A Maximum Likelihood Methodology for Estimating Length-at-Maturity with Application to Pacific Cod (Gadus macrocephalus) Population Dynamics

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Abstract
A maximum likelihood methodology for the analysis of maturity-at-length data is presented, and illustrated with data for female Pacific cod (Gadus macrocephalus) from Hecate Strait, British Columbia. Our approach explicitly accounts for the binomial nature of maturity data. Estimated maturity–length relationships show substantial differences for females sampled from different grounds within Hecate Strait, as well as large between-year differences in the maturity–length relationships for individual grounds. However, the maturity–length characteristics for a single ground are stable thoughout the spawning season, and we argue that the observed temporal variability is unlikely to be a sampling artefact. Assuming constant somatic growth rates, these differences correspond to shifts of slightly more than 1 yr in the median age-at-maturity; this shift implies that the instantaneous population growth rate rm, for Pacific cod can increase by up to 0.25 yr−1 in years when maturation occurs at smaller body size. This corresponds to an increase of over 50% in the sustainable fishing mortality rate, independent of other factors. Our results suggest that more attention should be focussed on assessing the reproductive dynamics of adult fish.

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