Modeling of age-dependent natural mortality rates for long-lived fishes based on the Richards model family

Natural mortality rates (M) are poorly quantified and commonly identified as a key source of uncertainty in fish stock assess-ments. Increasingly, stock assessments account for size-and age-dependence in M instead of using a constant M for all sizes and ages, as has traditionally been the default assumption. Empirical studies show that M is approximately inversely propor-tional to body length in fish populations, and this generalization has been used together with a von Bertalanffy growth curve to derive an age-dependent M. Here we extend this approach to the three commonly used growth functions of the Richards family (i.e., Logistic, von Bertalanffy, and Gompertz growth models). These models allow flexible production of various growth curves with a sigmoid shape and an upper asymptote, making them useful for displaying diverse growth curves for various long-lived fishes. The influences of growth parameters on predicted M were investigated, and the outcomes were compared among the three growth models. Age-dependent M for blue sharks (Prionace glauca) were estimated as an example.