Quantile regression models for fish recruitment–environment relationships: four case studies

Understanding and modelling the environmental control of fish recruitment has been a central question in fish population ecology for the last century. Most environment–recruitment models have primarily been developed to model mean recruitment using conventional regression techniques which assume that all environmental parameters are included and that the residual unexplained variability is unstructured. However, the complexity of environmental controls and the empirical evidence that many relationships have failed when retested suggest that these assumptions are generally not met. Most environmental controls may be considered as limiting factors to recruitment and act in interaction with other factors (often not measured or not known). We used quantile regression modelling, which is specifically designed to model limiting relationships, to reanalyse environment–recruitment relationships that have been published for 4 fish stocks: (1) Northeast Arctic cod (Barents Sea), (2) Atlanto-Scandian herring, (3) Bay of Biscay anchovy and (4) Pacific sardine. The method was adapted to the specific case of autocorrelated time series, a common feature of most environmental signals. The results from quantile regression were not straightforward extensions of conventional regressions. For Northeast Arctic cod and Pacific sardine, the original relationships with temperature were not statistically significant in the quantile model. For Atlanto-Scandian herring the relationship was confirmed and temperature clearly appeared as a limiting factor to recruitment. The published relationship for the Bay of Biscay anchovy with upwelling was not confirmed, but the previously undetected relationship with river runoff was established. In this specific case, it was only by using a quantile model that the relationship could be detected as statistically significant. These results confirm the ability of quantile regression models to provide robust interpretation of environment–recruitment relationships and to produce environmentally based advance warning when recruitment is expected to be low