Szerlong and Rundio, 2008

Szerlong, R. G., and D. E. Rundio. 2008. A statistical modeling method for estimating mortality and abundance of spawning salmon from a time series of counts. Canadian Journal of Fisheries and Aquatic Science 65:17-26.

We present a statistical modeling method for estimating mortality and abundance of spawning salmon from time-series counts that eliminates the need for separate information about mortality. We model arrival and mortality using differential equations, where mortality can be constant or changing linearly, and estimate mortality and abundance from counts using maximum likelihood when multiple estimates of detection rate are available. We also develop an approximate likelihood to estimate mortaility and abundance when only a single value for detection rate is available or th estimate only mortality when detection rates are entirely unknown. We demonstrate our approach using counts of coho salmon (Oncorhynchus kisutch) where mortality, abundance, and detection were determined from tagging at a weir. Our model for nonconstant mortality produced mortality estimates that closely matched the empirical data and were robust to variation in other parameters. It also provideed a better fit to the stream counts and a closer abundance estimate to the weir count that the constant mortality model. Monte Carlo simulations indicated that the approximate likelihood provided reasonable estimates of mortality over most of the ranges of parameters explored, particularly under the nonconstant mortality model, and produced relatively unbiased abundance estimates using a single value for detection.