# Predictive models of fish microhabitat selection in multiple sites accounting for abundance overdispersion

Laura Plichard, Maxence Forcellini, Yann Le Coarer, Hervé Capra, Georges

Carrel, René Ecochard, Nicolas Lamouroux

► To cite this version:

Laura Plichard, Maxence Forcellini, Yann Le Coarer, Hervé Capra, Georges Carrel, et al. Predictive models of fish microhabitat selection in multiple sites accounting for abundance overdispersion. River Research and Applications, 2020, 36 (7), pp.1056-1075. 10.1002/rra.3631. hal-02915577

HAL Id: hal-02915577

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1 PREDICTIVE MODELS OF FISH MICROHABITAT SELECTION IN

2 MULTIPLE SITES ACCOUNTING FOR ABUNDANCE OVERDISPERSION.

3

4 Running head: PREDICTIVE MODELS OF FISH MICROHABITAT SELECTION IN MULTIPLE SITES

5

6 Authors: Plichard Laura¹*, Forcellini Maxence¹, Le Coarer Yann², Capra Hervé¹, Carrel Georges²,

7 Ecochard René³, Lamouroux Nicolas¹

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9 ¹Irstea, UR RiverLy, Villeurbanne, France

10 ²Irstea, UR RECOVER, Aix-en-Provence, France

11 ³Université Lyon 1, Department of Health Biostatistics, CNRS 5558 - LBBE, Lyon, France

12 * Current address: Ecogea, 352 avenue Roger Tissandié 31600 Muret, France:

13 laura.plichard@protonmail.com

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15 Forcellini Maxence : maxence.forcellini@irstea.fr

16 Le Coarer Yann : yann.lecoarer@irstea.fr

17 Capra Hervé : herve.capra@irstea.fr

18 Carrel Georges : georges.carrel@irstea.fr

19 Ecochard René : rene.ecochard@chu-lyon.fr

20 Lamouroux Nicolas : nicolas.lamouroux@irstea.fr

21

22 ACKNOWLEDGEMENTS

23 For financial support, thanks to Agence Française pour la Biodiversité, Compagnie Nationale du

24 Rhône, Agence de l'eau Rhône-Méditerranée-Corse, Electricité De France, Région Rhône-Alpes,

25 Région Provence-Alpes-Côte d'Azur. For fish datasets, thanks to the LTSER platform « ZABR »,

26 University of Marseille, Ecotec, and all contributors who helped for numerous sampling surveys. For

27 Bayesian statistic and simulation guidance, thanks to Dominique Lamonica. For parallel computing
advice, thanks to Gérard Henry, Dominique Lamonica, Julie Crabot and Éliane Schermer. This
manuscript benefited from the meaningful comments from three anonymous reviewers.

30

31 Conflict of interest: No

32

33

ABSTRACT

Microhabitat selection models are frequently used in rivers to evaluate anthropogenic effects on aquatic organisms. Fish models are generally developed from few rivers, with debatable statistical treatments for coping with overdispersed abundance distributions. Analyses of data from multiple rivers are needed to test their transferability and increase their relevance for stakeholders. Using 3,528 microhabitats sampled in 9 French rivers during 129 surveys, we developed models for 35 specific-size classes of 22 fish species. We used mixed-effects GLMs (accounting for multiple surveys), involving B-spline transformations (accounting for non-linear responses) and assuming a Negative Binomial distribution (accounting for abundance overdispersion). We compared models of increasing complexity: no selection (M1), an "average" selection similar in all surveys (M2), two models with different selection across surveys (M3-4). Of 132 univariate cases (specific-size classes by habitat), 63% indicated selection for depth, 71% for velocity, 45% for substratum size and 13% for substratum heterogeneity. A total of 50 models were retained, involving 26/35 specific-size classes. Model fits indicated low explained deviance (R²MF<0.19) and higher rank correlations (rho<0.69) between observed and modeled values. However, Bayesian posterior predictive checks validated these results since excellent fits would generate R²MF lower than 0.59 and rho lower than 0.78. We found high transferability among rivers and dates, because (1) M2 was the most appropriate in 26/50 cases; (2) the R²MF and rho values by M2 were respectively 72% and 75% of that explained by the complex M4, and (3) independent river cross-validations showed good transferability. Bivariate models for selected specific-size classes improved univariate model fits (rho from 0.30 to 0.38). Overall, using a non-linear mixed-effect approach, our results confirmed the relevance of "average" models based on several rivers for developing helpful e-flow tools. Finally, our modeling approach opens opportunities for integrating additional effects as the spatial distribution of competitors.

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57 **Keyword:** Fish microhabitat selection modeling, Fish preference, mixed-effect models, abundance
58 overdispersion, Negative Binomial distribution, hydraulic habitat
59 INTRODUCTION

60 Habitat selection is the process by which an organism will choose the place to live (Odum, 1953; 61 Udvardy, 1959; Johnson, 1980). This choice will depend on several factors such as species or individual 62 traits (Wagner et al., 2011; Fisher, Anholt & Volpe, 2011; Bunce et al., 2013; Capra et al., 2017). In order 63 to optimize their fitness (Fretwell & Lucas, 1969), organisms will select different types of habitat 64 according to their activities (e.g., foraging, reproduction period; Baker, 2006; Conallin et al., 2014). To 65 describe this process, many habitat selection models are developed in terrestrial and in aquatic systems 66 (Manly et al. 2002). These models generally relate species abundance or occurrence to a variety of 67 habitat characteristics. They often involve habitat descriptions at the "local scale" of organisms, generally 68 referred to as microhabitats when the scale represents the immediate surroundings of organisms (Odum, 69 70 71 al., 2002).

72 Habitat selection models are particularly needed in rivers, where the increase in water demand and 73 global warming are altering the local environment of freshwater organisms. In particular, the 74 multiplication of water withdrawal, weirs or dams (Lehner et al., 2011) may affect ecosystem functioning 75 due to altered flow discharge, hydraulics, river morphology, habitat distribution and availability, and 76 dispersal possibilities (Poff, 1997; Vörösmarty et al., 2010; Olden et al., 2014). The development of 77 habitat selection models, in combination with hydraulic models and integrated into water management 78 software, has contributed to understand the variations in habitat suitability (often for fish and 79 macroinvertebrates) as a function of flow alteration (e.g., Tomsic et al., 2007; Hayes, Hughes & Kelly, 80 81 Conallin, Boegh & Jensen, 2010; Poff et al., 2010; Lamouroux et al., 2013; Garbe & Beeyers, 82 2017; Rosenfeld, 2017). Probably due to the strong variations in local hydraulics within rivers and their 83 strong dependence on discharge, many fish habitat selection models were developed at the microhabitat 84 scale (e.g., Lamouroux et al., 1999; Mouton et al., 2012; Booker & Graynoth, 2013), which represent the 85 immediate and daily habitat occupied by fish (Odum, 1953), or at the mesohabitat scale (e.g., Gosselin, 86 Maddock & Petts, 2012; Booker & Graynoth, 2013; Vezza et al., 2014), which represent the functional 87 habitat for fish activities (e.g., pools and riffles, Kemp, Harper & Crosa, 1999). Thus, microhabitat and 88 mesohabitat models allow studying local processes involved in fish ecology, considering fish sensitivity 89 to local hydraulic variations. These models generally link species abundance (or other proxies of habitat 90 selection) to hydraulic variables such as water depth or current velocity, considered to be both more 91 direct and ecologically relevant descriptors of habitat conditions than flow discharge alone.

91 Numerous microhabitat selection models have been developed for fish, differing for example by their 92 localization (e.g., Labonne, Allouche & Gaudin, 2003; Nykanen & Huusko, 2003 in Europe, Costa et al., 93 2013; Rosenfeld, 2017 in America; Fukuda, 2011; Shiroyama & Yoshimura, 2016 in Asia), the type of
94 rivers (e.g., Girard et al., 2014 for tropical streams, Papadaki et al., 2017 for Mediterranean streams) and
95 species involved (e.g., Dunbar, Alfredsen & Harby, 2012 for salmonids, Muñoz-Mas et al., 2017 for redfin
96 barbels), or the methodological approach used (e.g., Radinger, Kail & Wolter, 2017 using expert
97 judgments; Jowett & Davey, 2007 using Generalized Additive Models, GAM). In many studies,
98 microhabitat selection models involved one or a few species and a limited number of surveys (dates ×
99 sites combinations). This often limits the possibility to test the transferability of models to independent
100 rivers of different catchments and to apply habitat models at the larger scale of "riverscapes" (Harby et
101 al. 2017). For that purpose, it is crucial to improve methodological developments of such models for
102 enlarging their application in river management.

103 The joint analysis of ecological data collected from multiple surveys is often useful to detect general
104 ecological patterns, and to account for the influence of various environmental parameters that can
105 influence patterns observed in each individual survey. For example, having numerous field surveys
106 increases the statistical power to detect changes after restoration projects (Vaudor et al., 2015) and the
107 performance of species distribution models (Wisz et al., 2008). For microhabitat selection models,
108 analyzing numerous surveys can increase the statistical power to detect similarities and differences in
109 microhabitat selection among surveys. Using numerous surveys is also required for non-abundant
110 species, for which a single survey is often not powerful enough for identifying robust abundance-habitat
111 relationships. However, a challenge when using data from several surveys is to develop modeling
112 frameworks that clearly separate abundance/occurrence changes within surveys (that correspond to
113 microhabitat selection) from differences between surveys that can be due to numerous other factors
114 such as temperature, water quality, hydrology or species biogeography.

115 Among the abundant literature on habitat selection, many statistical models have been used to study
116 microhabitat selection (Ahmadi-Nedushan et al., 2006; Conallin, Boegh & Jensen, 2010). This includes
117 the simple comparison of microhabitat densities across habitat categories (e.g. habitat suitability curves
118 of Lamouroux et al., 1999; Mouton et al., 2012), generalized linear models (GLMs, e.g. Labonne,
119 Allouche & Gaudin, 2003; Jowett & Davey, 2007; Alcaraz-Hernandez et al., 2016), fuzzy-models (e.g.,
120 Muñoz-Mas et al., 2012) that compute a weighted average of different models, and more recent
121 machine-learning techniques such as random forests (e.g., Vezza et al., 2014; Shiroyama & Yoshimura,
122 2016) or neural networks (e.g., Fukuda, 2011; Muñoz-Mas et al., 2018) that are complex non-parametric
123 classification methods (Guisan & Zimmermann, 2000).

124 Due to their simplicity and flexibility, GLMs are powerful methods to assess fish habitat selection.
125 These models can be designed to cope for non-linear habitat selection relationships, for example by
126 using splines in generalized additive models (Pleydell & Chrétien, 2010; Girard et al., 2014, Zuur,
127 Saveliev & Ieno, 2014). These smoothing regressions use polynomial regressions to characterize the
128 range of habitat selected without overfitting models. In addition, they can deal with the spatial and
129 temporal variations generated by multiple surveys within multiple rivers using mixed-effect formulations
130 (Goldstein, 2003; Bates et al., 2015). They also can account for different hypothesis concerning the
131 statistical distribution of abundance counts, such as the Poisson or Negative Binomial distributions.
132 Because GLMs are parametric models, their parameters can be extracted for predictive purposes
133 (Ahmadi-Nedushan et al., 2006) and easily transferred to stakeholders as "preference curves" (e.g., ).
134 Combinations of multilevel GLMs and smoothing B-splines have already been used with longitudinal
135 data (i.e. multiple measurements on the same subject) in medicine, for modeling human growth (Pan &
136 Goldstein, 1998; Grajeda et al., 2016), but in our knowledge they have not been used in ecology for
137 modeling the relationship between species abundance and habitats. By combining a regression method
138 with a smoothing approach, this modeling method could help developing a powerful method for studying
139 complex microhabitat selection processes.

140 However, the overdispersion of fish abundance data (i.e. variance >> mean) complicates
141 microhabitat selection modeling. This overdispersion is characterized by a high number of samples
142 without organisms and a few samples containing the majority of the abundance. This overdispersion can
143 be accounted for by different methods. A first possibility is to transform the data (e.g., by log-
144 transformation; O'Hara & Kotze, 2010) in order to limit the impact of high variance on the models, but
145 transformations generate difficulties such as an underestimation of mean values (O'Hara & Kotze, 2010;
146 Warton, Wright & Wang, 2012; Ives, 2015). Another method is to use distribution assumptions that
147 involve an overdispersion parameter by definition, such as the overdispersed Poisson distribution, the
148 Negative Binomial distribution or zero-inflated distributions, which consider simultaneously an
149 abundance distribution and a presence-absence distribution (Warton, 2005; Potts & Elith, 2006; Vaudor
150 et al., 2015). Of these distributions, the Negative Binomial is particularly well adapted to freshwater
151 abundance data (Vaudor, Lamouroux & Olivier, 2011) and might be the most relevant for modeling fish
152 microhabitat selection.

153 Given these statistical limits of current approaches, the aim of this paper is to present and apply a
154 more suitable methodology for developing fish microhabitat selection models. Our approach is based on
155 the use of mixed-effect GLMs (to account for data collected in multiple surveys) involving B-spline
156 transformations of habitat variables (to account for non-linear responses) and Negative Binomial
157 assumptions (to account for overdispersed abundance data). We applied our approach to a unique data
158 set involving 3,528 microhabitats electrofished in a total of 129 surveys (date × reach combinations) in 9
159 French rivers. A total of 22 species × four size classes were considered. We first developed univariate
160 models relating fish abundance to microhabitat water depth, current velocity, substratum grain size and
161 substratum heterogeneity (i.e. grain size diversity). Models of increasing complexity were compared to
162 appreciate the degree of model transferability across surveys, and models were built for microhabitat
163 subsets with or without hydraulic refuges. Their performance was assessed using several metrics,
164 posterior predictive checks (Bayesian approach) and cross validations. Then, we developed bivariate
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models for a selection of species to appreciate their added values when compared with univariate
models.

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METHODS

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STUDY REACHES

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A total of 3,528 microhabitats were sampled between 1989 and 2014 during 129 surveys in 9 southern French rivers (Fig. 1, Table 1, Appendix 1). A first dataset was (n= 1709 microhabitats; rivers Ain, Ardèche, Drome, Garonne, Loire and Rhône) was already used by Lamouroux *et al.* (1999) to develop habitat selection models, with a different modeling approach and a debatable log-transformation of abundance. A second dataset (n= 1819 microhabitats) involved southern rivers. These two datasets were pooled to develop fish microhabitat selection models.

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FISH SAMPLING

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In both datasets, fish were electrofished at low flow rates with adjusted current (5 kW, 180-1000 V, 1-4 A, direct current) in microhabitats of varying surface areas (between 4 and 90 m² for 95% of microhabitats). Each microhabitat was selected in a given habitat type (e.g. a pool or a riffle) and electrofished using an open-sampling technique (Vadas & Orth, 1993; Lamouroux et al., 1999). For each survey, the total number of microhabitats represented the distribution of habitat types observed in the sampling reach on the sampling date. Fish lengths were recorded and classified into four classes cl1 (≤ 80 mm), cl2 (80 – 180 mm), cl3 (180 - 300 mm) and cl4 (> 300 mm).

To model fish microhabitat selection, for each specific size class (i.e. a size class associated to one species), surveys including less than six individuals observed in less than three microhabitats were removed from datasets. In addition, species observed in less than three surveys were not modelled. Some classes were pooled to develop and improve the models when individual classes did not contain enough individuals. For example, a pooled class 1-3 will be noted cl123 hereafter.

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MICROHABITAT CHARACTERISTICS

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Mean water depth and mean water column current velocity were calculated by the mean of several
verticals measurements (average = 7), randomly sampled and georeferenced within each microhabitat,
defining the microhabitat and weighted by their representative area for depth and representative volume
for velocity. Point water column velocities were measured from three measurements at distances above
the bed of 20%, 40% and 80% of the water depth, using a current meter. These calculations were
performed using the HydroSignature software (Le Coarer, 2007).
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Substratum grain size characterisation differed between the two datasets. In the first dataset, one or two dominant substratum grain sizes (covering most of the ~1m² area around the point) and the substratum with the maximum grain sizes were estimated at several points, as for depth and velocity, and assigned to one of 12 categories using a modified version of the Wentworth logarithmic scale (Wentworth, 1922). In the second dataset, the substratum grain size was measured at 10 points using the roughness height of substratum, defined as the relative height of particles relative to the bed (Gordon, McMahon & Finlayson, 1992). To merge datasets, we translated all substratum characterisations into frequencies of seven size classes within the microhabitat: silt, sand, gravel, pebble, cobble, boulder and block. Then, we computed the dominant substratum class and the number of distinct substratum classes. Finally, for each species, between 29% and 50 % of the data did not include substratum descriptions and were removed from dataset for developing models involving substratum (Table 2).

The presence of hydraulic refuges (grouping mineral refuges, vegetated refuges and bank refuges) was recorded. We separated the full dataset into two datasets, with or without refuges, to analyse the influence of refuges on microhabitat use. Most analyses were made on the dataset without refuges, and the data set with refuge was used to appreciate their influence.

## MODELING

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To compare predictive microhabitat selection models by specific size classes (and refuge types) we defined four mixed-effect models of increasing complexity (M1-M4, eqn.1 - eqn.4). In short, M1 was a model without microhabitat selection, M2 a model where selection was similar in all surveys and M3-4 models where selection could vary across surveys. All models linked the abundance of a specific size class to one of our four habitat variables, and accounted for difference between surveys by forcing a random effect on the model intercept. Models M3-4 also had random effects at the survey level associated with microhabitat characteristics, allowing variable microhabitat selection across surveys. Each model could be represented by its conditional expression, which corresponded to the full model fit (fixed and random effects) and thus could vary across surveys (e.g., Fig. 2), and its marginal component, which corresponded to its fixed effects only and had a similar form across surveys (e.g., Fig. 3).

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Fish overdispersion was accounted for by assuming that abundance values followed a Negative Binomial distribution NB(μ,θ), with different parameters of dispersion θ across species, size class and models, but a constant θ across surveys. Vaudor et al. (2015) justified the choice of using a constant parameter across surveys by the reduced temporal variation of θ for a given species. To check the relevance of our NB assumption, we estimated for each model the overdispersion coefficient defined as the sum of squared Pearson residuals divided by the difference between the sample size and the number of parameters (Zuur, Saveliev & Ieno, 2014). The values, close to 1, ranged between 0.4 and
232 2.4 and indicated a good adjustment of the NB to our abundance distributions (Zuur, Saveliev & Ieno, 2014).
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234 Because microhabitat selection is typically a non-linear process (e.g., Labonne, Allouche & Gaudin, 2003; Girard et al., 2014; Alcaraz-Hernandez et al., 2016), we introduced B-splines to transform the 235 microhabitat variables, which decomposed these variables into piecewise cubic regressions with fixed 236 knots (Pan & Goldstein, 1998; Grajeda et al., 2016). For each model, we previously selected the 237 appropriate number of knots between models with a single knot (fixed at 50 % of the distribution of the 238 microhabitat variable, 2 degrees of freedom) or models with two knots (fixed at 33 % and 67 % of the 239 distribution of the microhabitat variable, 3 degrees of freedom). The criterion used for this selection was 240 a modified Akaike Information Criterion for overdispersed count data, QAIC (Burnham & Anderson, 241 2002; Kim et al., 2014), which is a correction of the maximum-likelihood estimations by the 242 overdispersed coefficient of the global model and is calculated as: 243

244 QAIC = -2 log(Likelihood) / (ĉ$_{M4}$) + 2K

245 where K is the number of parameters of the model, and ĉ$_{M4}$ the overdispersion coefficient estimated 246 using our more detailed model M4.

247 Finally, to deal with differences in surface areas among microhabitats, which obviously could influence 248 abundance values, we introduced an offset (c$_{area}$) which was not a parameter of the models and 249 corresponded to the total area sampled by microhabitat.

250 The four models were built following:

251 $y_{ij}$ NB($\mu_{ij}$, $\theta$)

252 where $y_{ij}$ is the abundance of a specific size class of microhabitat i in survey j and $\mu_{ij}$ its expected mean 253 value. Relations between $\mu_{ij}$ and microhabitat variables varied across models:

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255 M1: No microhabitat selection

256 $\log(\hat{\mu}_{ij}) = \beta_0 + u_{0j} + c_{area}$ eqn.1

257 where $\beta_0$ represents the fixed component of the intercept and $u_{0j}$ N(0, $\sigma_0^2$) its random component. 258 Values of $u_{0j}$ were assumed normally distributed with a standard deviation of $\sigma_0$.

259 M1 is a model where microhabitat variables have no influence on abundance.

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261 M2: "Average" microhabitat selection
$$262 \qquad \log(\hat{\mu}_{ij}) = \beta_0 + u_{0j} + \beta_{x_{it}} * f(x_t \dot{=} n_{ij}) + c_{area} \dot{=} \qquad \text{eqn.2}$$

263 where $\beta_{x_{it}}$ are the fixed coefficients for each cubic regression spline $f(x_t \dot{=} t_n) \dot{=} $ of the microhabitat
264 variable x with n knots located at $t_n$ positions, and $u_{0j} N(0, \sigma_0^2)$.

265 M2 is a model where microhabitat variables have a similar influence on abundance across surveys, i.e. it
266 assumes that microhabitat selection is transferable across sites and dates.

267

268 **M3: Partially random microhabitat selection**

$$269 \qquad \log(\hat{\mu}_{ij}) = \beta_0 + u_{0j} + \beta_{x_{it}} * f(x_t \dot{=} n_{ij}) + u_{1j} x_{ij} + c_{area} \dot{=} \qquad \text{eqn.3}$$

270 where $\begin{pmatrix} u_{0j} \\ u_{1j} \end{pmatrix} N(0, \Omega)$ with a variance covariance matrix $\Omega = \begin{pmatrix} \sigma_0^2 & \sigma_{01} \\ \sigma_{01} & \sigma_1^2 \end{pmatrix}$.

271 M3 is a model where microhabitat variables have different influences on abundance across surveys.

272

273 **M4: Fully random microhabitat selection**

$$274 \qquad \log(\hat{\mu}_{ij}) = \beta_0 + u_{0j} + (\beta_{x_{it}} \dot{=} x_{it_n} + u_{1x_{it}}) * f(x_t \dot{=} n_{ij}) + c_{area} \dot{=} \qquad \text{eqn.4}$$

275 where $\begin{pmatrix} u_{0j} \\ u_{1x_{it}} \end{pmatrix} N(0, \Omega)$ and $\Omega = \begin{pmatrix} \sigma_0^2 & \cdots & \sigma_{0x_{it}} \\ \vdots & \ddots & \vdots \\ \sigma_{0x_{it}} & \cdots & \sigma_{it}^2 \end{pmatrix}$.

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277 M4 is a model where microhabitat variables have different influences on abundance across surveys as in
278 M3, but is more flexible than M3 because all coefficients of cubic regression splines may vary across
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280 In our study, M1 is considered as a null random model and thus a reference for appreciating the added
281 value of microhabitat selection models M2-M4. By contrast, M4 is the most complicated and
282 parametrized model and represents the best fitted microhabitat selection model.

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284 **MODEL EVALUATION**

285 *Model selection*

286 To compare models fit and parsimony, we calculated a ΔQAIC, defined as the difference in QAIC
287 between the model with the lowest QAIC and the QAIC of the three other models. Following Burnham &
Anderson (2002), models presenting a ΔQAIC≥10 were identified as failing to explain some substantial variation in the data.

290 Model fits: explained deviance (R²MF) and Spearman rho

291 Model fits were characterized using a McFadden's R² (R²MF; McFadden, 1974) or explained deviance, 292 which is the ratio between the explained deviance and the null deviance and is the equivalent for 293 maximum-likelihood of a R² in linear regression (Guisan & Zimmermann, 2000). Because R²MF are 294 based on null deviance, they can be compared between each model. A model with a higher value of 295 R²MF indicates a model with a higher explained deviance.

$$
296 \quad R^2 \text{ MF} = 1 - \frac{\log(\text{Likelihood}_{\text{Model}})}{\log(\text{Likelihood}_{\text{Nullmodel}})}
$$

297 To appreciate how the fully random model (M4) fitted the data compared to the model without 298 microhabitat selection (M1), we calculated a ΔR²MF which compared the difference between the R²MF of 299 M4 and the R²MF of M1.

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301 To appreciate how the “average” model M2 (considered as an average selection model shared by all 302 rivers) explained microhabitat selection compared to the most flexible model (M4), we calculated a 303 relative R²MF (RRMF), which compared the differences between the R²MF of the model M2 and the 304 R²MF of the simplest model M1, to the difference between the R²MF of the most parametrized model 305 (M4) and the least parametrized model (M1).

$$
306 \quad R \, RMF_{M2} = \frac{R^2 \, MF_{M2} - R^2 \, MF_{M1}}{R^2 \, MF_{M4} - R^2 \, MF_{M1}}
$$

307 We also use Spearman rho (i.e. rank correlation; Spearman, 1904), hereafter cited as Spearman rho, as 308 an alternative statistic to R²MF, in order to complement our appreciation of model fit (Guisan & 309 Zimmermann, 2000; Potts & Elith, 2006). Adding this statistic was important in our case of overdispersed 310 abundance values, which cause low R²MF values. Spearman rho is the correlation between the rank of 311 observed values and the rank of conditional fitted values (i.e. model adjusted by survey). A value close 312 to 1 suggests a positive correlation between the rank of observed values and the rank of conditional 313 fitted values, consequently a good rank correlation between the observed values and the predictions of 314 the observed values by the conditional model. By contrast, negative value of Spearman rho correlation 315 indicates negative correlation between the rank of observed values and the rank of fitted values, 316 consequently a poor rank correlation between the observed values and the predictions of the observed 317 values by the model. As for R²MF, we calculated a Δrho which compared the difference between the 318 Spearman rho of M4 and the Spearman rho of M1.
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Again, to appreciate the part of microhabitat selection explained by the "average" fixed model M2, we calculated a relative Spearman rho, which compared the differences between the Spearman rho of model M2 and the Spearman rho of the simplest model M1, to the difference between the Spearman rho of the most parametrized model (M4) and the least parametrized model (M1).

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$$Rrho_{M_2} = \frac{rho_{M_2} - rho_{M_1}}{rho_{M_4} - rho_{M_1}}$$

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## Posterior predictive check simulations

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We used posterior predictive check simulations (Chambert, Rotella & Higgs, 2014), widely used in Bayesian statistics, to assess the performance of models at predicting the data. The objective of this technique was to appreciate what quality of model fit (i.e. R²MF and Spearman rho) could be expectable with overdispersed abundance data such as ours. Specifically, simulations consisted in 1) assuming that the fitted model corresponded to the true response of abundance to habitat, 2) generating fictive, simulated observed values (n = 1500 fictive abundance datasets) taking into account the overdispersion of the taxa, 3) estimating the R²MF and Spearman rho of models fitted on these fictive data, and 4) comparing our initial model fit with the fictive ones.

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The choice of n = 1500 fictive datasets was made after trials with n values between 20 and 2000, indicating stable results for all models when n = 1500. To keep a similar structure between the observed dataset and the simulated datasets, each simulated dataset contained the same number of surveys as the observed dataset. In a simulated survey, we randomly picked the number of microhabitats within the range of microhabitats sampled by survey. For example, *Telestes soufia* class 2 was present in 60 surveys which contained between 7 and 96 microhabitats, consequently the simulated surveys randomly contained between 7 and 96 microhabitats. Then we randomly picked a value of the microhabitat characteristic for each sample. Given this microhabitat characteristic, we finally randomly picked the sampling area within the range of area observed for this microhabitat value. For example, the value of 0.1 m of water depth was observed in sampling area between 2 and 94 m² with a median at 21 m².

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Finally, the abundance $\hat{y}_{ij}$ was simulated following $NB(\hat{\mu}, \hat{\theta})$ using the 95 % confidence interval estimations for fixed effect and the variance estimated for the random effect from models. Because M4 is assumed to represent all the variability due to the hydraulic variables measured, we used in the simulations the $\hat{\theta}$ estimated from M4 for all simulations (M1-M4).

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## Leave-one_river_out cross-validations
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To evaluate the transferability of M2 across rivers, i.e. its ability to predict microhabitat selection on external data, we computed leave-one_river_out cross-validations after removing each river in turn. Specifically, for each specific class, we computed new models after excluding one river (i.e. training data set) and calculated the Spearman rho correlations between the observations and the predictions of each survey from this river (i.e. validation data set). The specific size classes included in these cross-validations where those showing a minimum magnitude of microhabitat selection (subjectively chosen as ΔR²MF >0.01 or Δrho > 0.09 between M4 and M1) and well described in the data (subjectively chosen as abundance ≥ 20 individuals per survey, occurrence ≥ 10 per survey).

*Comparison with the dataset with refuges and the results of Lamouroux et al. 1999*

The comparison of models for datasets with and without refuges was done for the selection of specific size classes showing a minimum magnitude of microhabitat selection (see just above).

Then, we compared our selection models with preference models showed in Lamouroux et al. (1999), derived with different methods (calculations of average log-densities in habitat classes in Lamouroux et al. 1999). For this purpose we represented the predicted abundance in our study (according to the marginal model M2, which corresponded to an average model across survey comparable to those developed in Lamouroux et al. 1999) as a function of the preferred microhabitat class identified in Lamouroux et al. (1999). This comparison was made only for specific size classes showing a minimum magnitude of microhabitat selection.

*Multivariate models*

To evaluate whether multivariate models increased the performance of univariate models, we developed multivariate models that include an additive selection for water depth and current velocity. Multivariate models were built for the "average" model M2 only and for specific size classes showing a minimum magnitude of microhabitat selection. We compared the R²MF and rho of multivariate models with values obtained by each univariate model (i.e. water depth and current velocity).

All modeling was performed with R software (version 3.4.1, R Core Team, 2017) using the function {glmer} from lme4 package (Bates et al., 2015) for mixed effects models, mgcv package (Wood, 2006) for Negative Binomial distributions.

# RESULTS

*Species characteristics*
A total of 87,177 individuals of 22 species, mainly cyprinids (Table 1), were considered in the dataset. They belonged to 37 specific size classes. The two most abundant species were *Barbatula barbatula* cl12 (N = 14,661 individuals) and *Phoxinus phoxinus* cl12 (N = 11,721), and the two least abundant species were *Zingel asper* cl12 (N = 29) and *Rhodeus amarus* cl12 (N = 66). The two species the most occurring were *Barbatula barbatula* cl12 (N = 1,124 presences in N = 2,359 sampled microhabitats) and *Phoxinus phoxinus* cl12 (N = 844 /1,854), and the two least occurring species were *Zingel asper* cl12 (N = 18 /196) and *Chondrostoma nasus* cl34 (N = 67 / 465). Around two third of specific size classes were sampled in more than 10 surveys.

Concerning the refuges, a quarter of specific size classes occurred more frequently in microhabitats containing refuges than others. Although refuge descriptions are not detailed here, the majority of refuges were vegetated refuges.

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## 393 MODEL EVALUATION

### 394 *Model selection*

Models were constructed using the dataset without refuges for a total of 132 cases (size class x variable combinations) that involved 35 specific size classes for water depth and current velocity, and 31 size classes for substratum variables. Following model selection according to ΔQAIC criteria, there was a significant microhabitat selection for 65/132 cases: 22/35 for water depth, 25/35 for current velocity, 14/31 for dominant substratum grain size, and 4/31 for substratum heterogeneity. In total, 18/22 species and 29/35 size classes significantly selected at least one habitat characteristic. In the remaining cases, model M1 was selected, suggesting no microhabitat selection.

Among the 65 significant selection models, we retained hereafter only the 50 cases (Table 3) with a minimal magnitude of habitat selection, subjectively defined as ΔR²MF between M4 and M1 strictly superior to 0.01 or a Δrho strictly superior to 0.09 (models listed in Table 3). These 50 cases involved 19/22 species and 26/35 specific size classes. For these models, M2 was selected in 26/50 cases (11 for water depth, 10 for current velocity, 4 for dominant substratum grain size, 1 for number of substratum classes), M3 in 21/50 cases (9 for water depth, 8 for current velocity, 3 for dominant substratum grain size, 1 for number of substratum classes) and M4 in 3/50 cases only (all for current velocity).

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### 410 *Model fits: explained deviance (R²MF) and Spearman rho*

The values of R²MF obtained were generally low (see Table 3 for a synthesis of model fits): between 0 and 0.10 for M1, from 0.02 to 0.16 for the "average" model M2, from 0.02 to 0.19 for the detailed M4. Because the level of complexity of M3 is between the level of complexity of M2 and M4, values for M3 were not shown in Table 3. When analyzing how the fully random model (M4) fitted the data compared to
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the model without selection (M1), we observed differences in R²MF from 0.02 to 0.17 (between 0.02 and 0.09 for water depth, 0.02 and 0.16 for current velocity, 0.02 and 0.17 for dominant substratum grain size, 0.02 and 0.08 for number of substratum classes).

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When analyzing how the “average” model (M2) fitted the data compared to the fully random model (M4) using the relative R²MF, we observed values from 0.15 to 1.03 with a median of 0.72. In other words, the “average” model M2 explained a median share of 72% of the deviance explained by the detailed model M4.

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Conditional Spearman rho (Table 3) confirmed these global results but rho values were much higher than R²MF values. Spearman rho obtained ranged from -0.25 to 0.38 for M1, from 0.04 to 0.67 for M2, and from 0.07 to 0.69 for M4. When analyzing how the fully random model (M4) fitted the data compared to the model without selection (M1), we observed differences in conditional Spearman rho from 0.10 to 0.62 (between 0.10 and 0.41 for water depth, 0.10 and 0.62 for current velocity, 0.11 and 0.51 for dominant substratum grain size, 0.10 and 0.41 for number of substratum classes).

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When analyzing how the “average” model (M2) fitted the data compared to the fully random model (M4) using the relative conditional Spearman rho, we observed values from -0.24 to 1.01 with a median of 0.75. In other words, the “average” model M2 had rho values that represented a median share of 75% of the rho values of model M4, consistently with the results obtained with deviance statistics.

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## *Posterior predictive check simulations*

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The posterior predictive check simulations (Table 3) suggested that, considering the overdispersion of microhabitat abundance data, the highest R²MF and Spearman rho values (95% percentile of our fictive simulations) that could be expected when fitting our models ranged between 0 and 0.59 (for R²MF) and 0.28 and 0.78 (for Spearman rho). Our model fits (up to 0.19 for R²MF and up to 0.69 for Spearman rho) therefore indicates satisfactory fits for overdispersed data.

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## *Univariate average microhabitat selection*

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Fig. 2 and Fig. 3 provide two examples of the univariate models described in Table 3. Fig. 2 shows how the different models M1-M4 fitted the observed variations in observed abundance of small *Barbatula barbatula* cl12 as a function of water depth and *Telestes soufia* cl1 as a function of current velocity. The *Barbatula barbatula* cl12 model has a strong magnitude of habitat selection, with a Δrho of 0.32, and the gain in Spearman rho with model M2 (Rrho) equals 93% of the gain in rho with M4 (Table 3). The “average” selection model is therefore very relevant for this size class. The *Telestes soufia* cl1 is an example with lower magnitude of habitat selection (Δrho = 0.26 and Rrho = 73%, current velocity,
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Table 3). For these taxa, the "average" model is also relevant but variations in selection across surveys are stronger (deviations between the red-line M2 and black line M4). Both graphs enable to appreciate the high degree of dispersion in these microhabitat data, with many points without fish and others with >100 individuals. Fig. 3 shows the marginal component of M2 for these two taxa, shared by all surveys, that represents the average shape of habitat selection model for the whole dataset.

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Fig. 4 summarizes the "average habitat selection" of habitat variables for all models in Table 3. This "average habitat selection" corresponds to the average value of the marginal component of M2 (as shown in the examples of Fig. 3) over the range of habitat characteristics observed in our dataset ([0, 3] m for water depth; [0, 1.94] m.s⁻¹ for water column current velocity). It corresponds to the average habitat value used by the size class if all habitat characteristics were equally available over these ranges. Fig. 4 indicates a wide diversity of habitat selection among specific size classes, with average selected depth ranging between ~0.2 and ~1.2 m, average selected velocities between ~0.05 and ~1 m.s⁻¹ and substratum sizes between sand and cobbles. For example, Fig. 4 indicates that small *Barbatula barbatula* cl12 select shallow habitats around ~0.2 m whereas *Telestes soufia* cl1 select intermediate velocities ~0.3 m.s⁻¹, consistently with Figs. 2&3. Other species such as *Barbus barbus* cl34 select deep and fast-flowing habitats, and large fish tend to select deeper habitats than small ones. Among the fewer significant selection of substrate characteristics, small *Perca fluviatilis* cl12 selects a reduced substratum heterogeneity (as opposed to *Squalius cephalus* cl2), preferably gravels.

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Leave one river out cross-validation

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Cross-validations of the models of Table 3 indicated the majority of models M2 presented positive correlation between the observations and the predictions of the validating data set (Fig. 5). Cross-validation rho values were of the same order of values than the differences in Spearman rho between M2 and M1 models during the fit on all rivers. Therefore, they reflected the potential of model M2 to predict abundance ranks in surveys of independent rivers. This was particularly true for example *Barbatula barbatula* cl12 (water depth, described in Fig. 3), *Telestes soufia* cl1 and *Barbus barbus* cl2 (current velocity, described in Fig. 3) but less for *Alburnus alburnus* cl1 (water depth, Fig. 3) whose cross-validations were less convincing.

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Comparison with the dataset with refuges and the results of Lamouroux et al. 1999

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After fitting selection models for the dataset with refuges (as was done for the dataset without refuges), a total of 24 significant models could be compared between the two datasets: 6 for water depth, 17 for current velocity, 1 for dominant substratum grain size and none for substrate heterogeneity. For all habitat variables, the majority of specific size classes presented similar average selection for models built on data with and without refuges (Fig. 6). A few deviations were observed for *Barbus barbus* cl2
484 and cl34, and *Alburnoides bipunctatus* cl23 that used lower velocities in the presence of refuges, and for
485 *Squalius cephalus* cl34 that selected a smaller substratum (gravel vs. pebble) in presence of refuges.

486 When comparing microhabitat selection (models of Table 3) with those available in Lamouroux et al
487 1999 (Fig. 7), we observed consistent results for water depth and current velocity but not for dominant
488 substratum grain size.

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490 *Multivariate models*

491 Multivariate models were developed for the 16 specific size classes that had significant selection (with
492 minimal magnitude of effect) for both water depth and current velocity (Table 3). The multivariate model
493 approach increased the performance of the majority of univariate models M2. This result was observed
494 with both metrics: median R²MF increased from 0.04 for water depth and 0.05 for current velocity to 0.06
495 and median rho increased from 0.30 for water depth and 0.33 for current velocity to 0.38 (Fig. 8).

496

DISCUSSION

497 Our results confirmed the generality of microhabitat selection because 29/35 specific size classes
498 showed significant microhabitat selection for at least one hydraulic variable, with a minimal magnitude.
499 Moreover, our results indicated the relevance of average models across surveys because (1) the
500 average model (M2) was selected by Akaike criteria in 26/50 cases, and (2) across all cases, the
501 average model explained more than 70 % of the variability explained by a fully random microhabitat
502 selection model (i.e. random intercept and slope by survey, model M4). However, if this fully random
503 microhabitat selection model explained a small proportion of variance, then the average model would not
504 be relevant either. Our results were also consistent with previous studies on fish habitat selection (e.g.,
505 Riffart et al., 2009), for example small *Barbatula barbatula* selected shallow microhabitats and small
506 *Barbus barbus* faster-flowing microhabitat.

507 In contrast to our expectations, no difference in microhabitat selection was found for both
508 conditions with and without refuge. Although refuges are crucial for fish ecology (e.g., Magoulick and
509 Kobza 2003), these results could suggest an absence of influence of refuge type on hydraulic
510 microhabitat selection. Nevertheless, our analysis of the influence of refuges could be complicated by
511 the influence of vegetated refuge such as woody debris on sampling technique efficiency (Thévenet &
512 Statzner, 1999) as well as difficulties to measure hydraulic conditions in refuges. In addition, the absence
513 of significant difference could be partly due to the lack of data with different type of refuges. We also
514 found that selection of substrate characteristics was weaker and less transferable across streams than
515 selection for hydraulics, as was observed earlier for fish and macroinvertebrates (Lamouroux, Dolédec &
516 Gayraud, 2004).
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Fish size appears to be an important factor explaining habitat selection. Here, it was partly accounted for by our use of specific size classes and its effects could deserve more detailed studies. Indeed, for some species the models showed differences in average microhabitat selection between size classes of the same species. *Barbus barbus* is a good example of the environmental gradient used by individuals throughout their life. Smallest individuals (< 80 mm, mainly juveniles) select slower and shallower habitat (velocity ~ 0.50 m.s⁻¹, depth ~ 0.25 m) than larger individuals (80 – 180 m), which select themselves shallower habitat (velocity ~ 1 m.s⁻¹, depth ~ 0.50 m) than largest individuals (velocity ~ 1 m.s⁻¹, depth ~0.75 m, size > 180 mm, mainly reproductive adult). Fish selection of deeper habitats over time can be related to predator avoidance and the use of riverine habitats where they can avoid high velocity variations. Nevertheless, considering the strong seasonal and annual variations in fish length between and within species, our use of fixed fish size categories remains questionable. We choose an arbitrary and uniform method for all species to define fish size classes, which was a compromise between expert opinion and statistical difficulties. Further developments may consider alternative groupings based on species life history strategies and traits (Schwartz 2016).

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The strong variability explained by average multi-survey models adds evidence to the relevance of generic habitat selection models, for many taxa, despite the variability of habitat selection across surveys (e.g., Lamouroux et al., 2013; Dixon & Vokoun, 2009). These results justify the application of habitat selection models over river networks and catchments for appreciating the ecological impact of flow management at large scale (e.g. Snelder, Booker & Lamouroux, 2011; Muñoz-Mas et al., 2012). The generality of habitat selection has also been explained by ecological strategies adapted to particular hydraulic conditions, such as the association between opportunistic species and stressful habitat conditions (Blanck, Tedesco & Lamouroux, 2007; Ayllón et al., 2014). However, in many studies involving fish or macroinvertebrates, it was found that habitat selection can vary a lot across space (Lancaster & Downes, 2010) or time (Vilizzi, Copp & Roussel, 2004) due to several potential causes such as variations in water quality or individual behavior. Our cross-validation values indicated also that an average model does not systematically transfer well to an independent river. These variations could be explained by the huge variation in river discharge (from 0.28 to 1490 m³.s⁻¹) and width (from 5 to 160 m), and the dominance of large rivers as the Rhône River and the Durance River regarding a few number of small rivers as the Loup River and Paillons Rivers. These differences in river characteristics were equally considered in our modeling approach and numerically limit the model transferability to small rivers. All these studies illustrate the need to better examine the variations in habitat selection across different regions or watersheds.

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Part of the variability in microhabitat selection across surveys may be due to identification biases of studied species. Indeed, recent studies revealed genetic differences within species identified using taxonomic criteria in France such as *Gobio gobio*, *Barbatula barbatula* or *Esox lucius* (Kottelat & Freyhof, 2007; Denys, 2015). These differences suggest the presence of multiple species considered as a single
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one in our study, and thus the development of microhabitat selection models at the genus level. Nevertheless, when species share taxonomic or functional traits, genus microhabitat selection models can be relevant as shown for macroinvertebrates genus such as Glossosoma or Protonemura (each grouping two species in Dolédec *et al.*, 2007). Similarly, microhabitat selection models developed for fish at the guild level showed common patterns of microhabitat selection and good transferability across populations and surveys (Lamouroux & Cattanéo, 2006, Martinez-Capel *et al.*, 2009). In addition, Chen & Olden (2018) showed that grouping species by guild based on their habitat use (i.e. species present in lower current velocity, for example *Cyprinus carpio* or *Gambusia affinis*) can provide relationships between flow and ecology that are transferable across rivers and basins, and thus relevant for catchment management.

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Although low, our values of explained deviance (R²MF) and correlations between observed and fitted values (Spearman rho) indicated good model quality and good adjustment. Indeed, there is no absolute value to determine whether the model performs well and the significance of each evaluation metric must be discussed for each specific study (Guisan & Thuiller, 2005). In particular, when working at small scales such as the scale of microhabitats of a few square-meters, one cannot expect obtaining strong deterministic models of species abundance (see also Fladung, Scholten & Thiel, 2003). Our Bayesian approach of fit statistic (posterior predictive checks) clearly confirmed that the magnitude of our fits were typically those we could expect when considering the overdispersed character of fish abundance. These results showed the relevance of average microhabitat selection models despite apparent weak fit metrics.

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Bivariate additive microhabitat selection, for water depth and water column current velocity, increased model performance. Indeed, for species presenting univariate selection for both hydraulic variables, model quality metrics increased in median from 0.04 to 0.06 for R²MF and from 0.30 to 0.38 for Spearman rho. These results confirm the need to further develop multivariate approach as described in previous studies on microhabitat and/or mesohabitat selection (e.g. Le Coarer, 2007; Dixon & Vokoun, 2009; Muñoz-Mas *et al.*, 2018). In contrast, for some species as *Barbus barbus*, the introduction of additive variable did not increase model performance and confirmed the assumption that in some cases univariate models perform better than multivariate ones (Millidine, Malcolm & Fryer, 2016). Several possibilities exist to investigate further the interactive effects of depth and velocity on microhabitat selection, such as describing habitats with the Froude number (Millidine et al. 2016), or using multivariate structural equation modeling (Leftwich et al. 1997), or Generalized Functional Response (Matthiopoulos et al. 2010). These approaches could improve model transferability across rivers.

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Microhabitat selection models were often criticized in the literature for considering abundance as a proxy of habitat selection. Indeed, abundance or density are not always equal to selection and can be strongly influenced by density-dependent population dynamics and individual behavior (Van Horne, 1983; Lancaster & Downes, 2010; Lamouroux *et al.*, 2010). For example, for territorial species, the most
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suitable microhabitat may be occupied by dominant individuals and thus correspond to low abundance (Rosenfeld, Beecher & Ptolemy, 2016). Alternatives to the use of abundance are to build selection models using presence or presence-absence data (e.g., Micheli-Campbell et al., 2013; Guerra et al., 2015), or to build bioenergetic models (Rosenfeld, Beecher & Ptolemy, 2016) that represent the energy gain or loss by organisms in a given microhabitat. Although encouraging, these bioenergetic models still deserve further field validation. Using other descriptors than abundance may raise other problems: for example, presence-absence data contain little information for species that have very low or very high occurrence. Our methodological approach considers overdispersion and has the advantage of taking into account the abundance information without giving too much importance to the samples with very high abundance. Specifically, our models treated differently gregarious species with schooling behavior, such as *Phoxinus phoxinus* (Garner, 1997), or less gregarious species such as *Barbus barbus*, and were well adapted to each condition.

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Finally, our selection models considered the temporal and spatial variations of abundance over space (between microhabitats) and time (across surveys). However, they did not account for the temporal and spatial variations of the microhabitat characteristics themselves. Microhabitats where fish individuals were found have their own history influenced by temporal events such as strong variations in discharge (e.g., floods or hydropower releases, Kennard et al., 2007, Capra et al., 2017) or drying events (e.g. Pires, Beja & Magalhães, 2014). Similarly, these microhabitats belong to particular microhabitat spatial configurations- or distributions- that can be more or less heterogeneous (e.g., Martelo et al., 2014) and more or less suitable for the different activities of the individuals over their dispersal distance (Radinger & Wolter, 2014). Ideally, these temporal and spatial variations in microhabitat characteristics around individuals should be described and included in microhabitat selection models. Our flexible mixed-effect methods could be further developed to integrate these aspects and provide more realistic, multi-scale models of complex habitat selection patterns.

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## DATA AVAILABILITY STATEMENT

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The authors confirm that the data supporting the findings of this study are available within the article. Any additional data requirements are available on request from the corresponding author.

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<table><caption>**Table 1:** River characteristics: number of reaches sampled, number of surveys, median number of microhabitats sampled during each survey, mean daily discharge [m³.s⁻¹] average by sampling date and for the entire reach, average width of the reach [m]</caption><thead><tr><th rowspan="3">River</th><th rowspan="3">Nb of reaches</th><th rowspan="3">Nb of surveys</th><th rowspan="3">Median Nb of microhabitats per survey</th><th colspan="2">Mean daily discharge</th><th>Average width</th></tr><tr><th colspan="2">Average by sampling date</th><th rowspan="2">Reach</th></tr><tr><th>Minimum</th><th>Maximum</th></tr></thead><tbody><tr><td>Ain</td><td>1</td><td>9</td><td>51</td><td>20.80</td><td>155.00</td><td>125</td><td>60</td></tr><tr><td>Ardèche</td><td>1</td><td>12</td><td>50</td><td>0.98</td><td>33.85</td><td>24</td><td>30</td></tr><tr><td>Drôme</td><td>1</td><td>2</td><td>37</td><td>13.10</td><td>27.20</td><td>7</td><td>20</td></tr><tr><td>Durance</td><td>18</td><td>1 to 12</td><td>15</td><td>1.01 to 78.50</td><td>1.01 to 270.00</td><td>6 to 20</td><td>15 to 100</td></tr><tr><td>Garonne</td><td>1</td><td>2</td><td>63</td><td>52.20</td><td>59.50</td><td>200</td><td>100</td></tr><tr><td>Le Loup</td><td>2</td><td>1</td><td>100</td><td>0.49</td><td>0.83</td><td>7</td><td>10</td></tr><tr><td>Les Paillons</td><td>6</td><td>1</td><td>30</td><td>0.16</td><td>0.24</td><td>0.28</td><td>5</td></tr><tr><td>Loire</td><td>5</td><td>1</td><td>15</td><td>10.50</td><td>19.00</td><td>50</td><td>75</td></tr><tr><td>Rhône</td><td>4</td><td>1 to 7</td><td>50</td><td>609.00</td><td>855.00</td><td>1030 to 1490</td><td>120 to 160</td></tr></tbody></table>

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843
<table><caption>**Table 2:** Species codes, size classes and characteristics. Total occurrence is the number of microhabitats where the size class occurred, among the total number of microhabitats sampled during the surveys where the size class occurred. Underlined specific size classes were considered for multivariate models.</caption><thead><tr><th rowspan="2">Family</th><th rowspan="2">Species</th><th rowspan="2">Code</th><th rowspan="2">Size class</th><th rowspan="2">Total Abundance</th><th rowspan="2">Total Occurrence</th><th rowspan="2">Total Nb of microhabitats</th><th rowspan="2">Nb of Surveys</th><th rowspan="2">% of data with substratum</th><th colspan="2">% of microhabitats with refuges</th></tr><tr><th>Absence</th><th>Presence</th></tr></thead><tbody><tr><td rowspan="2">Anguilidae</td><td rowspan="2">Anguilla anguilla</td><td rowspan="2">AnA</td><td>cl23</td><td>177</td><td>84</td><td>250</td><td>4</td><td>-</td><td>0.73</td><td>0.27</td></tr><tr><td>cl4</td><td>554</td><td>273</td><td>761</td><td>16</td><td>0.37</td><td>0.45</td><td>0.55</td></tr><tr><td rowspan="2">Balitoridae</td><td rowspan="2">Barbatula barbatula</td><td rowspan="2">BaBa</td><td>cl12</td><td>14661</td><td>1124</td><td>2359</td><td>98</td><td>0.41</td><td>0.72</td><td>0.28</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="2">Centrarchidae</td><td rowspan="2">Lepomis gibbosus</td><td rowspan="2">LeG</td><td>cl123</td><td>974</td><td>159</td><td>482</td><td>14</td><td>0.49</td><td>0.43</td><td>0.57</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="2">Cobitidae</td><td rowspan="2">Cobitis bilineata</td><td rowspan="2">CoB</td><td>cl12</td><td>518</td><td>127</td><td>396</td><td>19</td><td>0.29</td><td>0.87</td><td>0.13</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="2">Cottidae</td><td rowspan="2">Cottus gobio</td><td rowspan="2">CoG</td><td>cl12</td><td>200</td><td>77</td><td>312</td><td>11</td><td>0.46</td><td>0.56</td><td>0.44</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="2">Cyprinidae</td><td rowspan="2">Alburnoides bipunctatus</td><td rowspan="2">AlB</td><td>cl1</td><td>8506</td><td>831</td><td>1828</td><td>84</td><td>0.38</td><td>0.66</td><td>0.34</td></tr><tr><td>cl23</td><td>3349</td><td>512</td><td>1370</td><td>60</td><td>0.40</td><td>0.68</td><td>0.32</td></tr><tr><td rowspan="2">Alburnus alburnus</td><td rowspan="2">AlA</td><td>cl1</td><td>1918</td><td>193</td><td>811</td><td>22</td><td>0.48</td><td>0.53</td><td>0.47</td></tr><tr><td>cl23</td><td>895</td><td>124</td><td>451</td><td>14</td><td>0.48</td><td>0.62</td><td>0.38</td></tr><tr><td rowspan="2">Barbus barbus</td><td rowspan="2">BaBu</td><td>cl1</td><td>3848</td><td>691</td><td>1687</td><td>69</td><td>0.41</td><td>0.67</td><td>0.33</td></tr><tr><td>cl2</td><td>2393</td><td>528</td><td>1454</td><td>63</td><td>0.41</td><td>0.60</td><td>0.40</td></tr><tr><td rowspan="2">Barbus meridionalis</td><td rowspan="2">BaM</td><td>cl1</td><td>235</td><td>31</td><td>199</td><td>3</td><td>-</td><td>1.00</td><td>-</td></tr><tr><td>cl23</td><td>607</td><td>155</td><td>364</td><td>4</td><td>-</td><td>0.57</td><td>0.43</td></tr><tr><td>Blicca bjoerkna</td><td>BIB</td><td>cl12</td><td>360</td><td>44</td><td>219</td><td>8</td><td>0.46</td><td>0.58</td><td>0.42</td></tr><tr><td rowspan="2">Chondrostoma nasus</td><td rowspan="2">ChN</td><td>cl12</td><td>925</td><td>136</td><td>412</td><td>13</td><td>0.49</td><td>0.71</td><td>0.29</td></tr><tr><td>cl34</td><td>298</td><td>67</td><td>465</td><td>9</td><td>0.48</td><td>0.74</td><td>0.26</td></tr><tr><td rowspan="2">Gobio gobio</td><td rowspan="2">GoG</td><td>cl1</td><td>4580</td><td>643</td><td>1674</td><td>59</td><td>0.43</td><td>0.67</td><td>0.33</td></tr><tr><td>cl23</td><td>2376</td><td>596</td><td>1770</td><td>60</td><td>0.45</td><td>0.61</td><td>0.39</td></tr><tr><td rowspan="2">Leuciscus leuciscus</td><td rowspan="2">LeL</td><td>cl123</td><td>317</td><td>81</td><td>371</td><td>12</td><td>0.50</td><td>0.35</td><td>0.65</td></tr><tr><td>cl1</td><td>1195</td><td>136</td><td>534</td><td>16</td><td>0.44</td><td>0.74</td><td>0.26</td></tr><tr><td rowspan="2">Parachondrostoma toxosoma</td><td rowspan="2">PaT</td><td>cl1</td><td>338</td><td>85</td><td>423</td><td>12</td><td>0.48</td><td>0.65</td><td>0.35</td></tr><tr><td>cl23</td><td>11721</td><td>844</td><td>1854</td><td>71</td><td>0.37</td><td>0.71</td><td>0.29</td></tr><tr><td>Phoxinus phoxinus</td><td>PhP</td><td>cl12</td><td>66</td><td>13</td><td>37</td><td>3</td><td>0.50</td><td>-</td><td>1.00</td></tr><tr><td rowspan="2">Rhodeus amarus</td><td rowspan="2">RhA</td><td>cl12</td><td>66</td><td>13</td><td>558</td><td>20</td><td>0.49</td><td>0.51</td><td>0.49</td></tr><tr><td>cl1</td><td>1844</td><td>145</td><td>505</td><td>16</td><td>0.48</td><td>0.36</td><td>0.64</td></tr><tr><td rowspan="2">Rutilus rutilus</td><td rowspan="2">RuR</td><td>cl1</td><td>1373</td><td>148</td><td>211</td><td>6</td><td>0.34</td><td>0.42</td><td>0.58</td></tr><tr><td>cl34</td><td>1129</td><td>341</td><td>1238</td><td>46</td><td>0.48</td><td>0.46</td><td>0.54</td></tr></tbody></table>
<table><caption>Table 2. Continued</caption><thead><tr><th rowspan="2">Family</th><th rowspan="2">Species</th><th rowspan="2">Code</th><th rowspan="2">Size class</th><th rowspan="2">Total Abundance</th><th rowspan="2">Total Occurrence</th><th rowspan="2">Total Nb of microhabitats</th><th rowspan="2">Nb of Surveys</th><th rowspan="2">% of data with substratum</th><th colspan="2">% of microhabitats with refuges</th></tr><tr><th>Absence</th><th>Presence</th></tr></thead><tbody><tr><td rowspan="2">Cyprinidae</td><td rowspan="2">Telestes soufia</td><td rowspan="2">TeS</td><td>cl1</td><td>5231</td><td>625</td><td>1481</td><td>59</td><td>0.36</td><td>0.66</td><td>0.34</td></tr><tr><td>cl2</td><td>2857</td><td>517</td><td>1644</td><td>60</td><td>0.37</td><td>0.60</td><td>0.40</td></tr><tr><td rowspan="2">Percidae</td><td>Perca fluviatilis</td><td>PeF</td><td>cl12</td><td>188</td><td>72</td><td>419</td><td>12</td><td>0.49</td><td>0.43</td><td>0.57</td></tr><tr><td>Zingel asper</td><td>ZiA</td><td>cl12</td><td>29</td><td>18</td><td>196</td><td>3</td><td>0.50</td><td>1.00</td><td>-</td></tr><tr><td rowspan="2">Salmonidae</td><td rowspan="2">Salmo trutta fario</td><td rowspan="2">SaT</td><td>cl12</td><td>308</td><td>122</td><td>380</td><td>7</td><td>0.33</td><td>0.69</td><td>0.31</td></tr><tr><td>cl34</td><td>87</td><td>34</td><td>93</td><td>3</td><td>-</td><td>-</td><td>1.00</td></tr></tbody></table>
<table><caption>**Table 3:** Univariate model fits for microhabitat characteristics without refuge × specific size classes for specific size class showing minimum magnitude. ΔQAIC: difference with the lowest QAIC among models M1-M4, McFadden's R² (R²MF) observed with the dataset (Obs) and the R²MF observed in the 95-percentile of the posterior predictive checks simulations (Simu), the difference between the R²MF of M1 and M4 (ΔR²MF), the relative R²MF of M2 compared with M4 (RR²MF), and similar statistics for Spearman rho. The values were ordered of decreasing ΔR²MF. Underlined specific size classes were considered for multivariate models. Bold numbers represent the selected model according to an AIC's selection.</caption><thead><tr><th rowspan="3">Habitat</th><th rowspan="3">Species code</th><th rowspan="3">Class</th><th colspan="4">ΔQAIC</th><th colspan="4">McFadden's R²</th><th colspan="2">ΔR²MF</th><th colspan="2">RR²MF</th><th colspan="4">Spearman rho</th><th colspan="2">Δrho</th><th colspan="2">Rrho</th></tr><tr><th rowspan="2">M1</th><th rowspan="2">M2</th><th rowspan="2">M3</th><th rowspan="2">M4</th><th colspan="2">M1</th><th colspan="2">M2</th><th colspan="2">M4</th><th colspan="2">M1</th><th colspan="2">M2</th><th colspan="2">M4</th></tr><tr><th>Obs</th><th>Simu</th><th>Obs</th><th>Simu</th><th>Obs</th><th>Simu</th><th>Obs</th><th>Simu</th><th>Obs</th><th>Simu</th><th>Obs</th><th>Simu</th></tr></thead><tbody><tr><td colspan="21"><strong>Water depth</strong></td></tr><tr><td>BaBa</td><td>cl12</td><td>681</td><td>22</td><td>2</td><td>-</td><td>0.03</td><td>0.09</td><td>0.12</td><td>0.16</td><td>0.12</td><td>0.19</td><td>0.09</td><td>0.96</td><td>0.37</td><td>0.62</td><td>0.67</td><td>0.71</td><td>0.69</td><td>0.72</td><td>0.32</td><td>0.93</td></tr><tr><td>CoG</td><td>cl12</td><td>34</td><td>-</td><td>3</td><td>8</td><td>-</td><td>-</td><td>0.08</td><td>0.20</td><td>0.09</td><td>0.24</td><td>0.09</td><td>0.94</td><td>-0.10</td><td>0.35</td><td>0.29</td><td>0.52</td><td>0.31</td><td>0.73</td><td>0.41</td><td>0.95</td></tr><tr><td>BaM</td><td>cl23</td><td>29</td><td>-</td><td>2</td><td>5</td><td>0.03</td><td>0.06</td><td>0.09</td><td>0.15</td><td>0.10</td><td>0.26</td><td>0.08</td><td>0.87</td><td>0.27</td><td>0.51</td><td>0.42</td><td>0.64</td><td>0.43</td><td>0.68</td><td>0.16</td><td>0.91</td></tr><tr><td>BaBu</td><td>cl1</td><td>178</td><td>59</td><td>-</td><td>5</td><td>0.03</td><td>0.05</td><td>0.07</td><td>0.12</td><td>0.09</td><td>0.21</td><td>0.06</td><td>0.65</td><td>0.27</td><td>0.51</td><td>0.49</td><td>0.61</td><td>0.52</td><td>0.61</td><td>0.25</td><td>0.87</td></tr><tr><td>CoB</td><td>cl12</td><td>25</td><td>-</td><td>3</td><td>9</td><td>-</td><td>-</td><td>0.05</td><td>0.09</td><td>0.06</td><td>0.08</td><td>0.06</td><td>0.95</td><td>-0.12</td><td>0.32</td><td>0.22</td><td>0.43</td><td>0.26</td><td>0.45</td><td>0.39</td><td>0.89</td></tr><tr><td>GoG</td><td>cl23</td><td>111</td><td>5</td><td>5</td><td>-</td><td>0.01</td><td>0.03</td><td>0.05</td><td>0.07</td><td>0.06</td><td>0.08</td><td>0.04</td><td>0.82</td><td>0.07</td><td>0.37</td><td>0.24</td><td>0.57</td><td>0.31</td><td>0.64</td><td>0.24</td><td>0.73</td></tr><tr><td>BaBu</td><td>cl34</td><td>41</td><td>-</td><td>3</td><td>2</td><td>0.05</td><td>0.05</td><td>0.08</td><td>0.09</td><td>0.09</td><td>0.16</td><td>0.04</td><td>0.88</td><td>0.20</td><td>0.38</td><td>0.32</td><td>0.51</td><td>0.37</td><td>0.49</td><td>0.17</td><td>0.69</td></tr><tr><td>AlA</td><td>cl23</td><td>22</td><td>19</td><td>5</td><td>-</td><td>0.01</td><td>0.02</td><td>0.02</td><td>0.06</td><td>0.05</td><td>0.14</td><td>0.04</td><td>0.21</td><td>0.22</td><td>0.34</td><td>0.27</td><td>0.40</td><td>0.34</td><td>0.47</td><td>0.13</td><td>0.42</td></tr><tr><td>BaBu</td><td>cl2</td><td>91</td><td>4</td><td>-</td><td>2</td><td>0.02</td><td>0.04</td><td>0.06</td><td>0.07</td><td>0.06</td><td>0.15</td><td>0.04</td><td>0.82</td><td>0.27</td><td>0.43</td><td>0.38</td><td>0.53</td><td>0.40</td><td>0.74</td><td>0.13</td><td>0.83</td></tr><tr><td>PhP</td><td>cl12</td><td>208</td><td>66</td><td>1</td><td>-</td><td>0.02</td><td>0.05</td><td>0.05</td><td>0.08</td><td>0.06</td><td>0.08</td><td>0.04</td><td>0.67</td><td>0.26</td><td>0.44</td><td>0.46</td><td>0.51</td><td>0.52</td><td>0.54</td><td>0.26</td><td>0.75</td></tr><tr><td>SqC</td><td>cl34</td><td>11</td><td>2</td><td>-</td><td>8</td><td>0.02</td><td>0.03</td><td>0.06</td><td>0.07</td><td>0.06</td><td>0.17</td><td>0.04</td><td>0.84</td><td>0.09</td><td>0.31</td><td>0.20</td><td>0.43</td><td>0.27</td><td>0.41</td><td>0.18</td><td>0.64</td></tr><tr><td>AlB</td><td>cl23</td><td>71</td><td>2</td><td>-</td><td>8</td><td>0.02</td><td>0.04</td><td>0.04</td><td>0.07</td><td>0.05</td><td>0.08</td><td>0.03</td><td>0.85</td><td>0.30</td><td>0.43</td><td>0.40</td><td>0.53</td><td>0.45</td><td>0.56</td><td>0.15</td><td>0.71</td></tr><tr><td>AnA</td><td>cl4</td><td>12</td><td>6</td><td>-</td><td>5</td><td>0.10</td><td>0.11</td><td>0.11</td><td>0.13</td><td>0.13</td><td>0.20</td><td>0.03</td><td>0.48</td><td>0.37</td><td>0.57</td><td>0.41</td><td>0.63</td><td>0.48</td><td>0.78</td><td>0.11</td><td>0.38</td></tr><tr><td>TeS</td><td>cl2</td><td>62</td><td>18</td><td>6</td><td>-</td><td>0.02</td><td>0.02</td><td>0.04</td><td>0.05</td><td>0.05</td><td>0.17</td><td>0.03</td><td>0.57</td><td>0.17</td><td>0.36</td><td>0.28</td><td>0.44</td><td>0.34</td><td>0.44</td><td>0.17</td><td>0.63</td></tr><tr><td>GoG</td><td>cl1</td><td>83</td><td>18</td><td>-</td><td>8</td><td>0.02</td><td>0.05</td><td>0.04</td><td>0.08</td><td>0.05</td><td>0.18</td><td>0.03</td><td>0.76</td><td>0.21</td><td>0.41</td><td>0.37</td><td>0.47</td><td>0.41</td><td>0.57</td><td>0.19</td><td>0.80</td></tr><tr><td>TeS</td><td>cl1</td><td>98</td><td>10</td><td>-</td><td>3</td><td>0.01</td><td>0.03</td><td>0.03</td><td>0.06</td><td>0.03</td><td>0.06</td><td>0.03</td><td>0.82</td><td>0.10</td><td>0.41</td><td>0.32</td><td>0.46</td><td>0.37</td><td>0.47</td><td>0.27</td><td>0.80</td></tr><tr><td>SqC</td><td>cl2</td><td>32</td><td>7</td><td>2</td><td>-</td><td>0.02</td><td>0.02</td><td>0.03</td><td>0.05</td><td>0.04</td><td>0.06</td><td>0.03</td><td>0.56</td><td>0.06</td><td>0.34</td><td>0.18</td><td>0.40</td><td>0.26</td><td>0.40</td><td>0.20</td><td>0.62</td></tr><tr><td>SqC</td><td>cl1</td><td>111</td><td>30</td><td>2</td><td>-</td><td>0.01</td><td>0.02</td><td>0.03</td><td>0.05</td><td>0.03</td><td>0.12</td><td>0.03</td><td>0.68</td><td>-0.04</td><td>0.31</td><td>0.21</td><td>0.38</td><td>0.25</td><td>0.41</td><td>0.30</td><td>0.86</td></tr><tr><td>AlA</td><td>cl1</td><td>14</td><td>9</td><td>13</td><td>-</td><td>0.02</td><td>0.04</td><td>0.03</td><td>0.04</td><td>0.04</td><td>0.08</td><td>0.02</td><td>0.30</td><td>0.16</td><td>0.33</td><td>0.18</td><td>0.34</td><td>0.35</td><td>0.41</td><td>0.19</td><td>0.08</td></tr><tr><td>PaT</td><td>cl1</td><td>13</td><td>15</td><td>-</td><td>4</td><td>0.03</td><td>0.05</td><td>0.03</td><td>0.12</td><td>0.05</td><td>0.11</td><td>0.02</td><td>0.15</td><td>0.18</td><td>0.35</td><td>0.22</td><td>0.38</td><td>0.33</td><td>0.41</td><td>0.15</td><td>0.25</td></tr><tr><td colspan="21"><strong>Current velocity</strong></td></tr><tr><td>PeF</td><td>cl12</td><td>23</td><td>-</td><td>-</td><td>5</td><td>-</td><td>0.06</td><td>0.14</td><td>0.24</td><td>0.16</td><td>0.29</td><td>0.16</td><td>0.85</td><td>-0.25</td><td>0.40</td><td>0.22</td><td>0.49</td><td>0.29</td><td>0.52</td><td>0.54</td><td>0.88</td></tr><tr><td>BaM</td><td>cl1</td><td>29</td><td>1</td><td>-</td><td>4</td><td>0.05</td><td>0.10</td><td>0.16</td><td>0.25</td><td>0.19</td><td>0.36</td><td>0.15</td><td>0.82</td><td>0.05</td><td>0.52</td><td>0.34</td><td>0.52</td><td>0.37</td><td>0.54</td><td>0.33</td><td>0.88</td></tr><tr><td>CoB</td><td>cl12</td><td>118</td><td>-</td><td>2</td><td>3</td><td>-</td><td>-</td><td>0.12</td><td>0.19</td><td>0.13</td><td>0.15</td><td>0.13</td><td>0.94</td><td>-0.12</td><td>0.37</td><td>0.47</td><td>0.60</td><td>0.49</td><td>0.58</td><td>0.61</td><td>0.97</td></tr><tr><td>LeG</td><td>cl123</td><td>48</td><td>-</td><td>2</td><td>6</td><td>-</td><td>0.02</td><td>0.08</td><td>0.15</td><td>0.09</td><td>0.23</td><td>0.09</td><td>0.93</td><td>-0.22</td><td>0.35</td><td>0.37</td><td>0.54</td><td>0.40</td><td>0.64</td><td>0.62</td><td>0.96</td></tr></tbody></table>
<table><caption>Table 3. Continued</caption><thead><tr><th rowspan="2">Habitat</th><th rowspan="2">Species code</th><th rowspan="2">Class</th><th colspan="4">ΔQAIC</th><th colspan="6">McFadden's R<sup>2</sup></th><th colspan="2">ΔR<sup>2</sup>MF</th><th colspan="2">RR<sup>2</sup>MF</th><th colspan="4">Spearman rho</th><th colspan="2">Δrho</th><th colspan="2">Rrho</th></tr><tr><th>M1</th><th>M2</th><th>M3</th><th>M4</th><th>M1 Obs</th><th>Simu</th><th>M2 Obs</th><th>Simu</th><th>M4 Obs</th><th>Simu</th><th>M1 Obs</th><th>Simu</th><th>M2 Obs</th><th>Simu</th><th>M4 Obs</th><th>Simu</th><th>M1 Obs</th><th>Simu</th><th>M2 Obs</th><th>Simu</th><th>M4 Obs</th><th>Simu</th></tr></thead><tbody><tr><td colspan="21"><strong>Current velocity</strong></td></tr><tr><td>BlB</td><td>cl12</td><td></td><td>34</td><td>-</td><td>2</td><td>6</td><td>0.01</td><td>0.05</td><td>0.09</td><td>0.12</td><td>0.10</td><td>0.14</td><td>0.09</td><td>0.91</td><td>0.12</td><td>0.38</td><td>0.36</td><td>0.53</td><td>0.41</td><td>0.52</td><td>0.29</td><td>0.82</td></tr><tr><td>RuR</td><td>cl1</td><td></td><td>49</td><td>-</td><td>-</td><td>1</td><td>0.01</td><td>0.04</td><td>0.08</td><td>0.13</td><td>0.09</td><td>0.13</td><td>0.08</td><td>0.86</td><td>0.03</td><td>0.39</td><td>0.40</td><td>0.53</td><td>0.40</td><td>0.55</td><td>0.37</td><td>0.98</td></tr><tr><td>BaBu</td><td>cl2</td><td></td><td>112</td><td>52</td><td>14</td><td>-</td><td>0.02</td><td>0.04</td><td>0.05</td><td>0.10</td><td>0.08</td><td>0.10</td><td>0.05</td><td>0.51</td><td>0.27</td><td>0.46</td><td>0.42</td><td>0.53</td><td>0.47</td><td>0.57</td><td>0.20</td><td>0.76</td></tr><tr><td>SqC</td><td>cl1</td><td></td><td>244</td><td>26</td><td>5</td><td>-</td><td>0.01</td><td>0.03</td><td>0.05</td><td>0.09</td><td>0.06</td><td>0.08</td><td>0.05</td><td>0.86</td><td>-0.04</td><td>0.37</td><td>0.38</td><td>0.49</td><td>0.42</td><td>0.51</td><td>0.46</td><td>0.93</td></tr><tr><td>GoG</td><td>cl1</td><td></td><td>192</td><td>39</td><td>-</td><td>1</td><td>0.02</td><td>0.05</td><td>0.06</td><td>0.09</td><td>0.07</td><td>0.11</td><td>0.05</td><td>0.75</td><td>0.21</td><td>0.42</td><td>0.39</td><td>0.48</td><td>0.42</td><td>0.52</td><td>0.21</td><td>0.85</td></tr><tr><td>SqC</td><td>cl2</td><td></td><td>96</td><td>14</td><td>-</td><td>2</td><td>0.02</td><td>0.02</td><td>0.05</td><td>0.08</td><td>0.05</td><td>0.06</td><td>0.04</td><td>0.79</td><td>0.06</td><td>0.35</td><td>0.23</td><td>0.42</td><td>0.29</td><td>0.43</td><td>0.23</td><td>0.77</td></tr><tr><td>BaBu</td><td>cl34</td><td></td><td>31</td><td>22</td><td>7</td><td>-</td><td>0.05</td><td>0.04</td><td>0.06</td><td>0.08</td><td>0.08</td><td>0.13</td><td>0.04</td><td>0.28</td><td>0.20</td><td>0.35</td><td>0.35</td><td>0.42</td><td>0.39</td><td>0.48</td><td>0.18</td><td>0.78</td></tr><tr><td>AlA</td><td>cl1</td><td></td><td>38</td><td>5</td><td>8</td><td>-</td><td>0.02</td><td>0.04</td><td>0.04</td><td>0.07</td><td>0.05</td><td>0.09</td><td>0.04</td><td>0.72</td><td>0.16</td><td>0.34</td><td>0.23</td><td>0.39</td><td>0.33</td><td>0.44</td><td>0.17</td><td>0.44</td></tr><tr><td>AlB</td><td>cl23</td><td></td><td>80</td><td>44</td><td>14</td><td>-</td><td>0.02</td><td>0.04</td><td>0.03</td><td>0.07</td><td>0.05</td><td>0.13</td><td>0.04</td><td>0.36</td><td>0.30</td><td>0.43</td><td>0.42</td><td>0.50</td><td>0.46</td><td>0.56</td><td>0.16</td><td>0.74</td></tr><tr><td>PhP</td><td>cl12</td><td></td><td>184</td><td>44</td><td>4</td><td>-</td><td>0.02</td><td>0.05</td><td>0.05</td><td>0.08</td><td>0.06</td><td>0.08</td><td>0.04</td><td>0.71</td><td>0.26</td><td>0.45</td><td>0.44</td><td>0.49</td><td>0.52</td><td>0.54</td><td>0.26</td><td>0.69</td></tr><tr><td>AlA</td><td>cl23</td><td></td><td>12</td><td>5</td><td>4</td><td>-</td><td>0.01</td><td>0.02</td><td>0.03</td><td>0.05</td><td>0.05</td><td>0.10</td><td>0.04</td><td>0.43</td><td>0.22</td><td>0.34</td><td>0.24</td><td>0.40</td><td>0.35</td><td>0.46</td><td>0.13</td><td>0.19</td></tr><tr><td>AnA</td><td>cl4</td><td></td><td>14</td><td>9</td><td>-</td><td>4</td><td>0.10</td><td>0.10</td><td>0.11</td><td>0.14</td><td>0.13</td><td>0.18</td><td>0.03</td><td>0.38</td><td>0.37</td><td>0.57</td><td>0.41</td><td>0.60</td><td>0.46</td><td>0.60</td><td>0.09</td><td>0.44</td></tr><tr><td>PaT</td><td>cl1</td><td></td><td>25</td><td>-</td><td>3</td><td>7</td><td>0.03</td><td>0.05</td><td>0.06</td><td>0.09</td><td>0.06</td><td>0.11</td><td>0.03</td><td>0.91</td><td>0.18</td><td>0.36</td><td>0.32</td><td>0.40</td><td>0.36</td><td>0.42</td><td>0.18</td><td>0.78</td></tr><tr><td>TeS</td><td>cl1</td><td></td><td>114</td><td>10</td><td>11</td><td>-</td><td>0.01</td><td>0.03</td><td>0.03</td><td>0.07</td><td>0.04</td><td>0.06</td><td>0.03</td><td>0.84</td><td>0.10</td><td>0.41</td><td>0.29</td><td>0.47</td><td>0.36</td><td>0.50</td><td>0.26</td><td>0.73</td></tr><tr><td>ChN</td><td>cl12</td><td></td><td>12</td><td>3</td><td>-</td><td>5</td><td>0.02</td><td>0.07</td><td>0.04</td><td>0.12</td><td>0.05</td><td>0.13</td><td>0.03</td><td>0.64</td><td>0.26</td><td>0.46</td><td>0.34</td><td>0.55</td><td>0.37</td><td>0.53</td><td>0.11</td><td>0.74</td></tr><tr><td>GoG</td><td>cl23</td><td></td><td>59</td><td>20</td><td>-</td><td>2</td><td>0.01</td><td>0.02</td><td>0.03</td><td>0.04</td><td>0.03</td><td>0.06</td><td>0.02</td><td>0.62</td><td>0.07</td><td>0.34</td><td>0.13</td><td>0.36</td><td>0.23</td><td>0.41</td><td>0.16</td><td>0.41</td></tr><tr><td>BaBu</td><td>cl1</td><td></td><td>68</td><td>46</td><td>4</td><td>-</td><td>0.03</td><td>0.05</td><td>0.04</td><td>0.06</td><td>0.05</td><td>0.08</td><td>0.02</td><td>0.33</td><td>0.27</td><td>0.47</td><td>0.32</td><td>0.50</td><td>0.41</td><td>0.55</td><td>0.14</td><td>0.39</td></tr><tr><td>TeS</td><td>cl2</td><td></td><td>35</td><td>28</td><td>-</td><td>1</td><td>0.02</td><td>0.03</td><td>0.02</td><td>0.03</td><td>0.04</td><td>0.07</td><td>0.02</td><td>0.22</td><td>0.17</td><td>0.36</td><td>0.14</td><td>0.35</td><td>0.29</td><td>0.42</td><td>0.12</td><td>-0.24</td></tr><tr><td colspan="21"><strong>Dominant substratum</strong></td></tr><tr><td>PeF</td><td>cl12</td><td></td><td>34</td><td>-</td><td>4</td><td>3</td><td>-</td><td>0.06</td><td>0.14</td><td>0.28</td><td>0.17</td><td>0.26</td><td>0.17</td><td>0.84</td><td>-0.23</td><td>0.41</td><td>0.18</td><td>0.44</td><td>0.28</td><td>0.46</td><td>0.51</td><td>0.80</td></tr><tr><td>AlA</td><td>cl1</td><td></td><td>28</td><td>8</td><td>-</td><td>-</td><td>0.01</td><td>0.03</td><td>0.03</td><td>0.08</td><td>0.05</td><td>0.11</td><td>0.05</td><td>0.59</td><td>0.13</td><td>0.32</td><td>0.26</td><td>0.38</td><td>0.32</td><td>0.42</td><td>0.19</td><td>0.69</td></tr><tr><td>SqC</td><td>cl34</td><td></td><td>11</td><td>10</td><td>8</td><td>-</td><td>0.02</td><td>0.03</td><td>0.03</td><td>0.06</td><td>0.07</td><td>0.08</td><td>0.05</td><td>0.15</td><td>0.06</td><td>0.30</td><td>0.09</td><td>0.32</td><td>0.20</td><td>0.37</td><td>0.14</td><td>0.18</td></tr><tr><td>LeG</td><td>cl123</td><td></td><td>17</td><td>-</td><td>3</td><td>9</td><td>-</td><td>0.01</td><td>0.03</td><td>0.09</td><td>0.03</td><td>0.10</td><td>0.03</td><td>0.97</td><td>-0.22</td><td>0.30</td><td>0.13</td><td>0.34</td><td>0.16</td><td>0.38</td><td>0.38</td><td>0.92</td></tr><tr><td>RuR</td><td>cl1</td><td></td><td>13</td><td>-</td><td>4</td><td>8</td><td>0.01</td><td>0.03</td><td>0.03</td><td>0.09</td><td>0.03</td><td>0.09</td><td>0.03</td><td>0.88</td><td>0.05</td><td>0.32</td><td>0.21</td><td>0.38</td><td>0.21</td><td>0.39</td><td>0.17</td><td>0.96</td></tr><tr><td>AlB</td><td>cl23</td><td></td><td>36</td><td>22</td><td>-</td><td>6</td><td>0.02</td><td>0.06</td><td>0.03</td><td>0.07</td><td>0.04</td><td>0.16</td><td>0.02</td><td>0.39</td><td>0.31</td><td>0.45</td><td>0.37</td><td>0.47</td><td>0.42</td><td>0.56</td><td>0.11</td><td>0.52</td></tr><tr><td>TeS</td><td>cl2</td><td></td><td>15</td><td>12</td><td>-</td><td>4</td><td>0.02</td><td>0.03</td><td>0.02</td><td>0.06</td><td>0.04</td><td>0.22</td><td>0.02</td><td>0.24</td><td>0.12</td><td>0.35</td><td>0.19</td><td>0.38</td><td>0.24</td><td>0.45</td><td>0.12</td><td>0.61</td></tr><tr><td colspan="21"><strong>Substratum heterogeneity</strong></td></tr><tr><td>PeF</td><td>cl12</td><td></td><td>10</td><td>-</td><td>4</td><td>9</td><td>-</td><td>0.59</td><td>0.08</td><td>0.22</td><td>0.08</td><td>0.24</td><td>0.08</td><td>0.94</td><td>-0.23</td><td>0.28</td><td>0.10</td><td>0.35</td><td>0.18</td><td>0.38</td><td>0.41</td><td>0.81</td></tr><tr><td>SqC</td><td>cl2</td><td></td><td>24</td><td>17</td><td>7</td><td>-</td><td>0.02</td><td>0.04</td><td>0.03</td><td>0.05</td><td>0.04</td><td>0.09</td><td>0.03</td><td>0.28</td><td>0.06</td><td>0.37</td><td>0.05</td><td>0.37</td><td>0.19</td><td>0.41</td><td>0.13</td><td>-0.10</td></tr></tbody></table>
<figure><img src="image_1.png" /><figcaption>**Figure 1:** Location of sampling sites (points). Red points indicate location of two sites closely sampled.</figcaption></figure>
<figure><img src="image_2.png" /><figcaption>**Figure 2:** Observed microhabitat abundance (empty points) for conditional predictions of our four models (M1: black dashed lines, M2: red solid lines, M3: black dotted lines, M4: black solid lines) for the eight most abundant surveys for *Barbatula barbatula* cl12 and water depth (left) and for *Telestes soufia* cl1 and current velocity habitat (right). Each frame represents a survey. Because of their similarities (i.e. adjusted intercept and habitat selection shape by surveys), M3 and M4 lines are often superimposed on the graphs. Species codes are in Table 2.</figcaption></figure>

850

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<figure><img src="image_3.png" /></figure>

**Figure 3:** Marginal predictions of model M2 (red lines) with its 95-percent confidence interval (grey areas) for *Barbatula barbatula* cl12 and *Alburnus alburnus* cl1 in relation to water depth (left) and *Telestes soufia* cl1 and *Barbus barbus* cl2 in relation to current velocity (right). The Y-axis represents the average microhabitat selection corresponding to the ratio of the predicted abundance and the maximum predicted abundance of the “average” model M2. The dashes along the x-axis indicate the distribution of measurements of fish presence in the model. Species codes are from Table 2.
<figure><img src="image_4.png" /><figcaption>**Figure 4:** Average microhabitat selection corresponding to the average value of the marginal component of M2 (see examples in Fig. 2) over the range of habitat characteristics observed in our dataset. Codes of species and size classes are from Table 2. Blue codes represent specific size classes showing average microhabitat selection for two microhabitat types, red codes for three microhabitat types.</figcaption></figure>
<figure><img src="image_5.png" /></figure>

**Figure 5:** Distribution of Spearman rho values relating the observed ranks of abundance in surveys with predicted ranks (obtained for model M2 during our leave ONE out cross validations). These statistics indicate the potential of our "average" selection model M2 to predict blindly abundance ranks in an independent river. These cross-validations rho values are shown for the different specific size classes, ordered on the x-axis according to the differences of Spearman rho values between the full M2 and full M1. These differences indicate how M2 fits abundance ranks within surveys. Points indicate median values obtained across all the rivers tested for the specific size class.
<figure><img src="image_6.png" /><figcaption>**Figure 6:** Comparison of the average microhabitat selected (defined as in Fig. 3) between models M2 developed without (X-axis) and with (Y-axis) refuge. Dashed lines represent y=x, corresponding to a similar microhabitat selection with and without refuge.</figcaption></figure>
<figure><img src="image_7.png" /><figcaption>**Figure 7:** Comparison of habitat characteristics corresponding to maximum abundance values, between our models and those of Lamouroux *et al.* (1999). This comparison is made using the microhabitat classes from Lamouroux *et al.* (1999): **Water depth:** 0-0.2 m (D1); 0.2-0.4 m (D2); 0.4-0.8 m (D3); >0.8m (D4); **Dominant substratum:** 0-0.016 m (R1); 0.016-0.064 m (R2); 0.064-0.256 m (R3); >0.256 m (R4); large bedrocks (R5); **Current velocity** (i.e. water column water current velocity): 0-0.05 m.s⁻¹ (V1); 0.05-0.2 m.s⁻¹ (V2); 0.2-0.4 m.s⁻¹ (V3); 0.4-0.5 m.s⁻¹ (V4); >0.8 m.s⁻¹ (V5). Boxplots show the median, quartiles, 95% confidence intervals and extreme values across the different specific size classes.</figcaption></figure>

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<figure><img src="image_8.png" /><figcaption>**Figure 8:** Comparison of univariate (X-axis) and multivariate (Y-axis) performance of model M2, indicated by McFadden's R²MF (left) and conditional Spearman's rho (right). Circles and triangles represent respectively the performance of univariate models associated with water depth and current velocity. Grey segments link the performance for water depth and current velocity for a given specific class. Dashed lines represent the Y=X axis.</figcaption></figure>