Bridging mechanistic conceptual models and statistical species distribution models of riverine fish

Statistical species distribution models (SDMs) are widely used to quantify how taxa respond to environmental conditions and to predict their distribution. However, the application of SDMs to freshwater fish taxa is complicated by the active dispersal of fish taxa through river networks, and the species- and habitat-dependent observation process (i.e., the sampling method and effort) required to accurately sample their distributions. Many studies have applied presence-absence models (PAMs) to fish taxa, while more recent studies have proposed zero-inflated models (ZIMs) to account for count observations with many zeroes. However, relatively few studies have incorporated the observation process into the model structure, which would facilitate the combination of data from various monitoring programs that differ in their observation process. In this study, we use conceptual models to identify potentially dominant natural and anthropogenic environmental conditions with a direct, mechanistic effect on the distributions of freshwater fish taxa in Switzerland, a region with a large range of environmental conditions, from alpine streams that are mainly affected by hydromorphological alterations to lowland streams in densely populated areas with intensive agricultural land use. Moreover, numerous barriers impede fish migration along the entire river network. Using combined data from two fish monitoring programs in Switzerland, we applied an exhaustive cross-validation procedure to select a set of environmental variables with the highest (out-of-sample) predictive performance for the PAM and ZIM for fish density (individuals/m²) of the seven most prevalent fish taxa (Salmo spp., Cottus spp., Squalius spp., Barbatula spp., Barbus spp., Phoxinus spp., Gobio spp.). We used these variables to develop a PAM and ZIM for each taxon that accounts for differences in sampling methods and sampling effort. We quantified the quality of fit during calibration using all samples and predictive performance during 5-fold cross-validation of each model.Results show that stream temperature and stream morphology within the accessible habitat commonly appear among the best predictive presence-absence models for multiple taxa. Spatial variables that account for migration barriers and quantify morphological conditions within the accessible habitat were selected for 6 out of 7 taxa. The selected PAMs performed well for all taxa with an intermediate prevalence (10–40%), with an explanatory power (D2) of between 0.32 - 0.37 during calibration using all samples and only minor decreases in explanatory power during cross-validation (D2= 0.34 – 0.44). As expected, the PAM for the highly prevalent Salmo spp. (91%) failed to predict the few absence data points. By contrast, the ZIM model performed best for Salmo spp., with a standardized likelihood ratio of 1.56. For all other taxa besides Barbus spp. the ZIM models also had likelihood ratios above one, indicating a better predictive performance than the null model. We hope this study stimulates the development and application of fish species distribution models based on prior knowledge of causally linked environmental variables and incorporating observation errors to improve their predictive performance. This can facilitate learning from biomonitoring data to support management.