Succession of hide-seek and pursuit-evasion at heterogeneous locations

Counterintuitive prey strategies against predators with finite budgets: protection heterogeneity among sites matters more than their number

Combining the search and pursuit aspects of predator-prey interactions into a single game, where the payoff to the Searcher (predator) is the probability of finding and capturing the Hider (prey) within a fixed number of searches was proposed by Gal and Casas (J. R. Soc. Interface 11, 20140062 (doi:10.1098/rsif.2014.0062)). Subsequent models allowed the predator to continue its search (in another 'round') if the prey was found but escaped the chase. However, it is unrealistic to allow this pattern of prey relocation to go on forever, so here we introduce a limit of the total number of searches, in all 'rounds', that the predator can carry out. We show how habitat structural complexity affects the mean time until capture: the quality of the location with the lowest capture probability matters more than the number of hiding locations. Moreover, we observed that the parameter space defined by the capture probabilities in each location and the budget of the predator can be divided into distinct domains, defining whether the prey ought to play with pure or mixed hiding strategies.

Pursuit and evasion strategies in the predator-prey interactions of fishes

Predator-prey interactions are critical to the biology of a diversity of animals. Although prey capture is determined by the direction, velocity, and timing of motion by both animals, it is generally unclear what strategies are employed by predators and prey to guide locomotion. Here we review our research on fishes that tests the pursuit strategy of predators and the evasion strategy of prey through kinematic measurements and agent-based models. This work demonstrates that fish predators track prey with variations on a deviated-pursuit strategy that is guided by visual cues. Fish prey employ a mixed strategy that varies with factors such as the direction of a predator's approach. Our models consider the stochastic nature of interactions by incorporating measured probability distributions to accurately predict measurements of survivorship. A sensitivity analysis of these models shows the importance of the response distance of prey to their survival. Collectively, this work demonstrates how strategy affects the outcome of predator-prey interactions and articulates the roles of sensing, control, and propulsion. The research program that we have developed has the potential to offer a framework for the study of strategy in the predator-prey interactions of a variety of animals.

A stochastic game model of searching predators and hiding prey

When the spatial density of both prey and predators is very low, the problem they face may be modelled as a two-person game (called a 'search game') between one member of each type. Following recent models of search and pursuit, we assume the prey has a fixed number of heterogeneous 'hiding' places (for example, ice holes for a seal to breathe) and that the predator (maybe polar bear) has the time or energy to search a fixed number of these. If he searches the actual hiding location and also successfully pursues the prey there, he wins the game. If he fails to find the prey, he loses. In this paper, we modify the outcome in the case that he finds but does not catch the prey. The prey is now vulnerable to capture while relocating with risk depending on the intervening terrain. This generalizes the original games to a stochastic game framework, a first for search and pursuit games. We outline a general solution and also compute particular solutions. This modified model now has implications for the question of when to stay or leave the lair and by what routes. In particular, we find the counterintuitive result that in some cases adding risk of predation during prey relocation may result in more relocation. We also model the process by which the players can learn about the properties of the different hiding locations and find that having to learn the capture probabilities is favourable to the prey.

Prey should hide more randomly when a predator attacks more persistently

When being searched for and then (if found) pursued by a predator, a prey animal has a choice between choosing very randomly among hiding locations so as to be hard to find or alternatively choosing a location from which it is more likely to successfully flee if found. That is, the prey can choose to be hard to find or hard to catch, if found. In our model, capture of prey requires both finding it and successfully pursuing it. We model this dilemma as a zero-sum repeated game between predator and prey, with the eventual capture probability as the pay-off to the predator. We find that the more random hiding strategy is better when the chances of repeated pursuit, which are known to be related to area topography, are high. Our results extend earlier results of Gal and Casas, where there was at most only a single pursuit. In that model, hiding randomly was preferred by the prey when the predator has only a few looks. Thus, our new multistage model shows that the effect of more potential looks is opposite. Our results can be viewed as a generalization of search games to the repeated game context and are in accordance with observed escape behaviour of different animals.

Natural search algorithms as a bridge between organisms, evolution, and ecology

The ability to navigate is a hallmark of living systems, from single cells to higher animals. Searching for targets, such as food or mates in particular, is one of the fundamental navigational tasks many organisms must execute to survive and reproduce. Here, we argue that a recent surge of studies of the proximate mechanisms that underlie search behavior offers a new opportunity to integrate the biophysics and neuroscience of sensory systems with ecological and evolutionary processes, closing a feedback loop that promises exciting new avenues of scientific exploration at the frontier of systems biology.

When Optimal Strategy Matters to Prey Fish

Predator-prey interactions are commonly studied with an interest in determining the optimal strategy for prey. However, the implications of deviating from optimal strategy are often unclear. The present study considered these consequences by studying how the direction of an escape response affects the strategy of prey fish. We simulated these interactions with numerical and analytical mathematics and compared our predictions with measurements in zebrafish larvae (Danio rerio), which are preyed upon by adults of the same species. Consistent with existing theory, we treated the minimum distance between predator and prey as the strategic payoff that prey aim to maximize. We found that these interactions may be characterized by three strategic domains that are defined by the speed of predator relative to the prey. The "fast predator" domain occurs when the predator is more than an order of magnitude faster than the prey. The escape direction of the prey had only a small effect on the minimum distance under these conditions. For the "slow predator" domain, when the prey is faster than the predator, we found that differences in direction had no effect on the minimum distance for a broad range of escape angles. This was the regime in which zebrafish were found to operate. In contrast, the optimal escape angle offers a large benefit to the minimum distance in the intermediate strategic domain. Therefore, optimal strategy is most meaningful to prey fish when predators are faster than prey by less than a factor of 10. This demonstrates that the strategy of a prey animal does not matter under certain conditions that are created by the behavior of the predator.