A stochastic evolutionary dynamics of two strategies given by 2x 2 matrix games is studied in finite populations. We focus on stochastic properties of fixation: how a strategy represented by a single individual wins over the entire population. The process is discussed in the framework of a random walk with site dependent hopping rates. The time of fixation is found to be identical for both strategies in any particular game. The asymptotic behavior of the fixation time and fixation probabilities in the large population size limit is also discussed. We show that fixation is fast when there is at least one pure evolutionary stable strategy (ESS) in the infinite population size limit, while fixation is slow when the ESS is the coexistence of the two strategies.
The production of public goods by the contribution of individual volunteers is a social dilemma because an individual that does not volunteer can benefit from the public good produced by the contributions of others. Therefore it is generally believed that public goods can be produced only in the presence of repeated interactions (which allow reciprocation, reputation effects and punishment) or relatedness (kin selection). Cooperation, however, often occurs in the absence of iterations and relatedness. We show that when the production of a public good is a Volunteer's Dilemma, in which a fixed number of cooperators is necessary to produce the public good, cooperators and defectors persist in a mixed equilibrium, without iterations and without relatedness. The production of a public good that depends on the costly contribution of a number of individuals is a social dilemma because everybody relies on someone else. Imagine a group of individuals witnessing a crime: each can volunteer to pay a small contribution to call the police; if nobody volunteers everybody pays a higher cost because the criminal remains at large. Clearly it is better to volunteer if nobody else does it, but everybody prefers that it is someone else who pays the contribution. The dilemma is that, if the decision is simultaneous, it can happen that one volunteers in vain, or that nobody volunteers because everybody thinks that someone else is doing it. A similar dilemma occurs in animal groups, for example when individuals must decide whether to raise the alarm against a predator.Other situations require more than one volunteer to produce the public good. Public goods games are common in biology at all levels of organization, from the capture and sharing of large preys by groups of predators (Packer et al. 1990;Stander 1991;Creel 1997;Bednarz 1988) and cooperative nesting and breeding in birds (Rabenold 1984) The problem with the production of public goods (Olson 1965) is that, if contributing is costly, volunteers have a lower fitness than individuals that do not contribute; therefore an individual would rather avoid the cost of volunteering and exploit the public goods produced by others; someone must volunteer, however, otherwise the public good is not produced and everybody pays a cost higher than that of volunteering. Hence the social dilemma (Dawes 1980), which leads to the celebrated "tragedy of the commons" (Hardin 1968).In evolutionary biology it is generally believed (Rankin et al. 2007) that cooperation in public goods games is only possible in the presence of some form of assortment, which can be due to repeated interactions (which allow reciprocation, reputation effects and punishment; Axelrod and Hamilton 1981) or relatedness (kin selection; Hamilton 1964). Our scope here is to show that, instead, assortment is necessary only if the public good is modeled as an N-person Prisoner's Dilemma (NPD).It seems such common wisdom in the evolutionary biology literature to equate public goods games with the NPD, that in most papers the two ...
We review recent work at the interface of economic game theory and evolutionary biology that provides new insights into the evolution of partner choice, host sanctions, partner fidelity feedback and public goods. (1) The theory of games with asymmetrical information shows that the right incentives allow hosts to screen-out parasites and screen-in mutualists, explaining successful partner choice in the absence of signalling. Applications range from ant-plants to microbiomes. (2) Contract theory distinguishes two longstanding but weakly differentiated explanations of host response to defectors: host sanctions and partner fidelity feedback. Host traits that selectively punish misbehaving symbionts are parsimoniously interpreted as pre-adaptations. Yucca-moth and legume-rhizobia mutualisms are argued to be examples of partner fidelity feedback. (3) The theory of public goods shows that cooperation in multi-player interactions can evolve in the absence of assortment, in one-shot social dilemmas among non-kin. Applications include alarm calls in vertebrates and exoenzymes in microbes.
There is great interest in explaining how beneficial microbiomes are assembled. Antibiotic-producing microbiomes are arguably the most abundant class of beneficial microbiome in nature, having been found on corals, arthropods, molluscs, vertebrates and plant rhizospheres. An exemplar is the attine ants, which cultivate a fungus for food and host a cuticular microbiome that releases antibiotics to defend the fungus from parasites. One explanation posits long-term vertical transmission of P seudonocardia bacteria, which (somehow) evolve new compounds in arms-race fashion against parasites. Alternatively, attines (somehow) selectively recruit multiple, non-coevolved actinobacterial genera from the soil, enabling a ‘multi-drug’ strategy against parasites. We reconcile the models by showing that when hosts fuel interference competition by providing abundant resources, the interference competition favours the recruitment of antibiotic-producing (and -resistant) bacteria. This partner-choice mechanism is more effective when at least one actinobacterial symbiont is vertically transmitted or has a high immigration rate, as in disease-suppressive soils.
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