Models of Growth and Maturity for North Sea Cod

Abstract

Although North Sea cod do not show the large changes in growth and maturity seen in other North Atlantic cod stocks, there are systematic changes which may affect routine assessments. Using weight-at-age data from annual ICES assessments and the International Bottom Trawl Survey (IBTS), a descriptive model which explains weight-at-age in terms of a conventional von Bertalanffy curve and a year-class effect is developed. The fitted year-class effects are correlated with stock biomass indicating a density dependent effect. IBTS maturity data are examined which show that the proportion of fish mature at age is a function both of weight and age. A life history model is constructed which can explain the qualitative changes in maturity in terms of an optimal age of maturity given expectations of growth and natural mortality. A descriptive model based on age and weight is used to reconstruct the historical series of maturity ogives where no direct observations are available. Using the derived maturities, new spawning stock size estimates are calculated and compared with the conventional assessment. In general, taking into account the changes in growth and maturity for North Sea cod does not appear to substantially alter the estimates of sustainable exploitation rates for the stock.