John M Hoenig | Search USGS

USGS2016

The logic of comparative life history studies for estimating key parameters, with a focus on natural mortality rate

There are a number of key parameters in population dynamics that are difficult to estimate, such as natural mortality rate, intrinsic rate of population growth, and stock-recruitment relationships. Often, these parameters of a stock are, or can be, estimated indirectly on the basis of comparative life history studies. That is, the relationship between a difficult to estimate parameter and life history correlates is examined over a wide variety of species in order to develop predictive equations. The form of these equations may be derived from life history theory or simply be suggested by exploratory data analysis. Similarly, population characteristics such as potential yield can be estimated by making use of a relationship between the population parameter and bio-chemico–physical characteristics of the ecosystem. Surprisingly, little work has been done to evaluate how well these indirect estimators work and, in fact, there is little guidance on how to conduct comparative life history studies and how to evaluate them. We consider five issues arising in such studies: (i) the parameters of interest may be ill-defined idealizations of the real world, (ii) true values of the parameters are not known for any species, (iii) selecting data based on the quality of the estimates can introduce a host of problems, (iv) the estimates that are available for comparison constitute a non-random sample of species from an ill-defined population of species of interest, and (v) the hierarchical nature of the data (e.g. stocks within species within genera within families, etc., with multiple observations at each level) warrants consideration. We discuss how these issues can be handled and how they shape the kinds of questions that can be asked of a database of life history studies.

ICES Journal of Marine Science↗

USGS2014

Evaluating the predictive performance of empirical estimators of natural mortality rate using information on over 200 fish species

Many methods have been developed in the last 70 years to predict the natural mortality rate, M , of a stock based on empirical evidence from comparative life history studies. These indirect or empirical methods are used in most stock assessments to (i) obtain estimates of M in the absence of direct information, (ii) check on the reasonableness of a direct estimate of M , (iii) examine the range of plausible M estimates for the stock under consideration, and (iv) define prior distributions for Bayesian analyses. The two most cited empirical methods have appeared in the literature over 2500 times to date. Despite the importance of these methods, there is no consensus in the literature on how well these methods work in terms of prediction error or how their performance may be ranked. We evaluate estimators based on various combinations of maximum age ( t max ), growth parameters, and water temperature by seeing how well they reproduce >200 independent, direct estimates of M . We use tenfold cross-validation to estimate the prediction error of the estimators and to rank their performance. With updated and carefully reviewed data, we conclude that a t max -based estimator performs the best among all estimators evaluated. The t max -based estimators in turn perform better than the Alverson–Carney method based on t max and the von Bertalanffy K coefficient, Pauly’s method based on growth parameters and water temperature and methods based just on K . It is possible to combine two independent methods by computing a weighted mean but the improvement over the t max -based methods is slight. Based on cross-validation prediction error, model residual patterns, model parsimony, and biological considerations, we recommend the use of a t max -based estimator ( M = 4.899 t max − 0.916 "> M = 4.899 t − 0.916 max M=4.899tmax−0.916 , prediction error = 0.32) when possible and a growth-based method ( M = 4.118 K 0.73 L ∞ − 0.33 "> M = 4.118 K 0.73 L − 0.33 ∞ M=4.118K0.73L∞−0.33 , prediction error = 0.6, length in cm) otherwise.

ICES Journal of Marine Science↗