Combining change-in-ratio, index-removal, and removal models for estimating population size

There are three methods that can be used to estimate population size when s urvey data are collected just before and just after two or more known harve sts: change-in-ratio, index-removal, and catch-effort (removal) methods. In this paper, we introduce a methodology that combines all three methods. We begin by modeling the survey and removal processes as a Poisson point proc ess and a linear death process, respectively, and then we combine the two p rocesses. The complete-data likelihood can be factored into three parts: th e general likelihood function of the index-removal method, the general like lihood function of the change-in-ratio method, and the general likelihood f unction of the catch-effort method. We compute the maximum likelihood estim ates using the Powell search algorithm. Monte Carlo simulations are used to demonstrate that the estimates from combining change-in-ratio, index-remov al, and catch-effort methods are more precise than the estimates based on c ombining any two of them or only using a single method. An example based on snow crab data is presented to illustrate the methodology.