A length-based model for Korean chub mackerel (Scomber japonicus) stock

Abstract

When data are not available on the ages of fish sampled by a fishery or survey, it is necessary to resort to a size-based model, especially when time series data about fish body sizes are provided. Assessment of Korean chub mackerel (Scomber japonicus) stock was one such case. Building upon Quinn’s size-based model (Quinn et al. 1998), I assessed Korean chub mackerel stock. The merits of Quinn’s size-based model lie in constructing an ‘imaginary’ age structure for a fish population, and using this to estimate the year and age population sizes of cohorts. The data used were yield and lengths of fish caught by a large purse seine fishery from 2000 - 2017, and catch-per-unit-effort from 1996 - 2017. I extended Quinn’s model in three ways. First, I modified the objective function, which was the residual sum of squares in Quinn’s model, into a negative log-likelihood function in which the distributions of the annual length data and yield data were assumed to follow a multinomial and a log-normal distributions, respectively. Then I applied a prior distribution for natural mortality as opposed to using a fixed value as in Quinn’s model. Finally, using AD model builder, I estimated both the point estimates of the parameters and the uncertainty in those estimates. Estimates of annual biomass (including recruits) ranged from 1.06 x 106 MT to 2.26 x 106 MT. Estimates of fishing mortality rates were in the range of 0.11 - 0.31 year -1, while an estimate of natural mortality was 0.11 year-1.