that included gradients are appropriately modeled.
Furthermore, including some natural gradients may be counterproductive. For example, the size
of a stream is known to be strongly correlated with the type of organisms that are observed.
However, it is unlikely that stream size is the actual causal agent. Instead, stream size is
correlated with factors such as stream temperature and flow regime that directly influence the
abundance of different taxa. Thus, including some natural variables in our models can actually
impede our ability to accurately define taxon-environment relationships. Completely excluding
natural covariates is not a satisfactory solution either. If, for example, the stressor of interest is
stream temperature, then including stream size may partially control for the effects of flow
regime, which could be useful.
After covariates are included in models, the resulting taxon-environment relationship for
the stressor of interest can only be interpreted as being conditional on fixed values of the other
covariates. Thus, tolerance values based on these taxon-environment relationships are also
conditional on the values of the other covariates. This additional level of complexity in defining
tolerance values must be explored in detail and is beyond the scope of this report. In the analyses
presented here, we have used only a single explanatory variable in our models.
The strongest approach for increasing our confidence in causal relationships is to use
controlled experiments because responses determined through experiment provide powerful
evidence of causality. Laboratory experiments, however, are limited in the types of stressors that
can be tested and in the types of organisms that can be bred and they do not often replicate the
complexity of natural ecosystems. Thus, laboratory dosing tests can reveal that different
43
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macroinvertebrates undergo increased mortality at increased stress and show the different
physiological mechanisms that determine whether a particular species is tolerant or sensitive, but
these findings do not account for more complex ecological mechanisms (e.g., increased
predation, decreased competitive ability) that affect organism survival. A wealth of species-
specific sensitivity data that were developed from traditional laboratory toxicity tests are
available, and there is a great potential for using these data to inform and complement field-
derived tolerance values. However, more research is required to compare and contrast results
derived from laboratory experiments and those derived from field studies. Recent work
combining microcosm and field experiments have shown potential for bridging these gaps
(Clements, 2004).
5.2. DEFINING STRESSOR GRADIENTS
Another necessary step for broadening the applicability of tolerance values is developing
tolerance values for all of the stressors that are commonly observed in streams. In this report, we
have focused on elevated stream temperature and increased percentages of fine sediments as
examples of stressors. Previous efforts to develop tolerance values (e.g., Hilsenhoff, 1987) have
focused on nutrient enrichment and organic pollution gradients. Good data sets exist for some
stressors (e.g., increased metals and acidification), and the derivation of tolerance values using
the methods described in this report should be straightforward. More research will be required to
appropriately define and sample other common stressors before tolerance values can be
developed.
5.2.1. General-disturbance Gradients
The framework for the biological condition gradient (Davies, 2001) defines a set of
narrative descriptions of biological changes in response to a general human-disturbance gradient.
The response of sensitive and tolerant taxa figures prominently in this framework, but identifying
tolerant or sensitive taxa is hampered by the ambiguity inherent in defining a general human-
disturbance gradient. In this report, we have focused on stressor gradients that can be readily
quantified by field measurements. Unfortunately, no obvious environmental attribute or set of
attributes exists that can accurately define a general human-disturbance gradient. Various proxy
measures have been proposed, but all have important issues that must be resolved before they can
be applied to tolerance values. It has been suggested, for example, that a land use metric (e.g.,
percent urban land use in the catchment) provides a good proxy for the human-disturbance
gradient; indeed, in many cases, urban land use has served as a useful proxy for disturbance (e.g.,
Wang et al., 2001). However, the management decisions we hope to inform with tolerance
values are often concerned with directing future remediation efforts. If tolerance values are
44
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defined in terms of an urban gradient, then the only logical remediation or mitigation scheme
would be removal of the urban land use, an option that is rarely feasible. Thus, defining
tolerance values with regard to a land use gradient would not necessarily provide useful
suggestions for management. Moreover, the proxy measures of a human-disturbance gradient
would change between regions with different sets of dominant stressors; thus, no consistent
definition of the gradient or of the associated tolerance values would be possible.
An analytical approach for defining a general disturbance gradient would be to first apply
an ordination analysis (e.g., principle components analysis) to stressor data collected from the
study area and then estimate tolerance values with respect to the primary axis of the ordination.
For this exercise, the use of randomly collected data would be critical to accurately capture the
relative frequency with which different anthropogenic stressors affect streams within the study
area. The primary axis would then presumably capture a general disturbance gradient, and
tolerance values estimated with respect to this gradient would represent generally tolerant and
generally sensitive taxa for the study area. This approach would likely under-represent human
activities that may cause severe degradation but are limited in spatial extent. Furthermore,
natural gradients (e.g., elevation or catchment area) may confound the disturbance gradient
described by an ordination approach (as discussed in Section 5.1), so care should be taken to
select samples that minimize natural differences between streams.
An alternative to attempting to define a general disturbance gradient is the use of
tolerance values that do not require an explicit definition of a gradient. This type of approach has
not been described in this report because it differs fundamentally from methods based on taxon-
environment relationships. One such approach relies on predictive models (Hawkins, 2003) and
quantifies tolerance values from differences between an observed and a modeled frequency of
occurrence for a taxon. Thus, the relative tolerance value for a given taxon is based only on how
often the taxon is observed across an anthropogenically influenced study area relative to
reference expectations. If the tolerance values are derived using data that are collected in a
randomized design in a particular region, they could provide an accurate depiction of taxa that
increase and taxa that decrease in response to the dominant human activities in a region. In both
the predictive modeling and the ordination axis approaches, the general-disturbance tolerance
values derived would be unique to a particular region. This restriction seems reasonable, given
that dominant stressors differ between different regions. In contrast, the relative rankings of
tolerance and sensitivity derived with respect to individual stressor gradients would be expected
to be more stable between regions.
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5.2.2. Indirect Stressor Gradients
The models described in this report apply most effectively to environmental gradients that
directly influence the health and fecundity of a particular organism. These direct gradients would
include factors such as the temperature and acidity of the stream. Many other factors can
influence species survival but are difficult to measure directly. Usable physical habitat, for
example, is a requirement for all organisms, but a complete understanding of how different
stream macroinvertebrates utilize physical features in the stream is still lacking. We must
therefore resort to indirect measures to quantify many environmental gradients. The indirect
gradients for physical habitat may include measures of the percentage of fine sediment on the
stream bottom (Wood and Armitage, 1997) or measures of the quantity and distribution of large
woody debris (e.g., Lakly and McArthur, 2000). Another important indirect gradient is nutrient
concentration. High concentrations of nutrients generally do not directly influence
macroinvertebrates; rather, they alter the trophic status of a stream, placing certain insects at a
competitive disadvantage (Biggs, 2000). Taxon-environment relationships can be derived with
respect to any measured gradient, but the precision of the relationships, as well as their
applicability beyond the region in which they were derived, become more uncertain as the
mechanisms become less direct.
Resolving these issues requires that we improve our understanding of the mechanisms by
which different anthropogenic stressors affect stream biota. Tolerance values can then be defined
in terms of the appropriate proximal factor. With nutrients, for example, the optimal solution
may be to estimate tolerance values for different periphyton taxa instead of for
macroinvertebrates, because periphyton respond directly to nutrient concentrations in streams.
5.2.3. Sampling Issues
The number of stressors for which tolerance values can currently be defined is also
limited by the types of data that are readily available. Standard protocols for sampling streams
often rely on randomized sampling of riffles and a one-time visit to each stream. These protocols
constrain the types of stressors for which tolerance values can be derived. Randomized
sampling, while providing a statistical valid sample from which population statistics can be
estimated, does not always provide the best data for inferring taxon-environment relationships
because stressor gradients are also sampled in proportion to their distribution in the region. This
distribution would be suitable for computing tolerance values for some widely distributed
stressors. For other stressors that are not as prevalent, a randomized sampling design does not
provide enough samples at high levels of stress to accurately compute tolerance values. The
distribution of sediment measurements in the EMAP-West data (Section 4.1.3.1) provides a good
illustration of this phenomenon. Other sampling designs should be considered for such stressors.
46
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Riffles often contain the greatest density and diversity of macroinvertebrates, but sampling of
riffles can reduce our ability to discern the effects of stressors (such as sedimentation) that
initially would affect depositional areas in the stream. Depending on the stressor of interest,
different habitats may be more appropriate to sample. Transect designs, in which random
locations are sampled along prespecified reach transects, can also address this issue.
A one-time visit provides efficient sampling of a broad array of sites, but may not
provide information on stressors that have high temporal variability. Pulse additions of
sediment, toxicants, and nutrients are poorly quantified by a single visit. Understanding of such
stressors would be improved if sampled in temporally resolved studies. Other environmental
factors also exhibit high variability but can be effectively measured with a single grab sample as
long as the total number of samples is relatively high. For example, stream temperature varies
considerably on seasonal and daily cycles, so a single grab sample of temperature does not
necessarily provide useful information for a single stream. However, if one considers grab
temperature measurements from a large sample of streams, then the seasonal and daily variations
often are manifested as random noise, and useful patterns of taxon responses to temperature can
be extracted.
There is clearly much to be gained by analyzing existing data sets. However, directed
studies toward specific stressors, in which the samples are collected along the full gradient,
appropriate habitats are sampled, and temporal resolution of samples designed to accurately
characterize the stressor, would greatly enhance existing understanding of a broader array of
anthropogenic stressors. Other existing data sets collected with different designs and protocols
(e.g., Superfund) can potentially be mined. Controlled manipulations, either in the lab or in the
field, can supplement knowledge derived from field data, especially in cases where a well-
designed field sampling campaign to capture the same stressors is too costly.
5.3. FUNDAMENTAL ECOLOGY
The derivation and application of tolerance values are closely linked with a fundamental
understanding of stream ecology. Many uncertainties regarding tolerance values are also areas of
active research in stream ecology. Many examples of related basic ecological questions exist, but
here we focus only on two main areas: the role of biological interactions and the temporal
characteristics of stream ecosystems.
5.3.1. Biological Interactions
To derive tolerance values that are applicable beyond the immediate study area (see
Section 2.1), we need to assume that biological interactions are relatively unimportant and that
realized niches are similar to fundamental niches. These assumptions are broad and are likely
47
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violated in many cases. Different stream types will have different strengths of biological
interactions. For example, we would expect communities in streams with stable flow regimes to
be more strongly influenced by biological interactions than are communities in streams that are
disturbed by frequent floods (Allan, 1995). We would also expect certain taxa to be more subject
to biological interactions than others. A vast body of ecological research in both terrestrial and
aquatic systems exists that examines these effects (e.g., Ives, 1995). However, for the practical
purposes of applying tolerance values, we need specific guidelines on the types of streams and
the types of taxa for which biological interactions are likely to be important. Such specific data
are not widely available.
5.3.2. Temporal Characteristics of Stream Communities
Disturbance and recovery from disturbance are key factors in the structure of stream
communities. Stream communities are dynamic, constantly changing biological systems. Most
streams are exposed to strong, natural disturbances, and the stream community observed at any
point in time is a manifestation of the trajectory of recovery from the last major disturbance (e.g.,
flood). Other temporally influenced factors include natural cycles of hatching and emergence
and episodic anthropogenic disturbances, such as toxicant pulses. With regard to tolerance
values, we need to better understand the extent to which a single snapshot of a stream community
reflects a response to the environmental gradient of interest and the extent to which it reflects
temporally evolving factors. Other issues to be addressed include the extent to which the
conditions observed are a consequence of the initial conditions and zoogeographical history of
the stream and to what extent they are a consequence of legacy effects of past human activities.
All of these issues can potentially influence the generality of tolerance values derived from a
particular study area, and further research is required to identify scenarios in which temporally
evolving factors play an important role.
6. IMPLEMENTATION
As an assessment tool, tolerance values are applicable to many different aspects of water
quality management. They can help improve assessments of the condition of streams, identify
the sources of impairment for effective preparation of total daily maximum loads, and direct and
monitor restoration activities. Our intent in preparing this report was first to present and review
the methods for deriving tolerance values so that states and tribes can derive tolerance values for
use in their own programs. Second, our hope is that this report will lay the foundations for the
development of a national or several regional databases of tolerance values that can be used
48
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directly by states and tribes that may not have the resources to derive tolerance values from their
own data. For both of these objectives, two implementation issues must be addressed:
information management and taxonomic quality assurance.
6.1. INFORMATION MANAGEMENT
The applicability and utility of tolerance values would be vastly enhanced if analyses
conducted in different study areas were conveniently accessible. A repository of tolerance values
analyses would provide an opportunity for those developing their own tolerance values to
compare their results with others from similar locations. These comparisons would also help
accumulate evidence of causality, as described in Section 5.1. Finally, a database of tolerance
values (e.g., see Appendix C) could potentially be applied directly to assessment questions by
entities that do not have the resources to develop their own tolerance values. However, as
discussed earlier, a database of tolerance values may not be the most useful format for
assessments because absolute tolerance values vary with regional characteristics. The tolerance
values listed in Appendix C should be regarded as specific to the western United States and to
the range of conditions sampled in the data set. Storing information for the entire taxon-
environment relationship derived from different analyses would provide data that are more easily
compared between locations. Then, when tolerance values are required for assessment, the
stored taxon-environment relationships can be further processed.
A more ambitious vision of regional databases would involve storing and sharing the raw
data collected by different states, tribes, or regions. Pooling raw data collected by different
entities could lengthen the sampled environmental gradients of interest and increase sample
sizes, potentially increasing the accuracy of derived taxon-environment relationships.
Combining raw data however, requires that sampling protocols be compatible, and states differ in
the types of habitats they sample, the sampling intensity within those habitats, and the number of
individuals that they identify from each sample and in many other details of sampling procedures.
These differences must be reconciled before raw data can be effectively combined. Methods
exist for quantifying sampling differences (e.g., Cao et al., 2002) and reconciling different data
sets, so these issues are tractable. Providing a regional repository for raw data maybe less
immediately useful to state and tribal water quality programs.
6.2. TAXONOMIC QUALITY ASSURANCE
With tolerance values, assessments of site conditions can hinge on the presence or
absence of particular taxa, so ensuring the accuracy of taxonomic identifications is critically
important. Taxonomists are needed to catalogue the diversity of species in studies of biodiversity
(Blackmore, 2002). Unfortunately, fewer people are choosing taxonomy as field of study and
49
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there is a dearth of qualified taxonomists. A certification program for taxonomy could help
reinvigorate the field by raising the stature of the profession and establishing minimal levels of
expertise for taxonomists involved in biological assessment.
7. CONCLUSIONS AND RECOMMENDATIONS
Macroinvertebrate tolerance values have great potential for improving our ability to
effectively manage the waters of the United States. Tolerance values derive from fundamental
concepts of ecology and effectively represent variations in the relationships between different
species and environmental gradients of interest. In our review of methods for deriving and
applying tolerance values, we found that WA provides one of the simplest, most robust
approaches for estimating the relative sensitivity of different taxa. Weighted averages are
therefore recommended as a first estimate of the tolerance values for different taxa.
Other compositional metrics (e.g., relative abundance of sensitive taxa) provide
additional information regarding the effects of different stressors on stream assemblages and can
enhance diagnoses of the causes of impairment. However, these metrics require that differences
between sensitive and tolerant taxa be defined more clearly, and for this purpose, modeling the
taxon-environment relationship with GLMs or GAMs provides an invaluable tool. After taxon-
environment relationships are defined by regression models, different taxa can be categorized as
tolerant or sensitive on the basis of curve classification techniques, and then different
compositional metrics can be computed. An added benefit of explicitly modeling the taxon-
environment relationship is that the strength of the relationship between a particular taxon and a
particular environmental gradient can be quantified. Taxa that are only weakly associated with
the gradient of interest can then be excluded from use in metrics.
Tolerance values at both the family and the genus level were examined. Genus-level
values accounted for more variability in environmental observations; however, for certain
metrics, family-level identifications sufficed, and in all cases, family identifications still provided
useful information. We therefore recommend that organisms be identified to the finest
taxonomic level possible, but note that tolerance values can provide a useful tool for data
collected at coarser taxonomic resolutions.
Comparing the values of tolerance values metrics at test sites with baseline conditions at
least-impaired sites is a critical step for the effective application of tolerance values. Without
baseline conditions, it is difficult to establish expected values for tolerance value metrics and
therefore difficult to determine whether changes have occurred.
50
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To achieve the potential of tolerance values, more research is required to resolve specific
uncertainties regarding the importance of biological interactions and to expand our knowledge
base to all stressors that are important in streams. Research priorities include comparing and
contrasting species sensitivities derived from lab and field studies, mining existing databases to
derive tolerance value for other stressor gradients, and performing directed field studies for
stressors for which data do not currently exist.
On the practical side, the utility of tolerance values would be broadened if databases of
taxon-environment relationships were conveniently accessible, along with tools for deriving
different tolerance values from those taxon-environment relationships. Furthermore, a national
certification program for taxonomy would greatly strengthen the taxonomic basis for routinely
applying tolerance values in water quality management.
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APPENDIX A: ATTENDEES AT THE WESTERN TOLERANCE VALUES
WORKSHOP, CORVALLIS, OREGON (FEBRUARY 3-5, 2004)
Name
Steve Austin
Robert Bennetts
Wease Bollman
Darren Brandt
Daren Carlisle
Bruce Chessman
Will Clements
Bob Danehy
Doug Drake
Dave Feldman
Leska Fore
Jeroen Gerritsen
Rick Hafele
Jim Harrington
Chuck Hawkins
Lil Herger
Alan Herlihy
Shannon Hubler
Dave Huff
Susan Jackson
Jerry Jacobi
Phil Kauffman
Jeff Kershner
Tina Laidlaw
Phil Larsen
Dave Lenat
Gary Lester
Amanda Mays
Organization
Navajo Environmental Protection Agency
Greater Yellowstone Network
Rhithron Associates, Inc.
Idaho Department of Environmental Quality
U.S. Geological Survey
Center for Natural Resources, New South Wales Department of
Infrastructure, Planning and Natural Resources
Colorado State University
Weyerhauser
Oregon Department of Environmental Quality
Montana Department of Environmental Quality
Statistical Design
TetraTech
Oregon Department of Environmental Quality
California Game and Fish
Utah State University
U.S. EPA Region 10
Oregon State University
Oregon Department of Environmental Quality
Oregon Department of Environmental Quality
U.S. EPA Office of Water
New Mexico Department of Environmental Quality
U.S. EPA Office of Research and Development
U.S. Forest Service
U.S. EPA Region 8
U.S. EPA Office of Research and Development
North Carolina Department of Environment and Natural Resources
Eco Analysts
Council of State Governments
54
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Name
Sue Norton
Pete Ode
Yandong Pan
Mike Paul
Rob Plotnikoff
Amina Pollard
Andrew Rehn
Christina Relyea
Bobbye Smith
Patti Spindler
Jan Stevenson
Glenn Suter
Patti Tyler
John Van Sickle
Ian Waite
Lori Winters
Bob Wisseman
Lester Yuan
Jeremy ZumBerge
Organization
U.S. EPA Office of Research and Development
California Game and Fish
Portland State University
Howard University
Washington Department of Environmental Quality
U.S. EPA Office of Research and Development
California Game and Fish
Idaho State University
U.S. EPA Region 9
Arizona Department of Environmental Quality
Michigan State University
U.S. EPA Office of Research and Development A
U.S. EPA Region 8
U.S. EPA Office of Research and Development
U.S. Geological Survey
U.S. EPA Office of Research and Development
US EPA Office of Research and Development
Wyoming Department of Environmental Quality
55
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APPENDIX B: DATA DESCRIPTION
Two data sets were used to illustrate the analysis methods described in this report: one
contained data collected by the U.S. Environmental Protection Agency's Environmental
Management and Assessment Program-Western Pilot Project (EMAP-West) from 2000 to 2001,
and the other contained data collected in western Oregon by the Oregon Department of
Environmental Quality from 1999 to 2000 (Figures B-l and B-2). Both organizations used a
similar sampling protocol. A reach 40 times the wetted width of the stream was delineated for
sampling. Stream temperature was measured at the time of sampling. Substrate composition
was estimated by summarizing the size distribution of particles at five locations on 21 transects.
For the EMAP-West, macroinvertebrate samples were collected at eight randomized locations in
riffles using a modified D-frame kicknet (500 |_im mesh) by disturbing a 1 ft2 area for 30 seconds.
In Oregon, samples were collected by disturbing 2 ft2 areas at four randomized locations.
Samples from both studies were composited and spread on a gridded pan and picked from
randomly selected grid squares until at least 500 organisms were collected. Each organism was
then identified to the lowest possible taxonomic level (usually genus or species).
A total of 392 complete samples in EMAP-West and 271 complete samples from Oregon
were available for analysis.
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Figure B-l. Map of sampling locations for Western Environmental
Monitoring and Assessment Program (EMAP-West).
Figure B-2. Map of sampling locations in Oregon.
APPENDIX C: TOLERANCE VALUES
57
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Table C-l. Temperature tolerance values (°C) derived using EMAP-West data
Name
TROMBIDIFORMES
Atractides
Hygrobates
Lebertia
Protzia
Sperchon
Sperchonopsis
Testudacarus
Torrenticola
VENEROIDA
Pisidium
BASOMMATOPHORA
Physa
COLEOPTERA
Agabus
Cleptelmis
Dubiraphia
Eubrianax
Helichus
Heterlimnius
Hydraena
Lara
Microcylloepus
Narpus
Optioservus
Ordobrevia
Oreodytes
Psephenus
Zaitzevia
DIPTERA
Antocha
Atherix
Atrichopogon
Brillia
Cardiocladius
GLMMAX
2
11.9
15.7
11
15.1
17.1
29.1
14.6
29.1
16
16.8
7.7
11.9
29.1
14
16.8
17.1
16.5
22.3
16.5
13.8
29.1
29.1
8.6
19.8
GLMCL
S
I
I
I
I
I
T
I
T
I
I
I
I
T
I
I
I
I
I
I
I
T
T
I
I
GAMMAX
2
10.8
14.9
9.9
13.8
17.1
29.1
19.5
14
27.2
16.5
16.5
2
11.6
29.1
13.5
17.1
17.1
16
29.1
16
12.9
19.5
29.1
2
20.9
GAMCL
S
S
T
S
I
T
T
T
I
T
I
T
S
I
T
I
I
T
T
T
I
I
T
T
S
T
WA
14.5
14.7
12.8
12.9
14.3
14.4
12.2
14.2
15
16.9
15.5
14
16.8
15.4
15.6
10.9
14.6
12.1
19.2
13.7
14.9
16
15.2
18.7
14.8
13.6
16.2
16.9
12
17
CD75
17.4
17.6
15.2
15.2
17.8
16.3
14
16.2
18.2
19.5
19.5
15.7
19.8
17.3
17.3
13.2
17
14
22.9
15.7
17.5
18
16.5
21.3
17.3
15.5
18.2
20.7
14.6
19.6
58
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Table C-l. Temperature tolerance values (°C) derived using EMAP-West data
(continued)
Name
Chelifera
Chironomus
Cladotanytarsus
Clinocera
Corynoneura
Cricotopus
Cryptochironomus
Diamesa
Dicranota
Dicrotendipes
Dixa
Eukiefferiella
Glutops
Heleniella
Hemerodromia
Hexatoma
Hydrobaenus
Krenosmittia
Larsia
Limnophila
Limnophyes
Maruina
Micropsectra
Microtendipes
Nanocladius
Neoplasta
Nilotanypus
Oreogeton
Orthocladius
Pagastia
Parakiefferiella
Parametriocnemus
Paraphaenocladius
Paratanytarsus
Paratendipes
Parorthocladius
GLMMAX
2
29.1
29.1
2
10.8
29.1
29.1
2
2
29.1
12.4
2
7.5
2
22.3
14.3
2
2
2
29.1
2
20.3
15.1
16.5
29.1
2
2
5.6
11.6
2
17.6
29.1
2
GLMCL
S
T
T
S
I
T
T
S
S
T
I
S
I
S
I
I
S
S
S
T
S
I
I
I
T
S
S
I
I
S
I
T
S
GAMMAX
4.7
29.1
29.1
2
9.4
29.1
29.1
2
2
29.1
11.3
2
2
9.1
22.8
13.2
2
2
29.1
2
12.4
29.1
2
20.9
16.5
17.1
29.1
2
2
2
2
10.5
2
19
29.1
2
GAMCL
S
T
T
S
S
T
T
S
S
T
S
S
S
S
T
I
S
S
T
S
T
T
S
T
S
T
T
S
S
S
S
S
S
T
T
S
WA
12.3
17.7
16.6
10.7
13.2
15.2
17.6
11
13
18.8
13.1
13.4
10
12.6
17.3
13.9
9.8
10.4
15
12.6
14.4
17
12.6
16
14.3
15.5
18.6
10.2
12.1
11.9
13.4
13.6
10.5
15.7
17.1
10.3
CD75
14.6
22.9
19.5
12.7
15.3
18.8
21.5
13.1
15.6
20.3
15.2
16.1
11.7
14.7
19.6
16.1
12.7
12.4
19.6
15.2
17.3
21
15.1
18.9
18.2
18
20.9
11.9
14
14.7
17.8
16.3
12.9
19.1
22
12.5
59
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Table C-l. Temperature tolerance values (°C) derived using EMAP-West data
(continued)
Name
Pentaneura
Pericoma
Phaenopsectra
Polypedilum
Potthastia
Prosimulium
Pseudochironomus
Rheocricotopus
Rheotanytarsus
Simulium
Stempellina
Stempellinella
Synorthocladius
Tanytarsus
Th ienem anniella
Th ienem annim y ia
Tipula
Tvetenia
Wiedemannia
EPHEMEROPTERA
Acentrella
Ameletus
Baetis
Caenis
Caudatella
Cinygma
Cinygmula
Diphetor
Drunella
Epeorus
Ephemerella
Fallceon
Ironodes
Paralepto phleb ia
Rhithrogena
Serratella
GLMMAX
21.4
2
29.1
29.1
29.1
2
29.1
21.2
17.6
2
2
29.1
29.1
23.9
2
2
2
19.5
5.8
14
29.1
8.3
2
2
14
7.7
2
2
29.1
11.6
9.1
7.5
13.8
GLMCL
I
S
T
T
T
S
T
I
I
S
S
T
T
I
S
S
S
I
I
I
T
I
S
S
I
I
S
S
T
I
I
I
I
GAMMAX
24.4
2
20.6
29.1
17.9
2
29.1
11
25.3
17.6
2
2
29.1
29.1
29.1
2
2
8
20.6
2
13.8
29.1
6.7
2
2
13.8
6.4
2
2
29.1
11
2
3.4
13.2
GAMCL
T
S
T
T
T
S
T
S
T
T
S
S
T
T
T
S
S
S
T
S
S
T
S
S
S
I
S
S
S
T
S
S
S
I
WA
17.5
11
15.6
16
15.4
9.7
18.2
13.9
15.7
14.8
11.5
12.6
14.7
16.7
15
15.9
12.5
12.8
12.3
17
10.8
14.1
18.2
11.1
9.6
10.9
13.8
11.9
12.6
12.7
19.4
12.4
12.6
12.3
13.6
CD75
21.3
12.7
18.6
19.1
18.2
10.6
22.7
16.6
18.9
17.7
14
14.8
16.4
20.6
18.1
18.9
16.2
15.4
14.7
19.6
13.2
17
19.8
13
12.4
13.2
16.3
14
15.1
15.4
22.2
15.1
15
14.7
16
60
-------
Table C-l. Temperature tolerance values (°C) derived using EMAP-West data
(continued)
Name
Tricorythodes
HEMIPTERA
Ambrysus
LEPIDOPTERA
Petrophila
ODONATA
Argia
Ophiogomphus
PLECOPTERA
Calineuria
Despaxia
Doroneuria
Hesperoperla
Isoperla
Malenka
Megarcys
Pteronarcys
Skwala
Suwallia
Sweltsa
Visoka
Yoraperla
Zapada
TRICHOPTERA
Agapetus
Amiocentrus
Anagapetus
Apatania
Arctopsyche
Brachycentrus
Cheumatop sy che
Dicosmoecus
Dolophilodes
Ecclisomyia
Glossosoma
Helicopsyche
GLMMAX
29.1
29.1
29.1
22.5
29.1
15.7
11.3
9.1
12.9
14.6
7.5
13.8
2
2
5.3
6.7
8
2
15.7
2
2
11.6
11.3
28.6
29.1
2
2
9.7
29.1
GLMCL
T
T
T
I
T
I
I
I
I
I
I
I
S
S
I
I
I
S
I
S
S
I
I
I
T
S
S
I
T
GAMMAX
29.1
29.1
29.1
25
29.1
16
10.8
8
12.7
14.9
14.6
3.4
13.5
11.6
6.4
2
2
5.8
2
15.4
9.1
2
11.3
10.5
11.9
29.1
29.1
7.5
2
2
29.1
GAMCL
T
T
T
T
T
I
S
S
I
S
I
S
S
S
S
S
S
S
S
I
S
S
S
S
S
T
T
S
S
S
T
WA
18.5
18.9
20.5
18.5
18.5
14.8
11.8
11
13.2
13.8
14
9.8
13.6
13.3
11.5
11.4
10
10.9
11.7
14.8
13
10.2
12
12.2
13.3
18.9
15.7
11.6
10.3
12.2
17.2
CD75
22.4
22.7
23.8
22
24.5
17
13.1
13.2
15.2
17.4
16.1
11.7
16
15.6
13.2
13.6
11.9
13.1
14.1
16.3
15.1
12.4
13.4
13.7
16
22.7
20.7
13.1
11.9
14.9
20.4
61
-------
Table C-l. Temperature tolerance values (°C) derived using EMAP-West data
(continued)
Name
Hydropsyche
Hydroptila
Lepidostoma
Micrasema
Neophylax
Neothremma
Ochrotrichia
Oecetis
Oligophlebodes
Parapsyche
Polycentropus
Rhyacophila
Wormaldia
AMPHIPODA
Hyalella
TRICLADIDA
Polycelis
GLMMAX
22.3
22.5
12.1
8.8
11.9
6.4
29.1
29.1
9.1
6.9
29.1
2
17.1
20.1
2
GLMCL
I
I
I
I
I
I
T
T
I
I
T
S
I
I
S
GAMMAX
24.7
25
11.9
7.5
11
2
29.1
29.1
7.7
2
29.1
2
16.8
21.2
2
GAMCL
T
T
S
S
S
S
T
T
S
S
T
S
I
T
S
WA
16.4
17.8
13.1
12.9
12.7
9.5
17.5
16.6
10.5
11.4
17.6
11.9
15.3
16.5
10.4
CD75
19.2
20.4
15.7
15.6
14.9
10.5
20.6
22.9
12.1
14.2
20.4
14.8
17.8
19.1
12.4
CD75 = cumulative 75 percentile
GAMCL = generalized additive model - curve shape class
GAMMAX = generalized additive model - maximum point (optimum)
GLMCL = generalized linear model - curve shape class
GLMMAX = generalized line model - maximum point (optimum)
I = intermediately tolerant
S = sensitive
T = tolerant
WA = weighted averaging
62
-------
Table C-2. Sediment tolerance values (percent sands and fines) derived from EMAP-West
data
Name
TROMBIDIFORMES
Atractides
Hygrobates
Leb ertia
Protzia
Sperchon
Sperchonopsis
Testudacarus
Torrenticola
VENEROIDA
Pisidium
BASOMMATOPHORA
Physa
COLEOPTERA
Agabus
Cleptelmis
Dubiraphia
Eubrianax
Helichus
Heterlimnius
Hydraena
Lara
Microcylloepus
Narpus
Optioservus
Ordobrevia
Oreodytes
Psephenus
Zaitzevia
DIPTERA
Antocha
Atherix
Atrichopogon
Brillia
Caloparyphus
Cardiocladius
GLMMAX
0
0
0
0
21.6
0
97.1
97.1
97.1
97.1
11.8
0
0
34.3
0
97.1
0
0
7.8
0
25.5
0
33.4
24.5
GLMCL
S
S
S
S
I
S
T
T
T
T
I
S
S
I
S
T
S
S
I
S
I
S
I
I
GAMMAX
15.7
97.1
0
0
0
17.7
0
97.1
97.1
97.1
35.3
97.1
7.8
0
32.4
32.4
22.6
30.4
0
37.3
0
0
0
0
19.6
0
31.4
25.5
GAMCL
S
T
S
S
S
S
S
T
T
T
T
T
S
S
S
T
S
S
S
T
S
S
S
S
S
S
S
S
WA
22.9
31.2
22.4
14.4
25.9
19.6
19.3
16.1
42.5
38.3
39.4
26.4
55.7
12.6
24.6
20.7
25.5
22.7
29.6
22
26.3
10
29.9
17.4
20
15
14.2
21.8
20.2
25.9
20.9
CD75
34.3
41
29.8
19.2
37.1
25.7
27.6
22.1
67
57.1
56.2
38
74.3
17.1
35.2
29.5
36.2
32.4
34.3
35
37.1
12.4
37.1
24.8
27.6
21.9
16.2
37.1
31.4
36.2
29.5
63
-------
Table C-2. Sediment tolerance values (percent sands and fines) derived from
EMAP-West data (continued)
Name
Chelifera
Chironomus
Cladotanytarsus
Clinocera
Corynoneura
Cricotopus
Cryptochironomus
Diamesa
Dicranota
Dicrotendipes
Dixa
Eukiefferiella
Glutops
Heleniella
Hemerodromia
Hexatoma
Hydrobaenus
Krenosmittia
Larsia
Limnophila
Limnophyes
Maruina
Micropsectra
Microtendipes
Nanocladius
Neoplasta
Nilotanypus
Oreogeton
Orthocladius
Pagastia
Parakiefferiella
Parametriocnemus
Paraphaenocladius
Paratanytarsus
Paratendipes
Parorthocladius
GLMMAX
23.5
97.1
97.1
0
0
97.1
80.5
0
97.1
0
0
0
97.1
0
97.1
97.1
97.1
16.7
0
0
97.1
0
16.7
62.8
0
97.1
97.1
0
GLMCL
I
T
T
S
S
T
I
S
T
S
S
S
T
S
T
T
T
I
S
S
T
S
I
I
S
T
T
S
GAMMAX
21.6
97.1
97.1
0
0
97.1
86.3
0
97.1
0
17.7
0
64.8
0
74.6
97.1
97.1
14.7
0
60.8
0
97.1
0
10.8
70.6
29.4
0
97.1
0
GAMCL
S
T
T
S
S
T
T
S
T
S
S
S
T
S
T
T
T
S
S
S
T
S
S
T
S
S
T
S
WA
22.3
45.9
36
19.2
23.9
31
55.3
12.7
28.9
53.7
23.6
22.7
20.2
19.6
33.7
20.7
23.1
24
34.1
31.8
33.4
16.8
21.7
27.2
28.2
19.4
33.8
16.2
24.8
20.5
37.6
26.6
23.2
44.1
33.7
15.9
CD75
32.4
58.1
57.1
27.6
34.3
47.6
68.6
17.1
40
74
36.2
32.4
27.6
28.6
55.2
28.6
33.3
33.7
45.7
51.4
46.7
24.8
31.4
36.2
49
34.3
55.2
17.1
38.1
30.5
57.1
35.2
35
60
50.5
24.8
64
-------
Table C-2. Sediment tolerance values (percent sands and fines) derived from
EMAP-West data (continued)
Name
Pentaneura
Pericoma
Phaenop sectra
Polypedilum
Potthastia
Prosimulium
Pseudochironomus
Rheocricotopus
Rheotanytarsus
Simulium
Stempellina
Stempellinella
Synorthocladius
Tanytarsus
Th ienem anniella
Th ienem annim y ia
Tipula
Tvetenia
Wiedemannia
EPHEMEROPTERA
Acentrella
Ameletus
Baetis
Caenis
Caudatella
Cinygma
Cinygmula
Diphetor
Drunella
Epeorus
Ephemerella
Fallceon
Ironodes
Nixe
Paralepto phleb ia
Rhithrogena
GLMMAX
97.1
97.1
97.1
0
0
49.1
0
97.1
97.1
0
21.6
97.1
97.1
65.7
0
0
0
0
64.8
0
97.1
0
0
0
0
97.1
0
0
0
GLMCL
T
T
T
S
S
I
S
T
T
S
I
T
T
I
S
S
S
S
I
S
T
S
S
S
S
T
S
S
S
GAMMAX
97.1
97.1
69.7
0
0
50
0
77.5
85.4
0
22.6
97.1
97.1
73.6
0
0
97.1
0
0
72.6
0
97.1
0
0
0
0
97.1
0
97.1
0
0
GAMCL
T
T
T
S
S
T
S
T
T
S
S
T
T
T
S
S
T
S
S
T
S
T
S
S
S
S
T
S
S
S
WA
34.5
25.6
33.2
30.1
12.6
18
33.3
22.5
27.4
28.8
33.2
20
19.5
36.3
28
31.7
40.9
22.5
13.5
27
19.7
24.2
54.2
14.2
32.5
17.8
21.7
16.7
13.3
23.9
42.1
15.8
27.5
21.7
12
CD75
54.3
39.7
54.3
50.5
18.1
26.9
45.7
31.4
40
40
55.2
26.9
30.5
58.1
38.1
49
57.1
32.4
20
45.7
29.5
34.3
68.6
21
46.7
26.9
32.4
25.7
20
31.4
60.6
26.1
36.2
32.4
16.2
65
-------
Table C-2. Sediment tolerance values (percent sands and fines) derived from
EMAP-West data (continued)
Name
Serratella
Tricorythodes
HEMIPTERA
Ambrysus
LEPIDOPTERA
Petrophila
ODONATA
Argia
Ophiogomphus
PLECOPTERA
Calineuria
Despaxia
Doroneuria
Hesperoperla
Isoperla
Malenka
Megarcys
Pteronarcys
Skwala
Suwallia
Sweltsa
Visoka
Yoraperla
Zapada
TRICHOPTERA
Agapetus
Amiocentrus
Anagapetus
Apatania
Arctopsyche
Brachycentrus
Cheumatop sy che
Dicosmoecus
Dolophilodes
Ecclisomyia
Glossosoma
GLMMAX
0
97.1
48.1
97.1
97.1
0
0
12.8
0
37.3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
31.4
61.8
19.6
0
0
0
GLMCL
S
T
I
T
T
S
S
I
S
I
S
S
S
S
S
S
S
S
S
S
S
S
S
S
I
I
I
S
S
S
GAMMAX
0
97.1
47.1
30.4
97.1
73.6
0
0
0
0
35.3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
31.4
70.6
17.7
0
0
0
GAMCL
S
T
T
S
T
T
S
S
S
S
I
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
T
S
S
S
S
WA
18.1
39.5
37
25.1
40.4
39.1
12.8
16.1
17.8
18.2
28.4
23.9
13.7
14.4
21.4
12.9
17.3
16.6
19
21.2
22
19.8
15
15.2
11.3
24.6
39.4
17.7
14.6
14
16.9
CD75
25.7
60.6
47.6
33.7
66.7
62.7
17.9
24.4
26.9
27.6
36.2
34.3
15.2
26.7
30.5
17.1
24.4
26.9
27.6
31.4
26.7
31.4
26.1
18.1
14.3
35.2
60.6
26.7
26.1
20
26.7
66
-------
Table C-2. Sediment tolerance values (percent sands and fines) derived from
EMAP-West data (continued)
Name
Gumaga
Helicopsyche
Hydropsyche
Hydroptila
Lepidostoma
Micrasema
Neophylax
Neothremma
Ochrotrichia
Oecetis
Oligophlebodes
Parapsyche
Polycentropus
Rhyacophila
Wormaldia
AMPHIPODA
Hyalella
TRICLADIDA
Polycelis
GLMMAX
0
71.6
0
0
0
18.6
27.5
49.1
0
0
0
0
0
86.3
0
GLMCL
S
I
S
S
S
I
I
I
S
S
S
S
S
I
S
GAMMAX
0
35.3
97.1
0
0
0
18.6
23.5
57.9
0
0
0
0
12.8
97.1
0
GAMCL
S
T
T
S
S
S
S
S
T
S
S
S
S
S
T
S
WA
21.2
29.9
28.1
38.1
18.7
21.8
15.3
16.9
22.8
36.1
16.2
17.5
20.1
18
20
58.3
19.9
CD75
28.6
38.1
41
55.2
27.6
32.4
21.9
23.5
33.3
58.1
20
26.7
29.5
26.7
27.6
76.2
29.5
CD75 = cumulative 75th percentile
GAMCL = generalized additive model - curve shape class
GAMMAX = generalized additive model - maximum point (optimum)
GLMCL = generalized linear model - curve shape class
GLMMAX = generalized line model - maximum point (optimum)
I = intermediately tolerant
S = sensitive
T = tolerant
WA = weighted averaging
67
-------
APPENDIX D: EXAMPLE STATISTICAL SCRIPTS
This appendix provides short scripts that perform the statistical analyses described in the report.
R, a free software package for statistical computations, is used for these computations. More
information on R and the package itself are available from http://www.r-project.org/. If you wish
to run the scripts provided in this section, please visit the R web page and install R on your
computer.
D.I. R: BASIC SYNTAX
Variable names in R can be composed of combinations of letters, numbers, and periods. They
are case sensitive.
x, y, X, Y, flow.rate
(Note that in this and all subsequent sections, R commands can be run by typing text directly into
the R Console window. R commands are shown in the Courier font.)
Use the assignment operator, <-, to assign a value to a variable.
x <- 1 # Assign a single value to the variable x
x <- c(l,3,2) # Assign a vector of numbers to x
x <- c(T,F,T) # Assign a vector of logical values to x
x <- list(colors = c ( " r e d " , "blue", "black"), numbers = c(l,3))
# Assign a list of dissimilar objects to x
(Comments are preceded with a "#" and are ignored by R.)
The value of any variable can be examined by typing the variable name, or by using the print
command:
print(x)
Simple mathematical and statistical operations can be performed on different vectors.
x + y # Addition
x - Y # Subtraction
x * Y # Multiplication
x / Y # Division
mean(x) # Arithmetic mean
var(x) # Variance
sum(x) # The sum of all the elements of x
68
-------
The most commonly used format for storing data is the data frame, which is a list of objects of
the same length. Data frames allow one to combine logical, numerical, and factor data in a single
data structure.
site.name <- cC"A", "B", "C", "D") # A site label stored as a
# factor
pH <- c(7.6, 6.0, 4.0, 8.2) # Site pH stored as a
# numerical vector
abund.baetis <- c(103, 204, 602, 301) # Baetis abundance stored as
# a numerical vector
sampled.spring <- c(T, T, F, T) # Sampling season stored as a
# logical vector
all.data <- data.frame(site.name, pH, abund.baetis, sampled.spring)
# All data combined together
# as a data frame
The elements of a vector can be referred to in a variety of ways.
x[l] # The first element of the vector x
x[l:3] # The first three elements of vector x
x[c(T,T,F)] # The first two elements of x (assuming that x
# has three elements)
x[-l] # All of x except for the first element
We can also refer to different subsets of a data frame in a variety of ways.
all.data$pH # The element labelled "pH" from the data frame
# all.data
all.data[, "pH"] # The same column labelled "pH"
all.data[, 2] # The second column of the data.frame
all . data [ 1,] # The first row of the data.frame
Within R, you can access help pages on a particular command by typing,
help ()
For example:
help(glm)
help(mean)
D.2. LOADING DATA
Data formatted as tab-delimited text can be loaded easily with,
data.set <- read.delim() # Loads a tab-delimited data file
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A typical site-environment file would contain the environmental data for each site listed in each
row of the file, with each field delimited with tabs:
SITE.ID TEMP SED
A 13 40
B 17 20
C 15 10
In the above example, data on stream temperature (TEMP) and fine sediment (SED) is recorded
for each site.
A typical site-species file would contain the abundances of different species observed at a site:
SITE.ID BAETIS MALENKA ...
A 55 3
B 22 10
C 4 0
Assuming that both site-species and site-environment data are available as tab-delimited text
files, they can be loaded into R with the following commands.
# Load tab-delimited files
site.species <- read.delim("site.species.txt")
env.data <- read.delim("env.data.txt")
ls() # Check to see if new data frames are listed
The two data sets can be merged into a single data frame (matching environmental and biological
data) with the following command:
dfmerge <- merge(site.species, env.data, by = "SITE.ID")
D.3. ESTIMATING TOLERANCE VALUES FROM FIELD DATA
D.3.1. Weighted Averages
The basic formula for a weighted average tolerance value (eqn 1) can be represented in R as
follows:
WA <- sum (Y*x) /sum(Y)
where Y is a vector containing the abundance of the taxon of interest at each sample. Y can also
contain presence/absence data coded as 1 for present and 0 for absent, x is vector containing the
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value of the environmental variable of interest at each sample, and sum computes the sum of the
values of a numerical vector.
Use a for loop to create weighted averages for many different taxa using previously loaded data.
To run this script, first make sure that you have loaded biological data and merged them into a
single data frame (see previous section).
First designate the taxa for which you want to compute tolerance values.
taxa.names <- c("ACENTRELLA", "DIPHETOR", "AMELETUS")
The for loop then repeats the computation for each of the selected taxa.
WA <- rep(NA, times = length (taxa.names))
# Define a WA to be vector of a length the same as the
# number of taxa of i:
for (i in 1:length(taxa.names)) {
WA[i] <- sum(dfmerge[,taxa.names[i]]*dfmerge$ temp)/
sum(dfmerge[,taxa.names[i]])
}
names(WA) <- taxa.names
print(WA)
D.3.2. Cumulative Percentiles
Use a for loop similar to that used for weighted averages to compute cumulative percentile
tolerance values (eqn 2) for different taxa:
# Define a storage vector for the cumulative percentile
CP <- rep(NA, times = length(taxa.names))
# Sort sites by the value of the environmental variable
dftemp <- dfmerge[order(dfmerge$temp), ]
# Select a cutoff percentile
cutoff <- 0.75
# Specify three plots per page
par(mfrow = c(l,3), pty = "s")
for (i in 1:length(taxa.names)) {
# Compute cumulative sum of abundances
csum <- cumsum(dftemp[,taxa.names[i] ] )/sum(dftemp[,taxa.names[i] ] )
# Make plots like Figure 5
plot (dftemp$temp, csum, type = "1", xlab = "Temperature",
ylab = "Proportion of total", main = taxa.names[i])
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# Search for point at which cumulative sum is 0.75
ic <- 1
while (csum[ic] < 0.75) ic <- ic + 1
# Save the temperature that corresponds to this
CP[i] <- df temp$temp [ic]
}
names (CP) <- taxa. names
print (CP)
D.3.3. Parametric Regressions
Parametric regressions for presence/absence of different taxa (eqn 3) can be computed as
follows. We store each model in a list.
# Create storage list
modlist.glm <- as . list ( rep (NA, times = length ( taxa . names )))
for (i in 1 : length ( taxa . names )) {
# Create a logical vector that is true if taxon is
# present and false if taxon is absent.
resp <- df merge [, taxa . names [ i ]] >0
# Fit the regression model and store the results in a list.
# Here, poly(temp,2) specifies that the
# model is fitting using a second order polynomial of the
# explanatory variable. glm calls the function that fits
# Generalized Linear Models. We specify in this case that
# the response variable is distributed binomially.
modlist . glm [ [ i ] ] <- glm(resp ~ poly ( temp , 2 ) , data = dfmerge,
family = "binomial")
print ( summary (modlist. glm [ [i] ] ) )
Plot model results (similar to Figure 6) as follows.
par (mf row = c(l,3), pty = "s") # Specify 3 plots per page
for (i in 1 : length ( taxa . names )) {
# Compute mean predicted probability of occurrence
# and standard errors about this predicted probability.
predres <- predict (modlist . glm [[ i ]], type= "link", se.fit = T)
# Compute upper and lower 90% confidence limits
up . bound . link <- predres$fit + 1 . 65*predres$ se . f it
low . bound . link <- predres$fit - 1 . 65*predres$ se . f it
mean . resp . link <- predres$fit
# Convert from logit transformed values to probability.
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up. bound <- exp (up. bound. link) / ( 1+exp (up. bound. link))
low. bound <- exp (low. bound. link) / (1+exp (low. bound. link) )
mean.resp <- exp (mean. resp. link) /(1+exp (mean. resp. link))
# Sort the environmental variable.
lord <- order ( dfmerge$ temp )
# Define bins to summarize observational data as
# probabilities of occurrence
# Define the number of bins
nbin <- 20
# Define bin boundaries so each bin has approximately the same
# number of observations.
cutp <- quantile (df merge$ temp,
probs = seq(from =0, to = 1, length = 20) )
# Compute the midpoint of each bin
cutm <- 0 . 5* (cutp [-1 ] + cutp[-nbin])
# Assign a factor to each bin
cutf <- cut (dfmerge$ temp, cutp, include . lowest = T)
# Compute the mean of the presence/absence data within each
# bin.
vals <- tappl y (df merge [, taxa . names [ i ]] > 0, cutf, mean)
# Now generate the plot,
# Plot binned observational data as symbols.
plot (cutm, vals, xlab = "Temperature",
ylab = "Probability of occurrence", ylim = c(0,l),
main = taxa . names [ i ])
# Plot mean fit as a solid line.
lines (df merge $ temp [lord] , mean. resp [lord] )
# Plot confidence limits as dotted lines.
lines (dfmerge$ temp [lord], up.bound[iord], Ity = 2)
lines (dfmerge$ temp [lord], low. bound [lord], Ity = 2)
D.3.4. Nonparametric Regression
Nonparametric regressions (eqn 5) can be computed with a set of commands similar to those
of parameteric regressions.
library(gam) # Load GAM library
modlist.gam <- as. list (rep (NA, times = length (taxa. names)))
for (i in 1 : length ( taxa . names ) ) {
# Create a logical vector that is true if taxon is
# present and false if taxon is absent.
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# Fit the regression model, specifying two degrees of freedom
# to the curve fit.
modlist.gam[[i]] <- gam(resp ~ s(temp, df = 2 ) , data = dfmerge,
family = "binomial")
print ( summary(modlist.gam[ [i] ] ) )
Plot model results (similar to Figure 8) as follows.
par(mfrow = c(l,3), pty = " s " )
for (i in 1 : length(taxa.names) ) {
predres <- predict(modlist.gam[[i]], type= "link", se.fit = T)
up.bound.link <- predres$fit + 1.65*predres$se.fit
low.bound.link <- predres$fit - 1.65*predres$se.fit
mean.resp.link <- predres$fit
up.bound <- exp(up.bound.link)/(1+exp(up.bound.link))
low.bound <- exp(low.bound.link)/(1+exp(low.bound.link))
mean.resp <- exp(mean.resp.link)/(1+exp(mean.resp.link))
lord <- order(dfmerge$temp)
nbin <- 20
cutp <- quantile(dfmerge$temp, probs = seq(from = 0, to = 1,
length = 20))
cutm <- 0.5*(cutp[-l] + cutp [-nbin])
cutf <- cut(dfmerge$temp, cutp, include.lowest = T)
vals <- tapply(dfmerge[, taxa.names[i]] > 0, cutf, mean)
plot(cutm, vals, xlab = "Temperature",
ylab = "Probability of occurrence", ylim = c(0,l),
main = taxa.names[i])
lines (dfmerge$ temp[lord] , mean.resp[lord] )
lines(dfmerge$ temp[lord], up.bound[iord], Ity = 2)
lines(dfmerge$ temp[lord], low.bound[lord], Ity = 2)
D.3.5. Assessing Model Fit
The area under the ROC curve for each model can be computed by first imagining a pair of
sites where the species of interest is present at one site and absent at the other. We would
expect the probabilities of occurrence predicted by the regression model would be greater at
the site where the species is present than at the site where the species is absent. The area
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under the ROC is equivalent to the proportion of all such pairwise comparisons in which this
condition is satisfied. The following script performs this computation.
# Define storage vector for ROC
roc <- rep (NA, times = length ( taxa . names ))
for (i in 1 : length ( taxa . names )) {
# Compute mean predicted probability of occurrence
predout < - predict (modlist.glm[[i]], type = "response")
# Generate logical vector corresponding to presence/absence
resp <- dfmerge[, taxa.names[i]] > 0
# Divide predicted probabilities into sites where
# species is present ( " x " ) and sites where the species is
# absent ( " y " ) .
x <- predout [ resp ]
y <- predout [! resp]
# Now perform all pairwise comparisons of x vs. y
# and store results in a matrix
rocmat <- matrix(NA, nrow = length(x), ncol = length(y))
for (j in l:length(x)) {
rocmat [j,] <- as.numeric(x[j] > y)
# Summarize all comparisons to compute area under ROC
roc[i] <- sum(rocmat)/(length(x)*length(y))
}
names (roc) <- taxa. names
print ( roc )
D.3.6. Optima
The optimum tolerance value can be found by identifying the maximum point on the fitted
regression curve.
opt <- rep (NA, times = length ( taxa . names ))
for (i in 1 : length ( taxa . names )) {
predout <- predict (modlist . glm [[ i ]], type = "response")
# Find the index number of the maximum probability
imatch <- match (max (predout ), predout)
# The optimum is value of the environmental variable
# at the maximum probability.
opt[i] <- dfmerge$ temp [ imatch ]
}
names (opt) <- taxa. names
print ( opt )
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D.3.7. Curve Shape
Curves shapes can be classified into increasing, decreasing, or unimodal, by comparing the
mean responses to the confidence intervals. Note that unimod . test is an R function, a
series of commands that is executed when unimod. test is called.
unimod . test <- f unction (mnr, ubnd, Ibnd) {
# Find the maximum and minimum predicted mean probabilities
Imax <- max (mnr)
Imin <- min(mnr)
# Find index locations for these probabilities
imax <- match (Imax, mnr)
imin <- match(lmin, mnr)
x . out <- F
y . out <- F
# Compare mean predicted probability to the left of maximum point
# with upper confidence bound. Store a T in x.out if
# any point in the mean response deviates from the
# upper confidence limit
i f ( imax > 1 ) {
x.out <- sum(lmax == pmax(lmax, ubnd[l:(imax-l)])) > 0
# Store a T in y.out if any point in the mean probability
# to the right of the maximum point deviates from the upper
# confidence limit
if (imax < length(ubnd) ) {
y.out <- sum(lmax == pmax(lmax,
ubnd [ (imax+1) : length (ubnd) ] ) ) > 0
# Perform same set of tests for lower confidence limit
a . out <- F
b . out <- F
if (imin > 1) {
a. out <- sum(lmin == pmin(lmin, lbnd[l:(imin-l)])) > 0
}
if (imin < length ( Ibnd) ) {
b.out <- sum(lmin == pmin(lmin,
Ibnd [ (imin+1 ): length (Ibnd) ])) > 0
# The information on where the mean curve deviates from the
# confidence limits tells us its curve shape. . .
if (x . out & y . out ) {
return ("Unimodal")
if (a.out & b.out) {
return("Concave up")
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if (x.out | b.out) {
return ("Increasing")
}
if (y.out | a. out) {
return ("Decreasing")
}
if (! (x.out | y.out I a. out | b.out)) {
return (NA)
told <- repC"", times = length ( taxa . names ))
for (i in 1 : length ( taxa . names )) {
predres <- predict (modlist . gam [[ i ]], type= "link", se.fit = T)
# Compute upper and lower 90% confidence limits
up . bound . link <- predres$fit + 1 . 65*predres$ se . f it
low . bound . link <- predres$fit - 1 . 65*predres$ se . f it
mean . resp . link <- predres$fit
# Convert from logit transformed values to probability.
up. bound <- exp (up . bound . link) /( 1+exp (up . bound . link) )
low. bound <- exp ( low . bound . link) /( 1+exp ( low . bound . link) )
mean. resp <- exp (mean . resp . link) /( 1+exp (mean . resp . link) )
# unimod.test requires that the responses be sorted by
# the value of the environmental variable.
lord <- order (dfmerge$ temp )
tolcl[i] <- unimod . test (mean . resp [ lord] , up . bound [ lord] ,
low . bound [ lord] )
}
names (told) <- taxa. names
print ( told )
D.4. APPLYING TOLERANCE VALUES IN ASSESSMENT
In this section metric values are computed using the same data from which the tolerance
values were calculated. Typically, one would develop tolerance value using a calibration data
set, and then compute metrics for a second, independent set of test data.
First, expand the list of taxa to include all taxa in the data set that occur in at least 20 sites.
# Get names of all taxa in the data set
taxa.names.init <- names(site.species) [-1]
# Compute the number of occurrence of each taxon
getocc <- function(x) sum(x>0)
numocc <- apply(site.species [, taxa.names.init], 2, getocc)
# Save all taxa names that occur in at least 20 sites
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taxa.names <- taxa.names.init[numocc >= 20]
Now, recompute nonparametric regression and curve classifications for this expanded list of
taxa.
D.4.1. Richness
The richness of sensitive taxa can be computed as follows:
# Select only taxa for which tolerance values have been computed.
matl <- as.matrix(dfmerge[, taxa.names])
# Convert data to presence-absence.
mat2 <- as.numeric(matl > 0)
dim(mat2) <- dim(matl)
# Select sensitive taxa
sens <- as.numeric(told == "Decreasing")
# %*% performs a matrix multiplication, which gives the taxa
# present at a site that were classified as intolerant
sens.rich <- mat2 %*% sens
# Plot resulting metric against observed temperature.
plot(dfmerge$temp, sens.rich, xlab = "Temperature",
ylab = "Sensitive richness")
The same operation can be repeated to compute the richness of tolerant taxa.
D.4.2. Proportion Total Taxa
The proportion of observed taxa that are sensitive taxa can be computed using the sensitive
richness computed in the last section.
tot.rich <- apply(mat2, 1, sum) # Compute total richness
# The command "apply" applies the same operation to the
# rows or columns of a matrix.
# In this case, we compute the sum for each of the rows
# of the matrix.
# The proportion of taxa sensitive is computed with
# simple division.
ptax.sens <- sens.rich/tot.rich
# Plot resulting metric against observed temperature.
plot(dfmerge$temp, ptax.sens, xlab = "Temperature",
ylab = "Proportion taxa")
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D.4.3. Relative Abundance
The relative abundance of sensitive taxa can be computed as follows:
# have been computed.
mat1 <- as.matrix(dfmerge[, taxa.names])
# Select sensitive taxa
sens <- as.numeric(told == "Decreasing")
# Use matrix multiplication to compute the number of
# sensitive individuals collected
abn.sens <- matl %*% sens
# Compute total abundance.
abn.tot <- apply(matl, 1, sum)
# Compute relative abundance of sensitive taxa
relabn.sens <- abn.sens/abn.tot
# Plot resulting metric against observed temperature.
plot(dfmerge$temp, relabn.sens, xlab = "Temperature",
ylab = "Relative abundance")
The same operation can be repeated to compute the relative abundance of tolerance taxa.
D.4.4. Mean Tolerance Value
First, compute weighted averages or another continuous tolerance value for the expanded list
of taxa.
The mean tolerance value observed at a site can be computed as follows,
# Only select taxa for which tolerance values
# have been computed.
matl <- as.matrix(dfmerge[, taxa.names])
# First get total abundance
tot.abn <- apply(matl, 1, sum)
# Use matrix multiplication to compute the sum of all
# observed tolerance values, and then divide by total
# abundance to get the mean tolerance value.
mean.tv <- (matl %*% WA)/tot.abn
plot(dfmerge$temp, mean.tv, xlab = "Temperature",
ylab = "Mean weighted average")
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In this example, weighted average tolerance values have been used. Other continuous
tolerance values such as optima or cumulative percentiles can be substituted in as well. Also,
the mean computed here is weighted by abundance.
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