Estimating mortality rates from tag recoveries: incorporating over-dispersion, correlation, and change points

Abstract

In this article we studied the maximum-likelihood estimation of fishing and natural mortality rates with a change point from time series of tag recovery data. Our statistical models the change in the mortality rates and take account of over-dispersion and correlation involved in the recovery data. First, we considered a partial-likelihood approach for the multinomial model. Explicit estimators and variances of the fishing mortality rates were derived. However, the recovery data are usually over-dispersed, mainly because of aggregation in the population. For this problem. We considered the normal distribution model as an approximation of the Dirichlet compound multinomial distribution. When we compare the viability of different reared groups, it is important to note that the estimated parameters are correlated, even if they were obtained separately. This is because those groups were exposed to the same environments and therefore the resultant recovery data have correlation. We constructed a joint-likelihood function, taking account of the correlations among the time series of recoveries. Two groups of hatchery-reared red seabream were analyzed to demonstrate the methodology.

Author notes

Present address: Department of Aquatic Biosciences, Tokyo University of Fisheries, 4-5-7 Konan, Minato-ku, Tokyo 108, Japan

Present address: Department of Social and International Relations, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153, Japan