A game theoretical model of deforestation in human-environment relationships

We studied a two-person game regarding deforestation in human-environment relationships. Each landowner manages a single land parcel where the state of land-use is forested, agricultural, or abandoned. The landowner has two strategies available: forest conservation and deforestation. The choice of deforestation provides a high return to the landowner, but it degrades the forest ecosystem services produced on a neighboring land parcel managed by a different landowner. Given spatial interactions between the two landowners, each landowner decides which strategy to choose by comparing the expected discounted utility of each strategy. Expected discounted utility is determined by taking into account the current and future utilities to be received, according to the state transition on the two land parcels. The state transition is described by a Markov chain that incorporates a landowner's choice about whether to deforest and the dynamics of agricultural abandonment and forest regeneration. By considering a stationary distribution of the Markov chain for land-use transitions, we derive explicit conditions for Nash equilibrium. We found that a slow regeneration of forests favors mutual cooperation (forest conservation). As the forest regenerates faster, mutual cooperation transforms to double Nash equilibria (mutual cooperation and mutual defection), and finally mutual defection (deforestation) leads to a unique Nash equilibrium. Two different types of social dilemma emerge in our deforestation game. The stag-hunt dilemma is most likely to occur under an unsustainable resource supply, where forest regenerates extremely slowly but agricultural abandonment happens quite rapidly. In contrast, the prisoner's dilemma is likely under a persistent or circulating supply of resources, where forest regenerates rapidly and agricultural abandonment occurs slowly or rapidly. These results show how humans and the environment mutually shape the dilemma structure in forest management, implying that solutions to dilemmas depend on environmental properties.     

Stochastic sampling of interaction partners versus deterministic payoff assignment

Evolutionary game dynamics describes how successful strategies spread in a population. In well-mixed populations, the usual assumption, e.g. underlying the replicator dynamics, is that individuals obtain a payoff from interactions with a representative sample of the population. This determines their fitness. Here, we analyze a situation in which payoffs are obtained through a single interaction, so that individuals of the same type can have different payoffs. We show analytically that for weak selection, this scenario is identical to the usual approach in which an individual interacts with the whole population. For strong selection, however, differences arise that are reflected in the fixation probabilities and lead to deviating evolutionary dynamics.     

Cooperation in defence against a predator

The origin and the evolutionary stability of cooperation between unrelated individuals is one of the key problems of evolutionary biology. In this paper, a cooperative defence game against a predator is introduced which is based on Hamilton's selfish herd theory and Eshel's survival game models. Cooperation is altruistic in the sense that the individual, which is not the target of the predator, helps the members of the group attacked by the predator and during defensive action the helper individual may also die in any attack. In order to decrease the long term predation risk, this individual has to carry out a high risk action. Here I show that this kind of cooperative behaviour can evolve in small groups. The reason for the emergence of cooperation is that if the predator does not kill a mate of a cooperative individual, then the survival probability of the cooperative individual will increase in two cases. If the mate is non-cooperative, then—according to the dilution effect, the predator confusion effect and the higher predator vigilance—the survival probability of the cooperative individual increases. The second case is when the mate is cooperative, because a cooperative individual has a further gain, the active help in defence during further predator attacks. Thus, if an individual can increase the survival rate of its mates (no matter whether the mate is cooperative or not), then its own predation risk will decrease.     

Mutation-selection equilibrium in games with multiple strategies

In evolutionary games the fitness of individuals is not constant but depends on the relative abundance of the various strategies in the population. Here we study general games among n strategies in populations of large but finite size. We explore stochastic evolutionary dynamics under weak selection, but for any mutation rate. We analyze the frequency dependent Moran process in well-mixed populations, but almost identical results are found for the Wright-Fisher and Pairwise Comparison processes. Surprisingly simple conditions specify whether a strategy is more abundant on average than 1/n, or than another strategy, in the mutation-selection equilibrium. We find one condition that holds for low mutation rate and another condition that holds for high mutation rate. A linear combination of these two conditions holds for any mutation rate. Our results allow a complete characterization of n×n games in the limit of weak selection.     

Active linking in evolutionary games

In the traditional approach to evolutionary game theory, the individuals of a population meet each other at random, and they have no control over the frequency or duration of interactions. Here we remove these simplifying assumptions. We introduce a new model, where individuals differ in the rate at which they seek new interactions. Once a link between two individuals has formed, the productivity of this link is evaluated. Links can be broken off at different rates. In a limiting case, the linking dynamics introduces a simple transformation of the payoff matrix. We outline conditions for evolutionary stability. As a specific example, we study the interaction between cooperators and defectors. We find a simple relationship that characterizes those linking dynamics which allow natural selection to favour cooperation over defection.     

Spatial effects in social dilemmas

Social dilemmas and the evolutionary conundrum of cooperation are traditionally studied through various kinds of game theoretical models such as the prisoner's dilemma, public goods games, snowdrift games or by-product mutualism. All of them exemplify situations which are characterized by different degrees of conflicting interests between the individuals and the community. In groups of interacting individuals, cooperators produce a common good benefitting the entire group at some cost to themselves, whereas defectors attempt to exploit the resource by avoiding the costly contributions. Based on synergistic or discounted accumulation of cooperative benefits a unifying theoretical framework was recently introduced that encompasses all games that have traditionally been studied separately (Hauert, Michor, Nowak, Doebeli, 2005. Synergy and discounting of cooperation in social dilemmas. J. Theor. Biol., in press.). Within this framework we investigate the effects of spatial structure with limited local interactions on the evolutionary fate of cooperators and defectors. The quantitative effects of space turn out to be quite sensitive to the underlying microscopic update mechanisms but, more general, we demonstrate that in prisoner's dilemma type interactions spatial structure benefits cooperation-although the parameter range is quite limited-whereas in snowdrift type interactions spatial structure may be beneficial too, but often turns out to be detrimental to cooperation.     

No unique effect of intergroup competition on cooperation: non-competitive thresholds are as effective as competitions between groups for increasing human cooperative behavior

Explaining cooperation remains a central topic for evolutionary theorists. Many have argued that group selection provides such an explanation: theoretical models show that intergroup competition could have given rise to cooperation that is costly for the individual. Whether group selection actually did play an important role in the evolution of human cooperation, however, is much debated. Recent experiments have shown that intergroup competitions do increase human cooperation, which has been taken as evidence for group selection as a mechanism for the evolution of cooperation. Here we challenge this standard interpretation. Competitions change the payoff structure by creating a threshold effect whereby the group that contributes more earns an additional prize, which creates some incentive for individuals to cooperate. We present four studies that disentangle competition and thresholds, and strongly suggest that it is thresholds – rather than competitions per se – that increase cooperation. Thus, prior intergroup competition experiments provide no evidence of a unique or special role for intergroup competition in promoting human cooperation, and shed no light on whether group selection shaped human evolution.     

Signalling of information that is neither cryptic nor private

It is commonly assumed that in order for animal signals to be advantageous, the information being signalled could not have been obtained otherwise, and is therefore ‘cryptic’ or ‘private’. Here, we suggest a scenario in which individuals can gain an advantage by signalling ‘public’ information that is neither cryptic nor private. In that scenario, signalling increases the efficiency with which that ‘public’ information is transmitted. We formalize our idea with a game in which offspring can signal their condition to their parents. Specifically, we consider a resource‐strapped parent who can only invest in one of its two offspring, and we allow offspring the chance to influence parental investment through a signal. A parent in the game seeks to invest in the higher‐quality offspring, which it could identify either through a publicly available cue, such as body size, or by relying on a signal provided by the offspring. We find that if the signal can convey information about offspring quality more efficiently than cues, then signalling of condition between offspring and parents can be favoured by selection, even though parents could potentially have acquired the same information from the cue. Our results suggest that the biological function of signals may be broader than currently considered, and provide a scenario where low cost signalling can be favoured. More generally, efficiency benefits could explain signalling across a range of biological and economic scenarios.     

The evolution of strategic male mating effort in an information transfer framework

Sperm competition theory predicts that males should use cues indicating the risk and intensity of sperm competition to tailor their sperm investment accordingly. Rival males are an important source of social information regarding sperm competition risk. However, revealing such information may not be in the rival males' interest. Here, we use a theoretical approach based on informed and uninformed games to investigate when information transfer about sperm competition risk to competitors is beneficial for a male, and when it is not. The results show that signalling to potential future mates that a female has already mated is beneficial when the signalling male has a sperm competition disadvantage, whereas it is unfavourable when the signaller has an advantage. The reason for this counterintuitive result is that the rival males' optimal response is to reduce sperm investment when the signaller has a disadvantage and, conversely, to increase investment when the signaller has an advantage. Furthermore, we analysed scenarios where males use alternative reproductive tactics. In this situation, signalling the awareness of sperm competition risk rarely pays; instead, it is beneficial to maintain an information advantage. Thus, it may be beneficial for bourgeois males to accept cuckoldry instead of revealing their sperm competition awareness to reproductive parasites. These results provide new insight into the evolution of communication between rivals in the context of sperm competition.