Modeling fish numbers dynamically by age and length: Partitioning cohorts into "slices"

Fishery processes of selectivity and recruitment to legal size vary with fish length and are mediated by fish growth. Yet most fishery models are age-based. To model length-dependent change within each cohort, fish numbers must vary dynamically with length as well as with age in the model population array. The fishery model formalism described here achieves this by a partition of the continuous length-at-age distribution. This method is computationally efficient and cleanly differentiates legal from sublegal fish. Fish numbers within each cohort are partitioned into length bins, called slices. A slice is defined and calculated as the fish in each cohort length-at-age distribution that have grown into legal size since the start of the previous time step. When growth is estimated from catch length and age samples separately from the stock assessment, biases result from the implicit assumption that catch samples are representative of the population and from ignoring length-dependent change within cohorts. These biases are avoided by integrating recruitment, growth, and selectivity estimation into a stock assessment likelihood that represents changing population numbers by both age and length. Size dependence also permits a natural extension of fishery models to trophic interactions with the surrounding ecosystem.