A prior for steepness in stock-recruitment relationships, based on an evolutionary persistence principle

Priors are existing information or beliefs that are needed in Bayesian analysis. Informative priors are important in obtaining the Bayesian posterior distributions for estimated parameters in stock assessment. In the case of the steepness parameter (h), the need for an informative prior is particularly important because it determines the stock-recruitment relationships in the model. However, specifications of the priors for the h parameter are often subjective. We used a simple population model to derive h priors based on life history considerations. The model was based on the evolutionary principle that persistence of any species, given its life history (i.e., natural mortality rate) and its exposure to recruitment variability, requires a minimum recruitment compensation that enables the species to rebound consistently from low critical abundances (Nc). Using the model, we derived the prior probability distributions of the h parameter for fish species that have a range of natural mortality, recruitment variabilities, and Nt values.

Sex-change rules, stock dynamics, and the performance of spawning-per-recruit measures in protogynous stocks

Predicting and under-standing the dynamics of a population requires knowledge of vital rates such as survival, growth, and reproduction. However, these variables are influenced by individual behavior, and when managing exploited populations, it is now generally realized that knowledge of a species’ behavior and life history strategies is required. However, predicting and understanding a response to novel conditions—such as increased fishing-induced mortality, changes in environmental conditions, or specific management strategies—also require knowing the endogenous or exogenous cues that induce phenotypic changes and knowing whether these behaviors and life history patterns are plastic. Although a wide variety of patterns of sex change have been observed in the wild, it is not known how the specific sex-change rule and cues that induce sex change affect stock dynamics. Using an individual based model, we examined the effect of the sex-change rule on the predicted stock dynamics, the effect of mating group size, and the performance of traditional spawning-per-recruit (SPR) measures in a protogynous stock. We considered four different patterns of sex change in which the probability of sex change is determined by 1) the absolute size of the individual, 2) the relative length of individuals at the mating site, 3) the frequency of smaller individuals at the mating site, and 4) expected reproductive success. All four pat-terns of sex change have distinct stock dynamics. Although each sex-change rule leads to the prediction that the stock will be sensitive to the size-selective fishing pattern and may crash if too many reproductive size classes are fished, the performance of traditional spawning-per-recruit measures, the fishing pattern that leads to the greatest yield, and the effect of mating group size all differ distinctly for the four sex-change rules. These results indicate that the management of individual species requires knowledge of whether sex change occurs, as well as an understanding of the endogenous or exogenous cues that induce sex change.

The effects of size-selective fisheries on the stock dynamics of and sperm limitation in sex-changing fish

Fisheries models have traditionally focused on patterns of growth, fecundity, and survival of fish. However, reproductive rates are the outcome of a variety of interconnected factors such as life-history strategies, mating patterns, population sex ratio, social interactions, and individual fecundity and fertility. Behaviorally appropriate models are necessary to understand stock dynamics and predict the success of management strategies. Protogynous sex-changing fish present a challenge for management because size-selective fisheries can drastically reduce reproductive rates. We present a general framework using an individual-based simulation model to determine the effect of life-history pattern, sperm production, mating system, and management strategy on stock dynamics. We apply this general approach to the specific question of how size-selective fisheries that remove mainly males will impact the stock dynamics of a protogynous population with fixed sex change compared to an otherwise identical dioecious population. In this dioecious population, we kept all aspects of the stock constant except for the pattern of sex determination (i.e. whether the species changes sex or is dioecious). Protogynous stocks with fixed sex change are predicted to be very sensitive to the size-selective fishing pattern. If all male size classes are fished, protogynous populations are predicted to crash even at relatively low fishing mortality. When some male size classes escape fishing, we predict that the mean population size of sex-changing stocks will decrease proportionally less than the mean population size of dioecious species experiencing the same fishing mortality. For protogynous species, spawning-per-recruit measures that ignore fertilization rates are not good indicators of the impact of fishing on the population. Decreased mating aggregation size is predicted to lead to an increased effect of sperm limitation at constant fishing mortality and effort. Marine protected areas have the potential to mitigate some effects of fishing on sperm limitation in sex-changing populations.