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PubMed1999

Variable investment, the Continuous Prisoner's Dilemma, and the origin of cooperation.

Cooperation is fundamental to many biological systems. A common metaphor for studying the evolution of cooperation is the Prisoner's Dilemma, a game with two strategies: cooperate or defect. However, cooperation is rare all or nothing, and its evolution probably involves the gradual extension of initially modest degrees of assistance. The inability of the Prisoner's Dilemma to capture this basic aspect limits its use for understanding the evolutionary origins of cooperation. Here we consider a framework for cooperation based on the concept of investment: an act which is costly, but which benefits other individuals, where the cost and benefit depend on the level of investment made. In the resulting Continuous Prisoner's Dilemma the essential problem of cooperation remains: in the absence of any additional structure non-zero levels of investment cannot evolve. However, if investments are considered in a spatially structured context, selfish individuals who make arbitrarily low investments can be invaded by higher-investing mutants. This results in the mean level of investment evolving to significant levels, where it is maintained indefinitely. This approach provides a natural solution to the fundamental problem of how cooperation gradually increases from a non-cooperative state.

Biological Evolution↗
PubMed2004

Effects of neighbourhood size and connectivity on the spatial Continuous Prisoner's Dilemma.

The Prisoner's Dilemma, a two-person game in which the players can either cooperate or defect, is a common paradigm for studying the evolution of cooperation. In real situations cooperation is almost never all or nothing. This observation is the motivation for the Continuous Prisoner's Dilemma, in which individuals exhibit variable degrees of cooperation. It is known that in the presence of spatial structure, when individuals "play against" (i.e. interact with) their neighbours, and "compare to" ("learn from") them, cooperative investments can evolve to considerable levels. Here, we examine the effect of increasing the neighbourhood size: we find that the mean-field limit of no cooperation is reached for a critical neighbourhood size of about five neighbours on each side in a Moore neighbourhood, which does not depend on the size of the spatial lattice. We also find the related result that in a network of players, the critical average degree (number of neighbours) of nodes for which defection is the final state does not depend on network size, but only on the network topology. This critical average degree is considerably (about 10 times) higher for clustered (social) networks, than for distributed random networks. This result strengthens the argument that clustering is the mechanism which makes the development and maintenance of the cooperation possible. In the lattice topology, it is observed that when the neighbourhood sizes for "interacting" and "learning" differ by more than 0.5, cooperation is not sustainable, even for neighbourhood sizes that are below the mean-field limit of defection. We also study the evolution of neighbourhood sizes, as well as investment level. Here, we observe that the series of the interaction and learning neighbourhoods converge, and a final cooperative state with considerable levels of average investment is achieved.

Animals↗
PubMed2006

Cooperation prevails when individuals adjust their social ties.

Conventional evolutionary game theory predicts that natural selection favours the selfish and strong even though cooperative interactions thrive at all levels of organization in living systems. Recent investigations demonstrated that a limiting factor for the evolution of cooperative interactions is the way in which they are organized, cooperators becoming evolutionarily competitive whenever individuals are constrained to interact with few others along the edges of networks with low average connectivity. Despite this insight, the conundrum of cooperation remains since recent empirical data shows that real networks exhibit typically high average connectivity and associated single-to-broad-scale heterogeneity. Here, a computational model is constructed in which individuals are able to self-organize both their strategy and their social ties throughout evolution, based exclusively on their self-interest. We show that the entangled evolution of individual strategy and network structure constitutes a key mechanism for the sustainability of cooperation in social networks. For a given average connectivity of the population, there is a critical value for the ratio W between the time scales associated with the evolution of strategy and of structure above which cooperators wipe out defectors. Moreover, the emerging social networks exhibit an overall heterogeneity that accounts very well for the diversity of patterns recently found in acquired data on social networks. Finally, heterogeneity is found to become maximal when W reaches its critical value. These results show that simple topological dynamics reflecting the individual capacity for self-organization of social ties can produce realistic networks of high average connectivity with associated single-to-broad-scale heterogeneity. On the other hand, they show that cooperation cannot evolve as a result of "social viscosity" alone in heterogeneous networks with high average connectivity, requiring the additional mechanism of topological co-evolution to ensure the survival of cooperative behaviour.

Biological Evolution↗
PubMed2001

Experimental evidence for kin-biased helping in a cooperatively breeding vertebrate.

The widespread belief that kin selection is necessary for the evolution of cooperative breeding in vertebrates has recently been questioned. These doubts have primarily arisen because of the paucity of unequivocal evidence for kin preferences in cooperative behaviour. Using the cooperative breeding system of long-tailed tits (Aegithalos caudatus) in which kin and non-kin breed within each social unit and helpers are failed breeders, we investigated whether helpers preferentially direct their care towards kin following breeding failure. First, using observational data, we show that not all failed breeders actually become helpers, but that those that do help usually do so at the nest of a close relative. Second, we confirm the importance of kinship for helping in this species by conducting a choice experiment. We show that potential helpers do not become helpers in the absence of close kin and, when given a choice between helping equidistant broods belonging to kin and non-kin within the same social unit, virtually all helped at the nest of kin. This study provides strong evidence that kinship plays an essential role in the maintenance of cooperative breeding in this species.

Animals↗
PubMed1998

Working memory constrains human cooperation in the Prisoner's Dilemma.

Many problems in human society reflect the inability of selfish parties to cooperate. The "Iterated Prisoner's Dilemma" has been used widely as a model for the evolution of cooperation in societies. Axelrod's computer tournaments and the extensive simulations of evolution by Nowak and Sigmund and others have shown that natural selection can favor cooperative strategies in the Prisoner's Dilemma. Rigorous empirical tests, however, lag behind the progress made by theorists. Clear predictions differ depending on the players' capacity to remember previous rounds of the game. To test whether humans use the kind of cooperative strategies predicted, we asked students to play the iterated Prisoner's Dilemma game either continuously or interrupted after each round by a secondary memory task (i.e., playing the game "Memory") that constrained the students' working-memory capacity. When playing without interruption, most students used "Pavlovian" strategies, as predicted, for greater memory capacity, and the rest used "generous tit-for-tat" strategies. The proportion of generous tit-for-tat strategies increased when games of Memory interfered with the subjects' working memory, as predicted. Students who continued to use complex Pavlovian strategies were less successful in the Memory game, but more successful in the Prisoner's Dilemma, which indicates a trade-off in memory capacity for the two tasks. Our results suggest that the set of strategies predicted by game theorists approximates human reality.

Biological Evolution↗
PubMed2004

Folding stabilizes the evolution of catalysts.

Sequence folding is known to determine the spatial structure and catalytic function of proteins and nucleic acids. We show here that folding also plays a key role in enhancing the evolutionary stability of the intermolecular recognition necessary for the prevalent mode of catalytic action in replication, namely, in trans, one molecule catalyzing the replication of another copy, rather than itself. This points to a novel aspect of why molecular life is structured as it is, in the context of life as it could be: folding allows limited, structurally localized recognition to be strongly sensitive to global sequence changes, facilitating the evolution of cooperative interactions. RNA secondary structure folding, for example is shown to be able to stabilize the evolution of prolonged functional sequences, using only a part of this length extension for intermolecular recognition, beyond the limits of the (cooperative) error threshold. Such folding could facilitate the evolution of polymerases in spatially heterogeneous systems. This facilitation is, in fact, vital because physical limitations prevent complete sequence-dependent discrimination for any significant-size biopolymer substrate. The influence of partial sequence recognition between biopolymer catalysts and complex substrates is investigated within a stochastic, spatially resolved evolutionary model of trans catalysis. We use an analytically tractable nonlinear master equation formulation called PRESS (McCaskill et al., Biol. Chem. 382: 1343-1363), which makes use of an extrapolation of the spatial dynamics down from infinite dimensional space, and compare the results with Monte Carlo simulations.

Catalysis↗
PubMed2026

Pattern Formation in a Spatial Public Goods Dilemma due to Diffusive or Directed Motion.

The costly provision of public goods serves as a model problem for the evolution of cooperative behavior, presenting a social dilemma between the collective benefits of shared resources and the individual incentive to free-ride in resource production. The spatial structure of populations can also impact cooperation over public goods, as diffusion of public goods and intentional motion of individuals towards regions with greater resources can interact with population and public goods dynamics to produce heterogeneous patterns in the spatial distribution of strategies and resources. In this paper, we build off a model introduced by Young and Belmonte for the reaction dynamics of interacting individuals and an explicit public good, deriving a system of PDEs that describes the spatial profiles of strategies and the public good in the presence of both diffusive motion of individuals and resources and chemotaxis-like directed motion of individuals in response to gradients in the concentration of public goods. Through linear stability analysis, we show that spatial patterns in strategic and public goods profiles can emerge due to either Turing instability with high defector diffusivity or a directed-motion instability through strong sensitivity of cooperators towards increasing resource concentration. We further explore the emergent spatial patterns with a mix of weakly nonlinear stability analysis and numerical simulation, showing that, for a wide range of reaction parameters, diffusion-driven instability appears to increase cooperation and public goods across the spatial domain, while directed motion of cooperators towards public goods tends to decrease cooperation and environmental quality across the environment.

Models, Biological↗
PubMed1996

The robustness of cognitively simple judgment in ecologies of Prisoner's Dilemma games.

Various authors have pointed to the fitness advantage from a capacity to recognize others' intentions in prisoner's dilemma games, yet cognitive mechanisms supporting such perceptiveness might be no more efficient than the simple and presumably inexpensive rule to 'assume that potential partners have the same behavioral intentions as yourself.' Laboratory findings have shown that this projecting heuristic can support the evolution of cooperative behavior absent perceptiveness, but that rule might be vulnerable to invasion by perceptive mutations. This paper shows that perceptive mutants are more likely to destroy an entire ecology of projectors (that would otherwise survive and prosper) than to successfully invade it, while projecting mutants have considerable success invading a population of perceptives. Mutant projectors' success happens when a cooperative ecology is created for them by the initial success of perceptive cooperators; within such an ecology, cooperative projectors have a competitive advantage over cooperative perceptives. Critical parameters are (1) the incidence of cooperativeness in the population and (2) the price of perceptiveness.

Biological Evolution↗
PubMed2000

Towards a unified theory of cooperative breeding: the role of ecology and life history re-examined.

We present quantitative models that unify several adaptive hypotheses for the evolution of cooperative breeding in a single framework: the ecological constraints hypothesis, the life-history hypothesis and the benefits-of-philopatry hypothesis. Our goal is to explain interspecific variation in the occurrence of cooperative breeding in terms of interspecific variation in life-history traits and ecological conditions. We analyse two models, according to whether or not helpers can inherit their parents' territory. Major results are (i) territory inheritance always promotes cooperative breeding; (ii) if territories are not inherited, neither ecological constraints nor variation in life-history traits predict interspecific variation in cooperative breeding; and (iii) if territories are inherited, the mechanism of density regulation is crucial in determining which factors promote cooperative breeding. If density dependence acts on the probability to obtain a free territory or on the survival of dispersers, variation in ecological constraints cannot explain variation in cooperative breeding. Lower adult mortality favours helping, not because it reduces the availability of free territories, but because it enhances the direct benefits of helpers. If density dependence acts on fecundity, lower probability of obtaining a free territory and lower survival of dispersers promote cooperative breeding. In this case, lower adult mortality works against the evolution of helping. We suggest that the difference between birds and social insects in the covariance between cooperative breeding and life-history traits is due to different mechanisms of density regulation that operate in these taxa, and we explain how natural selection on habitat choice might have caused these different mechanisms to operate.

Animals↗
PubMed2004

The evolutionary origin of cooperators and defectors.

Coexistence of cooperators and defectors is common in nature, yet the evolutionary origin of such social diversification is unclear. Many models have been studied on the basis of the assumption that benefits of cooperative acts only accrue to others. Here, we analyze the continuous snowdrift game, in which cooperative investments are costly but yield benefits to others as well as to the cooperator. Adaptive dynamics of investment levels often result in evolutionary diversification from initially uniform populations to a stable state in which cooperators making large investments coexist with defectors who invest very little. Thus, when individuals benefit from their own actions, large asymmetries in cooperative investments can evolve.

Altruism↗
PubMed2005

Contingent movement and cooperation evolve under generalized reciprocity.

How cooperation and altruism among non-relatives can persist in the face of cheating remains a key puzzle in evolutionary biology. Although mechanisms such as direct and indirect reciprocity and limited movement have been put forward to explain such cooperation, they cannot explain cooperation among unfamiliar, highly mobile individuals. Here we show that cooperation may be evolutionarily stable if decisions taken to cooperate and to change group membership are both dependent on anonymous social experience (generalized reciprocity). We find that a win-stay, lose-shift rule (where shifting is either moving away from the group or changing tactics within the group after receiving defection) evolves in evolutionary simulations when group leaving is moderately costly (i.e. the current payoff to being alone is low, but still higher than that in a mutually defecting group, and new groups are rarely encountered). This leads to the establishment of widespread cooperation in the population. If the costs of group leaving are reduced, a similar group-leaving rule evolves in association with cooperation in pairs and exploitation of larger anonymous groups. We emphasize that mechanisms of assortment within populations are often behavioural decisions and should not be considered independently of the evolution of cooperation.

Animals↗
PubMed1996

Human cooperation in the simultaneous and the alternating Prisoner's Dilemma: Pavlov versus Generous Tit-for-Tat.

The iterated Prisoner's Dilemma has become the paradigm for the evolution of cooperation among egoists. Since Axelrod's classic computer tournaments and Nowak and Sigmund's extensive simulations of evolution, we know that natural selection can favor cooperative strategies in the Prisoner's Dilemma. According to recent developments of theory the last champion strategy of "win--stay, lose--shift" ("Pavlov") is the winner only if the players act simultaneously. In the more natural situation of players alternating the roles of donor and recipient a strategy of "Generous Tit-for-Tat" wins computer simulations of short-term memory strategies. We show here by experiments with humans that cooperation dominated in both the simultaneous and the alternating Prisoner's Dilemma. Subjects were consistent in their strategies: 30% adopted a Generous Tit-for-Tat-like strategy, whereas 70% used a Pavlovian strategy in both the alternating and the simultaneous game. As predicted for unconditional strategies, Pavlovian players appeared to be more successful in the simultaneous game whereas Generous Tit-for-Tat-like players achieved higher payoffs in the alternating game. However, the Pavlovian players were smarter than predicted: they suffered less from defectors and exploited cooperators more readily. Humans appear to cooperate either with a Generous Tit-for-Tat-like strategy or with a strategy that appreciates Pavlov's advantages but minimizes its handicaps.

Journal Article↗
PubMed2003

Evolution of signal emission by non-infested plants growing near infested plants to avoid future risk.

Several plant species indirectly defend themselves against herbivory by attracting natural enemies of herbivores by releasing signal chemicals when infested. Previous empirical research suggested that the chemical signals also reflexively induce signal emission by neighboring undamaged plants. We hypothesize that such a reflexively induced signal is a defensive strategy used by undamaged plants to avoid possible future risk. Using a mathematical model, we show that this defense against future risk can evolve if the following conditions are met: (1) the cost of the signal is small relative to the cost of damage by infestation, (2) the attractiveness of the signal to natural enemies is positively correlated with the local density of the signal chemical, (3) plants with infested neighbors are at greater risk than those without infested neighbors, and (4) the lifespan of plants is long compared with that of herbivores. We also discuss the relationship between our model and recent models of the evolution of cooperation.

Animals↗
PubMed2005

Importance of cooperation and affiliation in the evolution of primate sociality.

The idea that competition and aggression are central to an understanding of the origins of group-living and sociality among human and nonhuman primates is the dominant theory in primatology today. Using this paradigm, researchers have focused their attention on competitive and aggressive behaviors, and have tended to overlook the importance of cooperative and affiliative behaviors. However, cooperative and affiliative behaviors are considerably more common than agonistic behaviors in all primate species. The current paradigm often fails to explain the context, function, and social tactics underlying affiliative and agonistic behavior. Here, we present data on a basic question of primate sociality: how much time do diurnal, group-living primates spend in social behavior, and how much of this time is affiliative and agonistic? These data are derived from a survey of 81 studies, including 28 genera and 60 species. We find that group-living prosimians, New World monkeys, Old World monkeys, and apes usually devote less than 10% of their activity budget to active social interactions. Further, rates of agonistic behaviors are extremely low, normally less than 1% of the activity budget. If the cost to the actors of affiliative behavior is low even if the rewards are low or extremely variable, we should expect affiliation and cooperation to be frequent. This is especially true under conditions in which individuals benefit from the collective environment of living in stable social groups.

Activity Cycles↗
PubMed1994

Spatial games and the maintenance of cooperation.

The Prisoner's Dilemma (PD) is a widely employed metaphor for problems associated with the evolution of cooperative behavior. We have recently proposed an alternative approach to the PD, by exploring "spatial games" in which players--who are either pure cooperators, C, or pure defectors, D--interact with neighbors in some spatial array; in each generation, players add up the scores from all encounters, and in the next generation a given cell is retained by its previous owner or taken over by a neighbor, depending on who has the largest score. Over a wide range of the relevant parameters, we find that C and D persist together indefinitely (without any of the complex strategies that remember past encounters, and anticipate future ones, which characterize essentially all previous work on the iterated PD). Our earlier work, however, dealt with symmetric spatial lattices in two dimensions, deterministic winning and discrete time. We show here that the essential results remain valid in more realistic situations where the spatial distributions of cells are random in two or three dimensions, and where winning is partly probabilistic (rather than being determined by the largest local total). The essential results also remain valid (pace Huberman and Glance [Huberman, B. A. & Glance, N. S. (1993) Proc. Natl. Acad. Sci. USA 90, 7716-7718]) when interactions occur in continuous rather than discrete time.

Cooperative Behavior↗
PubMed1996

Cooperation and conflict in the evolution of individuality. II. Conflict mediation.

Evolutionary transitions in the units of selection require the promotion of cooperation and the regulation of conflict among the lower level units. For multicellular organisms to emerge as a new unit of selection, the selfish tendencies of their component cells had to be controlled. Theoretical results indicate organisms may regulate this internal conflict and competition in several ways: by reducing the somatic mutation rate, by sequestering cells in a germ line and by directly reducing the benefits to cell of defecting.

Animals↗