Annual spawning migrations in modelling brown trout population dynamics inside an arborescent river network

In the present paper, the annual spawning migration of adults is introduced into a model, describing the Salmo trutta population dynamics in a hierarchically organized river network (four levels and 15 interconnected patches) model based on previous work. The model describes simultaneously demographic and migration processes taking place at different time scales: migrations of individuals between patches at a fast time scale (e.g. the week or the month), the annual spawning migration of adults and the demography at the slow time scale of the year. The S. trutta population is sub-divided into three age-classes (young of the year, juveniles, and adults). We used a Leslie-type model, coupled with a migration matrix associated with the annual spawning process, and a second migration matrix associated with fast movements of individuals between patches throughout the year. All demographic and migratory parameters are constant, leading to a linear model governing 45 state variables (15 patches×three age-classes). By taking advantage of the two time scales and using aggregation techniques for the case of discrete time models, the complete model was approximated by a reduced one, with only three global variables (one per age-class) evolving at the slow time scale. Demographic indices were calculated for the population, and a sensibility analysis was performed to detect which parameters influence the most model predictions. We also quantified how modifications of the river network structure, by channels (change in connections between patches) or dams (patch deletion), influence the global population dynamics. We checked that the strategy of annual spawning migrations is actually beneficial for the population (the asymptotic population growth rate is increased), and that dams may have a more detrimental effect on the whole population dynamics than channelling.