Density-dependence can be revealed by modelling the variance in the stock–recruitment process: an application to flatfish

Recruitment success in marine species is mostly driven by the high and variable mortality of first life stages, and the relationships between stock and recruitment are then largely dominated by residual variability. We show that analysing the residual variability may provide insights on the density-dependence process occurring during the recruitment. Following the seminal formulation of Minto et al. (Survival variability and population density in fish populations. Nature, 2008), we show that when recruitment is considered as a sequence of a pelagic stage with stochastic density-independent mortality followed by a second stage with stochastic density-dependent mortality, then the variability of the recruitment rate per spawning biomass (RPSB) should be a decreasing function of the spawning biomass. Using stock-recruit data of 148 stocks from the RAM legacy database, we provide a test of this hypothesis by showing that the variability of RPSB is lower for fish species with the higher concentration during juvenile stages. Second, a hierarchical Bayesian model (HBM) is built to derive a meta-analysis of stock-recruit data for 39 flatfish stocks, characterized by a high concentration of juveniles in coastal nursery habitats. Results of the HBM show that the variance of the RPSB decreases with the spawning biomass for almost all stocks, thus providing strong evidence of density-dependence during the recruitment process. Finally, we attempt to relate patterns in recruitment variance to relevant life-history traits of flatfish species