Should Natural Mortality Estimators Based on Maximum Age Also Consider Sample Size?. Issue 1 (2nd January 2017) - Hoenig, John M.
Abstract: Natural mortality rate can be difficult to estimate; consequently, indirect methods based on life history correlations are frequently used to infer values for stock assessments. One common class of predictors is based on the relationship between natural mortality rate and maximum age in unexploited or lightly exploited populations. The oldest age in a sample depends on the sample size, but there is confusion in the literature over the correct expression. Those attributable to Sarhan (1954 ) and Holt (1965 ) are correct. Kenchington's (2014 ) estimators that incorporate sample size are mathematically flawed and should not be used. Expressions exist for the expected value and variance of order statistics from an exponential distribution (including the maximum age), and these account for sample size. However, the resulting estimators are not recommended without evaluation of their performance because (1) they may not be robust to failures of the parametric assumptions, (2) it is often difficult or impossible to determine the effective sample size, and (3) new estimators may not be needed because of the insensitivity of the maximum age to sample size. Empirical estimators based on regressing estimates of natural mortality rate from the literature on corresponding values of maximum age continue to be a viable approach. They do not use information on sample size, but fortunately the maximum observed age is insensitive to sample size provided the sample size is reasonably large. Sometimes, the maximum age from an exploited population is used with an empirical regression estimator. This can give an estimate close to the natural mortality rate if relict, old fish are largely protected by virtue of their habitat or their low vulnerability to capture. However, in general, use of maximum age from an exploited population tends to give an estimate somewhere between the natural mortality rate and the maximum total mortality that the stock has experienced. Received May 18, 2016; accepted October 12, 2016