Estimation of Instantaneous Rates of Fishing and Natural Mortalities from Mark–Recapture Data on the Western King PrawnPenaeus latisulcatusin the Gulf St. Vincent, Australia, by Conditional Likelihood

Abstract

The instantaneous rate of natural mortality is a fundamental quantity of a fish population and is often estimated through tagging experiments. In this work, we develop a simple probabilistic model that incorporates fishing mortality, natural mortality, type II tag shedding, probability of reporting, type I mortality, and type I tag shedding; derive a likelihood function for estimating model parameters; and use them to analyze a set of tagging data from a tagging experiment with the western king prawn Penaeus latisulcatus in the Gulf St. Vincent, Australia. For both males and females, the instantaneous rate of fishing or natural mortality of western king prawns above 20 mm in carapace length was not significantly affected by carapace length but varied slightly over truncated experimental tagging periods of 2,526, 2,567, and 2,933 d. Sexual differences existed in the instantaneous rate of fishing or natural mortality for each experimental tagging period. For a truncated experimental tagging period of 2,526 d, males had an 11.43% higher instantaneous rate of natural mortality and a 23.65% higher fishing mortality than females. Many other quantities could be computed by use of our model. For example, for an experimental tagging period of 2,526 d, the annual survival rate of tagged western king prawns from both fishing and natural death was 23.85 ± 0.61% for females, and 19.49 ± 0.62% for males. Finally, we explain why the instantaneous rate of natural mortality cannot be estimated reliably by use of existing models and conclude that the problem lies in our inability to measure the times of natural deaths in a population directly. The development of new technology is required to meet this challenge.