Comparison of growth models for sequential hermaphrodites by considering multi-phasic growth

Abstract

The von Bertalanffy (VB) growth model has been extensively used to describe fish growth. However, it may not be the best predictor of lifetime growth patterns for fish with complex life history (e.g., hermaphroditism). We sought to determine if growth models accounting for maturity and sex change were more appropriate than the VB model at capturing the growth and maturation patterns of Gag Mycteroperca microlepis, a protogynous hermaphrodite. To account for changes in growth at maturity, we used the Lester et al. (2004) growth model (bi-phasic Lester) and a modified Lester et al. (2004) model to account for an additional growth phase at sex change (tri-phasic Lester). We also compared management reference points from each model using a yield-per-recruit (YPR) framework. The tri-phasic Lester model described growth and reproductive schedules better than the bi-phasic Lester or VB models, indicating separate growth phases associated with maturation and sex change. Estimates of FMAX from the YPR analysis were lower when using the tri-phasic Lester model (0.21 year−1) compared to the VB model (0.33 year−1) when growth parameters were linked to natural mortality. Fishing mortality rates resulting in 35% of unfished total and male-specific spawning stock biomasses-per-recruit were similar for all models, but female-specific estimates were lower using the bi-phasic Lester model. Reference points from the VB model were generally lower compared to either Lester model using natural mortality rates that were not tied with the growth parameters. Our results support arguments that a single growth curve is insufficient to capture lifetime growth of fish. However, growth curves from the VB and tri-phasic Lester models were similar for all ages, especially less than age 12. This suggests the VB model can be used to describe mean length-at-age when information on reproductive status is not available, but may result in inappropriate management recommendations.