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 mortality and abundance when only a single value for detection rate is available or to 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 provided a better fit to the stream counts and a closer abundance estimate to the weir count than 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.
Detection and classification of vehicles for traffic video analytics
