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1. Predators impact prey populations not only by consuming individuals, but also by altering their behaviours. These nonlethal effects can influence food web properties as much as lethal effects. The mechanisms of nonlethal effects include chronic and temporary anti-predator behaviours, the nature of which depends on the spatial dynamics of predators and the range over which prey perceive risk. 2. The relation between chronic and ephemeral responses to risk determines predator–prey interactions, with consequences that can ripple across the food web. Nonetheless, few studies have quantified the spatio-temporal scales over which prey respond to predation threat, and how this response varies with habitat features. 3. We evaluated the reaction of radio-collared caribou and moose to the passage of radio-collared wolves, by considering changes in movement characteristics during winter and summer. We used an optimization algorithm to identify the rate at which the impact of prior passage of wolves decreases over time and with the predator's distance. 4. The spatial and temporal scales of anti-predator responses varied with prey species and season. Caribou and moose displayed four types of behaviour following the passage of wolves: lack of response, increased selection of safe land cover types, decreased selection of risky cover types and increased selection of food-rich forest stands. For example, moose increased their avoidance of open conifer stands with lichen in summer, which are selected by wolves in this season. Also in winter, caribou increased their selection of conifer stands with lichen for nearly 10 days following a wolf's passage. This stronger selection for food-rich patches could indicate that the recent passage of wolves informs caribou on the current predator distribution and reveals the rate at which this information become less reliable over time. 5. Caribou and moose used anti-predator responses that combine both long- and short-term behavioural adjustments. The spatial game between wolves and their prey involves complex and nonlinear mechanisms that vary between species and seasons. A comprehensive assessment of risk effects on ecosystem dynamics thus requires the characterization of chronic and temporary anti-predator behaviours.

Habitat connectivity influences the distribution dynamics of animals. Connectivity can therefore shape trophic interactions, but little empirical evidence is available, especially for large mammals. In forest ecosystems, logging alters functional connectivity among habitat patches, and such activities can affect the spatial game between large herbivores and their predators. We used graph theory to evaluate how harvesting-induced changes in habitat connectivity influence patch choice and residency time of GPS-collared caribou ( Rangifer tarandus caribou ) and moose ( Alces alces ) in winter in the boreal forest. We then investigated the predator-prey game by assessing how GPS-collared wolves ( Canis lupus ) adjusted their movements to changes in landscape properties and in the networks of their prey species. We built prey habitat networks using minimum planar graphs organized around species-specific, highly selected habitat patches (i.e., network nodes). We found that spatial dynamics of large herbivores were influenced not only by the intrinsic quality of habitat patches, but also by the connectivity of those network nodes. Caribou and moose selected nodes that were connected by a high number of links, and moose also spent relatively more time in those nodes. By limiting node accessibility, human disturbances influenced travel decisions. Caribou and moose avoided nodes that were surrounded by a high proportion of cuts and roads, but once within these nodes, moose stayed longer than in other nodes. Caribou selectively moved among nodes with low distance costs, and their residency time increased with distance costs required to reach the nodes. Wolves selected their prey's nodes, where vegetation consumed by caribou and moose was highly abundant. Furthermore, wolves discriminated among those nodes by selecting the most connected ones. In fact, selection by wolves was stronger for their prey's nodes than for the prey's utilization distribution per se, a difference that increased with the level of human disturbance. Considering the difficulty of keeping track of highly mobile prey, predators may benefit by targeting not only their prey's resource patches, but also the most highly connected patches. Matrix quality and connectivity are therefore key elements shaping the predator-prey spatial game in human-altered landscapes because of their impact on the spatial dynamics of the interacting species.

Evolutionary dynamics shape the living world around us. At the centre of every evolutionary process is a population of reproducing individuals. The structure of that population affects evolutionary dynamics. The individuals can be molecules, cells, viruses, multicellular organisms or humans. Whenever the fitness of individuals depends on the relative abundance of phenotypes in the population, we are in the realm of evolutionary game theory. Evolutionary game theory is a general approach that can describe the competition of species in an ecosystem, the interaction between hosts and parasites, between viruses and cells, and also the spread of ideas and behaviours in the human population. In this perspective, we review the recent advances in evolutionary game dynamics with a particular emphasis on stochastic approaches in finite sized and structured populations. We give simple, fundamental laws that determine how natural selection chooses between competing strategies. We study the well-mixed population, evolutionary graph theory, games in phenotype space and evolutionary set theory. We apply these results to the evolution of cooperation. The mechanism that leads to the evolution of cooperation in these settings could be called 'spatial selection': cooperators prevail against defectors by clustering in physical or other spaces.

Though contradicting with natural selection, cooperative behaviors widely exist in practice and seem to be an effective measure to maintain the functioning of complex systems. As revealed by previous studies, punishment is capable of promoting cooperation and therefore various types of punishment are proposed. Previously, scholars mainly focus on investigating either peer punishment or pool punishment, whereas in social and biological systems, an individual might function as different roles when facing different players. Thus, we mainly investigate these two types of punishment together and the effects of punishment-type transfer on the evolutionary dynamics are further provided with sufficient analyses in this manuscript. Role of different type of punishment on cooperation seems to be related to the number of punishers (being denoted as T ) among corresponding neighbors. Simulations are conducted in order to investigate the effect of threshold reflecting the punishment-type switching on evolutionary dynamics, while peer punishment is proved to be more effective than pool punishment in promoting cooperation. We hope our findings here can shed some lights on the investigation of punishment.

Evolutionary game dynamics on networks typically consider the competition among simple strategies such as cooperation and defection in the Prisoner’s Dilemma and summarize the effect of population structure as network reciprocity. However, it remains largely unknown regarding the evolutionary dynamics involving multiple powerful strategies typically considered in repeated games, such as the zero-determinant (ZD) strategies that are able to enforce a linear payoff relationship between them and their co-players. Here, we consider the evolutionary dynamics of always cooperate (AllC), extortionate ZD (extortioners), and unbending players in lattice populations based on the commonly used death-birth updating. Out of the class of unbending strategies that can foster reciprocal cooperation and fairness among extortionate players, we consider a particular candidate, pre-optimized through the machine-learning method of particle swarm optimization (PSO), called PSO Gambler. We derive analytical results under weak selection and rare mutations, including pairwise fixation probabilities and long-term frequencies of strategies. In the absence of the third unbending type, extortioners can achieve a half-half split in equilibrium with unconditional cooperators for sufficiently large extortion factors. However, the presence of unbending players fundamentally changes the dynamics and tilts the system to favor unbending cooperation. Most surprisingly, extortioners cannot dominate at all regardless of how large their extortion factor is, and the long-term frequency of unbending players is maintained almost as a constant. Our analytical method is applicable to studying the evolutionary dynamics of multiple strategies in structured populations. Our work provides insights into the interplay between network reciprocity and direct reciprocity, revealing the role of unbending strategies in enforcing fairness and suppressing extortion.

According to Thomas Hobbes' Leviathan [1651; 2008 (Touchstone, New York), English Ed], \"the life of man [is] solitary, poor, nasty, brutish, and short,\" and it would need powerful social institutions to establish social order. In reality, however, social cooperation can also arise spontaneously, based on local interactions rather than centralized control. The self-organization of cooperative behavior is particularly puzzling for social dilemmas related to sharing natural resources or creating common goods. Such situations are often described by the prisoner's dilemma. Here, we report the sudden outbreak of predominant cooperation in a noisy world dominated by selfishness and defection, when individuals imitate superior strategies and show success-driven migration. In our model, individuals are unrelated, and do not inherit behavioral traits. They defect or cooperate selfishly when the opportunity arises, and they do not know how often they will interact or have interacted with someone else. Moreover, our individuals have no reputation mechanism to form friendship networks, nor do they have the option of voluntary interaction or costly punishment. Therefore, the outbreak of prevailing cooperation, when directed motion is integrated in a game-theoretical model, is remarkable, particularly when random strategy mutations and random relocations challenge the formation and survival of cooperative clusters. Our results suggest that mobility is significant for the evolution of social order, and essential for its stabilization and maintenance.

1. Understanding why heterogeneity exists in animal-habitat spatial relationships is critical for identifying the drivers of animal distributions. Functional responses in habitat selection — whereby animals adjust their habitat selection depending on habitat availability — are useful for describing animal-habitat spatial heterogeneity. However, they could be yielded by different movement tactics, involving contrasting interspecific interactions. 2. Identifying functional responses in animal movement, rather than in emergent spatial patterns like habitat selection, could disentangle the effects of different movement behaviours on spatial heterogeneity in animal-habitat relationships. This would clarify how functional responses in habitat selection emerge and provide a general tool for understanding the mechanistic drivers of animal distributions. 3. We tested this approach using data from GPS-collared woodland caribou (Rangifer tarandus), a prey species under top-down control. We tested how caribou selected and moved with respect to a key resource (lichen-conifer stands) as a function of the availability of surrounding refuge land-cover (closed-conifer stands), using step selection functions. 4. Caribou selected resource patches more strongly in areas richer in refuge land-cover – a functional response in habitat selection. However, adjustments in multiple movement behaviours could have generated this pattern: stronger directed movement towards resource patches and/or longer residency within resource patches, in areas richer in refuges. Different contributions of these behaviours would produce contrasting forager spatial dynamics. 5. We identified functional responses in both movement behaviours: caribou were more likely to move towards resource patches in areas richer in refuge land-cover, and to remain in these patches during movement steps. This tactic enables caribou to forage for longer in safer areas where they can rapidly seek refuge in dense cover when predators are detected. 6. Our study shows that functional responses in movement can expose the context-dependent movement decisions that generate heterogeneity in animal-habitat spatial relationships. We used these functional responses to characterise anti-predator movement tactics employed by a large herbivore, but they could be applied in many different scenarios. The movement rules from functional responses in movement are well-suited to integration in spatial explicit individual-based models for forecasting animal distributions in landscapes undergoing environmental change.

Traditional evolutionary game theory explores frequency-dependent selection in well-mixed populations without spatial or stochastic effects. But recently there has been much interest in studying the evolutionary game dynamics in spatial settings, on lattices and other graphs. Here, we present an analytic approach for the stochastic evolutionary game dynamics on the simplest possible graph, the cycle. For three different update rules, called 'birth-death' (BD), 'death-birth' (DB) and 'imitation' (IM), we derive exact conditions for natural selection to favour one strategy over another. As specific examples, we consider a coordination game and Prisoner's Dilemma. In the latter case, selection can favour cooperators over defectors for DB and IM updating. We also study the case where the replacement graph of evolutionary updating remains a cycle, but the interaction graph for playing the game is a complete graph. In this setting, all three update rules lead to identical conditions in the limit of weak selection, where we find the '1/3-law' of well-mixed populations.

The puzzle of the emergence of cooperation between unrelated individuals is shared across diverse fields of behavioural sciences and economics. In this article we combine the public goods game originating in economics with evolutionary approaches traditionally used in biology. Instead of pairwise encounters, we consider the more complex case of groups of three interacting individuals. We show that territoriality is capable of promoting cooperative behaviour, as in the case of the Prisoner's Dilemma. Moreover, by adding punishment opportunities, the readiness to cooperate is greatly enhanced and asocial strategies can be largely suppressed. Finally, as soon as players carry a reputation for being willing or unwilling to punish, highly cooperative and fair outcomes are achieved. This group-beneficial result is obtained, intriguingly, by making individuals more likely to exploit their co-players if they can get away with it. Thus, less-cooperative individuals make more-cooperative societies.

Recent experimental research has revealed that the cooperation in dynamic social networks, has significant scope for enhancement because individuals in a social system break the links with defective neighbours. To investigate how the length of defection tolerance affects the cooperation of prisoner's dilemma game in dynamic ring networks, we study evolution of breaking and rewiring operations for social interaction as a response to the defection strategy. Defection tolerance is measured in terms of the time length that an individual tolerates a defector who continuously adopts the defective strategy. The results show that the dynamic nature of human social networks plays an essential role in promoting cooperation. Interestingly, there exists a critical value of the temptation to defect, below which the system is entirely dominated by cooperators, and a lower value of defection tolerance induces a larger threshold of temptation.