Comparing growth curves with asymmetric heavy-tailed errors: Application to the southern blue whiting (Micromesistius australis)

Abstract

Von Bertalanffy growth models (VBGMs) have been used in several studies of age, growth and natural mortality. Assuming that the residuals about this growth model are normal is, however, questionable. Here, we assume that these residuals are heteroskedastic and follow a log-skew-t distribution, a flexible distribution that is asymmetric and heavy-tailed. We apply the proposed methodology to length-at-age data for the southern blue whiting (Micromesistius australis) collected from Chilean austral continental waters between 1997 and 2010. The estimates of the VBGM parameters were L∞=57.042cm, K=0.173yr−1, t0=−2.423yr for males, and L∞=61.318cm, K=0.163yr−1, t0=−2.253yr for females. The BIC criteria suggest that females grow significantly faster than males and that length-at-age for both sexes exhibits significant heteroskedasticity and asymmetry.