A diffusion model for the downstream migration of sockeye salmon smolts

Abstract

Abstract The smolt migration (the migration from their nursery lake to the sea) of sockeye salmon ( Oncorhynchus nerka ) is modeled as one-dimensional diffusion with drift. The average downstream velocity of smolts is assumed proportional to the water velocity and water velocity is modeled based on Manning's roughness formula. This leads to the approximation that the expected transit time for a smolt is proportional to the minus two-fifths power of the river's discharge. The smolts disperse as they move downstream and their spatial positions at a given time after emigration are modeled as normally distributed with the variance proportional to the time after emigration. Mark-recapture data on smolts from Chilko Lake (Fraser River system, British Columbia) are fitted to this model by maximizing the conditional likelihood. Smolts from Chilko Lake emigrate daily at dusk during three distinct emigration events of a few days each between late April and mid May. By the time these smolts reach the mouth of the Fraser Estuary, the fitted model predicts that smolts from these three emigration events will have merged, so that their arrival times form a relatively smooth curve spanning five or six weeks.