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Email the author (Login required) Modeling and statistical analysis of growth and shape problems of the brown crab Callinectes bellicosus
Submited: 2024-01-24 17:57:14 | Published: 2024-10-30 20:32:52
DOI: https://doi.org/10.3856/vol52-issue5-fulltext-3218
Abstract
Allometric length-weight relationships are traditionally analyzed using the Huxley model, which assumes a lognormal distribution of errors. Still, other models have been successfully evaluated to describe these relationships, and it has been found that the distribution of errors is not necessarily lognormal. Two data sets of carapace width and weight, composed of 1,554 females and 2,531 males of Callinectes bellicosus (Stimpson, 1859), were fitted to five models to address this problem, which included: Huxley model, quadratic, cubic, breakpoint and two-segment. Lognormal distribution of the residuals was first assumed, but the goodness-of-fit test did not confirm this assumption, and the QQ plots revealed heavy tails. As an alternative, logistic distribution of the residuals was assumed, and the goodness-of-fit test and the QQ plots supported this. The Akaike information criterion (AIC) was used to select the best models. When a lognormal distribution of the residuals was assumed, the best model for females was the two-segment model and the cubic model for males. In contrast, with the logistic distribution, the best model was the two-segment model for both sexes. Furthermore, AIC was smaller in models with error loglogistic distribution than lognormal distribution. The two-segment model is associated with size at maturity in both sexes, and each segment represents juvenile and adult crabs. It is concluded that it is important to confirm the assumptions of the distribution of the residuals when fitting models to data because a wrong assumption can result in an erroneous model selection.
