When is bigger better? The effects of group size on the evolution of helping behaviours

Understanding the evolution of sociality in humans and other species requires understanding how selection on social behaviour varies with group size. However, the effects of group size are frequently obscured in the theoretical literature, which often makes assumptions that are at odds with empirical findings. In particular, mechanisms are suggested as supporting large‐scale cooperation when they would in fact rapidly become ineffective with increasing group size. Here we review the literature on the evolution of helping behaviours (cooperation and altruism), and frame it using a simple synthetic model that allows us to delineate how the three main components of the selection pressure on helping must vary with increasing group size. The first component is the marginal benefit of helping to group members, which determines both direct fitness benefits to the actor and indirect fitness benefits to recipients. While this is often assumed to be independent of group size, marginal benefits are in practice likely to be maximal at intermediate group sizes for many types of collective action problems, and will eventually become very small in large groups due to the law of decreasing marginal returns. The second component is the response of social partners on the past play of an actor, which underlies conditional behaviour under repeated social interactions. We argue that under realistic conditions on the transmission of information in a population, this response on past play decreases rapidly with increasing group size so that reciprocity alone (whether direct, indirect, or generalised) cannot sustain cooperation in very large groups. The final component is the relatedness between actor and recipient, which, according to the rules of inheritance, again decreases rapidly with increasing group size. These results explain why helping behaviours in very large social groups are limited to cases where the number of reproducing individuals is small, as in social insects, or where there are social institutions that can promote (possibly through sanctioning) large‐scale cooperation, as in human societies. Finally, we discuss how individually devised institutions can foster the transition from small‐scale to large‐scale cooperative groups in human evolution.     

Cooperation peaks at intermediate disturbance

Explaining cooperation is a challenge for evolutionary biology. Surprisingly, the role of extrinsic ecological parameters remains largely unconsidered. Disturbances are widespread in nature and have evolutionary consequences. We develop a mathematical model predicting that cooperative traits most readily evolve at intermediate disturbance. Under infrequent disturbance, cooperation breaks down through the accumulation of evolved cheats. Higher rates of disturbance prevent this because the resulting bottlenecks increase genetic structuring (relatedness) promoting kin selection for cooperation. However, cooperation cannot be sustained under very frequent disturbance if population density remains below the level required for successful cooperation. We tested these predictions by using cooperative biofilm formation by the bacterium Pseudomonas fluorescens. The proportion of biofilm-forming bacteria peaked at intermediate disturbance, in a manner consistent with model predictions. Under infrequent and intermediate disturbance, most bacteria occupied the biofilm, but the proportion of cheats was higher under less frequent disturbance. Under frequent disturbance, many bacteria did not occupy the biofilm, suggesting that biofilm dwelling was not as beneficial under frequent versus intermediate disturbance. Given the ubiquity of disturbances in nature, these results suggest that they may play a major role in the evolution of social traits in microbes.     

The hierarchy of virtue: mutualism, altruism and signaling in Martu women's cooperative hunting

Cooperative hunting is often assumed to be mutualistic, maintained through returns to scale, where, by working together, foragers can gain higher per capita return rates or harvest sizes than they can by hunting alone. We test this hypothesis among Martu hunters and find that cooperation only provides increased returns to poorer hunters while disadvantaging better hunters. Even so, better hunters still cooperate as frequently as poorer hunters. We ask whether better hunters are advantaged in secondary sharing distributions or whether they bias their partner choice to kin or household members. We find that better hunters are not more likely to pair up with kin and they do not gain consumption benefits from acquiring more. They share a greater proportion of their harvest than poorer hunters: no matter how much one produces — better hunter, worse hunter, cooperator, solitary hunter — all eat the same amount in the end. Such a result suggests the hypothesis that cooperation might be a costly signal of commitment to the public interest on the part of better hunters, which generates trust among camp members and facilitates strong social networks, particularly among women, who cooperate more than men. While some foragers may benefit through cooperation from returns to scale or risk reduction, others may benefit more through signaling commitment and generating trust.     

The ecology of cooperative breeding behaviour

Ecology is a fundamental driving force for the evolutionary transition from solitary living to breeding cooperatively in groups. However, the fact that both benign and harsh, as well as stable and fluctuating, environments can favour the evolution of cooperative breeding behaviour constitutes a paradox of environmental quality and sociality. Here, we propose a new model – the dual benefits framework – for resolving this paradox. Our framework distinguishes between two categories of grouping benefits – resource defence benefits that derive from group‐defended critical resources and collective action benefits that result from social cooperation among group members – and uses insider–outsider conflict theory to simultaneously consider the interests of current group members (insiders) and potential joiners (outsiders) in determining optimal group size. We argue that the different grouping benefits realised from resource defence and collective action profoundly affect insider–outsider conflict resolution, resulting in predictable differences in the per capita productivity, stable group size, kin structure and stability of the social group. We also suggest that different types of environmental variation (spatial vs. temporal) select for societies that form because of the different grouping benefits, thus helping to resolve the paradox of why cooperative breeding evolves in such different types of environments.     

Population bottlenecks promote cooperation in bacterial biofilms

Population bottlenecks are assumed to play a key role in the maintenance of social traits in microbes. Ecological parameters such as colonisation or disturbances can favour cooperation through causing population bottlenecks that enhance genetic structuring (relatedness). However, the size of the population bottleneck is likely to play a crucial role in determining the success of cooperation. Relatedness is likely to increase with decreasing bottleneck size thus favouring the evolution of cooperation. I used an experimental evolution approach to test this prediction with biofilm formation by the bacterium Pseudomonas fluorescens as the cooperative trait. Replicate populations were exposed to disturbance events every four days under one of six population bottleneck treatments (from 10(3) to 10(8) bacterial cells). In line with predictions, the frequency of evolved cheats within the populations increased with increasing bottleneck size. This result highlights the importance of ecologically mediated population bottlenecks in the maintenance of social traits in microbes.     

When to go with the crowd: Modelling synchronization of all-or-nothing activity transitions in grouped animals

For groups of animals to keep together, the group members have to perform switches between staying in one place and moving to another place in synchrony. However, synchronization imposes a cost on individual animals, because they have to switch from one to the other behaviour at a communal time rather than at their ideal times. Here we model this situation analytically for groups in which the ideal times vary quasinormally and grouping benefit increases linearly with group size. Across the parameter space consisting of variation in the grouping benefit/cost ratio and variation in how costly it is to act too early and too late, the most common optimal solutions are full synchronization with the group staying together and zero synchronization with immediate dissolution of the group, if the group is too small for the given benefit/cost ratio. Partial synchronization, with animals at the tails of the distribution switching individually and the central core of the group in synchrony, occurs only at a narrow stripe of the space. Synchronization cost never causes splitting of the group into two as either zero, partial or full synchronization is always more advantageous. Stable solutions dictate lower degree of synchrony and lower net benefits than optimal solutions for a large range of the parameter values. If groups undergo repeated synchronization challenges, they stay together or quickly dissolve, unless the animals assort themselves into a smaller group with less variation in the ideal times. We conclude with arguing that synchronization cost is different from other types of grouping costs since it does not increase much with increasing group size. As a result, larger groups may be more stable than smaller groups. This results in the paradoxical prediction that when the grouping benefit/grouping cost ratio increases, the average group sizes might decrease, since smaller groups will be able to withstand synchronization challenges.     

The concurrent evolution of cooperation and the population structures that support it

The evolution of cooperation often depends upon population structure, yet nearly all models of cooperation implicitly assume that this structure remains static. This is a simplifying assumption, because most organisms possess genetic traits that affect their population structure to some degree. These traits, such as a group size preference, affect the relatedness of interacting individuals and hence the opportunity for kin or group selection. We argue that models that do not explicitly consider their evolution cannot provide a satisfactory account of the origin of cooperation, because they cannot explain how the prerequisite population structures arise. Here, we consider the concurrent evolution of genetic traits that affect population structure, with those that affect social behavior. We show that not only does population structure drive social evolution, as in previous models, but that the opportunity for cooperation can in turn drive the creation of population structures that support it. This occurs through the generation of linkage disequilibrium between socio-behavioral and population-structuring traits, such that direct kin selection on social behavior creates indirect selection pressure on population structure. We illustrate our argument with a model of the concurrent evolution of group size preference and social behavior.     

Evolutionary causes and consequences of consistent individual variation in cooperative behaviour

Behaviour is typically regarded as among the most flexible of animal phenotypic traits. In particular, expression of cooperative behaviour is often assumed to be conditional upon the behaviours of others. This flexibility is a key component of many hypothesized mechanisms favouring the evolution of cooperative behaviour. However, evidence shows that cooperative behaviours are often less flexible than expected and that, in many species, individuals show consistent differences in the amount and type of cooperative and non-cooperative behaviours displayed. This phenomenon is known as ‘animal personality’ or a ‘behavioural syndrome’. Animal personality is evolutionarily relevant, as it typically shows heritable variation and can entail fitness consequences, and hence, is subject to evolutionary change. Here, we review the empirical evidence for individual variation in cooperative behaviour across taxa, we examine the evolutionary processes that have been invoked to explain the existence of individual variation in cooperative behaviour and we discuss the consequences of consistent individual differences on the evolutionary stability of cooperation. We highlight that consistent individual variation in cooperativeness can both stabilize or disrupt cooperation in populations. We conclude that recognizing the existence of consistent individual differences in cooperativeness is essential for an understanding of the evolution and prevalence of cooperation.     

Negative association between parental care and sibling cooperation in earwigs: a new perspective on the early evolution of family life?

The evolution of family life requires net fitness benefits for offspring, which are commonly assumed to mainly derive from parental care. However, an additional source of benefits for offspring is often overlooked: cooperative interactions among juvenile siblings. In this study, we examined how sibling cooperation and parental care could jointly contribute to the early evolution of family life. Specifically, we tested whether the level of food transferred among siblings (sibling cooperation) in the European earwig Forficula auricularia (1) depends on the level of maternal food provisioning (parental care) and (2) is translated into offspring survival, as well as female investment into future reproduction. We show that higher levels of sibling food transfer were associated with lower levels of maternal food provisioning, possibly reflecting a compensatory relationship between sibling cooperation and maternal care. Furthermore, the level of sibling food transfer did not influence offspring survival, but was associated with negative effects on the production of the second and terminal clutch by the tending mothers. These findings indicate that sibling cooperation could mitigate the detrimental effects on offspring survival that result from being tended by low‐quality mothers. More generally, they are in line with the hypothesis that sibling cooperation is an ancestral behaviour that can be retained to compensate for insufficient levels of parental investment.     

The Evolution of Quantitatively Responsive Cooperative Trade

The iterated Prisoner's Dilemma reflects the essence of repeated cooperative interactions with selfish incentives. However, the classical form of this game assumes that individuals either cooperate or defect, whereas in practice different degrees of cooperation are usually possible. To overcome this limitation, we present a model of alternating cooperative trade in which individuals controlled the costs they incurred in benefiting their partners. Since the range of possible strategies is enormous, competitively successful solutions were identified using a genetic algorithm, a powerful search technique in which good performers are iteratively selected and recombined from an initial "strategy soup". Beginning with a population of asocial individuals, altruistic behaviour readily emerged. Like the pre-defined strategy of "Raise-the-Stakes", the emerging strategies evolved protection from cheats by investing relatively little in strangers and subsequently responding quantitatively to a partner's altruism. Unlike "Raise-the-Stakes", they began trading relations at intermediate levels and, when the benefit-to-cost ratio of cooperation was relatively low, mean investment was considerably below the maximum level. Our approach is novel in allowing us to predict not just whether cooperation will occur, but how cooperative individuals will be, in relation to factors such as the number of rounds and the cost effectiveness of cooperative trade.     

Consequences of fluctuating group size for the evolution of cooperation

Studies of cooperation have traditionally focused on discrete games such as the well-known prisoner’s dilemma, in which players choose between two pure strategies: cooperation and defection. Increasingly, however, cooperation is being studied in continuous games that feature a continuum of strategies determining the level of cooperative investment. For the continuous snowdrift game, it has been shown that a gradually evolving monomorphic population may undergo evolutionary branching, resulting in the emergence of a defector strategy that coexists with a cooperator strategy. This phenomenon has been dubbed the ‘tragedy of the commune’. Here we study the effects of fluctuating group size on the tragedy of the commune and derive analytical conditions for evolutionary branching. Our results show that the effects of fluctuating group size on evolutionary dynamics critically depend on the structure of payoff functions. For games with additively separable benefits and costs, fluctuations in group size make evolutionary branching less likely, and sufficiently large fluctuations in group size can always turn an evolutionary branching point into a locally evolutionarily stable strategy. For games with multiplicatively separable benefits and costs, fluctuations in group size can either prevent or induce the tragedy of the commune. For games with general interactions between benefits and costs, we derive a general classification scheme based on second derivatives of the payoff function, to elucidate when fluctuations in group size help or hinder cooperation.     

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.     

Sex,long life and the evolutionary transition to cooperative breeding in birds

Long life is a typical feature of individuals living in cooperative societies. One explanation is that group living lowers mortality, which selects for longer life. Alternatively, long life may make the evolution of cooperation more likely by ensuring a long breeding tenure, making helping behaviour and queuing for breeding positions worthwhile. The benefit of queuing will, however, depend on whether individuals gain indirect fitness benefits while helping, which is determined by female promiscuity. Where promiscuity is high and therefore the indirect fitness benefits of helping are low, cooperation can still be favoured by an even longer life span. We present the results of comparative analyses designed to test the likelihood of a causal relationship between longevity and cooperative breeding by reconstructing ancestral states of cooperative breeding across birds, and by examining the effect of female promiscuity on the relationship between these two traits. We found that long life makes the evolution of cooperation more likely and that promiscuous cooperative species are exceptionally long lived. These results make sense of promiscuity in cooperative breeders and clarify the importance of life-history traits in the evolution of cooperative breeding, illustrating that cooperation can evolve via the combination of indirect and direct fitness benefits.     

DENSITY DEPENDENCE AND COOPERATION: THEORY AND A TEST WITH BACTERIA

Although cooperative systems can persist in nature despite the potential for exploitation by noncooperators, it is often observed that small changes in population demography can tip the balance of selective forces for or against cooperation. Here we consider the role of population density in the context of microbial cooperation. First, we account for conflicting results from recent studies by demonstrating theoretically that: (1) for public goods cooperation, higher densities are relatively unfavorable for cooperation; (2) in contrast, for self-restraint–type cooperation, higher densities can be either favorable or unfavorable for cooperation, depending on the details of the system. We then test our predictions concerning public goods cooperation using strains of the pathogenic bacterium Pseudomonas aeruginosa that produce variable levels of a public good—iron-scavenging siderophore molecules. As predicted, we found that the relative fitness of cheats (under-producers) was greatest at higher population densities. Furthermore, as assumed by theory, we show that this occurs because cheats are better able to exploit the cooperative siderophore production of other cells when they are physically closer to them.     

Understanding the evolution and stability of the G-matrix

The G-matrix summarizes the inheritance of multiple, phenotypic traits. The stability and evolution of this matrix are important issues because they affect our ability to predict how the phenotypic traits evolve by selection and drift. Despite the centrality of these issues, comparative, experimental, and analytical approaches to understanding the stability and evolution of the G-matrix have met with limited success. Nevertheless, empirical studies often find that certain structural features of the matrix are remarkably constant, suggesting that persistent selection regimes or other factors promote stability. On the theoretical side, no one has been able to derive equations that would relate stability of the G-matrix to selection regimes, population size, migration, or to the details of genetic architecture. Recent simulation studies of evolving G-matrices offer solutions to some of these problems, as well as a deeper, synthetic understanding of both the G-matrix and adaptive radiations.     

Chimpanzee grouping patterns and food availability in Mahale Mountains National Park,Tanzania

The aim of this study was to test for a correlation between party size and food (fruit) availability among the M group chimpanzees (Pan troglodytes) in the Mahale Mountains, Tanzania. Chimpanzee unit groups (or communities) show fission–fusion grouping patterns and form temporal parties. Fruit availability is assumed to be one of the important limiting factors in relation to the size of these parties. Different methods have been proposed to measure party size, but they all appear to focus mainly on two aspects of grouping phenomena. In “face-to-face parties”, party size is measured by scan sampling, whereas in “nomadic parties”, all members observed during a specific time period are counted. The mean monthly group size resulting from these two measures was compared with fruit availability, i.e. fruiting plant density and mean potential patch size. Nomadic party size was correlated with both values. Thus, party formation at this level was considered to be sensitive to overall fruit availability in the habitat. On the other hand, face-to-face party size remained stable and showed weak or no correlations with density and potential patch size. Although large patches are available during the peak fruiting season, Mahale chimpanzees depend on the liana species Saba comorensis, which, when fruiting, encourages individuals to spread out to eat. Thus, the lack of correlation between face-to-face-party size and fruit availability was attributed to the influence of physical limitations countervailing the fluctuation in fruit availability. Maximum face-to-face party size relative to unit-group size, regarded as the cohesiveness of a unit group, was compared among sites. The values differed largely: Mahale groups M and K, Bossou, and, in some years, Budongo, showed high cohesiveness, while others remained low. Thus, the distribution of the most important food during the fruiting season in each study site may be a crucial factor in the grouping phenomena of chimpanzees.     

The veil of ignorance can favour biological cooperation

Lack of information is a constraint but ignorance can sometimes assist the evolution of cooperation by constraining selfishness. We discuss examples involving both ignorance of role or pay-off and ignorance of relatedness. Ignorance can favour cooperative traits like grouping and warning coloration and reduce conflicts from meiotic drive, imprinting, greenbeards and various forms of nepotism.     

Ecological constraints, life history traits and the evolution of cooperative breeding

The ecological constraints hypothesis is widely accepted as an explanation for the evolution of delayed dispersal in cooperatively breeding birds. Intraspecific studies offer the strongest support. Observational studies have demonstrated a positive association between the severity of ecological constraints and the prevalence of cooperation, and experimental studies in which constraints on independent breeding were relaxed resulted in helpers moving to adopt the vacant breeding opportunities. However, this hypothesis has proved less successful in explaining why cooperative breeding has evolved in some species or lineages but not in others. Comparative studies have failed to identify ecological factors that differ consistently between cooperative and noncooperative species. The life history hypothesis, which emphasizes the role of life history traits in the evolution of cooperative breeding, offers a solution to this difficulty. A recent analysis showed that low adult mortality and low dispersal predisposed certain lineages to show cooperative behaviour, given the right ecological conditions. This represents an important advance, not least by offering an explanation for the patchy phylogenetic distribution of cooperative breeding. We discuss the complementary nature of these two hypotheses and suggest that rather than regarding life history traits as predisposing and ecological factors as facilitating cooperation, they are more likely to act in concert. While acknowledging that different cooperative systems may be a consequence of different selective pressures, we suggest that to identify the key differences between cooperative and noncooperative species, a broad constraints hypothesis that incorporates ecological and life history traits in a single measure of 'turnover of breeding opportunities' may provide the most promising avenue for future comparative studies. Copyright 2000 The Association for the Study of Animal Behaviour.     

Cooperation in defence against a predator

The origin and the evolutionary stability of cooperation between unrelated individuals is one of the key problems of evolutionary biology. In this paper, a cooperative defence game against a predator is introduced which is based on Hamilton's selfish herd theory and Eshel's survival game models. Cooperation is altruistic in the sense that the individual, which is not the target of the predator, helps the members of the group attacked by the predator and during defensive action the helper individual may also die in any attack. In order to decrease the long term predation risk, this individual has to carry out a high risk action. Here I show that this kind of cooperative behaviour can evolve in small groups. The reason for the emergence of cooperation is that if the predator does not kill a mate of a cooperative individual, then the survival probability of the cooperative individual will increase in two cases. If the mate is non-cooperative, then—according to the dilution effect, the predator confusion effect and the higher predator vigilance—the survival probability of the cooperative individual increases. The second case is when the mate is cooperative, because a cooperative individual has a further gain, the active help in defence during further predator attacks. Thus, if an individual can increase the survival rate of its mates (no matter whether the mate is cooperative or not), then its own predation risk will decrease.     

Grouping PCB Assembly Jobs with Feeders of Several Types

A variant of the classical job grouping problem (JGP) in printed circuit board (PCB) assembly is considered. Studies on JGPs have assumed a single feeder from which the components are retrieved and then placed on the PCB. Recent advances in technology have made it possible to use several different kinds (types) of feeders at the same time. In a JGP, the aim is to group the PCBs so that the cardinality of the grouping is minimal and each group can be processed without rearranging the contents of the feeder. In the job grouping problem with several feeder types (JGP-T) the goal is the same but instead of one linear feeder we have several feeders and each component is associated with a given feeder type which restricts its placement. We give a mathematical formulation for the JGP-T and show that it is hard to solve to optimality for problems of practical size. The connections of JGP-T to known problems are discussed. We also propose several efficient heuristics and compare their results against optimal solutions.