MULTIVARIATE ANALYSIS OF ECOTOXICOLOGICAL DATA USING ORDINATION: DEMONSTRATIONS OF UTILITY ON THE BASIS OF VARIOUS EXAMPLES

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1 MULTIVARIATE ANALYSIS OF ECOTOXICOLOGICAL DATA USING ORDINATION: DEMONSTRATIONS OF UTILITY ON THE BASIS OF VARIOUS EXAMPLES Paul J Van den Brink 1 *, Nio W Van den Brink 1 and Cajo JF Ter Braak 2 1 ALTERRA Green World Researh, Wageningen University and Researh Centre, PO Box 47, 6700 AA Wageningen, The Netherlands. 2 Biometris, Wageningen University and Researh Centre, PO Box 100, 6700 AC Wageningen, The Netherlands Manusript reeived, 16/10/02; revision reeived, 24/4/03; aepted, 16/5/03. ABSTRACT This paper desribes the usefulness of the group of multivariate tehniques belonging to ordination for the analysis of eotoxiologial data sets. It is argued that although eotoxiologists often gather multivariate data sets, they usually do not evaluate them with tehniques that an handle multivariate data. Ordination tehniques enable the researher to extrat an underlying struture out of a data set (eg. differenes in omposition of maro-invertebrate ommunity between sites) and, if measured, relate this struture to explanatory variables (eg. onentrations of toxiants at the same sites). Five example data sets are presented to illustrate the underlying theory and the possibilities of ordination tehniques. Two methods are presented, one based on weighted summation (eg. Prinipal Component Analysis, PCA) and one on weighted averaging (eg. Correspondene Analysis, CA). These tehniques differ in the shape of the modelled response (linear versus unimodal) as the type of data they model (absolute versus relative). Results of these two methods are illustrated using a data set omprising levels of different PCB ongeners measured in the blood of Adélie penguins in three periods. After this the onstrained forms of PCA and CA are disussed, ie. onstrained means that they are able to optimally display the differenes in speies omposition (here levels of PCB ongeners) due to explanatory variables (here period). Further examples illustrate the use of ovariables, ontinuous and nominal explanatory variables, supplementary explanatory variables and forward seletion of explanatory variables. Finally, two examples of Prinipal Response Curves (PRC) analyses are given. PRC is a tehnique that is espeially developed to analyse time-series in whih a ontrol or referene is present. The PRC results are disussed for a designed experiment and a monitoring data set. The paper ends with a disussion foussing on the omparison between ordination tehniques and other multivariate tehniques used in the field of eotoxiology. Keywords: multivariate analysis, prinipal omponent analysis, redundany analysis, prinipal response urves, ordination. INTRODUCTION To study the influene of abioti environmental variables on the bioti omposition of eosystems, multivariate tehniques have been used for many years in eology (Legendre and Legendre 1998). Dissimilarities in ommunity omposition between sampled sites are analysed and the differenes deteted are related to measured or observed variables suh as ph, habitat quality and dissolved oxygen. In partiular ordination has proved to be a very useful tehnique for this purpose beause it results in a diagram (biplot or triplot) displaying both the sites and the speies and, if measured, the environmental variables in a redued spae (Ter Braak 1995). It therefore enables the researher to evaluate differenes in speies omposition between sites and to identify the environmental variables responsible for these differenes in a single analysis. This property of ordination is the main advantage over other multivariate tehniques suh as, for instane, lustering and similarity analysis. In eotoxiology, multivariate analyses have been used in reent years to display differenes in ommunity omposition among treatments or sites and to relate these differenes to imposed hemial treatment or measured hemial stress (see for instane, Van Wijngaarden et al. 1995; Shaw and Manning 1996; Sparks et al. 1999; Kedwards et al. 1999a, b). The multivariate analysis of designed experiments with artifiial eosystems (miroosms and mesoosms) beame more informative by the new ordination tehnique Prinipal Response Curves (Van den Brink and Ter Braak 1999). The use of multivariate analysis, however, is not widely aepted yet in eotoxiology (Maund et al. 1999). In this paper we try to demonstrate that multivariate tehniques an be valuable in the analysis of a variety of eotoxiologial data. In this paper we will restrit ourselves to ordination tehniques that operate on the original data set for its analysis and thus allow a diret interpretation in terms of the original variables, in most ases speies (Ter Braak ). These tehniques are more diret than tehniques that operate on (dis)similarity indies (eg. similarity analysis, lustering and multidimensional saling). The tehniques used in this paper and those based on (dis)similarity indies will be ompared in the disussion setion. Ordination tehniques are apable of summarising very omplex responses beause they are not restrited to a single dimension (as for instane (dis)similarity analysis). When ombined with Monte Carlo permutation testing not only is a graphial summary of the struture present in the data set obtained, but also the statistial signifiane of hypothesised differenes (Ter Braak and smilauer 2002). This paper will present the analysis of five example data sets to illustrate the value of multivariate methods for the analysis of eotoxiologial data. We go beyond the traditional example in whih a sample by speies matrix is ompared with a sample by environmental/explanatory variables matrix. In our examples, toxiity values, ontaminant onentrations and physio-hemial parameters play the part of the speies; and time, geographial position, hemial treatment and moleule harateristis play the part of explanatory variables. *Author for orrespondene, paul.vandenbrink@wur.nl 141

2 BACKGROUND OF ORDINATION Sientifi investigation does not always allow the olletion of speies and environmental data simultaneously, often only speies data is gathered to monitor hanges in time. The data gathered an be omprised of samples ontaining either hemial or biologial speies or both. Ordination is able to express differenes in speies omposition between samples without the use of measured environmental or explanatory variables. In suh an analysis, ordination onstruts imaginary, latent explanatory variables whih maximise the variation in speies omposition between sites, ie. whih best represent the underlying struture in the data set (Ter Braak 1995). The first latent variable is onstruted in suh a way that it explains the largest part of the total variane, the seond one the largest part of the remaining variane et. The first two latent variables are normally used to onstrut an ordination diagram of whih they form the axes. Samples and speies are represented in the diagram by points (or arrows) plotted at the sores (values) they have on the latent variables (see for instane Figure 1). Samples with nearly idential speies omposition lie lose together in the diagram, while samples that lie far apart have very different speies omposition. In biplots, arrows (for speies or environmental variables) point in the diretion of higher values. In the example setion a preise interpretation of ordination diagrams will be given. When explanatory variables are measured, they an be inluded in the analysis in two ways. First, the explanatory variables an be laid over the ordination diagram using their values at the different sites. After the ordination analysis of the speies by sample matrix they are simply regressed upon the latent variables. This analysis is alled an indiret or unonstrained analysis with supplementary explanatory variables, ie. the explanatory variables do not play an ative role within the analysis. The analysis an also be onstrained to the part of the variane that is aptured by the explanatory variables. The analysis is performed using this explained variane only, and the latent variables onstruted are a linear ombination of the measured explanatory variables. This analysis is alled a diret or onstrained analysis. The row entries of Table 1 summarise the distintion between unonstrained and onstrained analysis. Sometimes the effets of some explanatory variables an a priori be expeted but one is not interested in the effets of these variables. On the one hand, these variables are important leading fators influening the data set, on the other hand one does not want these variables to dominate the analysis. The variane explained by suh variables an be exluded from the analysis. The resulting analysis is alled a partial ordination or an ordination with ovariables. Covariables an be used in both unonstrained and onstrained ordination. We disuss two groups of methods: methods based on Prinipal Component Analysis (PCA) and methods based on Correspondene Analysis (CA). PCA is based on a linear response model relating speies and environmental variables, whereas CA an be derived from a unimodal response model (olumn entries of Table 1). In Figure 1. PCA biplot, with fous on samples, showing the absolute differenes in onentrations of PCB ongeners in the different penguin blood samples. The different numbers refer to the different PCB ongeners, eg. the number 177 refers to the PCB177 ongener. Of all the variation in onentration of PCB ongeners, 55% is displayed on the first axis, and another 12% on the seond one. For larity samples taken at period 1, 2 and 3 are represented by different symbols. 142

3 eology mainly CA is used beause it fits the onept of nihespae partitioning with speies rising and falling along an eologial gradient (Ter Braak 1995). In this model eah speies an be haraterised by its position (optimum or entre) along the gradient. This position is estimated in CA by weighted averaging, whereas the sore of a speies in PCA is estimated by linear regression, whih in the ase of PCA simplifies to a weighted summation (Table 1; Ter Braak 1995; Legendre and Legendre 1998). The linearity of PCA must not be misinterpreted, as PCA is well able to show nonlinear patterns (eg. Figure 1). Sometimes the sampled sites represent only a small part of this eologial gradient, eg. when only sites with a ph value between 7.0 and 7.5 are sampled. In these ases a linear model is used beause it desribes the rise (or fall) along a short gradient better than a unimodal one. In eotoxiology it may be expeted that a speies normally does not have an optimum along the gradient of a stressor. Therefore attempts to use multivariate tehniques in eotoxiology mainly foussed on linear methods (Van Wijngaarden et al. 1995; Kedwards et al. 1999a and b). The hoie to either use PCA or CA an be based on two harateristis, the length of gradient present in the data set and the type of data gathered. The length of gradient is a measure for the degree of unimodality of a latent variable (ordination axis). If a length of gradient of the latent variable is short, PCA is the model to hoose, and when it is long CA is best (Table 1). This length of gradient an be alulated using Detrended Correspondene Analysis (DCA), a method we will not disuss in this paper beause of its limited use for eotoxiology. For a desription and the bakground of the DCA method is referred to Ter Braak (1995). A general rule of thumb is that when the length of gradient is longer than 4 Standard Deviations (SD), the speies data learly show a unimodal response along the latent variable and CA is preferred. Another differene between CA and PCA is that CA models relative abundane instead of the absolute abundane, whih is modelled using PCA (Ter Braak and smilauer 2002). The methods we disuss are ross-lassified in Table 1. INDIRECT AND DIRECT ORDINATION: THE PENGUIN EXAMPLE (1) The dynamis of the onentrations of PCB ongeners in the blood of Adélie penguins were studied during the breeding season (Table 2). From 15 birds, blood samples were olleted during three periods: 1) egg laying period, a period prior to breeding in whih the birds starve for a prolonged period on the nest; 2) egg-hathing period in whih parental birds takes shifts on the nest while the other goes out to sea foraging and 3) the rèhe-stage when hiks are left by the parents, although eah parent returns regularly to feed the hiks (. 1998). This resulted in 45 blood samples (15 individuals times 3 periods) whih were analysed for onentrations of 30 different PCB ongeners by GC-eletron apture detetion (ECD). All proedures and the univariate evaluation of the data are desribed in detail by Van den Brink et al. (1998). The onentrations were ln-transformed before analysis. All multivariate analyses in this paper were arried out using the Canoo for Windows pakage, version 4.5 (Ter Braak and smilauer 2002). In Canoo, one an hoose between predominantly interpreting relationships among samples or among speies from the ordination diagram. In our ase saling was foussed on intersample distanes beause differenes between periods were of interest, for all other questions the default options were hosen. Sine the length of gradient of the data set was very short (0.6 SD), the data are analysed by PCA. Figure 1 shows the ordination diagram resulting from the PCA analysis of the 45 samples by 30 PCB speies matrix. In this diagram, the blood samples are represented by squares and speies (different PCB ongeners) by irles. (In a linear biplot, speies ould be represented by arrows by onneting the points with the origin, but beause many speies are analysed simultaneously this would have resulted in a luttered biplot.) Figure 2 gives an example of the interpretation of linear biplots. In Figure 2 the irle denoting the speies point for the grouped ongener speies 138/163/164 is enlarged a bit and not filled for larity. For the interpretation a help line is drawn through this speies point and the origin of the plot. When all sample points are projeted perpendiularly onto this line, as is shown for a few samples as an example in Figure 2, the fitted onentration of the PCB ongener an easily be ordered from high to low. Sample A has the highest 143

4 Figure 2. PCA biplot, with fous on samples, that shows an example on how to interpret biplot ordination diagrams. The numbers refer to the different PCB ongeners, ie. the 138/163/164 point represents the summated levels of the ongeners PCB138, PCB163 and PCB164. The interpretation is only shown for a few example sample points for larity. For further explanation see text. fitted onentration, sample B the next highest fitted onentration and so on for the samples C, D, E, F and G (Figure 2). Low fitted onentrations our at the opposite end of the line (samples X, Y and Z), with the lowest onentration in sample Z. The distane between the speies point and the origin of the diagram is a relative measure for the magnitude of the differenes in onentrations between the samples, as indiated by the biplot. Thus, the further away the speies point is from the origin, the larger the differenes in PCB onentrations between the samples, as indiated by the biplot, are. The diagram an be evaluated in terms of the perentage variane displayed. The first prinipal omponent (latent variable, ie. horizontal axis of the biplot) displays 55% of the total variane in onentrations of PCB ongeners between the samples, the seond one (vertial axis) 12% (Figure 1), so together the axes display 67% of the variane. The third axis explained only 8% of the total variation, and is therefore left out of onsideration. Hene by applying PCA the speies by sample matrix is redued from 30 (speies) dimensions into 2 dimensions, retaining three-quarters of its variane. Most PCB ongeners are plaed on the right side of the origin of Figure 1, whih shows that the onentrations of most ongeners are somewhat ollinear with eah other. The onentrations tend to be high in samples plaed on the right side of the origin and low in those plaed on the left side. Figure 1 also shows differenes between periods. Samples taken in period 1 are plaed somewhat at the right side of the diagram, those taken in period 2 to the left-down and those taken in period 3 left-upper part of the diagram. This arrangement indiates that onentrations of most PCB ongeners were generally higher in the samples taken in period 1 ompared to those taken in periods 2 and 3. The onentrations of PCB ongeners plaed in the right-upper quadrant had espeially low onentrations in samples taken in period 2, while those plaed in the right-down quadrant are indiated to have the lowest onentrations in samples taken in period

5 Figure 3. A RDA biplot, with fous on samples (represented by periods), showing the absolute differenes in onentrations of PCB ongeners between the different periods. The numbers refer to the different PCB ongeners. Of all variation in onentrations of PCB ongeners in the penguin blood samples, 24% was explained by the nominal explanatory variables representing the periods. Of this explained variane, 84% is displayed on the first axis, the remaining 14% on the seond one. For larity the explanatory variables representing period 1, 2 and 3 are represented by different symbols. Indiated differenes are signifiant between all periods (p < 0.05, Monte Carlo permutation tests). Although Figure 1 indiates differenes in onentrations of PCB ongeners among the periods, these differenes are not optimally displayed. This data set ontains variation due to differenes between periods, individual penguins and measurement error, although the latter an not be distinguished from the seond beause no repliate samples were taken. The PCA biplot fouses on the differenes in onentrations of PCB ongeners between samples. The information on the period in whih a sample was taken is added post-ho, ie. after the analysis has been arried out. This is alled indiret or unonstrained ordination. The interpretation of the indiated differenes between samples takes plae in an indiret way, after the analysis has been performed. Redundany Analysis (RDA) is the diret form of PCA that enables the researher to fous the analysis on that partiular part of the variane that is explained by external explanatory variables (Table 1). In our example we used three nominal (1/0) variables denoting the period in whih a sample was taken as explanatory variables. The resulting RDA biplot (Figure 3) fouses on the differenes in onentrations of PCB ongeners between periods. For larity, the samples are not displayed, their important feature, ie. the period in whih they were sampled, is represented by the plaement of the three explanatory variables denoting the periods. As in the PCA biplot, higher onentrations of most PCB ongeners are indiated for period 1, the egg-laying period, and lower ones for periods 2 and 3. This an be explained by the atrophy of the petoral musle during period 1 (. 1998). This musle is a sink of PCBs, whih are released into the blood during atrophy. In period 2 this musle reovers due to the foraging in the sea so onentrations of PCBs go down. In period 3 a part of fat-reserve is onsumed but. (1998) argue that this is only a small sink for PCBs, ompared to the large petoral musle, so the onentrations do not hange that muh during that period. Of the total variane almost a quarter ould be explained by the indiator variables denoting period (Figure 3). Of this variane the majority is displayed on the first axis (84%), the remaining part on the seond one. RDA an be followed by Monte Carlo permutation tests to test 1) whether PCB ongener onentrations differ signifiantly between periods; 2) whether the first axis of the RDA biplot displays a signifiant part of the between period variation; and 3) whether differenes between the individual periods are signifiant. All periods were tested against eah other and all tests resulted in p-values < The results of the PCA and RDA analyses of this data set show that ordination an provide a lear summary of the underlying struture of the data set. It also enables the researher to fous on that part of the variane that is of interest, in this ase the differenes between periods. When onstrained ordination is ombined with Monte Carlo permutation tests, one an also test the signifiane of indiated differenes. The results of the multivariate analyses are omparable to the univariate one, with the results of multivariate analysis showing more details for individual ongeners. RDA VERSUS CCA: THE PENGUIN EXAMPLE (2) As mentioned in the bakground setion, PCA and its onstrained ounterpart RDA fous on the absolute differenes in speies abundanes (here PCB levels) between the samples, whereas CA and its onstrained ounterpart CCA fous on relative differenes. This differene between the two lasses of methods is illustrated by Figures 3 and 4. Figure 4 shows the CCA biplot of the same data set as Figure 3. The interpretation of the diagram is analogous to the RDA biplot (sine biplot saling was used, see Ter Braak and Verdonshot 1995 for details). In the CCA analysis the nominal variables denoting the periods explained 14% of the total variane, of whih approximately 50% is displayed on the first, horizontal axis and the remaining part on the seond, vertial one. Again, we 145

6 Figure 4. A CCA biplot, with fous on samples, showing the ompositional differenes of PCB ongeners between the different periods. The numbers refer to the different PCB ongeners. Of all variation in levels of PCB ongeners in the penguin blood samples, 14% was explained by the nominal explanatory variables representing the periods. Of this explained variane, 59% is displayed on the first axis, and the remaining 41% on the seond one. For larity the explanatory variables representing period 1, 2 and 3 are represented by different symbols. Indiated differenes are signifiant between all periods (p < 0.05, Monte Carlo permutation tests). see a separation of the three periods; period 1 and 2 are plaed at the bottom of the diagram, period 3 at the top. We also see that in this diagram, in ontrast to the RDA biplot, not all ongeners are plaed on one side of the diagram, but sattered around the origin. This is a result of the fat that CCA displays proportional, relative differenes. The figure indiates that the relative levels of some ongeners are higher in period 1 and others in period 3. This ould be a result of differenes in suseptibility to metabolisation between the ongeners. Compared to period 1, it may be that ongeners most suseptible to metabolisation inreased during period 2 due to feeding (foraging in the sea) and dereased during period 3 due to metabolisation. The same Monte Carlo permutation tests were performed as desribed in the RDA setion and again all tests yielded p-values < It is notable that a RDA using entring by samples and by speies on the log-onentrations (ie. a log-ratio analysis; Aithison 1990; Ter Braak and smilauer 2002) yielded almost idential results as the CCA analysis (results not shown). The results of the RDA and CCA analyses show that ordination suessfully deteted both absolute and ompositional (or relative) differenes in levels of PCB ongeners between the samples taken in the three periods. CONTINUOUS AND NOMINAL EXPLANATORY VARIABLES AND COVARIABLES: THE LECES EXAMPLE The Lees data set onsists of abundane of maro-invertebrate speies on five loations of the Lees River (East Java, Indonesia, Table 2). The ommunity was sampled from the riverside three times between September and November 1991 at eah loation using the kiking method, together with several physio-hemial parameters. Sampling station 1 was the most upstream station, sampling station 5 the most downstream one. Between sampling station 2 and 3 is a paper mill fatory, the effluent of whih was disharged into the river. The maro-invertebrate abundane data were ln(2x+1) transformed prior to the analysis (see Van den Brink et al for rationale). Sine the differenes between sampling dates were not of interest, three nominal variables denoting the three sampling dates were introdued as ovariables, ie. the part of the variane aptured by these variables was exluded from the analysis. Sampling date explained 14% of the total variane in abundane values of the maro-invertebrate ommunity between the samples. The remaining 86% an be attributed to differenes between sites. Figure 5 displays the first two axes of a PCA of this remaining variation. Figure 5 shows lear differenes between sites 1 and 2 on the one side (plaed on the left side of the diagram) and 3, 4 and 5 on the other side (right side), suggesting effets of the effluent of the paper mill fatory. For interpretation we also inluded nominal variables denoting the five sites, two indiating whether a sample was taken upstream or downstream of the fatory, and the ontinuous variables ph, urrent veloity, ondutivity, temperature, dissolved oxygen, hardness, hemial oxygen demand (COD) and ammonium onentration. In the resulting biplot, nominal variables 146

7 Figure 5. A PCA biplot, with fous on samples, of speies omposition showing the within-date differenes in speies omposition between samples taken upstream and downstream of the wastewater outlet in the Lees River. In this analysis, sampling date is defined as ovariable and explained 14% of the total variane in speies omposition. Of the remaining variane, 41% is displayed on the first axis, and another 15% on the seond one. The third axis (not shown) explained another 11% but was not related to the outlet. Also the relation with the supplementary variables sites and several physio-hemial parameters is displayed. For larity the explanatory variables representing upstream and downstream fatory are depited by different symbols than those representing the different sites. are represented by points, whereas ontinuous variables are represented by arrows. These variables are supplementary as they do not influene the PCA itself. The biplot (Figure 5) suggests that most taxa (espeially those belonging to Trihoptera, ie. Psyhomyiidae, Hydropsyhidae, Polyentropodidae, Philopotamidae, Rhyaophilidae and Limnephilidae) are negatively affeted by the effluent and that the levels of indiators of pollution (COD, ammonia, hardness, ondutivity) are indiated to have inreased due to the effluent. Carrying out a partial RDA by defining the supplementary variables as true explanatory variables yielded exatly the same result as the previous partial PCA. The reason is that the number of explanatory variables, inluding ovariables, is larger than the number of samples so that the explanatory variables do not really onstrain the analysis (Ter Braak and smilauer 2002). To test the statistial signifiane of the effluent of the mill fatory, we arried out a RDA with fatory as the only explanatory variable, and sampling date as nominal ovariable. A Monte Carlo permutation test using random permutation indiated that the plae relative to the fatory has a signifiant influene on the maroinvertebrate ommunity (p < 0.05). Random permutation takes the samples as independent whereas in pratie there may be orrelation of parameter values in spae (along the river) and time. When these are taken into aount (in a split-plot design with yli permutation of sites and of times, (see Ter Braak and smilauer 2002) the statistial evidene of an effet evaporates (p > 0.40). Note that the lak of statistial signifiane is not solely due to the redued number of permutations in this advaned permutational sheme as the number yielding different F-ratios is still over The example shows that partial ordination enables the researher to exlude a part of the variane that is not of interest. It allows the researher to yield an optimal summary of strutures in the remaining variation and relate this struture to nominal and measured explanatory variables simultaneously. CORRELATION TRIPLOT, SUPPLEMENTARY EXPLANATORY VARIABLES AND FORWARD SELECTION: THE TOXICITY EXAMPLE Deneer et al. (1987; 1989) performed toxiity tests with an alga (Chlorella pyrenoidosa), rustaean (Daphnia magna), fish (Poeilia retiulata) and a baterium (Photobaterium phosphoreum) with 13 mono-nitro ompounds together with a bioonentration experiment with the fish (Table 2). The goal of these experiments was to relate the toxiity of mono-nitro ompounds to two physio-hemial parameters of these ompounds, ie. to determine a Quantitative Struture Ativity Relationship (QSAR). The two parameters were the log(k ow ) (otanol-water partitioning oeffiient) and Hammett σ onstants (a measure for the reativity of the ompound, for its transformation into the ative n-hydroxy form). The toxiity was expressed by eight variables (EC50-, LC50- and/or LOEC-values for the test speies and a BCF value for the fish). A PCA analysis was performed in whih the ompounds play the role of samples, the toxiity measures the role of speies and the two physio-hemial parameters the role of supplementary explanatory variables (see bakground setion). All toxiity and BCF values were lntransformed and entred and standardised (giving mean = 0 and SD = 1 for eah variable) within Canoo for Windows, and the saling is foussed on variables, yielding a orrelation bi- or triplot. 147

8 Figure 6. PCA orrelation triplot showing the relation between different mono-nitro ompounds and their laboratory toxiity to several aquati organisms and BCF for Guppy. Also the relation between two physial parameters and the toxiity is indiated. Of all variation in toxiity, 71% is explained by these two parameters, of whih 89% is displayed on the first axis, another 10% on the seond one. Of all variane, 73% is displayed on the first axis, another 15% on the seond one. Both physial parameters explain a signifiant part of the variation in toxiity between the ompounds (p < 0.05, Monte Carlo permutation test). Standardisation treats all variables equally important regardless of their variability in the data. In a PCA analysis without standardising the endpoint with the largest variability would influene the analysis most. The triplot (Figure 6) shows that all toxiity values, exept the EC50 of Ph. phosphoreum, have a high positive orrelation with eah other and, as expeted, a negative one with the BCF of the fish. The log(k ow ) parameter has, as expeted, a high positive orrelation with BCF and herewith a negative one with most toxiity values. Also the Hammett σ onstants have a negative orrelation with all toxiity values exept for Ph. phosphoreum; a high Hammett σ onstant is assoiated with a low toxiity value (eg. a low EC50) and therefore a high toxiity. The different plaement of Ph. phosphoreum might indiate that mono-nitro ompounds do not only have an anaestheti mode of ation to this baterium. The toxiity of mono-nitro ompounds towards fish, D. magna and C. pyrenoidosa is somewhat higher than expeted for ompounds ating solely though an anaestheti mode of ation. This exess toxiity is probably aused by the formation of reative N-hydroxy metabolites. The rate of transformation of these metabolites is probably related to the Hammett σ onstant, whih explains the signifiane of this variable. For a omplete evaluation of this data set (and more), the reader is referred to Deneer et al. (1987; 1989). Together the two parameters explain 71% of the total variane in toxiity and BCF values between the ompounds, of whih 99% is displayed in the triplot. Within Canoo, forward seletion an be used for the ranking of the explanatory variables in importane for determining the speies data. In this way a large set of environmental variables an be redued to a meaningful small one. When forward seletion in ombination with Monte Carlo permutation tests is performed under the RDA option, first log(k ow ) is added to the model, explaining a signifiant 61% of the total variane (p < 0.05). After the inlusion of log(k ow ), the Hammett σ onstant is added to the model explaining another signifiant 10% of the total variane (p < 0.05). Sine the Hammett σ onstant alone explains 31% of the total variane, both parameters share 21% of the total variane. So for this example both log(k ow ) and the Hammett σ onstant explain a signifiant part of the toxiity and BCF values, although the two parameters share a large part of explained variane. Forward seletion is an important tehnique to limit the number of explanatory variables to a set that best explains the variation in the speies ommunity (here being toxiity and BCF values). One should be aware of two problems (Legendre and Legendre 1998). First, the type I error is far greater than the nominal 5% level, beause forward seletion involves multiple testing, Bonferroni adjustment of the signifiane level may be useful. Seond, forward seletion may lead to other results than stepwise seletion or bakward elimination of explanatory variables; there is thus no guarantee that forward seletion finds the best model. Despite these problems, forward seletion of explanatory variables has great data-analyti utility. 148

9 PRC ON A DESIGNED EXPERIMENT: THE FUNGICIDE EXAMPLE Prinipal Response Curves is a relatively new tehnique that is designed for the analysis of miroosm and mesoosm experiments (Van den Brink and Ter Braak 1999). It was first applied to the results of eotoxiologial experiments evaluating the effets of pestiides on freshwater eosystems (eg ) but appliations to terrestrial eosystems (eg. Smit et al. 2002) and the analysis of eologial field experiments (eg. Frampton et al. 2001) followed rapidly. The Prinipal Response Curves method was developed to overome very luttered biplots when the information of many sampling dates and many treatments is displayed in one diagram and time is not expressed as a single diretion in the biplot (see Kersting and Van den Brink 1997 as an example). In this setion the appliation of PRC and the interpretation of first and seond PRC diagrams will be disussed using an experiment desribed in Cuppen et al. (2000) and Van den Brink et al. (2000). The semi-field experiment for the evaluation of hroni exposure to arbendazim onsisted of indoor miroosms (1 m 3 ), whih represented marophyte-dominated drainage dithes. The systems were treated hronially for four weeks with 0, 3.3, 33, 100, 330 or 1000 µg/l arbendazim, with two repliates per onentration. The speies omposition of the phytoplankton, periphyton and invertebrate ommunities were monitored in time, together with hlorophyll-a ontent, various physio-hemial parameters and marophyte biomass. For a more detailed presentation and evaluation of the results, see Cuppen et al. (2000) and Van den Brink et al. (2000). In this paper we use the maro-invertebrate data set, onsisting of 86 different taxa, as an example (Table 2). No onsistent NOECs lower than 3.3 µg/l were reorded on the speies level. Diret effets on maro-invertebrates beame manifest following a treatment with 33 µg/l. Several worm-like taxa belonging to the groups of flatworms, leehes and oligohaete worms showed altered abundane values, together with two rustaean taxa. At this treatment onentration, indiret effets in the form of inreases of several snail taxa, were also observed, indiating food-web hanges due to inrease of food resoures of these speies. The effets of the arbendazim treatment at the maroinvertebrate ommunity level were analysed by the Prinipal Response Curves method (PRC). The PRC method is a multivariate tehnique speially designed for the analysis of data from miroosm and mesoosm experiments and an be obtained using RDA (Van den Brink and Ter Braak 1998; 1999). The model for the first PRC is: y d(j)tk = y 0tk + b k dt + ξ d(j)tk, where y d(j)tk is the log-abundane of speies k in repliate miroosm j of treatment d at time t, y 0tk is the mean log-abundane of speies k in week t in the ontrol (d = 0), dt is the sore of the d th treatment at time t, b k is the weight of the k th speies, and ξ d(j)tk is an error term with mean zero and variane σ k2. Note that by definition 0t = 0 for every t. The model is fitted to data by an RDA, using nominal variables denoting sampling date as ovariables and the produt of sampling date and treatment levels as nominal explanatory variables. This RDA yields least-squares estimates of the treatment sores { dt } and speies weights {b k }. See Van den Brink and Ter Braak (1998) and Ter Braak and smilauer (2002) for details. PRC results in a diagram showing the sampling weeks on the x-axis and the first Prinipal Component of the variane explained by treatment on the y-axis (see dt values in Figure 7A for an example). This yields a diagram showing the deviations, in time, of treatments ompared to ontrols. For instane, Figure 7A indiates that for the period after the start of the treatment, the greatest deviations from the ontrols ourred at the two highest treatment onentrations, while smaller deviations were found at the intermediate treatment onentrations. It also indiates minor differenes relative to the ontrols at the lower treatment onentrations. The speies weights shown on the right side of the diagram an be interpreted as the weight of eah speies for the response given in the diagram. Thus, the flatworm Dugesia tigrina, whih has the highest weight in the diagram, is shown to have dereased most at the higher treatment onentrations. The negative weight of the snail Lymnaea juvenile in the diagram indiates that its numbers inreased at the higher treatment onentrations. In quantitative terms, multiplying the weight b k of speies k by the regression oeffiient dt of a treatment d at a partiular sampling date t yields the fitted hange on a log-sale of this speies relative to the ontrols. In terms of abundane, taking the exponential of this quotient yields the relative abundane ompared to the ontrols. For instane, the relative abundane of Dugesia tigrina indiated by the first PRC (Figure 7A) for the miroosms with the highest treatment onentration in week 3 is exp(4.14*-1.25) = 0.57% of the abundane in the ontrols. Figure 7A shows the first PRC, expressing the most dominant effets of arbendazim on the omposition of the maro-invertebrate data set. It shows lear deviations from the ontrol for the four highest treatments onentrations (33 µg/l and higher). Between the treatment onentrations a lear dose-response was present, the higher the treatment onentrations the larger the deviations from the ontrol. No indiation of reovery was demonstrated. For all post treatment sampling dates a signifiant influene of the treatment regime as a whole was found (p < 0.05). This was tested by Monte Carlo permutation performed for eah sampling date using lntransformed treatment levels. For the sampling dates 1, 5, 7 and 9 post start of the treatment a NOEC ommunity of 3.3 µg/l was alulated (Williams ANOVA test applied on first prinipal omponent, see for more details). Monte Carlo permutation tests permuting whole time series indiated that the first PRC diagram displayed a signifiant part of the treatment variane (p < 0.05, see Van den Brink and Ter Braak 1999 for more details). The seond PRC also displayed a signifiant part of the treatment variane, the third did not. This means that no single dose-response type is present in the data set but several sub-dominant ones. The model for two PRC omponents is: y d(j)tk = y 0tk + b k1 dt1 + b k2 dt2 + ξ d(j)tk, where the sores { dt1 }[t = 1 T] represent the first prinipal response urve (PRC) for treatment d, ie. ourse of treatment d in time relative to the ontrols, the sores { dt2 }[t = 1 T] represent the seond prinipal response urve for treatment d, b k1 is the weight of speies k on the first PRC, and b k2 is the weight of speies k on the seond PRC. The seond PRC is shown in Figure 7B and displays the most important deviations from the first PRC present in the data set. It shows relatively large deviations from the ontrol for the 33 and 149

10 Figure 7. First (A) and seond (B) Prinipal Response Curves indiating the effets of the fungiide arbendazim on the maro-invertebrate ommunity. Of all variane, 30% ould be attributed to sampling date; this is displayed on the horizontal axis. Forty-nine perent of all variane ould be attributed to treatment, the remaining variane (21%) is between repliate variation. Of the treatment variane, 44% is displayed on the vertial axis of the first PRC (A), and another 17% on the vertial axis of the seond PRC (B). The lines represent the ourse of the treatment levels in time. The speies weight (b k ) an be interpreted as the affinity of the taxon with the Prinipal Response Curves ( dt ). Taxa with a speies weight between 0.5 and -0.5 are not shown for larity. The treatment explained a signifiant part of the total variane, of whih also a signifiant part is displayed in the first and seond PRC (p < 0.05, Monte Carlo permutation test with permuting whole time series only). The third PRC did not display a signifiant part of the treatment variane and is thus not shown (p > 0.05). 150

11 100 µg/l treatment onentrations. The seond PRC thus differentiates between taxa showing a response at the four highest treatment onentrations and those showing a response at the two highest treatment onentrations only. For instane, Dugesia tigrina has a positive weight with both diagrams. When both diagrams are onsidered in the interpretation, the indiated response for this taxon is a sum of both diagrams, in whih the diagrams are weighted by the speies sores of D. tigrina (Van den Brink and Ter Braak 1998). This indiates that this taxon suffered more severely from the 33 and 100 µg/l arbendazim treatment than was indiated by the first PRC diagram alone (Figure 8, see Cuppen et al for its real response). On the other hand Stylaria laustris has a positive weight with the first and a negative weight with the seond diagram. To dedue the indiated response of this taxon from the two PRC diagrams one has to subtrat the seond PRC from the first PRC diagram. The result of this subtration indiates that this taxon only suffered from the arbendazim treatment in the two highest treatment onentrations (Figure 8). By doing so all taxa an be grouped on the basis of the shape of their response to the arbendazim treatment (see Figure 8 for a graphial representation). For instane, all taxa with a positive response with both diagrams (eg. Dugesia lugubris, Dugesia tigrina, Pisidiidae) are indiated to have dereased in all but the lowest treatment levels; all taxa with a positive weight with the first PRC and a small weight with the seond one (eg. Gammarus juvenile, Gammarus pulex and Dero sp.) are indiated to have strongly dereased in the two higher treatment onentrations and only moderately in the intermediate ones; and all taxa having a positive weight with the first and a negative one with the seond PRC (eg. Stylaria laustris, Potamopyrgus antipodarum, Bithynia tentaulata and Proasellus meridianus) are only indiated to show effets for the two highest treatment onentrations. This grouping an be done for all ombination of weights (Van den Brink and Ter Braak 1998). This example shows that PRC is able to show the response of a whole ommunity into an easy to read diagram (Figure 7A), its outome is representative for the most sensitive speies (NOEC ommunity = 3.3 µg/l), it an easily be ombined with multivariate statistial testing (eg. Monte Carlo permutation test), and it is able to summarise very diverse response patterns when the seond PRC is also taken into aount. PRC ON MONITORING DATA: THE SEWAGE TREATMENT PLANT EXAMPLE PRC has only been applied to experimental data exept in a study by Leonard et al. (2000). Leonard et al. (2000) took samples at several sampling dates at several sites of a river, some of whih were influened by endosulfan exposure. The non-exposed sites served as the undosed ontrol, to whih the endosulfan influened samples were ontrasted. In this way the experimental design needed for PRC (treatment and ontrol) was imposed on the monitoring data. Often, however, no undosed ontrol is present, but a referene site an be assigned within the monitoring sheme. In this setion, PRC will be applied to a monitoring data set is whih a referene is assigned. Coad (2001) measured several physio-hemial parameters weekly at five sites: 1) 300 m upstream of a sewage treatment plant (STP) outlet, 2) 100 m upstream of the STP outlet, 3) in the STP outlet 4) 100 m downstream of the STP outlet and 5) 1 km downstream of the STP outlet (Table 2). The upstream part of the river (sites 1 and 2) was loated in an urban area. In total 795 samplings were performed at the five sites in the period 1994 through 2002 to evaluate the performane of the STP. All details are desribed in Coad (2001). It is lear when this data set is analysed with PCA or RDA and its results are displayed in a biplot, a very luttered and rowded diagram would be the result of the presene of many samples. Figure 9 shows the results of the PRC analysis using sampling month as ovariable and the produt of sampling month and site as explanatory variables. Site 3 (the outlet of the STP) was used as the referene beause it has the most omplete time-series. Figure 9 indiates the largest differenes from the STP outlet for the two upstream sites. For these sites, ompared to the outlet, lower levels of NOx, total nitrogen, ondutivity, salinity, total phosphorus and temperature are indiated together with higher levels of turbidity and faeal oliforms. For the two downstream sites smaller differenes are indiated, but in the same diretion. From the PRC analysis it is lear that the outlet of the STP lead to an inrease of onentrations of nitrogen and phosphorus, temperature and assoiated measures as ondutivity and salinity in the river. After the outlet, values of these parameters derease in the downstream sites, but not as low as in the upstream sites. The STP seems very suessful in reduing faeal oliforms, their level is even lower in the outlet ompared to the upstream sites whih are slightly ontaminated due to urbanisation. No trend in time is apparent, indiated differenes are relatively stable in time with a few outliers. This example shows that PRC an also be used for the evaluation of (bio)monitoring data, even when no apparent ontrol is present. PRC results in an easy to interpret overview of differenes, even when the sites are sampled very often, beause it displays time in a single diretion in the diagram. DISCUSSION In the eotoxiologial literature, Canonial Variate Analysis (CVA also alled Disriminant Analysis, DA) is often used to eluidate whih ombination of variables disriminate best between different treatment groups. Tehnially, CCA (Table 1) is a generalisation of CVA. To obtain a CVA through CCA, variables denoting groups are introdued as speies data and harateristis of these groups (eg. ontaminant data) as explanatory variables (Ter Braak and smilauer 2002). Bernet et al. (2001) used CVA to eluidate whih fish-serum parameters explained the differenes between ontrol and sewage impated sites. Their ordination diagram shows the size of group differenes. The diagram ould have been more informative if arrows for the fish-serum parameters had been added to the diagram, as the resulting biplot would allow one to interpret the group differenes in terms of the fish-serum parameters. Aptula et al. (2002) used CVA in quite a different ontext. They tried to explain the differenes in a priori assigned mehanisms of toxi mode of ation on the basis of their moleular desriptors. This analysis results in a Canonial Disriminant Funtion (CDF) in whih the explanatory variables are weighted on the basis of their ability to predit the lassifiation the best. It is interesting to ompare these uses of CVA with the methods we disussed. In our penguin and Lees examples (RDA and CCA) the harateristis (biologial or hemial speies ) are the responses to be explained by groups, a nominal explanatory variable (eg. denoting period or plae relative to the fatory). As mentioned above, in CVA it is the other way round. Beause harateristis are explanatory variables in CVA, CVA is hampered by multiollinearity among the 151

12 Figure 8. Two dimensional plot of the weights of the invertebrate taxa on the first and seond PRC, as given in Figure 7. The four diagrams in the orners apply to the taxa that have equal weights on the two PRCs (exept from the sign). 152

13 Figure 9. Prinipal Response Curves indiating the effets of the outlet of a sewage treatment plant on some monthly averages of physio-hemial harateristis of a river. Of all variane, 24% ould be attributed to between month variation; this is displayed on the horizontal axis. Fifty-seven perent of all variane ould be alloated to between site differenes, the remaining 19% to within month variation. Of the between site variation, 58% is displayed on the vertial axis. The lines represent the ourse of the sites in time with respet to the outlet. The weight of the physio-hemial variables (b k ) an be interpreted as the affinity of the variables with the Prinipal Response Curves ( dt ). harateristis, in partiular when the number of harateristis is greater than or of the same order of magnitude as the number of samples (Ter Braak 1995). For this reason, users of CVA apply stepwise seletion methods to redue the number of harateristis. This was not needed in our examples. Whih method is the method of hoie in a partiular appliation, will naturally depends on the researh question. In many QSAR studies multivariate Partial Least Squares is used (PLS2; eg. Eriksson et al. 2000; Drew et al. 1999). PLS2 is similar to RDA, but differs in that PLS2 guards automatially against multiollinearity among the explanatory variables whereas RDA does not (see Ter Braak and De Jong 1998 where RDA is termed redued rank regression, and Ter Braak and Verdonshot 1995). In RDA the problem of multiollinearity (when there are many explanatory variables) would be takled by forward seletion of variables (.f. CVA above). No other appliations of CA and related methods ould be found. The reason for the low use of CA and related methods in eotoxiology ould be that the researher is interested in logisti dose-response relationships between a stressor and the absolute abundane of speies, whih is better modelled by PCA and derived methods than CA (Van den Brink and Ter Braak 1997). We note that the logisti version of RDA an be fitted to presene/absene (1/0) speies data by the reent RR-VGLM software of Yee and Hastie (2003). In the eotoxiologial literature we found many appliations of PCA to link biologial data (eg. benthi ommunities) to hemial omposition of the habitat (eg. sediment). Some of them use ordination diagrams for the presentations of the results of the analyses (Vogt 1990; Berggrena et al. 1999; Carr et al. 2000, DelValls et al. 1998, Pedersen et al. 1999), but sometimes only tables with the site and speies sores of the different prinipal omponents are provided (Riba et al. 2002; DelValls et al. 2002; Boluda et al. 2002). The reason for this ould be that one wants to onsider more than two prinipal omponents. It must be stated that when using biplots often only the first two prinipal omponents are taken into onsideration without stating reasons why the third is not. It is reommended to use biplots beause (or)relations between speies and sites stand out more in biplots than in tables. Nevertheless a proper reasoning must be provided why a sueeding axis is not taken into onsideration. 153