Clements: “3357_c024” — 2007/11/9 — 18:34 — page 473 — #1 24 Application of Multimetric and Multivariate Approaches in Community Ecotoxicology The most distinct and beautiful statement of any truth must take at last the mathematical form. (Henry David Thoreau, in Walls 1999) 24.1 INTRODUCTION Methods to assess the effects of contaminants and other anthropogenic stressors on communities range from computationally simple indices such as species richness to complex, computer-dependent algorithms such as multivariate analyses. The simplest community indices use species pres- ence/absence or abundance data to show how individuals in the community are distributed among species. Theadvantagesof theseindices aretheir intuitivemeaningand theirability toreducecomplex data to a single number. Only slightly more involved but retaining more information, species abund- ance curves described in Chapter 22 characterize the distribution of individuals among the species by fitting abundance data to specified distributions. Estimated distributional parameters from species abundance models provide a parsimonious description of the community. Slightly more involved composite measures require additional knowledge about community qualities (e.g., the trophic status of a species) to produce indices developed specifically to gauge diminished community integrity due to anthropogenic stressors. Currently, the most popular of these composite indices is Karr’s (1981) index of biological integrity (IBI). These composite indices require more ecological knowledge of the community than measures of species richness or species abundance models but have the advant- age of being focused primarily on human effects on communities or species assemblages. More convenient, but perhaps applying less ecology than warranted, distributions of individual species effect metrics (e.g., distributions of 96-h LC50 values) are used to predict “safe concentrations” that presumably protect all but a specified, low percentage of the species making up the community. Even more computationally intense methods, such as multivariate analyses, aim to reduce the num- ber of data dimensions to an interpretable low number, and to quantify similarities or differences among sampling units. These last methods tend to generate interpretive parsimony at the expense of methodological simplicity and straightforward terminology; therefore, considerable caution is needed to avoid errors during their application. However, the value of these methods in identifying clear explanations from complex data sets makes worthwhile any effort spent wading through obtuse computer manuals or dealing with the associated jargon. Jargon, not argument, is your best ally in keeping him from the Church. (Lewis 1942) 473 © 2008 by Taylor & Francis Group, LLC Clements: “3357_c024” — 2007/11/9 — 18:34 — page 474 — #2 474 Ecotoxicology: A Comprehensive Treatment 24.1.1 COMPARISON OF MULTIMETRIC AND MULTIVARIATE APPROACHES Multimetric and multivariate approaches are applied to community data with the intent of render- ing the associated complex array of information to a more parsimonious form. Because ecological assessments of biological integrity generally require analysis of numerous biotic and abiotic vari- ables, sophisticated statistical approaches are often necessary to examine the complex relationships between species assemblages and multiple environmental factors. Multivariate approaches reduce complex, multidimensional data to two or three dimensions, thus allowing researchers to identify key environmental variables responsible for patterns of species abundance. In contrast, multimetric indices integrate a diverse suite of measures, often across several levels of biological organization, to assess biological integrity. It is appropriate to consider these two approaches together because the community data necessary to calculate a multimetric index or to conduct multivariate analyses are often the same (e.g., abundance, richness, and composition). In their comparison of multivariate and multimetric approaches, Reynoldson et al. (1997) con- cluded that multivariate approaches provided greater accuracy and precision for assessing reference conditions in streams. Terlizzi et al. (2005) showed that univariate measures ofmolluscan community structure (species richness) showed little response to contamination whereas multivariate analyses identified significant differences between reference and polluted sites. Thomas and Hall (2006) com- pared the ability of individual metrics, multivariate approaches, and multimetric indices to identify impairment in periphyton, macroinvertebrate, and fish communities. Although some individual met- rics were associated with large-scale habitat gradients, multivariate approaches were most useful for identifying spatial and temporal differences in each community. In a comprehensive analysis of community indices and multivariate approaches, Kilgour et al. (2004) compared the relative sensit- ivity of seven benthic community metrics and three multivariate indices to contamination associated with mines, pulp and paper mills, and urbanization. Multivariate approaches identified signific- ant differences associated with each of the perturbations and greater effect sizes compared to the community metrics. Although the examples described above seem to highlight the greater discrim- inatory ability of multivariate approaches, the usefulness of univariate and multivariate techniques for distinguishing between reference and contaminated sites will likely vary with the spatial scale of an investigation (Quintino et al. 2006). Despite their growing popularity in Canada and Europe, multivariate approaches have received considerably less attention in the United States (Resh et al. 1995). Multivariate analyses have been criticized because of their inherent statistical complexity and because results are often difficult to interpret (Fore et al. 1996, Gerritsen 1995). The com- plex graphical representations of multivariate results are often of limited value to non-ecologists and managers. Although strict reliance on complex statistical algorithms may obscure important biological results, we believe that multivariate approaches are an essential set of tools for biolo- gical assessments of water quality. Because community–environment relationships are inherently multidimensional, approaches such as multivariate analyses that consider interactions among pre- dictor variables and their effects on multiple response variables are necessary. New approaches, such as the application of principal response curves (Pardal et al. 2004), quantify multivariate community responses to contaminants in ways that are more accessible to managers and policy- makers. We agree with the recommendations of Reynoldson et al. (1997) that multivariate and multimetric approaches are complementary and should be used in conjunction. For example, the variables used in multivariate analyses such as principal components could include species rich- ness, abundance of sensitive groups, or other measures typically included in a multimetric index. Griffith et al. (2003) used this approach in their evaluation of the relationship between macroin- vertebrate assemblages and environmental gradients. Multivariate statistical analysis (redundancy analysis) using metrics derived from an index of biotic integrity provided complementary res- ults to canonical correspondence analysis based on macroinvertebrate abundance. Alternatively, © 2008 by Taylor & Francis Group, LLC Clements: “3357_c024” — 2007/11/9 — 18:34 — page 475 — #3 Application of Multimetric and Multivariate Approaches in Community Ecotoxicology 475 a multimetric index similar to Karr’s IBI could be developed using results of multivariate ana- lyses. Loading coefficients from canonical discriminant analyses, principal component analyses (PCA), and other multivariate procedures identify variables that are most important for separation of groups (generally locations, sampling stations). Variables shown to be responsible for separa- tion of reference and impacted stations could be combined in a multimetric index. Integration of multivariate and multimetric approaches may be necessary to detect perturbations when relatively weak relationships between stressors and community structure exist (Chenery and Mudge 2005). Finally, we note that our enthusiasm for multimetric and multivariate approaches in community- level bioassessment is not shared by all researchers. Weiss and Reice (2005) remind us that neither of these approaches provides causal linkages between stressors and community-level responses. These researchers advocate an alternative approach in which effects of stressors on individual taxa with known species-level tolerances are employed to develop an overall assessment of community-level impact. 24.2 MULTIMETRIC INDICES A principal objective of the 1972 Federal Water Pollution ControlAct and its 1977 and 1987 amendments is to restore and maintain the biological integrity of the nation’s waters. (Miller et al. 1988) One of the most significant advances in the field of biological assessments over the past 20 years was the development and application of multimetric approaches for measuring ecological integrity. Because no single measure of impairment will respond to all classes of contaminants, and because some individual metrics may show unexpected changes (e.g., increased species richness at polluted sites), multimetric indices are an effective tool for measuring effects of stressors (Fausch et al. 1990, Karr 1981, Kerans and Karr 1994, Plafkin et al. 1989). The individual metrics in a multimetric index reflect different characteristics of life history, community structure, and functional organization. In general, as the number of metrics increases (up to some reasonable number), the ability to separate contaminant effects from natural variation increases (Karr 1993) (Figure 24.1). In addition, because Level of stressorLevel of stressor Ecological attribute One metric Two metrics Threshold value FIGURE 24.1 Hypothetical relationships between stressor levels and ecological attributescharacterized using one or two metrics. The threshold value of the ecological attribute is defined as the response that is considered to be biologically significant. For example, a researcher may conclude that a 20% reduction in abundance of a sensitive species is a biologically significant response. The responses of the individual metrics are represented as clouds of points and the level of the stressor known to affect the ecological attribute is represented by the black bar. Note that addition of a second metric provides a more refined measure of the stressor level that causes a biologically significant response. (Modified from Figure 1 in Karr (1993).) © 2008 by Taylor & Francis Group, LLC Clements: “3357_c024” — 2007/11/9 — 18:34 — page 476 — #4 476 Ecotoxicology: A Comprehensive Treatment individual metrics respond differently to different classes of contaminants, multimetric approaches are useful for assessing a diverse suite of stressors and measuring impacts in systems receiving multiple stressors. The individual metrics included in a multimetric index may vary among perturba- tions, but should reflect important structural and functional characteristics of the system. In general, deviation of individual metrics from expected values at reference sites is estimated and a final value that includes the sum of all individual metrics is calculated. Karr’s (1981) IBI is the most widely used multimetric index for assessing the health of aquatic communities. The IBI was developed in response to the federally legislated mandate to “restore and maintain the chemical, physical, and biological integrity” of U.S. waters (Clean Water Act 1977, PL 95-217, also 1987 PL 100-4). Originally employed in Midwestern streams in the United States, the IBI is based on 12 attributes of fish assemblages in three general categories: species richness and composition, trophic composition, and fish abundance and condition. The individual metrics are assigned scores (1, 3, 5) based on their similarity to expected values in undisturbed or least impacted streams. Expected values for the individual metrics are obtained by sampling a large number of known reference sites in a region. Alternatively, expected values can be derived from surveys of reference and impacted sites and using the “best” values from these samples (Simon and Lyons 1995). Because expected values for species richness and total abundance vary with stream size, these metrics must be adjusted to reflect watershed area and other regional conditions. The scores of the 12 metrics are summed to yield a total IBI score for a site (which ranges from 12 to 60), with larger values indicating healthy fish assemblages. The IBI is sensitive to a diverse array of physical and chemical stressors, including industrial and municipal effluents, agricultural inputs, habitat loss, and introduction of exotic species. The IBI works especially well for characterizing fish communities because environmental requirements and historic distributions of this group are well known. This greatly facilitates estab- lishment of expected values for individual metrics. The structural and functional metrics included in the IBI are biologically relevant, and each individual metric responds to known gradients of degrad- ation (Fausch et al. 1990). The general approach outlined in the IBI has been modified for other ecosystems (e.g., lakes and estuaries) and applied to other taxonomic groups (e.g., benthic macroin- vertebrates and diatoms). Although the specific metrics vary among these applications, comparison of measured values to expected values and integration of a suite of metrics into a single index are consistent among approaches. A multimetric index for benthic macroinvertebrate communities was used to distinguish polluted from reference sites in rivers of the Tennessee Valley (Kerans and Karr 1994). The benthic IBI (B-IBI) was found to be highly effective because benthic macroin- vertebrates generally respond to chemical and physical degradation in a predictable fashion. The IBI now enjoys such popularity that the term, IBI, has come to be applied to any new composite or multimetric index. Calculating multimetric indices involves comparing individual metrics measured at an impacted site to the expected values for the region (Figure 24.2a). As described above, because some metrics (e.g., species richness) are greatly influenced by stream order and watershed area, these expected values must be adjusted to reflect natural variation (Figure 24.2b). Assuming that community responses to other landscape variables are predictable, a logical extension of this approach is to create models to account for natural variation across broad geographical areas. Bailey et al. (1998) found that simple geographic characteristics (distance from source, catch- ment area, elevation) and year sampled accounted for greater than 50% of the variation among reference sites. The performance of several bioassessment metrics was significantly improved when a predictive model that included this geographic variation was employed to identify impacted sites. The conventional approach of comparing metric values at impacted sites with expected values at reference sites has now advanced to the point where we can characterize hab- itat variation within subregions using more sophisticated multivariate statistics (Figure 24.2c). The application of multivariate techniques for assessing reference conditions is described below. © 2008 by Taylor & Francis Group, LLC Clements: “3357_c024” — 2007/11/9 — 18:34 — page 477 — #5 Application of Multimetric and Multivariate Approaches in Community Ecotoxicology 477 Metric value Metric 1 Metric 2 95% Confidence interval Habitat gradient Expected metric value Te st site Test site 1 Test site 1 Test site 2 Test site 3 Test site 2 Range of expected metric values at reference sites 95% Confidence ellipsoids Multivariate axis 1 Multivariate axis 2 (a) (c) (b) FIGURE 24.2 Multimetricand multivariateapproaches for comparing test sites to expected values atreference sites. (a) Two metric values at a test site (indicated by solid circles) are compared to expected values. Values are within the expected range for metric 1, but below the range of expected values for metric 2. (b) Metric values are adjusted to reflect expected changes in habitat characteristics along a gradient. Although the metric value at test site 2 is greater than at test site 1, it is less than the expected value and would indicate impact. (c) Multivariate analysis of expected metric values based on regional differences in habitat characteristics. Test sites 1 and 2 are within the expected values whereas test site 3 falls outside the 95% confidence ellipsoid. 24.2.1 MULTIMETRIC APPROACHES FOR TERRESTRIAL COMMUNITIES Although multimetric indices such as the IBI have been limited primarily to aquatic ecosystems, the general approach could be modified for terrestrial communities. Because of their sensitivity and rapid response to environmental stressors, terrestrial arthropods would be especially useful for assessing biological integrity (Kremen et al. 1993). Nelson and Epstein (1998) investigated the responses of lepidopterans to habitat modifications and concluded that butterfly communities integ- rate important structural and functional characteristics of terrestrial ecosystems. Kremen (1992) evaluated the indicator properties of butterfly communities and reported that this group was quite responsive to anthropogenic disturbance. Bird communities also offer opportunities for development of integrated measures of ecological integrity. The abundance, distribution, and habitat requirements of birds are generally well known, especially in North America. National monitoring programs, such as the Christmas Bird Counts conducted by the Audubon Society and Breeding Bird Sur- veys, have provided spatially extensive, long-term data on bird assemblages. Finally, responses of bird populations to some environmental stressors, especially pesticides and habitat alterations, have been well documented. However, given the logistical difficulties of sampling bird communit- ies, developing a suite of ecologically relevant indicators for this group will be a challenge. In © 2008 by Taylor & Francis Group, LLC Clements: “3357_c024” — 2007/11/9 — 18:34 — page 478 — #6 478 Ecotoxicology: A Comprehensive Treatment Species richness of birds 5 1015202530 Species richness of butterflies 2 4 6 8 10 12 14 16 FIGURE 24.3 The relationship between species richness of birds and butterflies at 6 sites along a gradient of urban development. Obtaining quantitative data for certain taxonomic groups, such as birds and small mammals is often expensive and logistically challenging. The close relationship between these measures suggests that butterflies, which are relatively easy to monitor, can be used as a surrogate to predict the response of birds to stressors. (Modified from Figure 1 in Blair (1999).) particular, surveys must be corrected to account for differences in detectability among species and among locations (Chambers et al. 1999). One promising alternative is to predict effects of anthropo- genic stressors on bird communities based on characteristics of surrogate taxonomic groups. Blair (1999) reported a strong relationship between species richness of birds and butterflies along a gradi- ent of urban development (Figure 24.3). Because butterfly surveys are relatively easy to conduct, Blair suggested that species richness of butterflies could be used as a surrogate for monitoring bird communities. 24.2.2 LIMITATIONS OF MULTIMETRIC APPROACHES One major advantage of multimetric approaches is that they integrate several ecologically relevant responses into a single measure, a characteristic that appeals to many water resource managers. However, some researchers are skeptical of multimetric indices and argue that a better approach is to assess an array of ecosystem responses, which provide a direct linkage between cause and effect (Suter 1993). Detailed critiques of multimetric indices as well as a discussion of their limitations have been published previously (Simon and Lyons 1995, Fausch et al. 1990, Suter 1993). Only a summary of the major limitations will be presented here. First, multimetric indices are data intensive. Regardless of the specific system or taxonomic group, development and application of multimetric approaches require a thorough understanding of the ecology andhabitat requirements of speciesas well as theirtolerances for environmental stressors. For some taxonomic groups and in some systems, these data will not be available. Second, most multimetric approaches cannot be employed to identify specific causes of environmental impacts. This criticism reflects two mutually exclusive goals of many biological monitoring programs. While chemical-specific, diagnostic indicators may allow researchers to identify a single source of perturb- ation, more general measures such as the IBI are required to characterize the integrity of systems receiving multiple stressors. It is possible that the responses of individual metrics in a multimetric index could offer some insight into the specific source of contamination. For example, a mul- timetric index for benthic macroinvertebrates might include metrics for abundance and species richness of mayflies, stoneflies, and caddis-flies. All three groups are generally sensitive to organic enrichment; however, many caddis-flies and some stoneflies are tolerant of heavy metals (Clem- ents et al. 1988, Clements and Kiffney 1995). Analysis of the responses of component metrics may © 2008 by Taylor & Francis Group, LLC Clements: “3357_c024” — 2007/11/9 — 18:34 — page 479 — #7 Application of Multimetric and Multivariate Approaches in Community Ecotoxicology 479 allow researchers to quantify the relative importance of individual stressors in systems affected by multiple perturbations. Third, multimetric indices may not respond to some types of perturbation because changes in one metric may be offset by changes in another metric. Again, the obvious solution to this problem is to report not only the integrated scores but also the responses of com- ponent metrics. Finally, multimetric indices based on attributes of community composition will be less effective in areas with low species richness or naturally impoverished assemblages. Fausch et al. (1990) note that the low species richness of fish assemblages in western coldwater streams requires that many of the community-level metrics be replaced by life history and population-level responses. 24.3 MULTIVARIATE APPROACHES Multivariate data sets are broadly defined here as those in which more than two dependent or inde- pendent variables are collected for each sampling unit. These variables typically include community characteristics (e.g., species abundances) that change or might be influenced together in complex ways. A wide range of multivariate statistical methods has been used to analyze these types of data. In contrast to the methods described to this point, multivariate analyses are not based on ecolo- gical concepts but are statistical constructs that reduce complex data sets to potentially meaningful patterns involving a few variables. Some, such as ordination methods, combine species abundance information for many sites or sampling units into functions that capture a portion of the total vari- ance in the data. A small number of uncorrelated, linear combinations of the species abundances might be identified. Ecotoxicological meaning can be assigned to the positions of sampling units (e.g., sites) along these linear functions. Alternatively, the researcher may simply use the results to describe trends among sampling units. Other methods, such as cluster analysis, separate samples into groups in hopes of identifying some ecological or toxicological pattern that may emerge to explain the groupings. Another type of analysis might be applied to species abundance data to identify which qualities weigh most heavily in discriminating among known groups. Regardless of the applied method, the overarching idea is that multivariate analysis of the measured variables can reveal hidden or unmeasured qualities. As with most parametric analyses, transformation of species abundance data is often advisable before applying a multivariate method. Transformation might be done to reduce the influence of one variable relative to others in the linear combinations of variables. One variable might have a much wider range of values and, in the absence of transformation, would have a disproportionately heavy influence on variance. In such a case, each variable (e.g., species’ abundances at all sampling sites) may be standardized to a mean of 0 and standard deviation of 1. If a skewed distribution was to occur with the species abundance distributions, some transformation such as the square root or another power of abundance might be employed prior to standardization and multivariate analysis. This is often necessary when a few species are very abundant at some sites. 24.3.1 S IMILARITY INDICES Although generally not included in treatment of multivariate analyses, similarity indices also reduce complex, multispecies data for the purpose of comparing communities among locations or over time. Similarity indices quantify the correspondence between two communities based on either presence–absence or abundance data. These indices are especially useful for comparing communities from regional reference sites to impacted sites. Alternatively, similarity indices are appropriate in studies of well-defined pollution gradients, where similarity to reference conditions is expected to increase with distance from a pollution source. The simplest and most frequently used similarity index based on presence–absence data is the Jaccard Index: J = j/(a +b −j), (24.1) © 2008 by Taylor & Francis Group, LLC Clements: “3357_c024” — 2007/11/9 — 18:34 — page 480 — #8 480 Ecotoxicology: A Comprehensive Treatment where a = the number of species in community a, b = the number of species in community b, and j = the number of species common to both sites. Because the Jaccard Index does not account for differences in abundance between locations, rare species and abundant species are weighted equally. Thus, it is likely that the Jaccard Index will be relatively insensitive to low or moderate levels of contamination. More sophisticated similarity indices, such as the Morisita–Horn measure, compare the relative abundance of taxa between two communities. The Morisita–Horn Index is given as MH = 2  (an i ×bn i )/(da + db)aN ×bN, (24.2) where an i = the number of individuals of the ith species at site a, bn i = the number of individuals of the ith species at site b, aN = the total number of individuals at site a, and bN = the total number of individuals at site b. The terms da and db in the Equation 24.2 are calculated as da =  an 2 i /aN 2 ,db =  bn 2 i /bN 2 . The Morisita–Horn measure of similarity is favored by some researchers because it is relatively insensitive to sample size and species richness (Magurran 1988, Wolda 1981). Dissimilarity among locations or between time points can also be used to evaluate responses to environmental stressors. Philippi et al. (1998) quantified spatial and temporal responses to perturb- ations by comparing the pairwise dissimilarity between sites with the average dissimilarity among replicate samples. These researchers noted that measures of dissimilarity (or similarity) can be employed to evaluate changes in community composition during recovery (Figure 24.4). If remedi- ation was effective, the relative dissimilarity between reference andimpactedsites would be expected to decrease over time. 01234567 0 0.2 0.4 0.6 0.8 1 Time since remediation Dissimilarity between/dissimilarity among FIGURE 24.4 Hypothetical changes in community similarity between reference and impacted sites as a function of time since remediation was initiated. The relationship shows that the index of dissimilarity (expressed as the ratio of dissimilarity between sites to the average dissimilarity among sites) is reduced over time as a result of remediation. © 2008 by Taylor & Francis Group, LLC Clements: “3357_c024” — 2007/11/9 — 18:34 — page 481 — #9 Application of Multimetric and Multivariate Approaches in Community Ecotoxicology 481 While similarity indices provide a simple way to compare community composition, there are potential problems with these measures. Boyle et al. (1990) evaluated the ability of similarity indices to discriminate effects of simulated perturbations based on initial community structure, sensitivity to community change, stability in response to reduced richness and abundance, and consistency. These researchers concluded that some similarity indices were misleading because results were strongly influenced by initial community composition and the nature of the perturbation. Although similarity indices are useful when comparing communities from two locations, more sophisticated techniques are necessary to compare multiple sites. Cluster analysis, a logical extension of sim- ilarity indices, is applicable for comparing communities from several locations or for comparing the similarity of a single site with a group of sites. Cluster analysis employs a variety of similar- ity measures based on either presence–absence or abundance data. These data are often expressed using a dendrogram, with the most similar sites combined into a single cluster. Additional sites are included based on their similarity to the existing clusters. Several different clustering algorithms have been developed, and relatively simple software packages are available for most analyses. Details of the different clustering techniques and the justification for deciding how different sites and clusters should be joined have been published (Gauch 1982). These methods will be described below. 24.3.2 ORDINATION Ordination is a process in which a large set of variables is reduced to a few variables with the intent of enhancing conceptual parsimony and tractability. With ordination analysis of community abundance data, the measured variables (e.g., abundance of each species for each sampling unit) are used to identify hidden patternsorunmeasured factors explaining the datastructure. Mathematicalconstructs are sought to help interpret correlations among variables. There are five steps to ordination analysis, regardless of the specific method applied (Comrey 1973). (1) The relevant data are generated and selected for analysis. As noted above, the data might require transformation prior to use. (2) The correlation matrix for the variables is calculated. (3) Factors (mathematical functions) are extracted. (4) Thefactorsmight be rotated to enhance interpretation. (5) Thefactorsare then interpreted. Ideally, plots of the sampling unit positions along the first few mathematical constructs reveal explanatory, or at least consistent, themes. As an example, linear functions can be defined such as Function 1 = b 1 X 1 +b 2 X 2 +b 3 X 3 +b 4 X 4 +··· , (24.3) where X i = the normalized ln(abundance +1) for each species sampled at the site. A first function is constructed that incorporates as much of the variance in the data as possible, and the process is repeated for additional functions with the remaining variance. Residual correlations after extraction of the first factor are used to produce a second, uncorrelated function that explains as much of the remaining variance as possible. The process is repeated to produce a series of functions. Ideally, most of the variance will be explained in the first few functions. A score for each sampling unit can be calculated for placement along each function. Plots for all sampling units using the formulated functions as axes should reveal an interpretable pattern. In this process, a matrix of many species abundances is reduced to a few sampling unit positions on a two- or three-dimensional plot. For example, the entire species abundance data set for a site might be reduced to one point in a two- or three-dimensional plot. The X, Y, andperhaps, Z dimensions are constructs that canbegiven physical meaning such as the influences of soil type (Function 1), heavy metal contamination (Function 2), and agricultural activity (Function 3) (Figure 24.5). Insight from additional information on soils, agricultural history, and soil metal concentrations might be used to interpret the distribution of the sampled plant communities along these three functions. The magnitude and signs of the b values (loading coefficients) in the linear functions are used to identify an underlying theme for each axis. © 2008 by Taylor & Francis Group, LLC Clements: “3357_c024” — 2007/11/9 — 18:34 — page 482 — #10 482 Ecotoxicology: A Comprehensive Treatment Grasslands with few metal-tolerant species Grasslands with numerous metal-tolerant species Metals Soil quality Agriculture Function 3 Function 2 Function 1 FIGURE 24.5 A hypothetical ordination analysis of plant communities relative to heavy metal contamination (top panel). Abundances of species are quantified at five sites near abandoned mines and another eight reference sites. Soil qualities and the history of agricultural use of the sites are also noted as potential confounding factors. After data transformation, ordination analysis results in three orthogonal, linear functions that are assigned interpretations of the influence of soil quality, soil metal concentrations, and agricultural history. The five mine sites clearly cluster away from the reference sites. There is a gradient of communities relative to soil quality and agricultural history. Ordination axes can be rotated to enhance interpretation using orthogonal and oblique methods (bottom panel). These loadings represent the extent to which the variables are related to the hypothetical factor. For most factor extraction methods, these loadings may be thought of as correlations between the variables and the function (Comrey 1973). For example, very high loadings in Function 2 for species known to be tolerant to toxic metals and low or negative loadings for metal-sensitive species would suggest the influence of metal exposure on community composition. For Function 3, high loadings for species known to flourish in active agricultural areas might suggest the impact of active agriculture on community structure. The final result at this stage for ordination analyses would be to construct a table with rows of variables and associated loadings for each relevant factor (i.e., a table of unrotated factor loadings). Several types of ordination methods exist (Boxes 24.1 and 24.2). PCA was the first, and remains the most popular method (Sparks 2000, Sparks et al. 1999). Using PCA, linear combinations of the original variables are extracted that sequentially account for the residual variance in a series of orthogonal (uncorrelated) components. The first component contains the most variance; the second © 2008 by Taylor & Francis Group, LLC [...]... Another general ordination method, factor analysis, is similar to PCA in that the variables are used to produce linear functions Instead of being called principal components, these linear functions of the data are called factors A factor is an unobservable variable that has attributes of a subset of the observed variables In contrast to PCA in which components are calculated directly as linear functions of... collected, but only canonical discriminant analysis of macroinvertebrate species abundance data are presented here Canonical variables, linear combinations of species abundance data that best distinguished among treatments, were produced for a series of times during the trial Analysis for one sampling date during the spiking period (August 31, 1 month after spiking began and 19 days after the last spiking)... as the log normal model, is often made without careful scrutiny (Jagoe and Newman 1997, Newman et al 2000, 2001) 24. 3.5 TAXONOMIC AGGREGATION IN MULTIVARIATE ANALYSES Our previous discussion in Chapter 22 concerning how taxonomic aggregation and the exclusion of rare taxa influence our ability to distinguish reference and contaminated sites is also relevant to multivariate analyses Ordination approaches... multivariate analyses are not based on ecological concepts but are statistical constructs that reduce complex data sets to illustrate potentially meaningful patterns involving a few variables • Multivariate data sets are broadly defined as those in which more than two dependent or independent variables are collected for each sampling unit • Ordination is a process in which a large set of variables is... Boldface Indicates a variable with high loading © 2008 by Taylor & Francis Group, LLC Clements: “3357_c 024 — 2007/11/9 — 18:34 — page 483 — #11 Ecotoxicology: A Comprehensive Treatment 484 1.46 1.86 1.60 2.01 FIGURE 24. 6 Ordination analysis (PCA) of physical and chemical qualities at sites along the James River (Virginia) Axes One and Two were interpreted as municipal waste discharge and industrial waste... along the first axis, reflecting an increase in abundance of Chironomidae, Planorbidae, Hirudinea, and Lymnaeidea, and a decrease in Gammaridae and Asellidae © 2008 by Taylor & Francis Group, LLC Clements: “3357_c 024 — 2007/11/9 — 18:34 — page 484 — #12 Application of Multimetric and Multivariate Approaches in Community Ecotoxicology 485 Axis two X S X Axis one X Temporal change in cypermethrin-spiked community... provided in Figure 24. 8 The results show clear separation among treatments based on community composition Surprisingly, species richness was not affected by copper spiking However, abundances of annelids, crustaceans, mayflies, and chironomids did change The mayfly Caenis was primarily responsible for separation among spiked treatments along the first canonical axis (Importantly, Caenis bioassays in the spiked... several tributaries Water quality data, including oxygen concentrations, were available for interpreting benthic species abundance information Site selection intentionally included those along salinity gradients, those with different sediment types, and those that experienced episodic anoxia Cluster analysis was done using logarithm-transformed species abundance data and the Bray-Curtis similarity... macrofauna (Clarke 1999), and benthic macroinvertebrates of the River Tees (Crane et al 2002) Methods for extracting functions aim to produce easily interpretable patterns The mathematical functions or axes that are initially generated are uncorrelated or perpendicular To enhance interpretation of these functions, some methods will rotate the axes at this stage of analysis based on some particular set... observed variables, the observed variables in factor analysis are envisioned as linear functions of the factors (unobserved variables) plus random error (Sparks et al 1999) Numerous other ordination methods are available for applications with specific needs Ordination can be done with discrete data using correspondence analysis or detrended correspondence analysis (Sparks et al 1999) Discrete data might . right along the first axis, reflecting an increase in abundance of Chironomidae, Planorbidae, Hirudinea, and Lymnaeidea, and a decrease in Gammaridae and Asellidae. © 2008 by Taylor & Francis. transformation, would have a disproportionately heavy influence on variance. In such a case, each variable (e.g., species’ abundances at all sampling sites) may be standardized to a mean of 0 and. measured variables can reveal hidden or unmeasured qualities. As with most parametric analyses, transformation of species abundance data is often advisable before applying a multivariate method. Transformation