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

Optimal search and ambush for a hider who can escape the search region

Search games for a mobile or immobile hider traditionally have the hider permanently confined to a compact ‘search region’ making eventual capture inevitable. Hence the payoff can be taken as time until capture. However in many real life search problems it is possible for the hider to escape an area in which he was known to be located (e.g. Bin Laden from Tora Bora) or for a prey animal to escape a predator’s hunting territory. We model and solve such continuous time problems with escape where we take the probability of capture to be the searcher’s payoff. We assume the searcher, while cruise searching, can cover the search region at unit rate of area, for a given time horizon T known to the hider. The hider can stay still or choose any time to flee the region. To counter this, the searcher can also adopt an ambush mode which will capture a fleeing hider. The searcher wins the game if he either finds the hider while cruise searching or ambushes him while he is attempting to flee; the hider wins if he flees successfully (while the searcher is cruising) or has not been found by time T. The optimal searcher strategy involves decreasing the ambush probability over time, to a limit of zero. This surprising behaviour is opposite to that found recently by Alpern et al. (2011, 2013) in a predator-prey game with similar dynamics but without the possibility of the hider escaping. Our work also complements that of Zoroa et al. (2015) on searching for multiple prey and Gal and Casas (2014) for a combined model of search and pursuit

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

Extended Adolescence: The Ecology and Endocrinology of Facultative Paedomorphosis

Phenotypic plasticity is an adaptation to unpredictable environments whereby an organism of a single genotype may express more than one phenotype under differing environmental conditions. Phenotypic plasticity can manifest as polyphenisms, which is an extreme form of phenotypic plasticity that produces two or more discrete, alternative phenotypes. The expression of alternative phenotypes is controlled by biotic and abiotic environmental factors, which variably affect the strength and direction of phenotypic outcomes. Using a model polyphenic salamander, I sought to understand the ecological and hormonal processes that regulate alternative phenotype expression. The mole salamander (Ambystoma talpoideum) and eastern newt (Notophthalmus viridescens) are facultatively paedomorphic, which is a polyphenism with two alternative adult phenotypes: paedomorphs and metamorphs. Paedomorphs retain juvenile characteristics at sexual maturity (i.e., gills and an aquatic morphology), while metamorphs transition to terrestrial environments. The expressed phenotype depends on the environment context in which the larvae develop, with paedomorphosis often occurring under favorable aquatic conditions. I conducted a series of experiments to investigate the roles of population density, predator presence, hydroperiod, and stress hormones in regulating the expression of paedomorphosis. Results indicated the regulation of paedomorphosis through multiple ecological factors may be reducible to density-mediated effects, with a few notable exceptions. I also show that elevated stress hormones play a central role in regulating metamorphosis suggesting that all ecological factors affecting facultative paedomorphosis may funnel through a simple stress physiology framework. In conclusion, environmental factors affecting this polyphenism may share a comthread of inducing a stress response that initiates metamorphosis, thereby regulating phenotype in the population

Perspectives on the relationship between local interactions and global outcomes in spatially explicit models of systems of interacting individuals

Understanding the behaviour of systems of interacting individuals is a key aim of much research in the social sciences and beyond, and a wide variety of modelling paradigms have been employed in pursuit of this goal. Often, systems of interest are intrinsically spatial, involving interactions that occur on a local scale or according to some specific spatial structure. However, while it is recognised that spatial factors can have a significant impact on the global behaviours exhibited by such systems, in practice, models often neglect spatial structure or consider it only in a limited way, in order to simplify interpretation and analysis. In the particular case of individual-based models used in the social sciences, a lack of consistent mathematical foundations inevitably casts doubt on the validity of research conclusions. Similarly, in game theory, the lack of a unifying framework to encompass the full variety of spatial games presented in the literature restricts the development of general results and can prevent researchers from identifying important similarities between models. In this thesis, we address these issues by examining the relationship between local interactions and global outcomes in spatially explicit models of interacting individuals from two different conceptual perspectives. First, we define and analyse a family of spatially explicit, individual-based models, identifying and explaining fundamental connections between their local and global behaviours. Our approach represents a proof of concept, suggesting that similar methods could be effective in identifying such connections in a wider range of models. Secondly, we define a general model for spatial games of search and concealment, which unites many existing games into a single framework, and we present theoretical results on its optimal strategies. Our model represents an opportunity for the development of a more broadly applicable theory of spatial games, which could facilitate progress and highlight connections within the field

Functional Morphology of Stereospondyl Amphibian Skulls

Stereospondyls were the most diverse clade of early tetrapods, spanning 190 million years, with over 250 species belonging to eight taxonomic groups. They had a range of morphotypes and have been found on every continent. Stereospondyl phylogeny is widely contested and repeatedly examined but despite these studies, we are still left with the question, why were they so successful and why did they die out? A group-wide analysis of functional morphology, informing us about their palaeobiology, was lacking for this group and was carried out in order to address the questions of their success and demise. Based on an original photograph collection, size independent skull morphometrics were used, in conjunction with analyses of the fossil record and comparative anatomy, to provide a synthesis of the functional morphology of stereospondyl amphibians. Stereospondyls originated in the Carboniferous and most taxonomic groups were extinct at the end of the Triassic. The early Triassic had exceptionally high numbers of shortlived genera, in habitats that were mostly arid but apparently experienced occasional monsoon rains. Genera turnover slowed and diversity was stable in the Middle Triassic, then declined with a series of extinctions of the Late Triassic. Stereospondyls showed the pattern of ‘disaster’ taxa: rapidly diversifying following a mass extinction, spreading to a global distribution, although this high diversity was relatively short-lived. Geometric morphometrics on characteristics of the skull and palate was carried out to assess general skull morphology and identified the orbital position and skull outline to be the largest sources of skull variation. Comparing anatomy of stereospondyls with extant species revealed that the differences in head shape and orbit positions between stereospondyls allows inference of a range of feeding behaviours, ranging from rapid head swipes, to crushing invertebrates with wide palatal bones, and crocodilian-type ambushing. The range of feeding modalities meant stereospondyl species were able to coexist with minimal competition. The success was, however, short lived, as highly specialised shapes in the middle and Late Triassic probably meant that stereospondyls were not able to adapt to a more generalised lifestyle when the end Triassic extinction eliminated ecosystems