Mechanistic models of recruitment variability in fish populations.

There are serious concerns worldwide about the decline of exploited fish stocks. The number of fish larvae surviving to be recruited into the adult population each year is fundamental to the long-term stability of a fish stock. Monitoring and predicting recruitment is a crucial component of managing economically important fisheries worldwide. Fish recruitment can vary by an order of magnitude, or more, between years, and the larval stage is a key determining factor. Fish larvae are born into an extremely variable environment, with high mortality rates, and so it is not surprising that the number surviving to join the adult population is highly variable. This thesis presents simple stochastic, mechanistic larval growth models, developed and utilised to investigate recruitment probabilities and variability. The models are mechanistic in that they are based on consideration of the key ecological processes at work, and not on statistical regression analyses or similar techniques. At the heart of the thesis lies a stochastic drift-diffusion model for the growth of an individual larva. Further mathematical and ecological complexity is built up through consideration of both the temporal and spatial heterogeneity of larval food sources, primarily zooplankton. Results illustrate the impact of stochasticity in the timing of peak food abundance, and the patchiness of the prey, on recruitment variability. The idea of non-constant variance in recruitment is also investigated, with the aim of testing its practical relevance to fisheries management. It is demonstrated that the currently available stock-recruitment time series are at least one order of magnitude too short to reliably fit such models. Management implications are illustrated using simple models and published recruitment data for two exploited stocks. The work developed within this thesis highlights the importance of stochasticity in fish larval growth and recruitment, and the power of simple mechanistic models in examining these ideas.