Oral Presentation Australian Society for Fish Biology Conference 2017

Accounting for sample size when estimating natural mortality from maximum age (#141)

Norman G Hall 1 2 , Ainslie Denham 1 , Alex Hesp 1
  1. Fisheries Department, Western Australia, Hillarys, WA, Australia
  2. Centre for Fish and Fisheries, Murdoch University, Murdoch, WA, Australia

A key parameter that is required for stock assessment is an estimate of the instantaneous rate of natural mortality, M, for the stock. This parameter is frequently estimated by substituting the maximum age recorded for the species into a regression equation that relates estimates of mortality for lightly-fished stocks to the maximum ages recorded for those stocks. Since Hoenig (1983) first published such a relationship, his approach has been cited over 1100 times, and estimates derived using his equation have been employed in numerous stock assessments. The approach has received criticism on occasion, however, as the equation does not include sample size and greater values of maximum age are likely to be observed as sample size increases. For many species, as time passes and the cumulative number of fish that have been aged increases, maximum age has crept upward. At the same time, fishing mortality has increased and the probability of survival has decreased. It is thus not possible to determine the size of an ‘equivalent’ random sample from the stock that, if the stock had remained at an unfished equilibrium, would have yielded a similar maximum age to that now employed when calculating M from the regression equation. Hoenig (2017) considers the criticism, and justifies continued use of equations estimating M from maximum age without accounting for sample size. It is interesting, however, to consider how the uncertainty associated with the observed value of maximum age varies with sample size and to explore an estimation approach that relates M to both maximum age and sample size. This presentation describes results from a preliminary exploration of this topic, which uses the probability mass function for the distribution of the maximum for a sample from a geometric distribution.

  1. Hoenig, J.M. 1983. Empirical use of longevity data to estimate mortality rates. Fishery Bulletin, 82: 898–903.
  2. Hoenig, J. M. 2017. Should natural mortality estimators based on maximum age also consider sample size? Transactions of the American Fisheries Society, 146: 136-146.