Estimation of fishing and natural mortalities from tag experiments with exact or grouped times at liberty

Abstract

A simple probabilistic model that incorporates fishing mortality, natural mortality, tag shedding, and differing reporting rates is developed, a likelihood function for estimating its parameters is derived, and a set of tagging data on newborn school shark, Galeorhinus galeus, is analysed to estimate their instantaneous natural and fishing mortalities. For a truncated tagging experimental period of 92 days, the instantaneous rate of natural mortality of newborn school sharks was estimated at 9.0427 × 10-3 (±2.4553 × 10-2)·day-1 or 3.3028 (±8.9680)·year-1 and is equal to a survival rate (from natural death only) of e-0.0090427 = 99.10%·day-1 or e-3.3028 = 3.68%·year-1. From this estimate and its corresponding estimates of catchability coefficients, we also calculated their instantaneous rate of fishing mortality in the study area from longlines, gill-nets, or both, and their survival rate, all as a function of time. This work extends previous work by incorporating fish tag shedding rates and reporting rates and by giving a detailed derivation of the likelihood function.