Optimal foraging in marine ecosystem models: selectivity, profitability and switching

Abstract

One of the most troubling aspects of ecosystem models is the use of rather arbitrary feeding and preference functions. The predictions of plankton functional type models have been shown to be highly sensitive to the choice of foraging model, particularly in multiple prey situations. Here we propose ecological mechanics and evolutionary logic as a solution to diet selection in ecosystem models. When a predator can consume a range of prey items, it has to choose which foraging mode to use, which prey to ignore and which ones to pursue, and animals are known to be particularly skilled in adapting their diets towards the most profitable prey items. We present a simple algorithm for plankton feeding on a size-spectrum of prey with particular energetic content, handling times and capture probabilities. We show that the optimal diet breadth changes with relative densities, but in a different way to the preference functions commonly used in models today. Indeed, depending on prey class resolution, optimal foraging can yield feeding rates that are considerably different from the 'switching functions' often applied in marine ecosystem models. Dietary inclusion is dictated by 2 optimality choices: (1) the diet breadth and (2) the actual feeding mode. The optimality model does not generate 'safety in low densities' for prey, as the 'switching function' does in ecosystem models, unless predators are shifting feeding mode adaptively. The actual diet, feeding rate and energy flux in ecosystem models can be determined by letting predators maximise energy intake or more properly, some measure of fitness where predation risk and cost are also included. An optimal foraging or fitness-maximising approach will give marine ecosystem models a sound principle to determine trophic interactions.

A biomechanical and optimality-based derivation of prey-size dependencies in planktonic prey selection and ingestion rates

“…3). Visser & Fiksen (2013) further developed those models by combining (heuristic) size dependencies for handling time, energetic content, and catchability.…”

“…Modeling either starts from empirical rules-of-thumb (Maury et al 2007, Petchey et al 2008, Williams et al 2010 or from kernel shape functions, such as Gaussian (Armstrong 2003, Troost et al 2008, Banas 2011 or Laplacian functions (Fuchs & Franks 2010), which until now lack thorough empirical testing and mechanistic explanations. Only recently, Visser & Fiksen (2013) proposed re-routing size-based feeding models towards biomechanical and evolutionarily sound principles, and assembled process-oriented formulations such as prey size dependencies of capture probability or energy content per item. However, Visser & Fiksen's resulting feeding kernels prescribe a relatively large diet breadth that even under food-replete and thus, selective grazing conditions spans 2 orders of magnitude, in contrast to the considerably smaller diet breadths observed in situ for selective copepod grazing (Wilson 1973, Richman et al 1977, Pagano et al 2003).…”

Copepod Life Strategy and Population Viability in Response to Prey Timing and Temperature: Testing a New Model across Latitude, Time, and the Size Spectrum

“…It is unclear whether this model behavior is a mathematical artifact-a limitation of combining actual lipid reserves and potential egg production into a single state variable-or whether it suggests that under some conditions the optimal level of foraging is intermediate between full activity and none. Incorporating a more mechanistic treatment of optimal foraging (Visser and Fiksen, 2013) and allowing a to vary continuously would address this. In this study, we have eliminated the phenomenon by approximating C dia as…”

“…This ambiguity is perhaps not surprising when one considers that ingestion as a function of chlorophyll or prey carbon is not a simple biomechanical property, but in fact a plastic behavioral choice. Accordingly, it might well be responsive not only to mean or maximum prey concentration but also to the prey distribution over the water column, the tradeoff between energy gain and predation risk (Visser and Fiksen, 2013), prey composition and nutritional value, and the context of the annual routine. These issues are fundamental to concretely modeling the effect of microplankton dynamics on mesozooplankton grazers.…”

Hazard warning: model misuse ahead

“…Andersen and Beyer, 2006), LotkaVolterra predator-prey dynamics (Wangersky, 1978), and analyses based on the optimization of Darwinian fitness (e.g. Visser and Fiksen, 2013). Finally, "mechanistic" models (Type III) are processbased and integrate the individual processes at one scale up to a higher scale: examples include bioenergetic and individual-based models (e.g.…”