A mathematical model predicting the abundance and spatio-temporal dispersal of adfluvial salmonid (Salvelinus malma) fry in a stream

Abstract

Models describing the spatial and temporal distributions of fishes are necessary for conservation and management of populations and their habitats. The early life stages of fishes are a particularly important period that can influence population dynamics and fisheries productivity. The fry of riverine migratory fish species are particularly influenced by downstream transport although relatively few models have been used to predict spatio-temporal abundance and dispersion of fry in combination with life history parameters in unperturbed habitats. We present a novel model predicting the downstream dispersal of age-0 adfluvial Dolly Varden in a spawning stream draining into Kronotskoye Lake basin, Kamchatka Peninsula, Russia. The model accounted for the number of and distance between known spawning grounds, diel activity, daily fish growth, and intra-specific diversity (i.e., morphotype) to describe how fry abundance changed at a specific stream location over the course of spring and summer. Data were collected using a trapnet monitored periodically during spring and summer to record changes in abundance, size (growth), and life history composition (‘nosed’ or ‘white’ morphotype) of fish between age-0 and -2. The experimental data were fitted to the model using a gradient descent optimization algorithm and a mean squared error loss function was used to verify how well experimental data fit to the theoretical model. The predicted abundance of age-0 fish was 18,831 with a mean dispersion rate of ∼36 m/day and a transit time between spawning area and stream mouth ranging 32–76 days. The catch was mainly comprised (81%) of the slower growing ‘nosed’ morphotype and exhibited variation in abundance over time and decreased considerably by the end of summer. Our comprehensive model will be useful to simulate the downstream dispersal of salmonid fishes whose early life stages inhabit riverine systems.