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Antal, Tibor

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Antal

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Antal, Tibor
Author's Publications: search.filters.isAuthorOfPublication.4312f93a-7b60-486d-ab75-568507c23516

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    Evolutionary Dynamics in Structured Populations
    (The Royal Society, 2010) Nowak, Martin; Tarnita, Corina; Antal, Tibor
    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.
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    Mutation-Selection Equilibrium in Games with Multiple Strategies
    (Elsevier, 2009) Antal, Tibor; Traulsen, Arne; Ohtsuki, Hisashi; Tarnita, Corina; Nowak, Martin
    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.
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    Evolution of Cooperation by Phenotypic Similarity
    (National Academy of Sciences, 2009) Antal, Tibor; Ohtsuki, Hisashi; Wakeley, John; Taylor, Peter D.; Nowak, Martin
    The emergence of cooperation in populations of selfish individuals is a fascinating topic that has inspired much work in theoretical biology. Here, we study the evolution of cooperation in a model where individuals are characterized by phenotypic properties that are visible to others. The population is well mixed in the sense that everyone is equally likely to interact with everyone else, but the behavioral strategies can depend on distance in phenotype space. We study the interaction of cooperators and defectors. In our model, cooperators cooperate with those who are similar and defect otherwise. Defectors always defect. Individuals mutate to nearby phenotypes, which generates a random walk of the population in phenotype space. Our analysis brings together ideas from coalescence theory and evolutionary game dynamics. We obtain a precise condition for natural selection to favor cooperators over defectors. Cooperation is favored when the phenotypic mutation rate is large and the strategy mutation rate is small. In the optimal case for cooperators, in a one-dimensional phenotype space and for large population size, the critical benefit-to-cost ratio is given by Formula. We also derive the fundamental condition for any two-strategy symmetric game and consider high-dimensional phenotype spaces.
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    Evolutionary Dynamics in Set Structured Populations
    (National Academy of Sciences, 2009) Tarnita, Corina; Antal, Tibor; Ohtsuki, Hisashi; Nowak, Martin
    Evolutionary dynamics are strongly affected by population structure. The outcome of an evolutionary process in a well-mixed population can be very different from that in a structured population. We introduce a powerful method to study dynamical population structure: evolutionary set theory. The individuals of a population are distributed over sets. Individuals interact with others who are in the same set. Any 2 individuals can have several sets in common. Some sets can be empty, whereas others have many members. Interactions occur in terms of an evolutionary game. The payoff of the game is interpreted as fitness. Both the strategy and the set memberships change under evolutionary updating. Therefore, the population structure itself is a consequence of evolutionary dynamics. We construct a general mathematical approach for studying any evolutionary game in set structured populations. As a particular example, we study the evolution of cooperation and derive precise conditions for cooperators to be selected over defectors.
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    Strategy Selection in Structured Populations
    (Elsevier, 2009) Tarnita, Corina; Ohtsuki, Hisashi; Antal, Tibor; Fu, Feng; Nowak, Martin
    Evolutionary game theory studies frequency dependent selection. The fitness of a strategy is not constant, but depends on the relative frequencies of strategies in the population. This type of evolutionary dynamics occurs in many settings of ecology, infectious disease dynamics, animal behavior and social interactions of humans. Traditionally evolutionary game dynamics are studied in well-mixed populations, where the interaction between any two individuals is equally likely. There have also been several approaches to study evolutionary games in structured populations. In this paper we present a simple result that holds for a large variety of population structures. We consider the game between two strategies, A and B, described by the payoff matrix View the MathML source. We study a mutation and selection process. For weak selection strategy A is favored over B if and only if σa+b>c+σd. This means the effect of population structure on strategy selection can be described by a single parameter, σ. We present the values of σ for various examples including the well-mixed population, games on graphs, games in phenotype space and games on sets. We give a proof for the existence of such a σ, which holds for all population structures and update rules that have certain (natural) properties. We assume weak selection, but allow any mutation rate. We discuss the relationship between σ and the critical benefit to cost ratio for the evolution of cooperation. The single parameter, σ, allows us to quantify the ability of a population structure to promote the evolution of cooperation or to choose efficient equilibria in coordination games.
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    Strategy Abundance in 2×2 Games for Arbitrary Mutation Rates
    (Elsevier, 2009) Antal, Tibor; Nowak, Martin; Traulsen, Arne
    We study evolutionary game dynamics in a well-mixed populations of finite size, N. A well-mixed population means that any two individuals are equally likely to interact. In particular we consider the average abundances of two strategies, A and B, under mutation and selection. The game dynamical interaction between the two strategies is given by the 2×2 payoff matrix [View the MathML source]. It has previously been shown that A is more abundant than B, if a(N-2)+bN>cN+d(N-2). This result has been derived for particular stochastic processes that operate either in the limit of asymptotically small mutation rates or in the limit of weak selection. Here we show that this result holds in fact for a wide class of stochastic birth–death processes for arbitrary mutation rate and for any intensity of selection.
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    Competition-Colonization Dynamics in an RNA Virus
    (National Academy of Sciences, 2010) Ojosnegros, Samuel; Beerenwinkel, Niko; Antal, Tibor; Nowak, Martin; Escarmis, Christina; Domingo, Esteban
    During replication, RNA viruses rapidly generate diverse mutant progeny which differ in their ability to kill host cells. We report that the progeny of a single RNA viral genome diversified during hundreds of passages in cell culture and self-organized into two genetically distinct subpopulations that exhibited the competition-colonization dynamics previously recognized in many classical ecological systems. Viral colonizers alone were more efficient in killing cells than competitors in culture. In cells coinfected with both competitors and colonizers, viral interference resulted in reduced cell killing, and competitors replaced colonizers. Mathematical modeling of this coinfection dynamics predicted selection to be density dependent, which was confirmed experimentally. Thus, as is known for other ecological systems, biodiversity and even cell killing of virus populations can be shaped by a tradeoff between competition and colonization. Our results suggest a model for the evolution of virulence in viruses based on internal interactions within mutant spectra of viral quasispecies.