DIMACS Center, CoRE Building, Rutgers University

**Organizers:****Vijay Vazirani**, Georgia Tech, vazirani@cc.gatech.edu**Denise Wolf**, Lawrence Berkeley Labs, dmwolf@lbl.gov**Adam Arkin**Lawrence Berkeley Labs and UC Berkeley

Title: Equilibrium selection in the evolution of mutualism: The Red King effect

Mutualistic associations, such as those between ants and lycaenid butterflies, cleaner fish and clients, or plants and mycorrhizal fungi, generate mutual benefits for the participants. How will these benefits be allocated among them? We address this question using a simple bargaining model with multiple Nash equilibria. We use evolutionary game theory to explore the ways in which the coevolutionary process selects among the possible equilibria. We focus on the importance of the relative rates of evolution of the mutualist species. Contrary to the Red Queen hypothesis, which suggests that fast evolution is favored in coevolutionary interactions, we find that slowly-evolving species are likely to gain a disproportionate share of the benefits arising through mutualism.

Title: Behavioral Game Theory, Evolutionary Game Theory, and the Explanation of Social Cooperation

Behavioral Game Theory has revealed forms of human behavior involving interaction among unrelated individuals that have proven difficult to explain in terms of self-interest. One such trait, strong reciprocity is a predisposition to cooperate with others, and to punish those who violate the norms of cooperation, at personal cost, even when it is implausible to expect that these costs will be repaid. Strong reciprocity is a form of altruism that can be explained using evolutionary game theory.

The talk will be based on Herbert Gintis, Samuel Bowles, Robert Boyd and Ernst Fehr, Moral Sentiments and Material Interests: On the Foundations of Cooperation in Economic Life (Cambridge: MIT Press, 2004).

Title: Cooperation in social dilemmas: Effects of population structures

Understanding the emergence of cooperation is a fundamental problem in evolutionary biology. To investigate this problem, evolutionary game theory has become a powerful framework. Two simple games have attracted most attention in theoretical and experimental studies: the Prisoner's Dilemma and the Snowdrift game (also known as the Hawk-Dove or Chicken game). In the Prisoner's Dilemma, the non-cooperative state is evolutionarily stable, which has inspired numerous investigations of suitable extensions that allow for cooperative behaviour to persist. In particular, based on spatial extensions of the Prisoner's Dilemma, it is widely accepted that spatial structure promotes the evolution of cooperation. This talk demonstrates that no such general predictions can be made for the effects of spatial structure in the Snowdrift game. In unstructured Snowdrift games, intermediate levels of cooperation persist. However, quite surprisingly, spatial structure reduces the proportion of cooperators for a wide range of parameters. In particular, spatial structure eliminates cooperation if the cost-to-benefit ratio of cooperation is high. In summary, these results caution against the common belief that spatial structure is necessarily beneficial for cooperative behaviour.

Title: Clinical Trials and Game Theory

The work focuses on a critique of the clinical trials process and the tensions in investment that pharma need to make in order to "win" vis a vis FDA as well as other pharmas who can change dynamically the rules of the game by introducing new treatments. The availability of the human genome has similarities with the Monty Hall door opening in the car-and-goat game. The implications are grounds for reevaluating the clinical trials design.

This is joint work with Samuel Broder (Celera) (the former Director of the National Cancer Institute for 25 years)

Title: Evolutionary game dynamics and the evolution of trait variation: will an ESS evolve?

Evolutionarily stable strategy (ESS) models are widely viewed as predicting the strategy of an individual that when monomorphic or nearly so prevents a mutant with any other strategy from entering the population. In fact, the prediction of some of these models is ambiguous when the predicted strategy is "mixed", as in the case of, say, a sex ratio, which may be regarded as a mixture of the subtraits "produce a daughter" and "produce a son." Some models that predict such a mixture predict only that it be manifested by the population as a whole, as an "evolutionarily stable state", instead of by each individual. The Hawk-Dove game and the sex ratio game in a panmictic population are models that make such a "degenerate" prediction. Here we analyze the consequences of incorporating population finiteness into degenerate models and show that it has effects for and against the evolution of an ESS that are of equal order in the population size. Therefore, we used Monte Carlo simulations in order to determine the probability that a finite population evolves to an ESS as opposed to an evolutionarily stable state. In contrast to previous analyses, we assessed how this probability depends on the type of competition among individuals, on the number of genotypes, and on the initial strategy distribution. We show that the probability that an ESS will evolve is generally much less than has been reported and that this probability depends upon on the population size, on the type of competition, on the number of genotypes in the initial population, and on the initial strategy distribution.

Title: Rock-Paper-Scissors for the Adult Player

Evolutionary game dynamics comes in many flavours. This talk compares discrete- and continuous-time replicator dynamics, fictitious play and best response dynamics, as well as other forms of myopic adjustments and spatial interactions, always using as touch-stone the humble Rock-Paper-Scissors game. Far from being a mathematical artificiality, this game is played by male lizards, by toxic bacteria, and by humans deciding whether or not to participate in a public goods experiment. Variants with similar structure show that no adjustment dynamics can lead , for all games, to an equilibrium solution.

Title: Bet-hedging in herpes viruses

Static latency is the hallmark of all herpes viruses. The varicella zoster virus, for instance, causes varicella (chickenpox), and after a latent phase of between 5 and 40 years, it can give rise to herpes zoster (shingles). This latency and the subsequent reactivation has intrigued and puzzled virologists. Although several factors have been suggested, it is unknown what triggers reactivation. However, evolution of latency can be explained with a simple mathematical model. Here, we demonstrate that a simple, yet efficient, bet-hedging strategy might have evolved in a number of viruses, especially those belonging to the herpes virus family and most importantly in varicella zoster virus. We show that the evolution of latency can be explained by the population dynamics of infectious diseases in fluctuating host populations.

Title: Evolutionary Game Dynamics in Finite Populations

We study the evolutionary game dynamics of a two-strategy game. In infinite populations, the well-known replicator equations describe the deterministic evolutionary dynamics. There are three generic selection scenarios. The dynamics of a finite group of players has received little attention. We provide a framework for studying stochastic evolutionary game dynamics in finite populations. We define a Moran process with frequency dependent fitness. We find that there are eight selection scenarios. And for a given payoff matrix, a number of these sceanrios can occur for different population size. Our results have interesting applications in biology and economics. In particular, we obtain new results on the evolution of cooperation in the classic repeated Prisoner's Dilemma game. We show that a single cooperator using a reciprocal strategy such as Tit-For-Tat can invade a population of defectors with a probability that corresponds to a net selective advantage. We specify the conditions for natural selection to favor the emergence of cooperation and derive conditions for evolutionary stability in finite populations.

Title: A game theoretic analysis of random phase variation and other microbial diversificaiton strategies

Population diversification strategies are ubiquitous in the microbial world, encompassing random phase variation of the expression of surface features on pathogenic bacteria, viral latency as observed in bacterial phages and HIV, and the non-genetic diversity of bacterial stress responses, among others. In this project we take an evolutionary game theoretic approach to investigating diversification strategies among microbes. We focus on random phase variation (RPV), an expression strategy involving random alternations between different cell states, as seen in type 1 pili expression of uropathic E. coli. Evolutionary game theory can help explore why cells behave as they do and elucidate the design principles of the regulatory circuits controlling cellular behaviors. This formulation allows one to address the question, what sort of selective forces give rise to RPV as an evolutionarily stable strategy (ESS)? Our analyses indicate that evolutionarily stable phenotype expression strategies depend strongly on the selective forces over the entire lifecycle of the organism, in conjunction with the ability of the organism to sense its environment, among other factors. In this talk we look at different types of sensor defects (unobservable environmental transitions, incorrect identification of environmental states, signal transduction delays, and additive noise), and different classes of environments (time-invariant vs. time-varying, stochastic, or frequency dependent), and analyze for combinations that give rise to random phase variation as an ESS. We show that a strategy that is evolutionarily stable under one set of environmental and sensing conditions can be impossible to implement or lead to extinction in other circumstances. Moreover, microbial populations with different sensor profiles in the exact same environment(s) will adopt different evolutionarily stable strategies depending on the types of sensing failures they experience.

Joint work with V. Vazirani and A. Arkin.

Title: Entering Stationary Phase: Senescence, Death and Selfish Survivors

At any given moment most microbial populations of the world are in a state of extremely slow or no growth; therefore the study of microbes in a non-dividing state is key for understanding microbial survival in general.

Entering the state of non-growth is accompanied by a genetic response resulting cessation of many metabolic activities, followed by rapid decline in viability. However, some cells can escape the non-dividing state entering in a competition with the rest of the non-dividing clone. This phenomenon is termed GASPing for Growth Advantage in Stationary Phase. Additional incubation can bring about successive rounds of selection in which new cells with additional GASP-conferring mutations cause new population changeovers. GASP-mutants can be thought of as defectors engaged in competition with the rest of the wild type population made of individuals cooperating in retaining the non-dividing state untill nutrients are available again. Understanding these complex population dynamics involves untangling mechanisms of senescence, cell death and various evolutionary strategies resulting in prolonged survival under limiting conditions.

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Document last modified on February 26, 2004.