Mean Field Games for Diel Vertical Migration with Diffusion.

We present a theoretical framework, based on differential mean field games, for expressing diel vertical migration in the ocean as a game with a continuum of players. In such a game, each agent partially controls its own state by adjusting its vertical velocity but the vertical position in a water column is also subject to random fluctuations. A representative player has to make decisions based on aggregated information about the states of the other players.

Population games with instantaneous behavior and the Rosenzweig-MacArthur model.

How to determine the spatial distribution and population dynamics of animals are some of the key questions in ecology. These two have been coupled before, but there is no general method for determining spatial distributions based on instantanous behavior coupled with population dynamics. We propose modeling interacting populations with instantaneous habitat choice through mean-field games.

Solving multispecies population games in continuous space and time.

Game theory has emerged as an important tool to understand interacting populations in the last 50 years. Game theory has been applied to study population dynamics with optimal behavior in simple ecosystem models, but existing methods are generally not applicable to complex systems. In order to use game-theory for population dynamics in heterogeneous habitats, habitats are usually split into patches and game-theoretic methods are used to find optimal patch distributions at every instant.

Evolution of toxins as a public good in phytoplankton.

Toxic phytoplankton blooms have increased in many waterbodies worldwide with well-known negative impacts on human health, fisheries and ecosystems. However, why and how phytoplankton evolved toxin production is still a puzzling question, given that the producer that pays the costs often shares the benefit with other competing algae and thus provides toxins as a 'public good' (e.g.

Spatial drivers of instability in marine size-spectrum ecosystems.

Size-spectrum models are a recent class of models describing the dynamics of a whole community based on a description of individual organisms. The models are motivated by marine ecosystems where they cover the size range from multicellular plankton to the largest fish. We propose to extend the size-spectrum model with spatial components.

Trophic interactions drive the emergence of diel vertical migration patterns: a game-theoretic model of copepod communities.

Diel vertical migration (DVM), the daily movement of organisms through oceanic water columns, is mainly driven by spatio-temporal variations in the light affecting the intensity of predator-prey interactions. Migration patterns of an organism are intrinsically linked to the distribution of its conspecifics, its prey and its predators, each with their own fitness-seeking imperatives. We present a mechanistic, trait-based model of DVM for the different components of a pelagic community.

Positioning of aquatic animals based on time-of-arrival and random walk models using YAPS (Yet Another Positioning Solver).

Aquatic positional telemetry offers vast opportunities to study in vivo behaviour of wild animals, but there is room for improvement in the data quality provided by current procedures for estimating positions. Here we present a novel positioning method called YAPS (Yet Another Positioning Solver), involving Maximum Likelihood analysis of a state-space model applied directly to time of arrival (TOA) data in combination with a movement model. YAPS avoids the sequential positioning-filtering-approach applied in alternative tools by using all available data in a single model, and offers better accuracy and error control.

Dynamic optimal foraging theory explains vertical migrations of Bigeye tuna.

Bigeye tuna are known for remarkable daytime vertical migrations between deep water, where food is abundant but the water is cold, and the surface, where water is warm but food is relatively scarce. Here we investigate if these dive patterns can be explained by dynamic optimal foraging theory, where the tuna maximizes its energy harvest rate. We assume that foraging efficiency increases with body temperature, so that the vertical migrations are thermoregulatory.

A Diffusion Approximation Based on Renewal Processes with Applications to Strongly Biased Run-Tumble Motion.

We consider organisms which use a renewal strategy such as run-tumble when moving in space, for example to perform chemotaxis in chemical gradients. We derive a diffusion approximation for the motion, applying a central limit theorem due to Anscombe for renewal-reward processes; this theorem has not previously been applied in this context. Our results extend previous work, which has established the mean drift but not the diffusivity.

Interrelations between senescence, life-history traits, and behavior in planktonic copepods.

The optimal allocation of resources to repair vs. reproduction in an organism may depend on the magnitude and pattern of the external mortality it is experiencing, which, in turn, may depend on its feeding and mate-finding behavior. Thus, the fundamental activities of an organism, i.

A model of extracellular enzymes in free-living microbes: which strategy pays off?

An initial modeling approach was applied to analyze how a single, nonmotile, free-living, heterotrophic bacterial cell may optimize the deployment of its extracellular enzymes. Free-living cells live in a dilute and complex substrate field, and to gain enough substrate, their extracellular enzymes must be utilized efficiently. The model revealed that surface-attached and free enzymes generate unique enzyme and substrate fields, and each deployment strategy has distinctive advantages.

Size-dependent diffusion promotes the emergence of spatiotemporal patterns.

Spatiotemporal patterns, indicating the spatiotemporal variability of individual abundance, are a pronounced scenario in ecological interactions. Most of the existing models for spatiotemporal patterns treat species as homogeneous groups of individuals with average characteristics by ignoring intraspecific physiological variations at the individual level. Here we explore the impacts of size variation within species resulting from individual ontogeny, on the emergence of spatiotemporal patterns in a fully size-structured population model.

Ctenophore population recruits entirely through larval reproduction in the central Baltic Sea.

The comb jelly Mertensia ovum, widely distributed in Arctic regions, has recently been discovered in the northern Baltic Sea. We show that M. ovum also exists in the central Baltic but that the population consists solely of small-sized larvae (less than 1.

Diffusive transport in Stokeslet flow and its application to plankton ecology.

In this paper we consider the advective/diffusive transport of a solute near a hovering zooplankter. We approximate the fluid flow with that of a Stokeslet, corresponding to the plankter exerting a point force on the water, and assume that the plankter acts as a point source for the transported solute, located at the same point as the force. We find an analytical expression in closed form for the steady-state concentration of the solute.

How optimal life history changes with the community size-spectrum.

This paper derives optimal life histories for fishes or other animals in relation to the size spectrum of the ecological community in which they are both predators and prey. Assuming log-linear size-spectra and well known scaling laws for feeding and mortality, we first construct the energetics of the individual. From these we find, using dynamic programming, the optimal allocation of energy between growth and reproduction as well as the trade-off between offspring size and numbers.