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The method of evolutionary stable strategies (ESS), in its current form, is confronted with a difficulty when it tries to explain how some social behaviors initiate their evolution. We show that this difficulty may be removed by changing the assumption made tacitly in game theory (and in ESS) of randomness of meetings or encounters. In reality, such randomness seems to be rare in nature. Family, population and social structure, customs, and habits impose various types of deviation from randomness. Introducing nonrandomness of meeting in a way formally similar to assortative mating, we show that the bar to initial increase of inherited cooperative or altruistic behaviors can be removed, provided there is sufficient assortment of meetings. Family structure may cause contacts predominantly between certain types of relatives, and one can reconstruct some results of classical kin selection in terms of evolutionary stable strategy with assortative meetings. Neighbor effects and group selection might be similarly treated. Assortment need not be a passive consequence of population and social structure, but it can also be actively pursued. Behaviors favoring the choice of cooperative companions will have the effect of favoring the evolution of cooperativeness. It can be shown that discrimination in the choice of companions, especially if combined with assortment, can favor the development of cooperativeness, making initial increase of cooperative behavior possible even at levels of assortment passively imposed which would not be adequate, per se, to guarantee the increase of cooperativeness. It is possible that, in some cases, cooperativeness and behavior favoring some type of assortment are coselected.
Iterated Prisoner's Dilemma models are proposed in which, at any trial, the probability of staying in the game depends on the outcome of the previous trial. If a player's choice depends on its own play (cooperate or defect) at the previous trial, it becomes possible for cooperative strategies to increase when rare in a population of egoists. A dynamic analysis is used to demonstrate that stable polymorphisms may result, and may involve more strategies than just Tit-for-Tat and all-Defect. The tendency for clustering among like strategists to enhance their initial increase when rare is also explored dynamically.
While vertebrate hemoglobins typically are tetrameric and show highly regulated and cooperative ligand binding, little is known of the evolution of these properties. We are studying the structural and functional properties of the hemoglobins from Caudina arenicola, an echinoderm. The echinoderms are in the lineage most closely related to the vertebrates to express hemoglobin. C. arenicola has three sets of red cells, in the water vascular system, the coelomic cavity, and in an intestinal vein. Each of these expresses a distinct array of globins. The hemoglobins are cooperative and exhibit unusual ligand-linked associative properties, being dimeric when oxygenated and forming tetramers and higher aggregates on deoxygenation. The major coelomic hemoglobins have been subjected to a detailed examination by a combination of ligand binding analyses and protein and DNA sequencing, as well as X-ray crystallography. Two typical globin introns were identified, along with a unique intron that bisects an N-terminal extension of the globin from the remainder of the gene. X-ray crystallographic analysis shows that the subunit interfaces of C. arenicola hemoglobins differ radically from those of vertebrate hemoglobins and indeed from some other invertebrate hemoglobins, but closely resemble the packing arrangements found in a clam hemoglobin (Scapharca). However, the residues implicated in cooperativity in these two types of hemoglobins differ substantially.
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A nonzero-sum three-person coalition game is presented to study the evolution of complexity and diversity in cooperation, where the population dynamics of players with strategies is given according to their scores in the iterated game and mutations. Two types of differentiation emerge initially: a biased one to classes and a temporal one to change their roles for coalition. Rules to change the hands are self-organized in a society through evolution. The coevolution of diversity and complexity of strategies and interactions (or communications) are found at later stages of the simulation. Relevance of our results to the biological society is briefly discussed.
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Evolutionary theory has not explained how competition among lower level units is suppressed in the formation of higher-level evolutionary units. For example, the key problem of early evolution is small, individual replicators formed cooperative groups of sufficient complexity to allow accurate copying of the genetic material. The puzzle is why parasites did not subvert the formation of cells by obtaining benefits from the group without contributing to shared traits that enhance reproduction. These parasites would outcompete other replicators within the cell, disrupting reproductive fairness among subunits and destroying the functional coherence of the group. A similar problem arose at a later evolutionary stage with the orderly mendelian segregation of subunits (chromosomes) within cells, and reproductive fairness continued to be a problem in the evolution of insect and human societies. Here I present a simple model to show how reproductive fairness evolves among subunits to create functional coherence and higher-level units. Self-restraint, which evolves according to the kin-selection coefficient of relatedness, is not sufficient: mutual policing and enforcement of reproductive fairness are also required for the evolution of increasing social complexity.
"Cooperation" defines any behavior that enhances the fitness of a group (e.g. a community or species), but which, by its nature, can be exploited by selfish individuals, meaning, firstly, that selfish individuals derive an advantage from exploitation which is greater than the average advantage that accrues to unselfish individuals. Secondly, exploitation has no intrinsic fitness value except in the presence of the "cooperative behavior". The mathematics is described by the simple Prisoner's Dilemma Game (PDG). It has previously been shown that koinophilia (the avoidance of sexual mates displaying unusual or atypical phenotypic features, such as mutations) stabilizes any inherited strategy in the simple or iterated PDG, meaning that it cannot be displaced by rare forms of alternative behavior which arise through mutation or occasional migration. In the present model equal numbers of cooperators and defectors (in the simple PDG) were randomly spread in a two-dimensional "cornfield" with uniformly distributed resources. Every individual was koinophilic, and interacted (sexually and in the PDG tournaments) only with individuals from within its immediate neighborhood. This model therefore tested whether cooperation can outcompete defection or selfishness in a straight, initially equally matched, evolutionary battle. The results show that in the absence of koinophilia cooperation was rapidly driven to extinction. With koinophilia there was a very rapid loss of cooperators in the first few generations, but thereafter cooperation slowly spread, ultimately eliminating defection completely. This result was critically dependent on sampling effects of neighborhoods. Small samples (resulting from low population densities or small neighborhood sizes) increase the probability that a chance neighborhood comes to consist predominantly of cooperators. A sexual preference for the most common phenotype in the neighborhood then makes that phenotype more common still. Once this occurs cooperation's spread becomes almost inevitable.
The problems of achieving mutual cooperation can be formalized in a game called the Prisoner's Dilemma in which selfish defection is always more rewarding than cooperation. If the two protagonists have a certain minimum probability of meeting again a strategy called TIT FOR TAT is very successful. In TIT FOR TAT the player cooperates on the first move and thereafter does whatever the opponent did on the previous move. I have studied the behaviour of fish when confronting a potential predator, because conflicts can arise within pairs of fish in these circumstances which I argue resemble a series of games of Prisoner's Dilemma. Using a system of mirrors, single three-spined sticklebacks (Gasterosteus aculeatus) approaching a live predator were provided with either a simulated cooperating companion or a simulated defecting one. In both cases the test fish behaved according to TIT FOR TAT supporting the hypothesis that cooperation can evolve among egoists.
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A long-standing problem in biological and social sciences is to understand the conditions required for the emergence and maintenance of cooperation in evolving populations. For many situations, kin selection is an adequate explanation, although kin-recognition may still be a problem. Explanations of cooperation between non-kin include continuing interactions that provide a shadow of the future (that is, the expectation of an ongoing relationship) that can sustain reciprocity, possibly supported by mechanisms to bias interactions such as embedding the agents in a two-dimensional space or other context-preserving networks. Another explanation, indirect reciprocity, applies when benevolence to one agent increases the chance of receiving help from others. Here we use computer simulations to show that cooperation can arise when agents donate to others who are sufficiently similar to themselves in some arbitrary characteristic. Such a characteristic, or 'tag', can be a marking, display, or other observable trait. Tag-based donation can lead to the emergence of cooperation among agents who have only rudimentary ability to detect environmental signals and, unlike models of direct or indirect reciprocity, no memory of past encounters is required.
We address the problem of how to reinforce learning in ultracomplex environments, with huge state-spaces, where one must learn to exploit a compact structure of the problem domain. The approach we propose is to simulate the evolution of an artificial economy of computer programs. The economy is constructed based on two simple principles so as to assign credit to the individual programs for collaborating on problem solutions. We find empirically that starting from programs that are random computer code, we can develop systems that solve hard problems. In particular, our economy learned to solve almost all random Blocks World problems with goal stacks that are 200 blocks high. Competing methods solve such problems only up to goal stacks of at most 8 blocks. Our economy has also learned to unscramble about half a randomly scrambled Rubik's cube and to solve several commercially sold puzzles.
A fundamental problem in biology is the evolutionary transition from single cells to multicellular life forms. During this transition the unit of selection shifts from individual cells to groups of cooperating cells. Although there is much theory, there are few empirical studies. Here we describe an evolutionary transition that occurs in experimental populations of Pseudomonas fluorescens propagated in a spatially heterogeneous environment. Cooperating groups are formed by over-production of an adhesive polymer, which causes the interests of individuals to align with those of the group. The costs and benefits of cooperation, plus evolutionary susceptibility to defecting genotypes, were analysed to determine conformation to theory. Cooperation was costly to individuals, but beneficial to the group. Defecting genotypes evolved in populations founded by the cooperating type and were fitter in the presence of this type than in its absence. In the short term, defectors sabotaged the viability of the group; but these findings nevertheless show that transitions to higher orders of complexity are readily achievable, provide insights into the selective conditions, and facilitate experimental analysis of the evolution of individuality.
A basic evolutionary problem posed by the Iterated Prisoner's Dilemma game is to understand when the paradigmatic cooperative strategy Tit-for-Tat can invade a population of pure defectors. Deterministically, this is impossible. We consider the role of demographic stochasticity by embedding the Iterated Prisoner's Dilemma into a population dynamic framework. Tit-for-Tat can invade a population of defectors when their dynamics exhibit short episodes of high population densities with subsequent crashes and long low density periods with strong genetic drift. Such dynamics tend to have reddened power spectra and temporal distributions of population size that are asymmetric and skewed toward low densities. The results indicate that ecological dynamics are important for evolutionary shifts between adaptive peaks.
Animals often aid others without gaining any immediate benefits. Although these acts seem to reduce the donor's fitness, they are only apparently altruistic. Donors typically help because they or their kin receive future benefits or avoid costly punishment. Reciprocal altruism--alternating the roles of donor and recipient--has been a well-studied form of cooperation among non-kin because of its intuitive appeal in explaining human cooperation. Despite immense theoretical interest, little empirical evidence substantiates the biological importance of reciprocal altruism in non-human animals. We propose that this is because psychological mechanisms constrain its application in cooperative contexts. In particular, we contend that cognitive limitations such as temporal discounting, numerical discrimination and memory make reciprocity difficult for animals.
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