István Scheuring

Fixation of Strategies for an Evolutionary Game in Finite Populations

A stochastic evolutionary dynamics of two strategies given by 2× 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.

Review: Game theory of public goods in one-shot social dilemmas without assortment.

We review the theory of public goods in biology. In the N-person prisoners dilemma, where the public good is a linear function of the individual contributions, cooperation requires some form of assortment, for example due to kin discrimination, population viscosity or repeated interactions. In most social species ranging from bacteria to humans, however, public goods are usually a non-linear function of the contributions, which makes cooperation possible without assortment. More specifically, a polymorphic state can be stable in which cooperators and non-cooperators coexist. The existence of mixed equilibria in public goods games is a fundamental result in the study of cooperation that has been overlooked so far, because of the disproportionate attention given to the two- and N-person prisoners dilemma. Methods and results from games with pairwise interactions or linear benefits cannot, in general, be extended to the analysis of public goods. Game theory helps explain the production of public goods in one-shot, N-person interactions without assortment, it leads to predictions that can be easily tested and allows a prescriptive approach to cooperation.

Coexistence of cooperation and defection in public goods games.

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 Volunteers 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. This mixed equilibrium is absent in the N‐person Prisoners Dilemma, in which the public good is a linear function of the individual contributions. We also show that the Prisoners Dilemma and the Volunteers Dilemma are the two opposite extremes of a general public goods game, and that all intermediate cases can have a mixed equilibrium like the Volunteers Dilemma. The coexistence of cooperators and defectors, therefore, is a typical outcome of most social dilemmas, which requires neither relatedness nor iterations.

In silico simulations reveal that replicators with limited dispersal evolve towards higher efficiency and fidelity

The emergence of functional replicases, acting quickly and with high accuracy, was crucial to the origin of life. Although where the first RNA molecules came from is still unknown, it is nevertheless assumed that catalytic RNA enzymes (ribozymes) with replicase function emerged at some early stage of evolution. The fidelity of copying is especially important because the mutation load limits the length of replicating templates that can be maintained by natural selection. An increase in template length is disadvantageous for a fixed digit copying fidelity, however, longer molecules are expected to be better replicases. An iteration for longer molecules with better replicase function has been suggested and analysed mathematically. Here we show that more efficient replicases can spread, provided they are adsorbed to a prebiotic mineral surface. A cellular automaton simulation reveals that copying fidelity, replicase speed and template efficiency all increase with evolution, despite the presence of molecular parasites, essentially because of reciprocal atruism (‘within-species mutualism’) on the surface, thus making a gradual improvement of replicase function more plausible.

Economic game theory for mutualism and cooperation.

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.

How to assemble a beneficial microbiome in three easy steps

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.

Application of multifractals to the analysis of vegetation pattern

. A method of characterizing the geometry and statistical nature of vegetation patterns and for studying their fractal dimension is proposed. The method utilizes the concept of multifractals, and is especially suited to the description of complex patterns. The properties of multifractals and their role in detecting the scale of vegetation patterns are explained. We suggest an extension of the term multifractal for use in landscape ecology and coenology connected with patterns of many different kinds of points. Relationships between information-statistical functions and the fractal dimensions introduced are shown. A computer-simulated example demonstrates the use of statistical functions and illustrates its applicability in vegetation science.

chaotic advection, diffusion, and reactions in open flows

We review and generalize recent results on advection of particles in open time-periodic hydrodynamical flows. First, the problem of passive advection is considered, and its fractal and chaotic nature is pointed out. Next, we study the effect of weak molecular diffusion or randomness of the flow. Finally, we investigate the influence of passive advection on chemical or biological activity superimposed on open flows. The nondiffusive approach is shown to carry some features of a weak diffusion, due to the finiteness of the reaction range or reaction velocity. (c) 2000 American Institute of Physics.

Competing populations in flows with chaotic mixing

We investigate the effects of spatial heterogeneity on the coexistence of competing species in the case when the heterogeneity is dynamically generated by environmental flows with chaotic mixing properties. We show that one effect of chaotic advection on the passively advected species (such as phytoplankton, or self-replicating macro-molecules) is the possibility of coexistence of more species than that limited by the number of niches they occupy. We derive a novel set of dynamical equations for competing populations.

The evolution of intermediate castration virulence and ant coexistence in a spatially structured environment

Theory suggests that spatial structuring should select for intermediate levels of virulence in parasites, but empirical tests are rare and have never been conducted with castration (sterilizing) parasites. To test this theory in a natural landscape, we construct a spatially explicit model of the symbiosis between the ant-plant Cordia nodosa and its two, protecting ant symbionts, Allomerus and Azteca. Allomerus is also a castration parasite, preventing fruiting to increase colony fecundity. Limiting the dispersal of Allomerus and host plant selects for intermediate castration virulence. Increasing the frequency of the mutualist, Azteca, selects for higher castration virulence in Allomerus, because seeds from Azteca-inhabited plants are a public good that Allomerus exploits. These results are consistent with field observations and, to our knowledge, provide the first empirical evidence supporting the hypothesis that spatial structure can reduce castration virulence and the first such evidence in a natural landscape for either mortality or castration virulence.