A probabilistic model characterizing fish assemblages of French rivers: a framework for...

Freshwater Biology (2001) 46, 399–415

APPLIED ISSUES

A probabilistic model characterizing fish assemblagesof French rivers: a framework for environmentalassessment

THIERRY OBERDORFF,* DIDIER PONT,† BERNARD HUGUENY† and DANIEL CHESSEL†*Institut d’Ecologie et de Gestion de la Biodiversite, Laboratoire d’Ichtyologie, Museum national d’histoire naturelle, 43 rueCuvier, 75231 Paris cedex 05, France†Laboratoire de Biometrie et Biologie Evolutive, Universite Lyon I, 43 Bld du 11 Novembre 1918, 69622 Villeurbanne cedex,France

SUMMARY

1. Management of running waters and assessment of water quality trends require theuse of biological methods. Among potential indicators, fish assemblages are of particu-lar interest because of their ability to integrate environmental variability at differentspatial scales.2. The French Water Agencies and the Ministry of the Environment initiated a re-search programme to develop a fish-based index that would be applicable nation-wide.Such an index should encompass the relative importance of geographic, ecoregionaland local factors influencing the distribution of riverine fishes.3. An effective way of using the information available from fish assemblages to estab-lish such an index is through the use of the ‘reference condition approach’ whichinvolves testing a fish assemblage exposed to a potential stress against a referencecondition that is unexposed to such a stress.4. Logistic regression procedures were applied, using a fish data set of 650 referencesites fairly evenly distributed across French rivers and defined by some easily mea-sured regional and local characteristics, to elaborate the simplest possible responsemodel that adequately explains the observed patterns of occurrence for each species ofa fish assemblage at a given site of any given river. This allows us to predict a‘theoretical’ assemblage at a site.5. The models were validated using a second independent data set of 88 referencesites. Using a third data set of 88 disturbed sites, the observed assemblages were thencompared against the reference condition as defined by the ‘theoretical’ assemblages.The amount of deviation between the expected and observed assemblages within thesesites is used as a measure of degradation.6. This approach could be used as a framework for adapting and calibrating a multi-metric index, thereby serving as a practical technical reference for conducting cost-effective biological assessments of lotic systems.

Correspondence: Thierry Oberdorff, Laboratoire d’Ichtyologie, Museum national d’histoire naturelle, 43, rue Cuvier, 75005 Paris,France.E-mail: [email protected]

© 2001 Blackwell Science Ltd 399

T. Oberdorff et al.400

Keywords : biological assessment, fish assemblages, fish-based index, French rivers, logisticregressions

Introduction

In developed countries, the modern goal of waterpolicy is not only to preserve ecosystems, but also torehabilitate them and to restore their functions. Thus,it is necessary to develop practical biological toolsusing a community-based approach for monitoringwater resource quality. One of the most effectiveways of using the information available from theseassemblages to establish such biocriteria is throughthe use of the ‘reference condition approach’ (Baileyet al., 1998), which involves testing an ecosystemexposed to a potential stress against a reference con-dition that is unexposed to such a stress. For aquaticecosystems, biological indicators can be chosen froma variety of animal or plant assemblages, but fish areof particular interest because (1) they are present inmany water bodies, (2) their taxonomy, ecologicalrequirements and life history are generally betterknown than for other assemblages, (3) they occupy avariety of trophic levels and habitats, and (4) theyhave both economic and aesthetic values, and thushelp raise awareness about the necessity of conserv-ing aquatic habitats.

Ecologists have developed biological indexes tomonitor water quality beginning with the pioneeringefforts of Kolkwitz & Marsson (1908, 1909). Since thisearly work, the concept of biological monitoring hasbeen greatly refined with a general trend away fromthe indicator species concept and/or diversity indicestowards an integrated, community-based approach(see Fausch et al., 1990 for a review). In France, theMinistry of the Environment, the Water Agencies andthe National Council of Fishing have established apartnership to define a fish-based index with nation-wide application.

One such integrated approach (using a ‘referencecondition approach’) to quantify the impact of humanactivities on the aquatic ecosystem via fish assem-blages is the Index of Biotic Integrity (IBI), first for-mulated by Karr (1981). The IBI employs a series ofmetrics based on assemblage structure and functionto calculate an index score at a site, which is thencompared with the score expected at an unimpairedcomparable site (Scott & Hall, 1997).

Nevertheless, effectively adapting such an indexover a broad geographic area (i.e. France) requires a

detailed understanding of both the patterns of assem-blage composition and distribution within andamong water bodies under natural conditions, andthe nature of the major environmental gradients thatcause, or at least explain, these patterns (Lyons, 1996).Patterns of assemblage richness and composition arestrongly influenced by the spatial scale of investiga-tion. On a local scale (within a site), previous studiesof stream fish assemblages have shown that habitats(as a function of depth, current velocity, temperature,substrate (Huet, 1959; Gorman & Karr, 1978; Anger-meier & Schlosser, 1989; Rahel & Hubert, 1991)), andincreasing stream size (gradient, stream width, dis-charge, stream-order, catchment area (Sheldon, 1968;Horwitz, 1978; Paller, 1994; Belliard, Boet & Tales,1997)) can influence not only species richness, butalso trophic composition (Schlosser, 1982; Anger-meier & Karr, 1983; Oberdorff, Guilbert & Luchetta,1993).

Patterns and processes observed in local fish as-semblages are not only determined by local mecha-nisms acting within assemblages, but also result fromprocesses operating at larger spatial scales (Hugueny& Paugy, 1995; Angermeier & Winston, 1998; Ober-dorff et al., 1998). At regional scales (basins or eco-regions), physical factors such as river size (Hugueny,1989; Welcomme, 1990; Guegan, Lek & Oberdorff,1998), geomorphology and climate (Hughes, Rexstad& Bond, 1987; Whittier, Hughes & Larsen, 1988;Changeux & Pont, 1995) are the major determinantsof assemblage richness and composition, thereby reg-ulating the importance of local-scale factors. Thus,before assemblage response can be useful in the as-sessment of stream condition and/or in the compari-son of stream condition within an aquatic system(and from one region to another), using indices suchas the IBI, it is essential to take into account the wayassemblage attributes are related to actual streamconditions (Hoefs & Boyle, 1995; Smogor & Anger-meier, 1998).

In this study we model, using logistic regressions,the occurrence of the 34 most common fish species ofFrance in relation to regional and local environmentalfactors. Using this methodology, the probability ofoccurrence of an event (a fish species in our case) canbe predicted as a function of one or more indepen-

© 2001 Blackwell Science Ltd, Freshwater Biology, 46, 399–415

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Predicting riverine fish assemblages 401

dent variables (Ter Braak & Looman, 1986; Hosmer &Lemeshow, 1989; Trexler & Travis, 1993; Edwin,Peeters & Gardeniers, 1998). Our method is designedto predict the fish assemblage at a particular site frommodels of species occurrence. First, we randomlydivided a set of reference sites into two subsets. Onesubset was used to calibrate the models, and theother to validate the models (by checking for theirpredictive power). Secondly, using a data set of ex-posed (disturbed) sites, we measured the deviationbetween the expected and observed assemblages atthese sites to assess the ability of our models to detectanthropogenic perturbations. The probabilistic natureof our approach allows a rigorous quantification ofthe degree to which a disturbed assemblage deviatesfrom a comparable but relatively undisturbed assem-blage. This method could be used as a framework foradapting and calibrating a multimetric index basedon species occurrence, thereby serving as a practicaltechnical reference for conducting cost-effective bio-logical assessments of lotic systems.

Methods

Fish data

We extracted two data sets from the database held bythe Conseil Superieur de la Peche (Banque Hydrobi-ologique et Piscicole), covering a period of 10 years ofsurvey. (i) A set of 738 reference sites (RS738), fairlyevenly distributed across French rivers (Fig. 1). (ii) Aset of 88 exposed (disturbed) sites (DS88). The selec-tion was done by regional experts (fish biologists) onthe basis of water quality map inspection and fieldreconnaissance. Factors considered in the field inspec-tion included the amount of stream channel modifica-tion, channel morphology, substrate character andcondition, and the general representativness of thesite within the region. Reference sites were notpristine nor totally undisturbed but were those thathave suffered the least impact within a particularbiogeographical region (Hughes, 1995). Most of theupstream sites selected were virtually undisturbedbut it was impossible to identify completly undis-turbed sites for large rivers (at large catchment-levelscales). Consequently, reference sites, as defined inthis paper, should rather be viewed as ‘typical’ of aparticular biogeographical region. RS738 data set wasfurther randomly divided in two subsets: one set of

650 sites (RS650) that was used to calibrate the mod-els, and one set of 88 sites (RS88) that was used tovalidate the models. The size of this last data set(RS88) was defined to match the size of the data set ofdisturbed sites (DS88). Sites were sampled during1985–98 by the Conseil Superieur de la Peche byelectrofishing conducted during low-flow periods(from August to October) to evaluate fish assem-blages throughout France. These included referencesites on large streams, mainstream rivers and head-water streams throughout the country. Depending onriver width and depth, two different sampling meth-ods were used. When it was possible (small rivers)each site was sampled by wading. In large rivers,sampling was undertaken by boat in near shore areas.Although this last approach may not have yielded acomplete inventory of all species, we combined thesedata with those obtained for small rivers because webelieved most species in large French rivers to beconcentrated in near shore areas. This hypothesis wascorroborated by a study using sonar techniques toevaluate fish assemblages in the main channel of theSeine River (P. Boet et al., unpublished data). The sizeof each sample was sufficient to include the homerange of the dominant fish species as defined by Stott(1967), Nicolas, Pont & Lambrechts (1994) and Minns

Fig. 1 Map of France showing eight hydrological units andthe 650 reference sites used to build a probabilistic modelcharacterizing riverine fish communities. H1=North Seabasins; H2=Seine basin; H3=English Channel basins;H4=Atlantic basins; H5=Loire basin; H6=Garonne basin;H7=Rhone basin; H8=Mediterranean basins.



(1995), and to encompass complete sets of the charac-teristic river form (e.g. pools, riffles, runs) (generally\100 m for wading sites and \500 m for boat sites)(Yoder & Smith, 1998). Fish were identified to species,measured and weighed in the field, and thenreleased.

Local scale environmental variables

Eight abiotic environmental variables were measuredat each site: gradient (‰) (derived from topographicmaps) (GRA), elevation (m) (derived from topo-graphic maps) (ELE), July mean daily maximum airtemperature (TJuly), January mean daily maximum airtemperature (TJanuary), stream width (m) (WID), meandepth (m) (DEP), distance from headwater sources(km) (measured using a digital planimeter on a1:1000000-scale map) (DIS), and surface area of thedrainage basin (km2) (measured using a digitalplanimeter on a 1:1000000-scale map) (SAD).

We used DIS and SAD as synthetic variablesreflecting the position of each site in the upstream–downstream gradient. Principal component analysis(PCA) was used to reduce dimensionality and elimi-nate co-linearity in the two variables (James & Mc-Culloch 1990). The first principal component (PC1)was retained as a synthetic independent variablereflecting the longitudinal gradient (G) for furtheranalyses:

G=3.015−0.347�log(SADkm2 )−0.543�log(DISkm).

A measure of local water velocity was calculatedusing a velocity index (V) derived from the Chezyformula (Chow, Maidment & Mays, 1988):

V= log(WIDm)+ log(DEPm)+ log(GRA‰)

−log(WIDm+2�DEPm)

Elevation was introduced in the models as E=log(ELE). Climatic variables that have a spatial com-ponent represent potential explanations for fishdistribution patterns (T. Oberdorff et al., unpublisheddata). Two climate variables were used: July meandaily maximum temperature (TJuly) and January meandaily maximum temperature (TJanuary). The baselineclimate data set was generated from mean monthlyvalues for 1951–93 for all recording stations supply-ing data to the Meteorological Office. These data wereinterpolated on the basis of the National Grid. Wethen introduced in the models two independent vari-

ables related to temperature requirements of fish spe-cies (see Sokal & Rohlf, 1995):

(i) T1=Tjuly+TJanuary

(ii) T2=Tjuly−TJanuary

Regional scale variables

A regional classification can provide a useful frame-work for studying and managing rivers in differentgeographic areas. There are several approaches todeveloping these geographic frameworks (Omernik& Bailey, 1997). One of the fundamental units forunderstanding fish assemblage structure in rivers isthe hydrological unit. Hydrological units are discretephysical units that provide well-defined boundarieswith a real biological significance for riverine assem-blages (Strange, 1998). The insular nature of rivers(Sheldon, 1968; Hugueny, 1989; Oberdorff, Guegan &Hugueny, 1995; Oberdorff, Hugueny & Guegan, 1997;Guegan, Lek & Oberdorff, 1998) stipulates that themaximum number of species able to colonize a givenlocal habitat is the number of species present in thewhole drainage basin (Hugueny & Paugy, 1995;Oberdorff et al., 1998). Here, hydrological units werecoded as eight different nominal variables. Four rep-resent large river basins (i.e. Seine River (H2), LoireRiver (H5), Garonne River (H6), and Rhone River(H7)), and four (i.e. North Sea basins (H1), EnglishChannel basins (H3), Atlantic basins (H4), and Med-iterranean basins (H8)) were established on the basisof fauna lists published by Persat & Keith (1997).Hydrological units were entered into the regressionsas dummy variables (Fig. 1).

Statistical analyses

Thirty-four species that were captured at more than1% of the 650 sites were used in analyses (Table 1).Rare species were not included because they typicallyhave little effect on results and because their inclu-sion substantially complicates statistical computa-tions and interpretations (Gauch, 1982).

Logistic regression was applied to the presence/ab-sence data for all 34 species; S-PLUS (1995) was usedto analyse the relationship between each species andthe explanatory variables. This technique was firstintroduced in ecology by Austin (1980) and Austin,Cunningham & Fleming (1984). The ‘presence/ab-



Table 1 The 34 most common freshwater fish species ofFrance

Family/species (code) Common name

PetromyzontidaeBrook lampreyLampetra planeri (Lap)

SalmonidaeSalmo salar (Sas) Salmon

Brown troutSalmo trutta fario (Sat)GraylingThymallus thymallus (Tht)

EsocidaePikeEsox lucius (Esl)

CyprinidaeAbramis sp. (Abs) Common bream

BleakAlburnus alburnus (Ala)Stream bleakAlburnoides bipunctatus (Alb)BarbelBarbus barbus (Bab)Mediterranean barbelBarbus meridionalis (Bam)Crucian carpCarassius carassius (Cac)Common naseChondrostoma nasus (Chn)French naseChondrostoma toxostoma (Cht)Common carpCyprinus carpio (Cyc)GudgeonGobio gobio (Gog)ChubLeuciscus cephalus (Lec)

Leuciscus leuciscus (Lel) DaceLeuciscus soufia (Les) Blageon

MinnowPhoxinus phoxinus (Php)RoachRutilus rutilus (Rur)

Rhodeus sericeus (Rhs) BitterlingRuddScardinius erythrophtalmus (Sce)TenchTinca tinca (Tit)

CobitidaeStone loachNemacheilus barbatulus (Neb)

IctaluridaeBlack bullheadIctalurus melas (Icm)

AnguillidaeEelAnguilla anguilla (Ana)

GadidaeBurbotLota lota (Lol)

GasterosteidaeGasterosteus aculeatus (Gaa) Three-spined StickelbackPungitius pungitius (Pup) Nine-spined Stickelback

PercidaeRuffeGymnocephalus cernua (Gyc)

Perca fluviatilis (Pef) PerchPikeperchStizostedion lucioperca (Stl)

CentrarchidaePumpkinseedLepomis gibbosus (Leg)

CottidaeCottus gobio (Cog) Bullhead

log� p(x)

1−p(x)�

=a0+a1x+a2x2

Up(x)=1

1+e−a0−a1x−a2x2 (1)

The parameters a1 and a2 of equation (1) are regres-sion coefficients with a0 as the intercept or constantterm. The resulting response curve is symmetricaland bell-shaped. As a2 approaches zero, the modelproduces a sigmoidal increase or decrease in theprobability of occurrence (ter Braak & Looman, 1986;McCullagh & Nelder, 1989). The maximum likelihoodprinciple is used to estimate the values for theparameters a0, a1 and a2 (Hosmer & Lemeshow, 1989).Equation (1) can be extended to include more thanone variable. The contribution of parameters in alogistic regression model is assessed by comparingthe predictive value of models with and withoutthem using the likelihood ratio test based on thedifference of the deviance (D= −2log (likelihoodratio)) between two models (see Trexler & Travis1993; Edwin, Peeters & Gardeniers, 1998 for moredetails). In order to determine the minimum adequateset of variables for predicting the probability of oc-currence of each species we applied stepwise logisticprocedures which automatically add and removeterms from a given general linear model (GLM) toconstruct a new GLM model in a ‘stepwise’ fashion.At each step, a new parameter is added to the mini-mal model if it significantly reduces the unexplaineddeviance using the Akaike criterion (Hastie & Pregi-bon, 1993).

Using the independent set of 88 reference sites(RS88), we first validated each of the species-specificmodels obtained by comparing the observed occur-rence Oocc (number of sites occupied by a species) tothe expected one Eocc=Sj Pij, where pij is the proba-bility of observing species i in site j according to thelogistic model and j=1 to 88 sites and i=1 to 34species.

For each species (i ), the amount of deviation be-tween the expected and observed occurrence is thengiven by:

Docc=Oocc−Eocc'%j

pij(1−pij)

Docc corresponds to the standardized residualsaround the prediction line of observed vs. predictedoccurrences.

sence response curve’ of a species (Ter Braak &Looman, 1986) describes the probability of the speciesbeing present, p(x), as a function of a measuredenvironmental variable x. The general expression forthis probability is:



If the models are valid we expect: (1) that theintercept of the regression line of observed versuspredicted occurrences will not be statistically differ-ent from zero and that the slope will not be statisti-cally different from one; (2) the quantity Docc to beLN(0,1) distributed. The same tests have been appliedfor the independent data set of 88 perturbed sites(DS88). Assuming that anthropogenic perturbationsreduce fish species occurrence, we expect that: (1) theslope will be lower than one and/or the intercept willbe lower than zero; (2) the mean of Docc will be lessthan zero.

For each species the predicted standard deviation(SDocc) is given by:

SDocc='%

j

pij(1−pij)

The theoretical variance then differs between spe-cies, which violates the assumption of homogeneityof variance needed in regression tests. To circumventas far as possible this problem we used weightedleast squares (Draper & Smith, 1966) in regressingobserved occurrence values against predicted values.Weights used were the reciprocals of the theoreticalvariance in species occurrence.

In a second step we predicted presence/absence ofeach species for a site by rounding off each species’sexpected probability to 0 (if the predicted probabilityis lower than 0.5) or 1 (if the predicted probabilty ishigher than 0.5) (Leftwich, Angermeier & Dolloff,1997). The similarity between observed and predicteddistributions is then assessed by computing the pro-portion of correct predictions of presence or absence.

To validate the models at the assemblage level wequantify, using RS88 data set, the amount of devia-tion between the predicted and observed assem-blages. To do so, we used two assemblagedescriptors: the assemblage species richness (SR), andthe likelihood of observing the assemblage (given themodels).

For a given site the expected species richness isgiven by ESR=Si Pij and its predicted standard devia-tion by:

SDSR='%

i

pij(1−pij)

For each site (j ), we also define the amount ofdeviation between the expected and observed speciesrichness (DSR):

DSR=OSR−ESR'%i

pij(1−pij)

If the models are valid and if species are indepen-dently distributed, we expect that: (1) the intercept ofthe regression line of observed vs. predicted occur-rences will not be statistically different from zero andthat the slope will not be statistically different fromone; (2) the quantity DSR to be LN(0,1) distributed.The theoretical variance in species richness differsamong sites. To take into account this heteroscedas-ticity we used weighted least squares in regressingobserved species richness values against predictedvalues. Weights used were the reciprocals of the theo-retical variance in species richness.

The same tests were applied for the independentdata set of 88 perturbed sites (DS88). Assuming thatanthropogenic perturbations reduce fish species rich-ness, we expect that: (1) the slope will be lower thanone and/or the intercept lower than zero; (2) the meanof DSR will be less than zero.

Probabilities obtained from logistic regressions canbe combined to compute the likelihood of an ob-served list of species at a site. This value representsthe probability (given by the models) of observingthis particular list of species. The log of this value isused for convenience. The Log-likelihood (LL) is thengiven by:

LL= −%i

log(p(obs)ij)

where p(obs)ij=pij when species i is present at site j,or p(obs)ij= (1−pij) when species i is absent at site j.LL is always positive and high values indicate ob-served assemblages diverging from ‘theoretical’ ones.A drawback of using the LL function is that there isno theoretical model of distribution for its values(Collett, 1999). This drawback led us to performMonte-Carlo simulations. At each site, a randomnumber (between 0 and 1) is assigned to each species.If this number is higher than the probability pij for thespecies at the site, then the species is considered to bepresent in the simulated assemblage. When the com-position of the simulated assemblage is completed,



the resulting LL is computed. At each site, 10000random assemblages were generated this way. Foreach site, we computed the proportion of iterationsfor which LL simulated ]LL observed. This valuegives the probability a of rejecting the null hypothesis(species distributed independently of each other andaccording to logistic models) when it is true (type Ierror). If species are distributed according to the nullhypothesis in our set of reference sites, then a mustbe uniformly distributed over the 0–1 interval(Hedges & Olkin, 1985) because, by definition, it isexpected that 5% of the assemblages have a 0.05, 10%have a 50.1 and so on.

Assuming that anthropogenic perturbations mod-ify fish species composition, we expect observed LLvalues (DS88 data set) to be higher than expectedleading to an a distribution that differs from a uni-form distribution by an excess of low values (siteswith unlikely LL values according to the models).

Results

Logistic regression models for each of the 34 species

Table 2 shows the models retained for each of the 34species. The ecological significance of each specificmodel will be reported in another paper. Most spe-cies show statistically significant fits with G (32/34), V(23/34), T1 (20/34), T2 (27/34), H (26/34), E (28/34) butrespond in different ways to the environmental vari-ables studied. For example, 68% of the species aresignificantly linked to hydrological units, 68% to alti-tude and 71% are dependent on both longitudinalgradient and current velocity. These results suggestthat regional factors together with local factors sig-nificantly influence fish assemblage structure inFrench rivers.

As an example, Fig. 2 shows the probabilities ofoccurrence of nine of the 34 species against the longi-tudinal gradient (G). For Salmo trutta, higher proba-bilities of occurrence occur at lower values of G, butthe species occurs over the full range of these values.Conversely for the catadromous species Anguilla an-guilla, the probability of occurrence decreases regu-larly with G. For Alburnus alburnus, Barbus barbus,Leuciscus cephalus, and Rutilus rutilus, a higher proba-bility is reached at higher values of G, but probabili-ties of occurrence become zero or nearly so for thelowest values of G. Cottus gobio, Leuciscus leuciscus,

and Phoxinus phoxinus occur over the full range of Gvalues, but show a distinct preference for mediumposition in the upstream–downstream gradient.These results are similar to those of previous studiesdealing with occurrence profiles of these speciesalong the longitudinal gradient (Huet, 1959;Verneaux, 1977; Belliard et al., 1997).

Validation of the models and assessment of theircapacity in dicriminating perturbations

Fig. 3 shows the relationships between Eocc and Oocc

values for RS88 and DS88. In the case of RS88 (Fig.3a) the regression is highly significant (n=88, R2=0.981, PB0.001). Student’s t-tests show that the inter-cept of the regression line is not statistically differentfrom zero (n=88, t=1.164, P\0.05) and that theslope is not different from one (n=88, t=1.552, P=0.130). The mean of Docc does not differ from zero(0.327, t(33)=1.602, P=0.119) and its variance(1.414) does not differ from one according to a x2

distribution of 33 ddl (Sokal & Rohlf, 1995) (95%confidence limits: 0.920–2.450). For DS88 (Fig. 3b), therelationship between Eocc and Oocc values is weaker(n=88, R2=0.737, PB0.001). The intercept of theregression line is not statistically different from zero(n=88, t=2.022, P=0.052) but the slope is statisti-cally lower than one (n=88, t= −2.786, P=0.009).The mean of Docc does not differ from zero (0.129,t(33)=0.285, P=0.778) and its variance (7.006) dif-fers from one (95% confidence limits: 4.558–12.138).Furthermore, the species-specific models correctlypredict presence and absence of species for 71–99%of sampled sites depending on the species (mean=0.903; median=0.920; CV=0.08). Thus, species-spe-cific models performed well in the validationprocedures despite a slightly significant underestima-tion in the occurrence of two species (i.e. Leuciscuscephalus (Lec) and Gasterosteus aculeatus (Gaa)), and aslightly significant overestimation in the occurrenceof one species (i.e. Stizostedion lucioperca (Stl)) (Table3). As expected, the models are much less efficient inpredicting species occurrence for the data set of dis-turbed sites. There is a high dispersion of pointsaround the prediction (Fig. 3b). Moreover, Table 3shows significant underestimation in the occurrenceof nine species (i.e. Alburnus alburnus (Ala), Abramissp. (Abs), Carassius carassius (Cac), Cyprinus carpio(Cyc), Gobio gobio (Gog), Lepomis gibosus (Leg), Leucis-




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Fig. 2 Probability of occurrence of the nine species for eight classes of equal distribution of inversed G values. The solid linesjoin the mean probabilities for each class. The dashed lines give the 95% confidence limits of the expected frequency (see Table1 for species code).



Fig. 3 Plots of expected vs. observed species occurrencevalues for the two independent data sets RS88 and DS88 (seetext for abbreviations): (a) RS88, R2=0.974, PB0.001; (b)DS88, R2=0.848, PB0.001.

(n=650, t=1.457, P=0.145). The mean of Dsr does notdiffer from zero (−0.024, t(649)=−0.437, P=0.662)but its variance (1.996) differs from one (95% confi-dence limits: 1.796–2.233). In the case of RS88, theregression is highly significant (n=88, R2=0.602,PB0.001). The intercept of the regression line is mar-ginally different from zero (Student’s t-test, n=88,t=2.110, P=0.038), and the slope is not statisticallydifferent from one (n=88, t= −1.607, P=0.112). Themean of Dsr does not differ from zero (0.238, t(87)=1.480, P=0.142) and its variance (2.278) differs fromone (95% confidence limits: 1.728–3.142). Finally, forDS88 (Fig. 4c), the relationship between expected andobserved SR values is weaker (n=88, R2=0.241,PB0.001). The intercept of the regression line is statis-tically different from zero (n=88, t=2.074, P=0.041),and the slope is statistically different from one (n=88,t= −2.525, P=0.013). The mean of Dsr does not differfrom zero (0.123, t(87)=0.518, P=0.606) and its vari-ance (4.973) differs from one (95% confidence limits:3.772–6.858).

Fig. 5 shows the distribution of probabilities of LLvalues obtained for RS650, RS88 and DS88 (i.e. numberof iterations from 10000 for which LL predicted \LLobserved) plotted against a uniform distribution. Forboth data sets of reference sites (RS650 and RS88) theprobabilities of LL values approach a uniform distribu-tion (Figs 5a & b). In contrast, as expected, the proba-bilities of LL values for disturbed sites (DS88) are notuniformly distributed, but mostly occur in the left partof the graph where P values tend towards zero (Fig.5c).

Discussion

Habitat models relating physical characteristics to pop-ulation features (occurrence or density), are widelyused in applied ecology (Boyce & McDonald, 1999). Inreviewing such models for stream fishes, Fausch,Hawkes & Parsons (1988) emphasized that they arefrequently based on small sample sizes and are rarelyvalidated on a new and independent data set. Further-more, habitat models are often not easily transferableamong systems or lack precision for the system inwhich they were developed (Leftwich et al., 1997).Finally, integrating different spatial scales in habitatmodels is also identified as a key component forincreasing model reliability (McCreadie & Adler, 1998;Smogor & Angermeier, 1998; Chessman, 1999; Turaket al., 1999).

cus cephalus (Lec), Perca fluviatilis (Pef), rutilus rutilus(Rur), and significant overestimation in the occurrenceof six species (i.e. Barbus barbus (Bab), Cottus gobio(Cog), Lota lota (Lol), Lampetra planeri (Lap), Phoxinusphoxinus (Php), Salmo trutta (Sat). Furthermore, thespecies-specific models are less efficient in predictingpresence and absence of species for the DS88 data set.The models correctly predict presence and absence ofspecies for 61–99% of sampled sites (mean=0.825;median=0.841; CV=0.152).

Fig. 4 shows the relationships between predicted andobserved SR values for RS650, RS88 and DS88. ForRS650, the regression is highly significant (n=650,R2=0. 623, PB0.001) and Student’s t-test show thatthe intercept of the regression line is not statisticallydifferent from zero (n=650, t= −1.063, P=0.288)and that the slope is not statistically different from one



Table 3 Observed species occurrences (Oocc), expected species occurrence (Eocc) and standardized deviation between theexpected and observed species occurrences within the data set of 88 reference sites and the data set of 88 perturbed sites.Values in bold indicate species for which the expected occurrence differs significantly from the observed one

Data set RS88 Data set DS88

Species Oocc Eocc Docc Oocc Eocc Docc

8.676 −1.937 18Abs 10.5835 2.94013.121Ala −0.712 20 17.012 1.227125.151 1.705 108 11.792 −0.741Alb

32Ana 30.013 0.638 38 38.268 −0.07715Bab 11.530 1.555 15 21.104 −2.060

4.072 −0.667 13 1.057 −0.064Bam1.987 0.010 5 2.078 2.068Cac 27.113 −1.687 64 9.981Chn −1.667

3Cht 1.923 0.882 3 1.559 1.19845.759 0.597 29 54.813Cog −6.63948

4.316 0.386 85 4.014Cyc 2.12513Esl 11.436 0.630 21 18.447 0.782

9Gaa 5.001 2.120 9 7.207 0.77830.583 1.847 6037 49.451 2.608Gog

2Gyc 4.579 −1.522 7 6.384 0.3142Icm 2.466 −0.349 4 3.003 0.638

17.207 1.139 1521 22.455 −1.954Lap34 26.482 2.664 47 38.124 2.517Lec

8.157 −0.992 206 9.840 3.905Leg16Lel 13.632 0.877 25 26.214 −0.337

3Les 3.301 −0.208 2 2.562 −0.7414.076 1.126 36 8.506 −2.698Lol

43.415 0.985 57 60.551Neb −0.9824715.335 −0.132 3615 22.718 4.036Pef

46Php 46.949 −0.241 48 59.452 −3.0275Pup 4.807 0.112 11 9.440 0.650

3.840 −0.516 93 5.137 1.933Rhs22.605 1.251 49 36.976 3.357Rur 263.678 0.871 35 4.804Sas −1.090

76Sat 73.447 1.120 45 68.876 −7.9076Sce 5.336 0.346 14 7.842 2.601

3.388 −2.372 40 2.328 1.235Stl2.482 1.696 2 5.483 −1.657Tht 58.266 −0.111 16 12.514 1.1278Tit

Our approach overcomes all of these identifieddrawbacks. First, we used a large number (650 sites)of reference sites to build our models. Furthermore,these reference sites were evenly distributed acrossall available types of French rivers. Second, we testedthe performance of the model with two independentdata sets of reference and disturbed sites. Third, weincorporated in the model both local and regionalscale natural environmental factors to integrate thebiological variability that occurs naturally bothwithin and between water bodies. As a result, ourspecies-specific models performed well in the valida-tion tests. We did not validate the models outside

France. However, as it was possible to develop asingle prediction system for France, despite its com-plex and heterogeneous geology and climate, we feelconfident that the model may be appropriate forrivers in other European countries.

The species-specific models developed here areecologically meaningful when comparing referenceand disturbed sites. When analysing disturbed siteswe noticed a significant increase in the mean occur-rence of nine species (i.e. Alburnus alburnus, Abramissp., Carassius carassius, Cyprinus carpio, Gobio gobio,Lepomis gibosus, Leuciscus cephalus, Perca fluviatilis, ru-tilus rutilus) and a significant decrease in the mean



Fig. 4 Plots of expected vs. observed species richness valuesfor the three independent data sets RS650, RS88, DS88 (seetext for abbreviations): (a) RS650, R2=0.787, PB0.001; (b)RS88, R2=0.759, PB0.001; (c) DS88, R2=0.314, PB0.001.

Fig. 5 Distribution of probabilities of LL values observed (i.e.number of iterations over 10000 for which LL predicted \LLobserved) against an expected normal probabilitydistribution: (a) RS650; (b) RS88; (c) DS88.

occurrence of six species (i.e. Barbus barbus, Cottusgobio, Lota lota, Lampetra planeri, Phoxinus phoxinus,Salmo trutta). The first group is mainly composed ofubiquitous species well known to be strongly tolerantof perturbations (Belliard, Berrebi dit Thomas & Mon-nier, 1999) whereas the second group comprises moresensitive species known to disappear early with the

onset of environmental degradation (Crisp, 1996;Mann, 1996).

At the assemblage level, the two descriptors (as-semblage species richness and the LL) gave goodpredictions with the independent data set. The mod-els explained around 60% of the total variation inspecies richness, which is comparable to predictions



from artificial neural networks (ANNs) (Mastrorillo etal. 1998) and exceeds the richness variation usuallyexplained in related studies using traditional mod-elling approaches (Hugueny, 1990; Pont et al. 1995).Nevertheless, during the validation phase, we noticeda significant underestimation of the variance in spe-cies richness. By using DSR, we suppose that assem-blages are composed of statistically independentspecies (i.e. all the covariances between species arenull). In other words, we suppose that species inter-actions do not lead to negative covariances betweenspecies occurrences. This assumption is partly ver-ified here as no significant negative associations be-tween species could be found (D. Chessel,unpublished data). This result is in accordance withthe conclusions of Jackson, Somers & Harvey (1992)and Oberdorff et al. (1998) suggesting that inter-spe-cific competition is not the major force structuringfish assemblages. However, we found some signifi-cant positive associations between species belongingto the same family (i.e. Cyprinidae). Taxonomicallyrelated pairs tend to co-occur more than randomlychosen pairs of species (a detailed examination of thisresult will be reported elsewhere). An explanation forthis pattern is that some species respond in the sameway to some unknown environmental factor not in-cluded in the model. A consequence is that we cannotpredict species richness variance because it is inflatedby positive covariances to an unknown extent (i.e.underestimation of the species richness variance inour validation test). Similar explanations for excessivespecies richness variance have been proposed forcynipid wasps (Hugueny & Cornell, 2000) and islandbirds (Diamond & Gilpin, 1980).

The simple ecological assumption we made thatanthropogenic perturbations should reduce speciesoccurrence (or species richness) is not totally confi-rmed (as none of the Docc and DSR values differ fromzero). This means that sites may exhibit an increase inspecies richness as well as a decrease in response tohuman disturbance. However, this last result is notreally surprising as under certain circumstances (e.g.eutrophication, removal of riparian vegetation) in-creasing productivity or water temperatures can leadto an increase in species richness (Brookes, Knight &Shields, 1996; Mundahl & Simon, 1998).

The objective of this study was to develop a proba-bilistic model characterizing riverine fish assemblagesfor French rivers that could be used as a framework

for the adaptation of a fish-based index with nation-wide application. At this stage, the method uses theamount of deviation between the expected and ob-served assemblages within sites as an indicator of thedegradation of sites. However, there is no way todirectly assess which aspect(s) of the assemblage re-sponds to the perturbation. To overcome this limita-tion it is now possible to follow the conceptual basisof the IBI (Karr, 1981) by describing the expectedassemblage with several attributes (metrics) to assessbiotic integrity of a given site. Each metric shouldreflect the quality of a different aspect of the fishassemblage that responds in a different manner toaquatic ecosystem stressors (Fausch, Karr & Yant,1984; Hughes & Noss, 1992). Many advantages of anIBI-like approach can be cited including: (1) it isquantitative; (2) it reflects distinct attributes of biolog-ical systems; and (3) there is no loss of informationfrom the constituent metrics when the total index isdetermined because each metric contributes to thetotal evaluation (Karr, 1991). Nevertheless, a draw-back of this method is that it does not implicitlyintegrate the major environmental factors that cause,or at least explain, the patterns of assemblages com-position and distribution within, and among, waterbodies at various spatio-temporal scales under natu-ral conditions. This makes the process of establishingappropriate, sensitive metric expectations difficult(Lyons, 1996; Smogor & Angermeier, 1998). Our ap-proach should overcome the limitation exposedabove by taking into account the way assemblageattributes are related to actual stream conditions.

In this study we applied logistic models to pres-ence–absence data, thus concentrating only on as-semblage richness. However, numerical or relativeabundances may be useful in assessing biologicalconditions of streams (Karr, 1991). Nonetheless,Hoefs & Boyle (1995), working on a southeasternMissouri river, noted that attributes of fish assem-blages responding to stream condition were based onspecies occurrence rather than individual abundance.This suggests that species occurrence may be a betterindicator of stream condition than numbers of indi-viduals present. Consequently, the next steps will be:(1) to divide the expected assemblage given by thepredictive models (based on species occurrence) intoa variety of metrics, chosen on their potential toindicate degradation (Hughes & Oberdorff, 1998); (2)to integrate LL value as a potential metric; (3) to



integrate and validate new metrics based on abun-dance data. The metrics that will prove most effectivein discriminating between reference and exposed siteswill then be developed into a national index by assign-ing scoring criteria for each metric according towhether the value statistically approximates, deviatessomewhat from, or deviates strongly from the valueexpected; and (4) to classify the data set of disturbedsites into broadly similar degradation categories (e.g.habitat alterations, water quality alterations) and ex-amine variation in fish assemblages (by checking met-ric by metric response) over this range of degradation.This will permit a more accurate assessment of thesignificance of changes caused by each category ofdegradation.

This strategy will allow for the objective develop-ment of an effective indicator while maintaining theIBI’s theoretical foundations (Lyons, 1996; Scott &Hall, 1997; Hughes & Oberdorff, 1998; Karr, 1999; Karr& Chu, 1999) and should overcome some limitationsin the IBI methodology particularly those for establish-ing metric criteria, that are sometimes subjective(Fausch et al., 1990; Rankin & Yoder, 1998).

AcknowledgmentsThanks to Andrea Bullock for improving the Englishversion of the manuscript. We appreciate Bob Hughes’and Knut Seip’s thoughtful and constructive reviewsof earlier versions of the manuscript. Two anonymousreferees and Colin R. Townsend offered many helpfulcriticisms of the manuscript. This work was supportedby the Water Agencies and the French Ministry of theEnvironment under contracts 1302 and 1303 to theConseil Superieur de la Peche. We are grateful to allmembers of the Conseil Superieur de la Peche forproviding data.

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(Manuscript accepted 23 May 2000)


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