Geostatistical distribution modelling of two invasive crayfish across dendritic stream networks

Species distribution models combining environmental and spatial components are increasingly used to understand and forecast species invasions. However, modelling distributions of invasive species inhabiting stream networks requires due consideration of their dendritic spatial structure, which may strongly constrain dispersal and colonization pathways. Here we evaluate the application of novel geostatistical tools to species distribution modelling in dendritic networks, using as case study two invasive crayfish (Procambarus clarkii and Pacifastacus leniusculus) in a Mediterranean watershed. Specifically, we used logistic mixed models to relate the probability of occurrence of each crayfish to environmental variables, while specifying three spatial autocorrelation components in random errors. These components described spatial dependencies between sites as a function of (1) straight-line distances (Euclidean model) between sites, (2) hydrologic (along the waterlines) distances between flow-connected sites (tail-up model), and (3) hydrologic distances irrespective of flow connection (tail-down model). We found a positive effect of stream order on P. clarkii, indicating an association with the lower and mid reaches of larger streams, while P. leniusculus was affected by an interaction between stream order and elevation, indicating an association with larger streams at higher altitude. For both species, models including environmental and spatial components far outperformed the pure environmental models, with the tail-up and the Euclidean components being the most important for P. clarkii and P. leniusculus, respectively. Overall, our study highlighted the value of geostatistical tools to model the distribution of riverine and aquatic invasive species, and stress the need to specify spatial dependencies representing the dendritic network structure of stream ecosystems.