Properties of age compositions and mortality estimates derived from cohort slicing of length data

ICES Journal of Marine Science ICES Journal of Marine Science (2015), 72(1), 44– 53. doi:10.1093/icesjms/fsu088 Original Article Properties of age compositions and mortality estimates derived from cohort slicing of length data Lisa E. Ailloud, Matthew W. Smith, Amy Y. Then, Kristen L. Omori, Gina M. Ralph, and John M. Hoenig* Virginia Institute of Marine Science, College of William & Mary, P.O. Box 1346, Gloucester Point, VA 23062, USA *Corresponding author: tel: +1 804 684 7125; e-mail: Ailloud, L. E., Smith, M. W., Then, A. Y., Omori, K. L., Ralph, G. M., and Hoenig, J. M. Properties of age compositions and mortality estimates derived from cohort slicing of length data. – ICES Journal of Marine Science, 72: 44– 53. Received 2 September 2013; revised 22 April 2014; accepted 23 April 2014; advance access publication 3 June 2014. Cohort slicing can be used to obtain catch-at-age data from length frequency distributions when directly measured age data are unavailable. The procedure systematically underestimates the relative abundance of the youngest age groups and overestimates abundance at older ages. Cohortsliced catch-at-age data can be used to estimate total mortality rate (Z) using a regression estimator or the Chapman – Robson estimator for right truncated data. However, the effect of cohort slicing on accuracy and precision of resulting Z estimates remains to be determined. We used Monte Carlo simulation to estimate the per cent bias and per cent root mean square error of the unweighted regression, weighted regression, and Chapman –Robson mortality estimators applied to cohort-sliced data. Incompletely recruited age groups were truncated from the cohortsliced catch-at-age data using previously established recommendations and a variety of plus groups was used to combine older age groups. The sensitivity of the results to a range of plausible biological combinations of Z, growth parameters, recruitment variability, and length-at-age error was tested. Our simulation shows that cohort slicing can work well in some cases and poorly in others. Overall, plus group selection was more important in high K scenarios than it was in low K scenarios. Surprisingly, defining the plus group to start at a high age worked well in some cases, although length and age are poorly correlated for old ages. No one estimator was uniformly superior; we therefore provide recommendations concerning the appropriate estimator and plus group to use, depending on the parameters characterizing the stock. We further recommend that simulations be performed to determine exactly which plus group would be most appropriate given the scenario at hand. Keywords: age composition, age distribution, age slicing, catch-at-age, cohort slicing, mortality. Introduction While there has been a recent shift in stock assessment methods towards using catch-at-length-based models, much of modern stock assessment remains based on catch-at-age models, which estimate population sizes and derive exploitation history by summing catches over time on a cohort-by-cohort basis. Size-structured models like MULTIFAN-CL (Fournier et al., 1998) and Stock Synthesis (Methot, 2005) are often more informative than the simpler catch-at-age models, but these highly complex integrated assessment methods also tend to require more data, leaving simpler models like virtual population analysis (VPA) still used for data-poor species. The catch-at-age approach is predicated on having reliable data on the age composition of the catch in each year. Age data can often be obtained from hard parts (e.g. otoliths, vertebrae, spines), but such techniques are labour-intensive and time-consuming, and not applicable to many invertebrates. This information is therefore not always available to stock assessment scientists who have to extract age composition from the available fisheries catch-at-length data. The most common approaches used when no age estimates are available are Pauly and David’s (1981) ELEFAN, and Fournier et al.’s (1990) MULTIFAN. When limited direct observations on age are available, an inverse age – length key (Hoenig and Heisey, 1987; Kimura and Chikuni, 1987) or a combined forward and inverse key (Hoenig et al., 1994) might be used. While these tools reduce the need for direct ageing studies, they still require some age – length data to be collected, which is not always practical. An alternative is to estimate the age composition from the length frequency distribution of the catch using cohort slicing (also known as age slicing). This requires a growth equation to be available but does not require information on variability in size at age. With this method, a length interval or “bin” is specified for each age # International Council for the Exploration of the Sea 2014. All rights reserved. For Permissions, please email: Properties of age compositions and mortality estimates group and the number at each age is estimated as the number of observations in the corresponding length bin. The bin definitions are determined from a von Bertalanffy (or other) growth equation, following the assumption that ages are clearly separated by length bounds. The oldest age groups are lumped together in a catch-all “plus” group because, as fish grow, the relationship between body size and age weakens to the point that the oldest nominal ages are largely mixtures of ages (Figure 1). This method is currently being used in the assessment of many highly migratory species, including swordfish, Xiphias gladius, yellowfin tuna, Thunnus albacares, bigeye tuna, Thunnus obesus, Atlantic bluefin tuna, Thunnus thynnus, and North Atlantic albacore, Thunnus alalunga (International Commission for the Conservation of Atlantic Tunas, 2010, 2011, 2012a, b, 2014) as well as a number of demersal fisheries, including the witch flounder, Glyptocephalus cynoglossus (International Council for the Exploration of the Sea, 2012), European hake, Merluccius merluccius, red mullet, Mullus barbatus, red shrimp, Aristeus antennatus, and deep-water pink shrimp, Parapenaeus longirostris (General Fisheries Commission for the Mediterranean, 2012). Cohort slicing is predicated on the assumption that there is no overlap in length among cohorts. Strictly speaking, this assumption is never met—size distributions for the oldest age groups always overlap. While the properties of cohort slicing have not yet been evaluated comprehensively, a few studies have explored the implications of its assumptions for the estimation of age composition. Mohn (1994) and Restrepo (1995) were the first to point out that cohort slicing tends to underestimate recruitment variability. When the cohorts are of equal abundance, the younger cohort contributes as much to the estimate of the older cohort as the older cohort contributes to the estimate of the younger cohort. Hence, the errors of misclassification cancel out. But, when the cohorts are of unequal size, the more abundant cohort contributes more to pe (...truncated)