Evolution of cooperation with shared costs and benefits

The quest to determine how cooperation evolves can be based on evolutionary game theory, in spite of the fact that evolutionarily stable strategies (ESS) for most non-zero-sum games are not cooperative. We analyse the evolution of cooperation for a family of evolutionary games involving shared costs and benefits with a continuum of strategies from non-cooperation to total cooperation. This cost-benefit game allows the cooperator to share in the benefit of a cooperative act, and the recipient to be burdened with a share of the cooperator's cost. The cost-benefit game encompasses the Prisoner's Dilemma, Snowdrift game and Partial Altruism. The models produce ESS solutions of total cooperation, partial cooperation, non-cooperation and coexistence between cooperation and non-cooperation. Cooperation emerges from an interplay between the nonlinearities in the cost and benefit functions. If benefits increase at a decelerating rate and costs increase at an accelerating rate with the degree of cooperation, then the ESS has an intermediate level of cooperation. The game also exhibits non-ESS points such as unstable minima, convergent-stable minima and unstable maxima. The emergence of cooperative behaviour in this game represents enlightened self-interest, whereas non-cooperative solutions illustrate the Tragedy of the Commons. Games having either a stable maximum or a stable minimum have the property that small changes in the incentive structure (model parameter values) or culture (starting frequencies of strategies) result in correspondingly small changes in the degree of cooperation. Conversely, with unstable maxima or unstable minima, small changes in the incentive structure or culture can result in a switch from non-cooperation to total cooperation (and vice versa). These solutions identify when human or animal societies have the potential for cooperation and whether cooperation is robust or fragile.     

A new route to the evolution of cooperation

The Prisoner's Dilemma (PD) constitutes a widely used metaphor to investigate problems related to the evolution of cooperation. Whenever evolution takes place in well-mixed populations engaged in single rounds of the PD, cooperators cannot resist invasion by defectors, a feature, which is somewhat alleviated whenever populations are spatially distributed. In both cases the populations are characterized by a homogeneous pattern of connectivity, in which every individual is equivalent, sharing the same number of neighbours. Recently, compelling evidence has been accumulated on the strong heterogeneous nature of the network of contacts between individuals in populations. Here we describe the networks of contacts in terms of graphs and show that heterogeneity provides a new mechanism for cooperation to survive. Specifically, we show that cooperators are capable of exploring the heterogeneity of the population structure to become evolutionary competitive. As a result, cooperation becomes the dominating trait in scale-free networks of contacts in which the few highly connected individuals are directly inter-connected, in this way contributing to self-sustain cooperation.     

The importance of mechanisms for the evolution of cooperation

Studies aimed at explaining the evolution of phenotypic traits have often solely focused on fitness considerations, ignoring underlying mechanisms. In recent years, there has been an increasing call for integrating mechanistic perspectives in evolutionary considerations, but it is not clear whether and how mechanisms affect the course and outcome of evolution. To study this, we compare four mechanistic implementations of two well-studied models for the evolution of cooperation, the Iterated Prisoner''s Dilemma (IPD) game and the Iterated Snowdrift (ISD) game. Behavioural strategies are either implemented by a 1 : 1 genotype–phenotype mapping or by a simple neural network. Moreover, we consider two different scenarios for the effect of mutations. The same set of strategies is feasible in all four implementations, but the probability that a given strategy arises owing to mutation is largely dependent on the behavioural and genetic architecture. Our individual-based simulations show that this has major implications for the evolutionary outcome. In the ISD, different evolutionarily stable strategies are predominant in the four implementations, while in the IPD each implementation creates a characteristic dynamical pattern. As a consequence, the evolved average level of cooperation is also strongly dependent on the underlying mechanism. We argue that our findings are of general relevance for the evolution of social behaviour, pleading for the integration of a mechanistic perspective in models of social evolution.     

The nearly neutral and selection theories of molecular evolution under the fisher geometrical framework: substitution rate, population size, and complexity

The general theories of molecular evolution depend on relatively arbitrary assumptions about the relative distribution and rate of advantageous, deleterious, neutral, and nearly neutral mutations. The Fisher geometrical model (FGM) has been used to make distributions of mutations biologically interpretable. We explored an FGM-based molecular model to represent molecular evolutionary processes typically studied by nearly neutral and selection models, but in which distributions and relative rates of mutations with different selection coefficients are a consequence of biologically interpretable parameters, such as the average size of the phenotypic effect of mutations and the number of traits (complexity) of organisms. A variant of the FGM-based model that we called the static regime (SR) represents evolution as a nearly neutral process in which substitution rates are determined by a dynamic substitution process in which the population's phenotype remains around a suboptimum equilibrium fitness produced by a balance between slightly deleterious and slightly advantageous compensatory substitutions. As in previous nearly neutral models, the SR predicts a negative relationship between molecular evolutionary rate and population size; however, SR does not have the unrealistic properties of previous nearly neutral models such as the narrow window of selection strengths in which they work. In addition, the SR suggests that compensatory mutations cannot explain the high rate of fixations driven by positive selection currently found in DNA sequences, contrary to what has been previously suggested. We also developed a generalization of SR in which the optimum phenotype can change stochastically due to environmental or physiological shifts, which we called the variable regime (VR). VR models evolution as an interplay between adaptive processes and nearly neutral steady-state processes. When strong environmental fluctuations are incorporated, the process becomes a selection model in which evolutionary rate does not depend on population size, but is critically dependent on the complexity of organisms and mutation size. For SR as well as VR we found that key parameters of molecular evolution are linked by biological factors, and we showed that they cannot be fixed independently by arbitrary criteria, as has usually been assumed in previous molecular evolutionary models.     

Cooperation and the evolution of intelligence

The high levels of intelligence seen in humans, other primates, certain cetaceans and birds remain a major puzzle for evolutionary biologists, anthropologists and psychologists. It has long been held that social interactions provide the selection pressures necessary for the evolution of advanced cognitive abilities (the 'social intelligence hypothesis'), and in recent years decision-making in the context of cooperative social interactions has been conjectured to be of particular importance. Here we use an artificial neural network model to show that selection for efficient decision-making in cooperative dilemmas can give rise to selection pressures for greater cognitive abilities, and that intelligent strategies can themselves select for greater intelligence, leading to a Machiavellian arms race. Our results provide mechanistic support for the social intelligence hypothesis, highlight the potential importance of cooperative behaviour in the evolution of intelligence and may help us to explain the distribution of cooperation with intelligence across taxa.     

The evolution of altruism: Correlation,cost, and benefit

A simple and general criterion is derived for the evolution of altruism when individuals interact in pairs. It is argued that the treatment of this problem in kin selection theory and in game theory are special cases of this general criterion.My thanks to James Crow, Carter Denniston, Lee Dugarkin, David Wilson, and an anonymous referee of this journal for helpful discussion.     

The option to leave: Conditional dissociation in the evolution of cooperation

Conditional dissociation, i.e. the option to leave an interacting partner in response to his behaviour, is a mechanism that has been shown to promote cooperation in several settings, but the fundamental features that make conditional dissociation work in this way are not yet fully understood. This paper identifies some of the key conditions that make conditional dissociation lead to high levels of cooperation, explains how this mechanism can support the evolutionary coexistence of cooperative and non-cooperative behaviour typically observed in nature, and provides an analytical formula to estimate the expected degree of cooperation thus achieved. Our model involves a population of individuals who are paired to play an iterated prisoner’s dilemma. All individuals share the same capacity to react to the action previously chosen by their partner and, without any other a priori constraint or exclusion, they may use any behavioural rule that is compatible with this capacity. The dynamic evolution of the population eventually enters either a non-cooperative or a partially cooperative regime, depending mainly on the expected lifetime of individuals. Whenever the partially cooperative regime materializes, the cornerstone of its long-run stability is the coexistence of defectors and “Out-for-Tat” strategists, the latter being those who start cooperating and respond to defection by merely leaving. We find, therefore, that conditional dissociation is the essential disciplinary device supporting cooperation, whilst other conditional strategies (such as Tit-for-Tat) remain present only in small population shares. These conclusions are obtained both by extensive numerical simulations and through analytical mean-field methods that approximate the stochastic simulation dynamics and deliver accurate predictions for general parameter configurations.     

The contribution of the y chromosome to hybrid male sterility in house mice

Hybrid sterility in the heterogametic sex is a common feature of speciation in animals. In house mice, the contribution of the Mus musculus musculus X chromosome to hybrid male sterility is large. It is not known, however, whether F(1) male sterility is caused by X-Y or X-autosome incompatibilities or a combination of both. We investigated the contribution of the M. musculus domesticus Y chromosome to hybrid male sterility in a cross between wild-derived strains in which males with a M. m. musculus X chromosome and M. m. domesticus Y chromosome are partially sterile, while males from the reciprocal cross are reproductively normal. We used eight X introgression lines to combine different X chromosome genotypes with different Y chromosomes on an F(1) autosomal background, and we measured a suite of male reproductive traits. Reproductive deficits were observed in most F(1) males, regardless of Y chromosome genotype. Nonetheless, we found evidence for a negative interaction between the M. m. domesticus Y and an interval on the M. m. musculus X that resulted in abnormal sperm morphology. Therefore, although F(1) male sterility appears to be caused mainly by X-autosome incompatibilities, X-Y incompatibilities contribute to some aspects of sterility.     

To kill a kangaroo: understanding the decision to pursue high-risk/high-gain resources

In this paper, we attempt to understand hunter–gatherer foraging decisions about prey that vary in both the mean and variance of energy return using an expected utility framework. We show that for skewed distributions of energetic returns, the standard linear variance discounting (LVD) model for risk-sensitive foraging can produce quite misleading results. In addition to creating difficulties for the LVD model, the skewed distributions characteristic of hunting returns create challenges for estimating probability distribution functions required for expected utility. We present a solution using a two-component finite mixture model for foraging returns. We then use detailed foraging returns data based on focal follows of individual hunters in Western Australia hunting for high-risk/high-gain (hill kangaroo) and relatively low-risk/low-gain (sand monitor) prey. Using probability densities for the two resources estimated from the mixture models, combined with theoretically sensible utility curves characterized by diminishing marginal utility for the highest returns, we find that the expected utility of the sand monitors greatly exceeds that of kangaroos despite the fact that the mean energy return for kangaroos is nearly twice as large as that for sand monitors. We conclude that the decision to hunt hill kangaroos does not arise simply as part of an energetic utility-maximization strategy and that additional social, political or symbolic benefits must accrue to hunters of this highly variable prey.     

Co-evolution of behaviour and social network structure promotes human cooperation

The ubiquity of cooperation in nature is puzzling because cooperators can be exploited by defectors. Recent theoretical work shows that if dynamic networks define interactions between individuals, cooperation is favoured by natural selection. To address this, we compare cooperative behaviour in multiple but independent repeated games between participants in static and dynamic networks. In the latter, participants could break their links after each social interaction. As predicted, we find higher levels of cooperation in dynamic networks. Through biased link breaking (i.e. to defectors) participants affected their social environment. We show that this link-breaking behaviour leads to substantial network clustering and we find primarily cooperators within these clusters. This assortment is remarkable because it occurred on top of behavioural assortment through direct reciprocity and beyond the perception of participants, and represents a self-organized pattern. Our results highlight the importance of the interaction between ecological context and selective pressures on cooperation.     

The behavioural ecology of personality: consistent individual differences from an adaptive perspective

Individual humans, and members of diverse other species, show consistent differences in aggressiveness, shyness, sociability and activity. Such intraspecific differences in behaviour have been widely assumed to be non‐adaptive variation surrounding (possibly) adaptive population‐average behaviour. Nevertheless, in keeping with recent calls to apply Darwinian reasoning to ever‐finer scales of biological variation, we sketch the fundamentals of an adaptive theory of consistent individual differences in behaviour. Our thesis is based on the notion that such ‘personality differences’ can be selected for if fitness payoffs are dependent on both the frequencies with which competing strategies are played and an individual's behavioural history. To this end, we review existing models that illustrate this and propose a game theoretic approach to analyzing personality differences that is both dynamic and state‐dependent. Our motivation is to provide insights into the evolution and maintenance of an apparently common animal trait: personality, which has far reaching ecological and evolutionary implications.     

Invasion of cooperators in lattice populations: Linear and non-linear public good games

A generalized version of the N-person volunteer's dilemma (NVD) Game has been suggested recently for illustrating the problem of N-person social dilemmas. Using standard replicator dynamics it can be shown that coexistence of cooperators and defectors is typical in this model. However, the question of how a rare mutant cooperator could invade a population of defectors is still open.     

The evolution of the animals: introduction to a Linnean tercentenary celebration

Celebrating 300 years since the birth of Carl Linnaeus (1707-1778), a meeting was held in June 2007 to review recent progress made in understanding the origins and evolutionary radiation of the animals. The year 2008 celebrates the 250th anniversary of the publication of the 10th edition of Linnaeus' Systema Naturae, generally considered to be the starting point of zoological nomenclature. With subsequent advances in comparative taxonomic and systematic studies, Darwin's discovery of evolution by natural selection, the birth of phylogenetic systematics, and the wider interest in biodiversity, it is salutary to consider that many of the major advances in our understanding of animal evolution have been made in recent years. Phylogenetic systematics, drawing from evidence provided by genotype, phenotype and an understanding of the link between them through comparative embryological and evolutionary developmental studies, has provided a wide consensus of the major branching patterns of the tree of life. More importantly, the integrated approaches discussed in the 16 contributions to this volume highlight the identity and nature of problematic taxa, the missing data, errors in existing analytical procedures and the promise of a wealth of additional characters from genomes that need to be accumulated and assessed in providing a definitive Systema Naturae.     

Modulating DNA configuration by interfacial traction: an elastic rod model to characterize DNA folding and unfolding

As a continuum model of DNA, a thin elastic rod subjected to interfacial interactions is used to investigate the equilibrium configuration of DNA in intracellular solution. The interfacial traction between the rod and the solution environment is derived in detail. Kirchhoff’s theory of elastic rods is used to analyze the equilibrium configuration of a DNA segment under the action of the interfacial traction. The influences of the interfacial energy factor and bending stiffness on the toroidal spool formation of the DNA segment are discussed. The results show that the equilibrium configuration of DNA is mainly determined by competition between the interfacial energy and elastic strain energy of the DNA itself, and the interfacial traction is one of the forces that drives DNA folding and unfolding.     

Effects of allometry,productivity and lifestyle on rates and limits of body size evolution

Body size affects nearly all aspects of organismal biology, so it is important to understand the constraints and dynamics of body size evolution. Despite empirical work on the macroevolution and macroecology of minimum and maximum size, there is little general quantitative theory on rates and limits of body size evolution. We present a general theory that integrates individual productivity, the lifestyle component of the slow–fast life-history continuum, and the allometric scaling of generation time to predict a clade''s evolutionary rate and asymptotic maximum body size, and the shape of macroevolutionary trajectories during diversifying phases of size evolution. We evaluate this theory using data on the evolution of clade maximum body sizes in mammals during the Cenozoic. As predicted, clade evolutionary rates and asymptotic maximum sizes are larger in more productive clades (e.g. baleen whales), which represent the fast end of the slow–fast lifestyle continuum, and smaller in less productive clades (e.g. primates). The allometric scaling exponent for generation time fundamentally alters the shape of evolutionary trajectories, so allometric effects should be accounted for in models of phenotypic evolution and interpretations of macroevolutionary body size patterns. This work highlights the intimate interplay between the macroecological and macroevolutionary dynamics underlying the generation and maintenance of morphological diversity.     

The evolution of matrilineal kinship organization

Matrilineal kinship organization is a human social system that emphasizes interactions between matrilineal kin, i.e. individuals related only through females. The ‘matrilineal puzzle’ refers to the potential for tension characteristic of this social system, owing to the conflict between the interests and responsibilities of men in their roles as brother/uncle versus husband/father. From an evolutionary perspective, matrilineal kinship organization is puzzling when it diverts investment of resources from the individuals who provide the potentially highest reproductive returns. I use a game-theoretic framework to investigate a particular form of matrilineal inheritance—the transfer of property from a maternal uncle to a sororal nephew. The analysis reveals two mechanisms that may make this strategy a stable evolutionary outcome. First, a polygynous male has multiple wives, and hence multiple brothers-in-law; with matrilineal inheritance, each additional brother-in-law may transfer resources to the male''s wife''s offspring, thus potentially contributing to the male''s inclusive fitness. Second, the husband of a polyandrous female is effectively ‘sharing’ paternity with other men; depending on the number of husbands, he may be better off investing in his sister''s offspring. I conclude by discussing how these results address the challenges posed by the occurrence of matrilineal kinship organization.     

Simulation of the evolution of root water foraging strategies in dry and shallow soils

Background and Aims

The dynamic structural development of plants can be seen as a strategy for exploiting the limited resources available within their environment, and we would expect that evolution would lead to efficient strategies that reduce costs while maximizing resource acquisition. In particular, perennial species endemic to habitats with shallow soils in seasonally dry environments have been shown to have a specialized root system morphology that may enhance access to water resources in the underlying rock. This study aimed to explore these hypotheses by applying evolutionary algorithms to a functional–structural root growth model.

Methods

A simulation model of a plant''s root system was developed, which represents the dynamics of water uptake and structural growth. The model is simple enough for evolutionary optimization to be computationally feasible, yet flexible enough to allow a range of structural development strategies to be explored. The model was combined with an evolutionary algorithm in order to investigate a case study habitat with a highly heterogeneous distribution of resources, both spatially and temporally – the situation of perennial plants occurring on shallow soils in seasonally dry environments. Evolution was simulated under two contrasting fitness criteria: (1) the ability to find wet cracks in underlying rock, and (2) maximizing above-ground biomass.

Key Results

The novel approach successfully resulted in the evolution of more efficient structural development strategies for both fitness criteria. Different rooting strategies evolved when different criteria were applied, and each evolved strategy made ecological sense in terms of the corresponding fitness criterion. Evolution selected for root system morphologies which matched those of real species from corresponding habitats.

Conclusions

Specialized root morphology with deeper rather than shallower lateral branching enhances access to water resources in underlying rock. More generally, the approach provides insights into both evolutionary processes and ecological costs and benefits of different plant growth strategies.     

Negotiation may lead selfish individuals to cooperate: the example of the collective vigilance game

Game-theoretical models have been highly influential in behavioural ecology. However, these models generally assume that animals choose their action before observing the behaviour of their opponents while, in many natural situations, individuals in fact continuously react to the actions of others. A negotiation process then takes place and this may fundamentally influence the individual attitudes and the tendency to cooperate. Here, I use the classical model system of vigilance behaviour to demonstrate the consequences of such behavioural negotiation among selfish individuals, by predicting patterns of vigilance in a pair of animals foraging under threat of predation. I show that the game played by the animals and the resulting vigilance strategies take radically different forms, according to the way predation risk is shared in the pair. In particular, if predators choose their target at random, the prey respond by displaying moderate vigilance and taking turns scanning. By contrast, if the individual that takes flight later in an attack endures a higher risk of being targeted, vigilance increases and there is always at least one sentinel in the pair. Finally, when lagging behind its companion in fleeing from an attacker becomes extremely risky, vigilance decreases again and the animals scan simultaneously.