A general growth model for mark-recapture data

Abstract

The general four-parameter size-age growth model of Schnute incorporates many classical formulations, such as the von Bertalanffy, Gompertz, and Richards, as submodels. The general model has different submodels depending on the values of two model parameters a and b. We develop here the equivalent model representations for mark-recapture data, consisting of size measurements at the times of marking and recapture and the times at large. The general mark-recapture model for these data contains only three distinct parameters, because actual fish age is not included in the data set. Thus, mark-recapture data can be used to determine a general growth model only if one of the parameters, most likely size at the starting age, is specified beforehand. The model is applied to two data sets with both size-age and mark-recapture data: Arctic char in the Wood River system, Alaska and rainbow trout in the Kenai River, Alaska. Different growth formulations are isolated for the two data sets, illustrating the versatility of Schnute's formalism of growth. In only one instance is the ubiquitous von Bertalanffy growth model selected, suggesting that alternative growth models should be considered more frequently. We discuss how growth variations of individuals may be incorporated into the general model.