Modelling fish physico-thermal habitat selection using functional regression

In this paper, a new fish habitat modelling approach is introduced using the full probability density functions (PDF), rather than single measurements or central tendency metrics, to describe each predictor. To model habitat selection using PDFs, functional regression models (FRM) are used to allow for the inclusion of curves or functions (smoothed empirical PDFs) in regression models compared to scalars or vectors in classical contexts. The benefits of FRM are exemplified by comparing results with those obtained using generalized additive models (GAM), one of the most recent and performing models in the field. Abundance of juvenile Atlantic salmon sampled at 26 sites (75 m-long x river width) of the Sainte-Marguerite River (Quebec, Canada) was modelled with PDFs of four potential predictors: flow velocity, water depth, substrate size and water temperature. The latter has been less frequently used in habitat modelling and the results showed that it was the most significant predictor. Overall, FRM explained more of the variability in habitat selection than GAM (+14.9% for fry and +8.1% for 1+ parr), mainly due to their ability to use complete distributions of the habitat variables rather than aggregated values (mean). A leave-one-out cross validation showed that both GAM and FRM had similar performance to predict fish abundance. The use of FRM in fish habitat modelling is innovative and its potential should be further developed, especially in the current context where habitat variables are becoming increasingly easy to obtain due to rapid progress of remote measurement techniques.