A deterministic eco-genetic model for the short-term evolution of exploited fish stocks

- One of the first deterministic eco-genetic population models of an exploited fish stock.
- The first modeling the short-term evolution of the probabilistic maturation reaction norm.
- Results agree with those of stochastic individual-based models and with empirical trends.
- Depletion of genetic diversity is found as a new consequence of size-selective harvest.
- The loss of genetic diversity might delay the collapse of the stock.

Eco-genetic models describe the contemporary evolution of quantitative genetic traits by integrating the key ecological aspects with the modes of inheritance. Because of the flexibility in incorporating physiological, ecological, and genetic detail, eco-genetic models are typically individual-based and stochastic. Here we propose a deterministic eco-genetic population model to study the evolution of maturation schedules in exploited fish stocks. It is the first deterministic model addressing the evolution of the probabilistic maturation reaction norm (PMRN)-the genetic trait recognized to control maturation in fish species. The PMRN is the probability of interseasonal maturation as a function of age and size of juvenile individuals. Being independent of the growth trajectory followed by the individual, it can be considered a non-plastic phenotype, under limited change in temperature and climate. We consider the continuous age and size structures of the fish stock and explicitly represent foraging on a single food resource and mating under 1:1 sex ratio. Inheritance follows a single-locus-two-alleles Mendelian rule to limit the number of genotypes. We adapt the standard escalator boxcar train method for the simulation of physiologically structured population models to the case of two-dimensional age distributions-mature individuals being also distributed according to the age at maturation. The model simulations qualitatively reproduce empirical trends, specifically the genotypic redistribution toward early-maturing types under increasing exploitation and the eventual collapse of the stock. Interestingly, increased effort targeted at large sizes seems to erode the genetic diversity, an effect missed by stochastic models that might serve as warning to fishery managers and policy makers.