A method for estimating dynamics of carrying capacity using time series of stock and recruitment

ABSTRACT:  The present paper proposes a method for estimating the dynamics of carrying capacity using estimates of number of recruits and stock biomass with the stock recruitment curve. The paper assumes that both biological parameters at saturation level and the type of stock recruitment curve are invariant and independent of the size of the carrying capacity. The carrying capacity size is incorporated into a density dependent parameter in a model of stock and recruitment and size is expressed as a function of time. Normal independent variable, autoregressive process of order one and moving average process of order one are used for candidates of process error. Unknown parameters are estimated maximizing likelihood function. The best model is selected statistically using the finite corrected criterion of the Akaike Information Criterion. The method was applied to the recruits and biomass estimates of the Pacific stock of chub mackerel Scomber japonicus and estimates of the stock of Japanese sardine Sardinops melanostictus along the Pacific coast. Issues and problems for applications and modification of the model are discussed.