A new likelihood for simultaneously estimating von Bertalanffy growth parameters, gear selectivity, and natural and fishing mortality

Abstract

Gear selectivity and the cumulative effects of size-selective fishing produce bias in the length-at-age samples used to estimate the von Bertalanffy growth parameters. In fished populations, fast-growing young fish and slow-growing old fish are overrepresented in size–age samples. To account for such effects, we treated size-at-age observations as multinomial samples, with expected catches in each size–age category dependent on growth parameters, growth variation, size selectivity, abundance at age, and the history of exploitation. Using simulated data sets, estimated growth parameters using the multinomial likelihood were unbiased when fishing mortality was not too high and the shape of the vulnerability function was correct. In contrast, estimated growth parameters using a least squares approach overestimated the metabolic growth coefficient (K) and underestimated mean asymptotic length (L∞). Models that do not explicitly account for the effects of fishing and size selectivity underestimated L∞ and overestimated K. We estimate growth parameters for northern pikeminnow (Ptychocheilus oregonensis) as an example of the method and document a stunted "pigmy" population with an L∞ of 175-mm fork length, attributing its small size to effects of high density and (or) a short growing season.