Stock and recruitment: generalizations about maximum reproductive rate, density dependence, and variability using meta-analytic approaches

I describe the development and application of meta-analytic techniques to understand population dynamics. These methods have been applied to a compilation of over 700 populations of fish, which includes multivariate time-series of egg production, population size, natural mortality, and anthropogenic mortality. The key requirements of this approach are to make all units comparable and to make all model parameters random variables that describe the variation among populations. Parameters are then estimated using hierarchical Bayesian or classical mixed models. This approach allows patterns to be determined that are not detected otherwise. For example, the maximum annual reproductive rate is relatively constant for all species examined: between 1 and 7 replacement spawners are produced per spawner per year at low population size. Using these approaches, I also show a 20-fold variation in carrying capacity per unit area for cod, and a decrease in carrying capacity with temperature. Recruitment variability generally increases at low population sizes, for species with higher fecundity, for populations at the edge of their range, and in regions with less oceanographic stability. The spatial scale of recruitment correlations for marine species is approximately 500 km, compared with less than 50 km for freshwater species; anadromous species fall between these two scales. Recruitment variability generally decreases with age for marine demersal fish, but often increases with age for some salmonids.