Game-theoretic methods for functional response and optimal foraging behavior

Resource Patchiness as a Resolution to the Food Paradox in the Sea

AbstractAverage concentrations of biota in the ocean are low, presenting a critical problem for ocean consumers. High-resolution sampling, however, demonstrates that the ocean is peppered with narrow hot spots of organism activity. To determine whether these resource aggregations could provide a significant solution to the ocean's food paradox, a conceptual graphical model was developed that facilitates comparisons of the role of patchiness in predator-prey interactions across taxa, size scales, and ecosystems. The model predicts that predators are more reliant on aggregated resources for foraging success when the average concentrations of resources is low, the size discrepancy between predator and prey is great, the predator has a high metabolic rate, and/or the predator's foraging time is limited. Size structure differences between marine and terrestrial food webs and a vast disparity in the overall mean density of their resources lead to the conclusion that high-density aggregations of prey are much more important to the survival of oceanic predators than their terrestrial counterparts, shaping the foraging decisions that are available to an individual and setting the stage on which evolutionary pressures can act. Patches of plenty may be rare, but they play an outsized role in behavioral, ecological, and evolutionary processes, particularly in the sea.

From the distributions of times of interactions to preys and predators dynamical systems

We consider a stochastic individual based model where each predator searches and then manipulates its prey or rests during random times. The time distributions may be non-exponential and density dependent. An age structure allows to describe these interactions and get a Markovian setting. The process is characterized by a measure-valued stochastic differential equation. We prove averaging results in this infinite dimensional setting and get the convergence of the slow-fast macroscopic prey predator process to a two dimensional dynamical system. We recover classical functional responses. We also get new forms arising in particular when births and deaths of predators are affected by the lack of food.

State-controlled epidemic in a game against a novel pathogen

The pandemic reminded us that the pathogen evolution still has a serious effect on human societies. States, however, can prepare themselves for the emergence of a novel pathogen with unknown characteristics by analysing potential scenarios. Game theory offers such an appropriate tool. In our game-theoretical framework, the state is playing against a pathogen by introducing non-pharmaceutical interventions to fulfil its socio-political goals, such as guaranteeing hospital care to all needed patients, keeping the country functioning, while the applied social restrictions should be as soft as possible. With the inclusion of activity and economic sector dependent transmission rate, optimal control of lockdowns and health care capacity management is calculated. We identify the presence and length of a pre-symptomatic infectious stage of the disease to have the greatest effect on the probability to cause a pandemic. Here we show that contrary to intuition, the state should not strive for the great expansion of its health care capacities even if its goal is to provide care for all requiring it and minimize the cost of lockdowns.

Predation in Many Dimensions: Spatial Context Is Important for Meaningful Functional Response Experiments

For simplicity and to minimize variation, functional response experiments frequently use environments of simple physical structure and small size. Less attention is paid to similarity of the experimental environment to the natural environment where predation occurs. Assumptions about predator and prey use of space are often implied in the choice of experimental environment. We illustrate how these assumptions may affect conclusions with an experiment testing how arena size affects a functional response. Toxorhynchites rutilus preyed upon larval Culex restuans in containers differing in volume by 15x, but spanning a similar range of prey/liter. The most plausible Type II model included attack rates that were statistically indistinguishable, but in the larger volume, had handling time that was lower by > 30x compared to the smaller volume, suggesting a major change in predator behavior with container volume. When we altered our assumption that predation scales with prey/liter, assuming instead that aggregation causes predation to scale with prey/area of surface or bottom, the conclusions changed: neither attack rate nor handling time differed with container size. Thus, our assumption about how predator and prey used space altered the conclusions of the experiment. We then summarize recently published experiments showing that spatial context affects estimated functional responses. We suggest that functional response experiments would be improved by using larger experimental spaces that represent physical complexity of environments where predation occurs. Greater spatial extent and complexity are likely to cause aggregation of predation. Effects of more realistic spatial context are likely to yield more complete understanding of quantitative aspects of predation.

Top-down effects of foraging decisions on local, landscape and regional biodiversity of resources (DivGUD)

Foraging by consumers acts as a biotic filtering mechanism for biodiversity at the trophic level of resources. Variation in foraging behaviour has cascading effects on abundance, diversity, and functional trait composition of the community of resource species. Here we propose diversity at giving-up density (DivGUD), i.e. when foragers quit exploiting a patch, as a novel concept and simple measure quantifying cascading effects at multiple spatial scales. In experimental landscapes with an assemblage of plant seeds, patch residency of wild rodents decreased local α-DivGUD (via elevated mortality of species with large seeds) and regional γ-DivGUD, while dissimilarity among patches in a landscape (ß-DivGUD) increased. By linking theories of adaptive foraging behaviour with community ecology, DivGUD allows to investigate cascading indirect predation effects, e.g. the ecology-of-fear framework, feedbacks between functional trait composition of resource species and consumer communities, and effects of inter-individual differences among foragers on the biodiversity of resource communities.

Nash equilibria in human sensorimotor interactions explained by Q-learning with intrinsic costs

The Nash equilibrium concept has previously been shown to be an important tool to understand human sensorimotor interactions, where different actors vie for minimizing their respective effort while engaging in a multi-agent motor task. However, it is not clear how such equilibria are reached. Here, we compare different reinforcement learning models to human behavior engaged in sensorimotor interactions with haptic feedback based on three classic games, including the prisoner's dilemma, and the symmetric and asymmetric matching pennies games. We find that a discrete analysis that reduces the continuous sensorimotor interaction to binary choices as in classical matrix games does not allow to distinguish between the different learning algorithms, but that a more detailed continuous analysis with continuous formulations of the learning algorithms and the game-theoretic solutions affords different predictions. In particular, we find that Q-learning with intrinsic costs that disfavor deviations from average behavior explains the observed data best, even though all learning algorithms equally converge to admissible Nash equilibrium solutions. We therefore conclude that it is important to study different learning algorithms for understanding sensorimotor interactions, as such behavior cannot be inferred from a game-theoretic analysis alone, that simply focuses on the Nash equilibrium concept, as different learning algorithms impose preferences on the set of possible equilibrium solutions due to the inherent learning dynamics.

Revisiting the "fallacy of averages" in ecology: Expected gain per unit time equals expected gain divided by expected time

Fitness is often defined as the average payoff an animal obtains when it is engaged in several activities, each taking some time. We point out that the average can be calculated with respect to either the time distribution, or to the event distribution of these activities. We show that these two averages lead to the same fitness function. We illustrate this result through two examples from foraging theory, Holling II functional response and the diet choice model, and one game-theoretic example of Hamilton's rule applied to the time-constrained Prisoner's dilemma (PD). In particular, we show that in these models, fitness defined as expected gain per unit time equals fitness defined as expected gain divided by expected time. We also show how these fitnesses predict the optimal outcome for diet choice and the prevalence of cooperation in the repeated PD game.

Beauveria bassiana (Ascomycota: Hypocreales)-treated Diamondback Moth (Lepidoptera: Plutellidae) Larvae Mediate the Preference and Functional Response of Euborellia annulipes (Dermaptera: Anisolabididae) Nymphs

Biological control is one of the strategies to reduce populations of diamondback moth, Plutella xylostella (Linnaeus) (Lepidoptera: Plutellidae), the major pest of brassica. Entomopathogen-based biopesticides are recommended and used for its control, reducing the constant use of chemical pesticides. Predators and/or fungal entomopathogens have an increasing interest to be used against diamondback moth, and the compatibility of these control agents in the field is important for pest management. Here we experimentally investigate the effects of diamondback moth larvae treated with a biopesticidal formulation of Beauveria bassiana (Balsamo) Vuillemin in the feeding preference and functional response of the ring-legged earwig. We used untreated and B. bassiana-treated diamondback moth fourth instars (over a 24-h period of exposure) and Euborellia annulipes (Lucas) fifth instars. The nymphs were included in choice condition tests and different larval densities to the analysis of feeding preference and functional responses, respectively. Euborellia annulipes nymphs exhibited no feeding preference under choice conditions but presented different types of functional response: Type II on untreated and type III on fungus-treated diamondback moth larvae. The interaction between E. annulipes and B. bassiana observed in our study contributes to the understanding of the predator-prey-pathogen relationships with implications for P. xylostella integrated management strategies.

iTRAQ-based proteomic analysis to identify molecular mechanisms of the selenium deficiency response in the Przewalski's gazelle

The Przewalski's gazelle shows long-term survival in a selenium (Se)-deficient environment, but fails to exhibit obvious pathological manifestations. To reveal proteomic changes in the Przewalski's gazelle in response to Se-deficiency, twenty Przewalski's gazelle were randomly divided into control group and Se-deficient group. After induction of Se-deficiency animal model, blood samples were collected from eight animals. An isobaric tag for relative and absolute quantitation (iTRAQ)-liquid chromatography-tandem mass spectrometry (LC-MS/MS) proteomics approach was employed to explore blood protein alterations and potential mechanisms of the response to Se-deficiency challenge. Se deficiency contributed to a remarkable change in blood Se levels and routine blood indexes. In proteomic analyses, 130 proteins were differentially accumulated in the Se-deficient and control groups. The differentially expressed proteins were annotated mainly as single-organism process, extracellular region, or binding, respectively, and they were highly enriched in the coagulation and complement cascades. Protein-protein interaction analysis showed several important nodal proteins involved in the regulation of binding, cellular biochemical processes, and signal transduction pathways. To our knowledge, this study is the first to comprehensively analyze blood protein changes in the Przewalski's gazelle under Se-deficient conditions, which reveal that this species has developed physiological mechanisms of adaptation in response to Se-deficiency stress. SIGNIFICANCE: The present study is the first to comprehensively analyze alterations in the protein profiles induced by Se deficiency in the blood of the Przewalski's gazelle, showing that Se-deficiency contributed to a significant reduction in blood Se levels and marked changes in blood parameters, which will likely contribute to a better understanding of the molecular mechanisms of the changes in protein abundance in the Przewalski's gazelle in response to Se-deficiency stress.

Opportunistic random searcher versus intentional search image user

We consider two types of optimal foragers: a random searcher and a search image user. A search image user can find its desired prey with higher and undesired prey with lower probability than a random searcher. Our model considers the density-dependent travelling time and the time duration of reproduction (oviposition). In the framework of optimal foraging theory for one predator-two prey systems, we find that there are ranges of prey densities in which the search image user has a higher net energy intake, and there are other ranges of prey densities in which the random searcher has higher net energy intake. The damsel bug Nabis pseudoferus Remane (Hemiptera: Nabidae) is a generalist predator rather than an omnivore. This species has a wide range of arthropod prey (predominantly insects and mites). Several aspects of the biology of this species have been studied, especially its cannibalistic behaviour, which is a quite important feature because N. pseudoferus is often used as a biological control agent against lepidopteran pests in greenhouse crops. Experimentally, we found that Nabis is a search image user in the above sense.

Linear functional response by two pupal Drosophila parasitoids foraging within single or multiple patch environments

Functional response describes the number of prey or hosts attacked by a predator or parasitoid as a function of prey or host density. Using three different experimental designs, we found a linear functional response by two insect parasitoids (the pteromalid Pachycrepoideus vindemiae and the diapriid Trichopria drosophilae) to their hosts (the drosophilids Drosophila suzukii and D. melanogaster). A linear function response is considered unusual for insect parasitoids. The first design was a 'fixed time within patch experiment' where individual parasitoids were exposed to a range of host densities for 24 h; the second two designs were a 'variable time functional response' and a 'selective functional response' experiments where individual parasitoids were presented with a range of host patches and allowed to freely select and explore only one patch (variable time) or forage for 24 h (selective). In all experimental designs, the number of hosts parasitized increased linearly until reaching an upper limit. Under the laboratory conditions used, the functional response of P. vindemiae was limited by its egg supply and time (host handling time) whereas T. drosophilae was limited by time only. The linear functional response by both parasitoids likely resulted from a constant attack rate and an incremental foraging strategy where the parasitoids left a poor (low density) host patch or remained in a higher quality host patch when there was successful oviposition and adequate host density.

Live substrate positively affects root growth and stolon direction in the woodland strawberry, Fragaria vesca

Studies of clonal plant foraging generally focus on growth responses to patch quality once rooted. Here we explore the possibility of true plant foraging; the ability to detect and respond to patch resource status prior to rooting. Two greenhouse experiments were conducted to investigate the morphological changes that occur when individual daughter ramets of Fragaria vesca (woodland strawberry) were exposed to air above live (non-sterilized) or dead (sterilized) substrates. Contact between daughter ramets and substrate was prohibited. Daughter ramet root biomass was significantly larger over live versus dead substrate. Root:shoot ratio also increased over live substrate, a morphological response we interpret as indicative of active nutrient foraging. Daughter ramet root biomass was positively correlated with mother ramet size over live but not dead substrate. Given the choice between a live versus a dead substrate, primary stolons extended preferentially toward live substrates. We conclude that exposure to live substrate drives positive nutrient foraging responses in F. vesca. We propose that volatiles emitted from the substrates might be effecting the morphological changes that occur during true nutrient foraging.

Functional response and population dynamics for fighting predator, based on activity distribution

The classical Holling type II functional response, describing the per capita predation as a function of prey density, was modified by Beddington and de Angelis to include interference of predators that increases with predator density and decreases the number of killed prey. In the present paper we further generalize the Beddington-de Angelis functional response, considering that all predator activities (searching and handling prey, fight and recovery) have time duration, the probabilities of predator activities depend on the encounter probabilities, and hence on the prey and predator abundance, too. Under these conditions, the aim of the study is to introduce a functional response for fighting the predator and to analyse the corresponding dynamics, when predator-predator-prey encounters also occur. From this general approach, the Holling type functional responses can also be obtained as particular cases. In terms of the activity distribution, we give biologically interpretable sufficient conditions for stable coexistence. We consider two-individual (predator-prey) and three-individual (predator-predator-prey) encounters. In the three-individual encounter model there is a relatively higher fighting rate and a lower killing rate. Using numerical simulation, we surprisingly found that when the intrinsic prey growth rate and the conversion rate are small enough, the equilibrium predator abundance is higher in the three-individual encounter case. The above means that, when the equilibrium abundance of the predator is small, coexistence appears first in the three-individual encounter model.

The replicator equation and other game dynamics

The replicator equation is the first and most important game dynamics studied in connection with evolutionary game theory. It was originally developed for symmetric games with finitely many strategies. Properties of these dynamics are briefly summarized for this case, including the convergence to and stability of the Nash equilibria and evolutionarily stable strategies. The theory is then extended to other game dynamics for symmetric games (e.g., the best response dynamics and adaptive dynamics) and illustrated by examples taken from the literature. It is also extended to multiplayer, population, and asymmetric games.