Size-dependent mortality formulation for isochronal fish species based on their fecundity: An example of Pacific cod ( Gadus macrocephalus) in the eastern coastal areas of Korea

Abstract

We developed a matrix projection method to estimate and validate size-dependent instantaneous rates of natural mortality ( M) for isochronal fishes, based on their fecundity and growth. Here we show an example of application to the Pacific cod ( Gadus macrocephalus) in Korean sea waters. The parameters of the first row of the Leslie matrix, which represent fecundity, were estimated by combining a von Bertalanffy growth equation covering all life stages, a logistic equation of maturity with body size, and a relationship between body size and fecundity, which were derived from otolith and gonad analyses of cods collected from the East Sea of Korea from 2003 to 2007. For survival rates in the Leslie matrix, we derived a theoretical mortality curve after assuming M as an inverse function of total length (TL) and long-term equilibrium status of stock. The derived constant for size-specific instantaneous mortality ( q) was 46.26 yr −1 cm in TL. The estimates of age-specific M ranged from 9.1 yr −1 for age 0 cod to 0.49 yr −1 for age 8 cod, on average for age 1 to 8 yr, 0.82 yr −1 which is greater by a factor of 4 than the estimate derived by Pauly's equation, 0.2 yr −1. Our estimate of q is sensitive to the embryonic survival rate, which could vary greatly depending on water temperature, but we assumed as a constant of 10%. However, sensitivity analyses showed that, except age 0, derived age-specific M is robust with varying embryonic survival rate from 1% to 100%. Moreover, comparisons of the length frequencies derived from our Leslie matrix with those derived from catch data did not show any significant difference, suggesting that our theoretically derived M is reliable enough for the purpose of stock assessment. Our approach of estimating and validating size-dependent M based on fecundity can be applied and extended to other freshwater and marine fish species, improving reliability of stock assessments for fisheries management.