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

ICES Journal of Marine Science (2016), 73(10), 2453–2467. doi:10.1093/icesjms/fsw089 Quo Vadimus The logic of comparative life history studies for estimating key parameters, with a focus on natural mortality rate John M. Hoenig1,*, Amy Y.-H. Then1,2, Elizabeth A. Babcock3, Norman G. Hall4,5, David A. Hewitt6, and Sybrand A. Hesp5 1 Virginia Institute of Marine Science, College of William & Mary, PO Box 1346, Gloucester Point, VA 23062, USA Institute of Biological Sciences, Faculty of Science, University of Malaya, Kuala Lumpur, 50603, Malaysia 3 University of Miami, 4600 Rickenbacker Causeway, Miami, FL 33149, USA 4 Centre for Fish and Fisheries Research, Murdoch University, 90 South Street, Murdoch, Western Australia 6150, Australia 5 Department of Fisheries, Western Australian Fisheries and Marine Research Laboratories, PO Box 20, North Beach, Perth, Western Australia 6920, Australia 6 U.S. Geological Survey, Western Fisheries Research Center, 2795 Anderson Avenue Suite 106, Klamath Falls Field Station, Klamath Falls, OR 97603, USA 2 *Corresponding author: tel: 18046847125; e-mail: Hoenig, J. M., Then, A. Y.-H., Babcock, E. A., Hall, N. G., Hewitt, D. A., and Hesp, S. A. The logic of comparative life history studies for estimating key parameters, with a focus on natural mortality rate. – ICES Journal of Marine Science, 73: 2453–2467. Received 7 September 2015; revised 11 March 2016; accepted 4 April 2016; advance access publication 21 June 2016. 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 illdefined 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. Keywords: biological reference points, data selection bias, empirical relationships, Fmsy, hierarchical Bayesian models, indirect methods, intrinsic rate of population growth, life history correlates, mixed effects models, steepness parameter, stock-recruit relationships. Introduction The models used by resource assessment biologists, ecosystem modellers and other applied scientists frequently require values of certain key parameters that are difficult to estimate reliably and precisely. In these cases, it is natural to examine similar situations for guidance on possible values of the parameters. Such guidance can be derived from observations from similar locations, species, time periods, observation systems (e.g. fisheries), and so forth. Indeed, even when an estimate of a parameter is believed to be reliable and precise, it is prudent to check its reasonableness by C International Council for the Exploration of the Sea 2016. All rights reserved. V For Permissions, please email: 2454 comparing it to estimates in the realm of experience. For example, Hewitt et al. (2007) estimated the natural mortality rate of blue crabs (Callinectes sapidus) from field data and compared the results to values obtained from several methods based on comparative life history studies. Sometimes, a parameter can be estimated within a population dynamics model but the estimates may be imprecise and highly correlated with those of other parameters. In this case, it may be of interest to provide additional information about the parameter to the modelling process. In a Bayesian analysis, auxiliary information can be used to develop a prior distribution for the parameter which is incorporated into the estimation scheme; the prior distribution may be developed on the basis of comparative life history data (see Hamel, 2015). Another approach is to assess several stocks simultaneously, allowing the parameter to be estimated as a compromise between what the data say about an individual stock and what other stocks say about the parameter value (Punt et al., 2011). In essence, a penalty is imposed for departure from a shared value; the amount of penalty decreases as the information about the particular species of interest increases. The problem of obtaining values for these difficult to estimate parameters can be of tremendous importance. For example, the instantaneous natural mortality rate, M, enters into almost all aspects of fishery stock assessment but can be difficult to estimate. Consequently, a number of indirect methods based on life history correlations have found widespread use. One, due to Pauly (1980), has been cited over 2400 times and another, due to Hoenig (1983), has been cited almost 1100 times according to Google Scholar (http://scholar.google.com/, accessed 5 March 2016). Another example of a widely used parameter that is difficult to estimate is the intrinsic rate of population increase (maximum per capita rate of population growth). This parameter occurs in surplus production models of yield, is directly related to the fishing mortality rate that gives maximum sustainable yield (Fmsy), and occurs in methods for calculating allowable biological catch and for formulating stock rebuilding plans. It also occurs in models of population dynamics of low fecundity species and in LotkaVolterra and similar models of predator-prey interactions. Although this parameter can be estimated in a surplus production model, the estimates tend to be imprecise especially when observations are available over only a limited range of population size. The intrinsic rate of population increase can also be estimated by observing population growth at low population density, or by observing growth rate (...truncated)