Abstract. It is well established that resource variability generated by spatial patchiness and turbulence is an important influence on the growth and recruitment of planktonic fish larvae. Empirical data show fractal-like prey distributions, and simulations indicate that scale-invariant foraging strategies may be optimal. Here we show how larval growth and recruitment in a turbulent environment can be formulated as a hitting time problem for a jump-diffusion process. We present two theoretical results. Firstly, if jumps are of a fixed size and occur as a Poisson process (embedded within a drift-diffusion), recruitment is effectively described by a diffusion process alone. Secondly, in the absence of diffusion, and for "patchy" jumps (of negative binomial size with Pareto inter-arrivals), the encounter process becomes superdiffusive. To synthesise these results we conduct a strategic simulation study where "patchy" jumps are embedded in a drift-diffusion process. We conclude that increasingly Lévy-like predator foraging strategies can have a significantly positive effect on recruitment at the population level.
Recent analyses propose that the key regulatory processes in fisheries are stochastic, characterized by increased recruitment variance at low stock sizes (heteroscedasticity). Here, we investigate the consequences of this idea, with the aim of testing its practical relevance to fisheries management. We argue that stock‐recruitment time series are at least one order of magnitude too short to reliably fit heteroscedastic models; indeed, they are typically insufficient even to establish in which direction recruitment variance changes with stock size. Unreliable estimates of heteroscedasticity can have important management implications, depending on the sign of the coefficient of heteroscedasticity. Maximum sustainable yield (MSY) estimates from simple models, which include heteroscedasticity can be volatile, unrealistically high and sometimes non‐existent, as illustrated by an analysis of North Sea cod (Gadus morhua) data. In contrast, for North Sea herring (clupea harengus) data, heteroscedasticity has a negligible effect on MSY estimates. Statistical models are useful to elucidate broad‐scale regulatory processes, but will need to combined with the mechanistic understanding offered by models of population dynamics before being applied in a management setting.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.