A stochastic, compartmental model of the migration of juvenile anadromous salmonids in the Columbia River Basin

Abstract

A probabilistic model is developed which describes the juvenile migration of Pacific salmon and steelhead trout ( Oncorhynchus sp.) in the Columbia River Basin in western North America. The downstream passage of smolts through a series of reservoirs or river reaches is modeled as an irreversible particle diffusion process through a series of compartments. The probability of live passage from one compartment to the next t time units after having entered the compartment can be viewed as the product of the probability of having survived to time t, the probability of transiting the compartment in t time units, and the probability of a successful transition between compartments at time t. From this basic premise, a general passage model is developed. Focusing on survival through Columbia and Snake River reservoirs (as opposed to dam-related mortality), a specific model which uses a Poisson death process and a gamma distribution to describe transmit time is presente. Analytical solutions to the single-compartment system are derived with extensions to the multi-compartment system. Empirical data from the Columbia River is used to demonstrate the utility of the model as well as to highlight problems that exist in fitting the model using existing data. Graphical techniques are presented for using the model to assess the effectiveness of management actions that are designed to improve the reservoir survival of smolts.