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 survey data are collected just before and just after two or more known harvests: 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 process and a linear death process, respectively, and then we combine the two processes. The complete-data likelihood can be factored into three parts: the general likelihood function of the index-removal method, the general likelihood function of the change-in-ratio method, and the general likelihood function of the catch-effort method. We compute the maximum likelihood estimates using the Powell search algorithm. Monte Carlo simulations are used to demonstrate that the estimates from combining change-in-ratio, index-removal, and catch-effort methods are more precise than the estimates based on combining any two of them or only using a single method. An example based on snow crab data is presented to illustrate the methodology.