Evolution of cooperation under -person snowdrift games

In the animal world, performing a given task which is beneficial to an entire group requires the cooperation of several individuals of that group who often share the workload required to perform the task. The mathematical framework to study the dynamics of collective action is game theory. Here we study the evolutionary dynamics of cooperators and defectors in a population in which groups of individuals engage in N-person, non-excludable public goods games. We explore an N-person generalization of the well-known two-person snowdrift game. We discuss both the case of infinite and finite populations, taking explicitly into consideration the possible existence of a threshold above which collective action is materialized. Whereas in infinite populations, an N-person snowdrift game (NSG) leads to a stable coexistence between cooperators and defectors, the introduction of a threshold leads to the appearance of a new interior fixed point associated with a coordination threshold. The fingerprints of the stable and unstable interior fixed points still affect the evolutionary dynamics in finite populations, despite evolution leading the population inexorably to a monomorphic end-state. However, when the group size and population size become comparable, we find that spite sets in, rendering cooperation unfeasible.     

Evolutionary matrix games and optimization theory

An evolutionarily stable strategy (ESS) is only required to be capable of resisting invasion by rare mutant strategies. In contrast, an absolute invader strategy (AIS) is a rare mutant strategy that can invade any established strategy. We show that the predictions of the outcome of evolution made by optimization models are compatible with those made by the classical expected payoff comparisons in matrix games. We also show that if a matrix game has an AIS that AIS is unique and is also an ESS. But an ESS need not be an AIS. In pure-strategy submodels, an AIS need not be unique. An AIS of a matrix game has global asymptotic stability property in the game dynamics which involve only pure strategies including the AIS.     

Evolution of cannibalistic traits: scenarios derived from adaptive dynamics

The evolution of cannibalistic traits in consumer populations is studied in this paper with the approach of adaptive dynamics theory. The model is kept at its minimum complexity by eliminating some environmental characteristics, like heterogeneity and seasonalities, and by hiding the size-structure of the population. Evolutionary dynamics are identified through numerical bifurcation analysis, applied both to the ecological (resident-mutant) model and to the canonical equation of adaptive dynamics. The result is a rich catalog of evolutionary scenarios involving evolutionary stable strategies and branching points both in the monomorphic and dimorphic dynamics. The possibility of evolutionary extinction of highly cannibalistic populations is also ascertained. This allows one to explain why cannibalism can be a transient stage of evolution.     

Strategic analysis in evolutionary genetics and the theory of games

This paper is written in memory of John Maynard Smith. In a brief survey it discusses essential aspects of how game theory in biology relates to its counterpart in economics, the major transition in game theory initiated by Maynard Smith, the discrepancies between genetic and phenotypic models in evolutionary biology, and a balanced way of reconciling these models. In addition, the paper discusses modern problems in understanding games at the genetic level using the examples of conflict between endosymbionts and their hosts, and the molecular interactions between parasites and the mammalian immune system.     

Ecological public goods games: cooperation and bifurcation

The Public Goods Game is one of the most popular models for studying the origin and maintenance of cooperation. In its simplest form, this evolutionary game has two regimes: defection goes to fixation if the multiplication factor r is smaller than the interaction group size N, whereas cooperation goes to fixation if the multiplication factor r is larger than the interaction group size N. Hauert et al. [Hauert, C., Holmes, M., Doebeli, M., 2006a. Evolutionary games and population dynamics: Maintenance of cooperation in public goods games. Proc. R. Soc. Lond. B 273, 2565-2570] have introduced the Ecological Public Goods Game by viewing the payoffs from the evolutionary game as birth rates in a population dynamic model. This results in a feedback between ecological and evolutionary dynamics: if defectors are prevalent, birth rates are low and population densities decline, which leads to smaller interaction groups for the Public Goods game, and hence to dominance of cooperators, with a concomitant increase in birth rates and population densities. This feedback can lead to stable co-existence between cooperators and defectors. Here we provide a detailed analysis of the dynamics of the Ecological Public Goods Game, showing that the model exhibits various types of bifurcations, including supercritical Hopf bifurcations, which result in stable limit cycles, and hence in oscillatory co-existence of cooperators and defectors. These results show that including population dynamics in evolutionary games can have important consequences for the evolutionary dynamics of cooperation.     

Evolutionary graph theory: breaking the symmetry between interaction and replacement

We study evolutionary dynamics in a population whose structure is given by two graphs: the interaction graph determines who plays with whom in an evolutionary game; the replacement graph specifies the geometry of evolutionary competition and updating. First, we calculate the fixation probabilities of frequency dependent selection between two strategies or phenotypes. We consider three different update mechanisms: birth-death, death-birth and imitation. Then, as a particular example, we explore the evolution of cooperation. Suppose the interaction graph is a regular graph of degree h, the replacement graph is a regular graph of degree g and the overlap between the two graphs is a regular graph of degree l. We show that cooperation is favored by natural selection if b/c>hg/l. Here, b and c denote the benefit and cost of the altruistic act. This result holds for death-birth updating, weak-selection and large population size. Note that the optimum population structure for cooperators is given by maximum overlap between the interaction and the replacement graph (g=h=l), which means that the two graphs are identical. We also prove that a modified replicator equation can describe how the expected values of the frequencies of an arbitrary number of strategies change on replacement and interaction graphs: the two graphs induce a transformation of the payoff matrix.     

Repeated games and direct reciprocity under active linking

Direct reciprocity relies on repeated encounters between the same two individuals. Here we examine the evolution of cooperation under direct reciprocity in dynamically structured populations. Individuals occupy the vertices of a graph, undergoing repeated interactions with their partners via the edges of the graph. Unlike the traditional approach to evolutionary game theory, where individuals meet at random and have no control over the frequency or duration of interactions, we consider a model in which individuals differ in the rate at which they seek new interactions. Moreover, once a link between two individuals has formed, the productivity of this link is evaluated. Links can be broken off at different rates. Whenever the active dynamics of links is sufficiently fast, population structure leads to a simple transformation of the payoff matrix, effectively changing the game under consideration, and hence paving the way for reciprocators to dominate defectors. We derive analytical conditions for evolutionary stability.     

On sperm competition games: raffles and roles revisited

 In principle there are two approaches to modelling a trade-off between the positive and negative outcomes of a behavior: after suitably defining a value for the behavior in the absence of any trade-off, one can either multiply that value by an appropriate discount or subtract an appropriate cost. In a prospective analysis of sperm competition, Parker (Proc. Roy. Soc. Lond. B (1990) 242, 120–126) adopted the multiplicative approach to model the trade-off between the value of a mating and the cost of its acquisition. He obtained two paradoxical results. First, if two males ‘know’ whether they are first or second to mate, but these roles are assigned randomly, then sperm numbers should be the same for both males whether the ‘raffle’ for fertilization is fair or unfair. Second, if mating order is constant, then a favored male should expend less on sperm. His results are puzzling not only in terms of intuition about nature, but also in terms of his model’s consistency. In other words, they present both an external and an internal paradox. Parker assumed the fairness of the raffle to a disfavored male to be independent of how much sperm a favored male deposits. This article both generalizes Parker’s analysis by allowing fairness to decrease with sperm expenditure by the favored male and compares Parker’s results to those obtained by the additive approach. In many respects, results are similar. Nevertheless, if the costs of mating are assumed to increase with sperm expenditure but not to depend on the role in which sperm is expended, as Parker assumed, then the additive approach is more fundamentally correct. In particular, Parker’s constant-role paradox is an artifact of his approach. His random-role paradox is internally rationalized in terms of standard microeconomic theory. When fairness decreases, however slightly, with sperm expenditure by the favored male, both models demonstrate that the evolutionarily stable strategy is for more sperm to be deposited during a favored mating than during a disfavored mating. The lower the costs, the greater the divergence. Thus a possible resolution of the external paradox is that fairness is not constant in nature. Received: 7 December 1998     

Designing a connected nature reserve using a network flow theory approach

Establishing nature conservation reserves is an effective and widely accepted practice to protect biodiversity. In order to promote the effectiveness and efficiency of the reserve, spatial attributes of the reserve should be considered. Connectedness (contiguity) is one of these important spatial attributes. Currently in the biological literature there are only a few formal/exact optimization approaches to endogenously designing a connected nature reserve. This article adds a new approach by adapting a spatial unit allocation model to the reserve design problem. Using concepts from network flow theory, the model defines a sink site from which no flow directs out and ensures contiguity by specifying the outflow and inflow relationship of the potential sites. Computational performance of the model is tested using hypothetical problems with various sizes including up to 400 potential sites. Results show that the time needed to solve the problem to optimality increases exponentially both as number of potential sites increases and as species distribution gets more sparse. An empirical application involving 80 potential sites and 15 bird species in part of Fox River watershed, Illinois USA is presented. Factors influencing an IP model’s computational performance and potential extensions of the model were discussed.     

Evolution of structure,order and complexity in biological systems: Part III of a general theory

In this, Part III of a general theory, the large-scale features of evolution of structure, order, and complexity are considered as characteristic features of the biological state of matter. This starts with a rigorous formal definition of structure, classes of structural order, complexity, measures of complexity, and how these arise through evolution by a cumulative process of storing information in memory systems. Three such memory systems have evolved: the genetic memory, the immune memory, and the memories of the nervous system. The evolution, characteristic parameters and the limitations of these memory systems are explored. From these considerations emerge the large-scale features of the evolutionary pathways of biological structure, function, and complexity.     

Positive feedback and alternative stable states in inbreeding, cooperation, sex roles and other evolutionary processes

A large proportion of studies in systems science focus on processes involving a mixture of positive and negative feedbacks, which are also common themes in evolutionary ecology. Examples of negative feedback are density dependence (population regulation) and frequency-dependent selection (polymorphisms). Positive feedback, in turn, plays a role in Fisherian 'runaway' sexual selection, the evolution of cooperation, selfing and inbreeding tolerance under purging of deleterious alleles, and the evolution of sex differences in parental care. All these examples feature self-reinforcing processes where the increase in the value of a trait selects for further increases, sometimes via a coevolutionary feedback loop with another trait. Positive feedback often leads to alternative stable states (evolutionary endpoints), making the interpretation of evolutionary predictions challenging. Here, we discuss conceptual issues such as the relationship between self-reinforcing selection and disruptive selection. We also present an extension of a previous model on parental care, focusing on the relationship between the operational sex ratio and sexual selection, and the influence of this relationship on the evolution of biparental or uniparental care.     

John Maynard Smith and the importance of consistency in evolutionary game theory

John Maynard Smith was the founder of evolutionary game theory. He has also been the major influence on the direction of this field, which now pervades behavioural ecology and evolutionary biology. In its original formulation the theory had three components: a set of strategies, a payoff structure, and a concept of evolutionary stability. These three key components are still the basis of the theory, but what is assumed about each component is often different to the original assumptions. We review modern approaches to these components. We emphasis that if a game is considered in isolation, and arbitrary payoffs are assumed, then the payoffs may not be consistent with other components of the system which are not modelled. Modelling the whole system, including not only the focal game, but also the future behaviour of the players and the behaviour of other population members, allows a consistent model to be constructed. We illustrate this in the case of two models of parental care, showing how linking a focal game to other aspects of the system alters what is predicted.     

Game Dynamics with Learning and Evolution of Universal Grammar

We investigate a model of language evolution, based on population game dynamics with learning. First, we examine the case of two genetic variants of universal grammar (UG), the heart of the human language faculty, assuming each admits two possible grammars. The dynamics are driven by a communication game. We prove using dynamical systems techniques that if the payoff matrix obeys certain constraints, then the two UGs are stable against invasion by each other, that is, they are evolutionarily stable. Then, we prove a similar theorem for an arbitrary number of disjoint UGs. In both theorems, the constraints are independent of the learning process. Intuitively, if a mutation in UG results in grammars that are incompatible with the established languages, then the mutation will die out because mutants will be unable to communicate and therefore unable to realize any potential benefit of the mutation. An example for which these theorems do not apply shows that compatible mutations may or may not be able to invade, depending on the population's history and the learning process. These results suggest that the genetic history of language is constrained by the need for compatibility and that mutations in the language faculty may have died out or taken over due more to historical accident than to any straightforward notion of relative fitness. MSC 1991: 37N25 · 92D15 · 91F20     

Physical violence,child abuse,and child homicide

The study of child abuse and child homicide has been based on the often implicit assumption that there is a continuum of violence ranging from mild physical punishment to severe abuse and homicide. Empirical data supporting this assumption are sparse. Existing data can be shown, however, to support an assumption that there are distinct forms of violence, not a continuum. This paper reviews these data and discusses their implications for the study of violence, abuse, and homicide in terms of substantive and methodological explanations. In addition, the implications of the assumption that violence consists of distinct behaviors as opposed to a continuum are discussed in light of sociobiological and evolutionary explanations of child abuse and child homicide. This paper was written under the auspices of the Family Violence Research Program at the University of Rhode Island. A complete list of books and articles is available upon request. Richard J. Gelles is Professor of Sociology and Anthropology and the Director of the Family Violence Research Program at the University of Rhode Island. He is the author or coauthor of 14 books and more than 90 articles and chapters on family violence. His most recent books areIntimate Violence, published in 1988 by Simon and Schuster;Physical Violence in American Families: Risk Factors and Adaptations in 8,145 Families, published by Transaction Books in 1990; andIntimate Violence in Families, published in 1990 by Sage Publications.     

Global mutations and local mutations have very different effects on evolution, illustrated by mixed strategies of asymmetric binary games

We study the evolutionary effect of rare mutations causing global changes in traits. We consider asymmetric binary games between two players. The first player takes two alternative options with probability x and 1−x; and the second player takes options with probability y and 1−y. Due to natural selection and recurrent mutation, the population evolves to have broad distributions of x and y. We analyze three cases showing qualitatively different dynamics, exemplified by (1) vigilance-intrusion game, (2) asymmetric hawk-dove game and (3) cleaner-client game. We found that the evolutionary outcome is strongly dependent upon the distribution of mutants’ traits, more than the mutation rates. For example in the vigilance-intrusion game, the evolutionary dynamics show a perpetual stable oscillation if mutants are always close to the parent (local-mutation mode), whilst the population converges to a stable equilibrium distribution if mutants can be quite different from the parent (global-mutation mode), even for extremely low mutation rate. When common local mutations and rare global mutations occur simultaneously, the evolutionary outcome is controlled by the latter.     

Aging, evolvability, and the individual benefit requirement; medical implications of aging theory controversies

There is a class of theories of aging (variously termed adaptive aging, aging by design, aging selected for its own sake, or programmed death theories) that hold that an organism design that limits life span conveys benefits and was selected specifically because it limits life span. These theories have enjoyed a resurgence of popularity because of the discovery of genes that promote aging in various organisms.However, traditional evolution theory has a core tenet that excludes the possibility of evolving and retaining an individually adverse organism design, i.e. a design characteristic that reduces the ability of individual organisms to survive or reproduce without any compensating individual benefit. Various theories of aging dating from the 1950s and based on traditional evolution theory enjoy substantial popularity. Therefore, any theorist proposing an adaptive theory of aging must necessarily also propose some adjustment to traditional evolution theory that specifically addresses the individual benefit issue. This paper describes an adaptive theory of aging and describes how one of the proposed adjustments (evolvability theory) supports adaptive aging.This issue is important because adaptive theories are generally more optimistic regarding prospects for medical intervention in the aging process and also suggest different approaches in achieving such intervention.     

Effects of waterfowl, large fish and periphyton on the spring growth of Potamogeton pectinatus L. in Lake Mogan, Turkey

It has been argued that waterfowl and fish may threaten growth of submerged macrophytes, especially in spring during the early growth phase when plant biomass is low. A small reduction of biomass at that time might delay growth or decrease subsequent productivity. We investigated the impact of waterfowl and large fish on the spring growth of fennel pondweed (Potamogeton pectinatusL.) by employing an exclosure experiment in the macrophyte-dominated clear-water Lake Mogan, Turkey. Birds and large fish were excluded from eight plots and both in situvegetation and macrophytes kept in pots were compared to eight open plots. Also, to investigate the effect of periphyton on plant growth it was removed from half of the pot plants. Exclusion of waterfowl and fish may decrease predation on macroinvertebrates, which in turn may affect periphyton, and macrophyte growth, why macroinvertebrates also were sampled. Waterfowl density was high (15–70 ind. of coot, Fulica atraL. ha^–1), abundance of submerged plants was also high with a surface coverage of 70–80%, and benthivorous fish were present, mainly tench, (Tinca tincaL.) and carp, (Cyprinus carpioL.). Exclusion of waterfowl and large fish did not significantly affect the spring growth of pondweed; neither plants growing in situnor kept in pots. Removal of periphyton from the plants in the pots did not favour growth. The density of macroinvertebrates was not affected by the exclusion of waterfowl and large fish, but it was positively related to aboveground biomass of fennel pondweed. We suggest that even if waterfowl and large fish are in high densities, their effect on fennel pondweed spring growth in lakes with abundant submerged vegetation, such as Lake Mogan, is low.     

Descriptions of superparasitism by optimal foraging theory,evolutionarily stable strategies and quantitative genetics

Many parasitoids superparasitize, in which an insect attacks a previously parasitized host, laying an egg in the host even though only one offspring will emerge from the host. In this paper superparasitism is considered from the perspectives of optimal foraging theory, evolutionarily stable strategies, and quantitative genetics. The focal question is: at what point in its life should an individual parasitoid begin attacking previously parasitized hosts? Each of the three theoretical methods can be used to answer the question and by doing so, we see how the three methods are connected. Qualitative, empirical predictions based on the theories are described.