The robustness of altruism as an evolutionary strategy

Kin selection, reciprocity and group selection are widely regarded as evolutionary mechanisms capable of sustaining altruism among humans andother cooperative species. Our research indicates, however, that these mechanisms are only particular examples of a broader set of evolutionary possibilities.In this paper we present the results of a series of simple replicator simulations, run on variations of the 2–player prisoner's dilemma, designed to illustrate the wide range of scenarios under which altruism proves to be robust under evolutionary pressures. The set of mechanisms we explore is divided into four categories:correlation, group selection, imitation, and punishment. We argue that correlation is the core phenomenon at work in all four categories.     

Evolution of cooperation: cooperation defeats defection in the cornfield model

"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.     

Cooperation driven by mutations in multi-person Prisoner's Dilemma

The n-person Prisoner's Dilemma is a widely used model for populations where individuals interact in groups. The evolutionary stability of populations has been analysed in the literature for the case where mutations in the population may be considered as isolated events. For this case, and assuming simple trigger strategies and many iterations per game, we analyse the rate of convergence to the evolutionarily stable populations. We find that for some values of the payoff parameters of the Prisoner's Dilemma this rate is so low that the assumption, that mutations in the population are infrequent on that time-scale, is unreasonable. Furthermore, the problem is compounded as the group size is increased. In order to address this issue, we derive a deterministic approximation of the evolutionary dynamics with explicit, stochastic mutation processes, valid when the population size is large. We then analyse how the evolutionary dynamics depends on the following factors: mutation rate, group size, the value of the payoff parameters, and the structure of the initial population. In order to carry out the simulations for groups of more than just a few individuals, we derive an efficient way of calculating the fitness values. We find that when the mutation rate per individual and generation is very low, the dynamics is characterized by populations which are evolutionarily stable. As the mutation rate is increased, other fixed points with a higher degree of cooperation become stable. For some values of the payoff parameters, the system is characterized by (apparently) stable limit cycles dominated by cooperative behaviour. The parameter regions corresponding to high degree of cooperation grow in size with the mutation rate, and in number with the group size. For some parameter values, we find more than one stable fixed point, corresponding to different structures of the initial population.     

The commons dilemma: A simulation testing the effects of resource visibility and territorial division

In a commons dilemma laboratory analog subjects were allowed individually to draw valuable points from a slowly regenerating pool. Subjects participated in groups of four and faced the dilemma of either rapidly drawing a large number of points for themselves (but thereby destroying the pool), or limiting their own harvesting so that the pool would regenerate, benefiting the group. All subjects were, in addition, informed of the optimum strategy for harvesting before the game began, but results showed that this strategy was rarely used. Two factors were added to the basic game: (1) dividing the resource pool into individual harvesting territories, and (2) making the varying levels of resources visible. Each of these increased the harvest and production of the resource, but only territoriality increased the supply. Only when both factors were applied together did the groups approach the optimal harvesting strategy earlier spelled out to them. Possible mediating variables and applications are discussed.This paper is based on a dissertation thesis by the first author conducted at Arizona State University entitled Territoriality and the Tragedy of the Commons: A Social Trap Analysis. Grateful appreciation is extended to D. Linder, R. Hershberger, S. Braver, I. Sandler, A. Betz, R. Cialdini, and E. P. Willems for their assistance and advice.     

Evolutionary dynamics of the continuous iterated prisoner's dilemma

The iterated prisoner's dilemma (IPD) has been widely used in the biological and social sciences to model dyadic cooperation. While most of this work has focused on the discrete prisoner's dilemma, in which actors choose between cooperation and defection, there has been some analysis of the continuous IPD, in which actors can choose any level of cooperation from zero to one. Here, we analyse a model of the continuous IPD with a limited strategy set, and show that a generous strategy achieves the maximum possible payoff against its own type. While this strategy is stable in a neighborhood of the equilibrium point, the equilibrium point itself is always vulnerable to invasion by uncooperative strategies, and hence subject to eventual destabilization. The presence of noise or errors has no effect on this result. Instead, generosity is favored because of its role in increasing contributions to the most efficient level, rather than in counteracting the corrosiveness of noise. Computer simulation using a single-locus infinite alleles Gaussian mutation model suggest that outcomes ranging from a stable cooperative polymorphism to complete collapse of cooperation are possible depending on the magnitude of the mutational variance. Also, making the cost of helping a convex function of the amount of help provided makes it more difficult for cooperative strategies to invade a non-cooperative equilibrium, and for the cooperative equilibrium to resist destabilization by non-cooperative strategies. Finally, we demonstrate that a much greater degree of assortment is required to destabilize a non-cooperative equilibrium in the continuous IPD than in the discrete IPD. The continuous model outlined here suggests that incremental amounts of cooperation lead to rapid decay of cooperation and thus even a large degree of assortment will not be sufficient to allow cooperation to increase when cooperators are rare. The extreme degree of assortment required to destabilize the non-cooperative equilibrium, as well as the instability of the cooperative equilibrium, may help explain why cooperation in Prisoner's Dilemmas is so rare in nature.     

A theory for exaggerated secondary sexual traits in animal-pollinated plants

We analyze two mathematical models of adaptive investment in rewarding plant traits. In both models, the attractiveness of a particular trait value declines as the mean value in the population increases (asymmetric competition), giving relatively rewarding traits a competitive advantage. Including this competition for pollinator visits in a standard model of hermaphroditic sex allocation shifts additional allocation to pollinator rewards at the expense of allocation to pollen and seeds. In the second model, plants can invest additional resources in pollinator rewards but suffer reduced viability and rising costs due to excess pollen removal and within-plant selfing (geitonogamy). Despite these accumulating costs, increasing the magnitude of asymmetric competition exaggerates the ESS investment in rewards beyond the equilibrium in cases where attractiveness depends only on a plant’s absolute reward value. We suggest that the type of frequency dependent selection modeled here is fundamentally equivalent to sexual selection in animal populations (with some unique exceptions). Testing the main assumptions of our models may reveal whether seemingly “extravagant” floral traits are strictly analogous to the exaggerated secondary sexual traits of animals. An erratum to this article can be found at     

具有Allee效应的合作进化

Allee效应对物种的续存是潜在的干扰因素,在很大程度上将增加种群局部甚至全局灭绝的可能性。对许多物种,尤其是濒临物种更容易受其影响。将Allee效应引入囚徒困境博弈模型,通过理论分析与数值模拟相结合的方法分析讨论了Allee效应对合作进化的影响。研究结果表明:在恶劣的环境条件下,Allee效应极易使物种灭绝,不利于合作进化;在相对优越的环境条件下(死亡率较低),Allee效应促进合作进化,且Allee效应强度越强,更有利于合作进化,不过种群的空间斑块占有率也会随着Allee效应强度的增强而降低,使物种最终灭绝。     

Carnivorous Cats,Vegetarian Dogs,and the Resolution of the Vegetarian's Dilemma

The present research sought to further clarify the vegetarian's dilemma, the conflict that pits feeding one's pet an animal-based diet that may be perceived as best promoting their well-being with concerns over animal welfare and environmental degradation threatened by such diets. It specifically examined whether non-meat eaters would distinguish between pet dogs and cats in the percentage of their diet derived from animal products, guilt experienced from such diets, and perceived appropriateness of non-vegetarian diets. Survey responses from 290 vegans and vegetarians indicated that participants fed their pet dogs a diet significantly more vegetarian than they fed their pet cats, and reported experiencing less guilt feeding their cats a diet derived highly from animals than in feeding their dogs such a diet. This lack of guilt largely arose from greater endorsement that vegetarian diets were more inappropriate for cats than dogs. For dogs, then, the vegetarian's dilemma was resolved primarily through feeding them diets reduced in meat/fish. For cats, the primary attempt at resolving the dilemma was not behavioral but perceptual in that vegetarian diets were deemed inappropriate. As discussed, this latter strategy was met with mixed success. Overall, the reaction of participants reflected prevailing medical wisdom that vegetarian diets are somewhat acceptable for dogs but problematic for cats.     

Size-dependent discrimination of mating partners in the simultaneous hermaphroditic cestode Schistocephalus solidus

The cestode Schistocephalus solidus is a simultaneous hermaphroditethat reproduces in the gut of birds, or for this study in an in vitro system that simulates the gut of the bird. Like manyother helminth parasites, S. solidus can reproduce by self-and cross-fertilization. Hermaphrodites are expected to matenot primarily to get their own eggs fertilized, but ratherto get the opportunity to fertilize a partner's eggs. BecauseS. solidus has a size-dependent sex allocation (i.e., largerworms are more biased toward female allocation and producemore egg mass), we expect larger individuals to be attractivemating partners for smaller ones. However, this may be a one-directionalpreference, as smaller individuals may not be attractive tolarger ones. We tested this experimentally by studying thereaction of focal worms of different sizes to a compartmentcontaining a potential mating partner that was either smalleror larger than the focal worm. The focal worms were, on average,closer to the compartment containing the stimulus than to anempty control compartment. Moreover, they indeed showed a preferencefor larger stimulus worms than for smaller ones. They eventended to avoid being close to stimulus worms of very smallsize compared to themselves. This may reveal a general preferencefor cross-fertilization over selfing, but it also indicatesthat all the genetic benefits from outcrossing do not necessarilyoutweigh the costs of mating with a relatively small individualand that the worms may take this into account in their reproductivedecisions.