Environmental adversity and uncertainty favour cooperation
© Andras et al; licensee BioMed Central Ltd. 2007
Received: 24 May 2007
Accepted: 30 November 2007
Published: 30 November 2007
A major cornerstone of evolutionary biology theory is the explanation of the emergence of cooperation in communities of selfish individuals. There is an unexplained tendency in the plant and animal world – with examples from alpine plants, worms, fish, mole-rats, monkeys and humans – for cooperation to flourish where the environment is more adverse (harsher) or more unpredictable.
Using mathematical arguments and computer simulations we show that in more adverse environments individuals perceive their resources to be more unpredictable, and that this unpredictability favours cooperation. First we show analytically that in a more adverse environment the individual experiences greater perceived uncertainty. Second we show through a simulation study that more perceived uncertainty implies higher level of cooperation in communities of selfish individuals.
This study captures the essential features of the natural examples: the positive impact of resource adversity or uncertainty on cooperation. These newly discovered connections between environmental adversity, uncertainty and cooperation help to explain the emergence and evolution of cooperation in animal and human societies.
The drive to understand the emergence of cooperation – actions of benefit to both actor and recipient – in communities of selfish individuals has generated a large body of theoretical and empirical research in recent decades [1–14]. This research focuses on the dynamics of interactions between individuals and pays relatively little attention to the effects of the environment. However, evidence is growing, in many taxa, that as the adversity (harshness) and uncertainty of the environment increase cooperation is enhanced and we present a model here that attempts to explain this phenomenon as an adaptive facultative response favoured by selection.
An organism's environment is more adverse if some quality such as resources, physical structure, climate, competitors, parasites or predators changes in such a way as to decrease darwinian fitness. Environmental adversity is species-specific, e.g. high temperature may be adverse for some organisms, but not for thermophilic bacteria. As an example of the uncertainty or unpredictability of the environment , feeding in a patchy area, where some places are rich in food and others barren, results in greater uncertainty of nutritional status compared to foraging where food is distributed homogeneously. Uncertainty can be measured as the variance of a distribution of environmental quality, and adversity as the mean . Both adversity and uncertainty have been conceptualised as aspects of environmental 'risk' .
At many levels of life, from plants to human societies, cooperation thrives in conditions where the environment is most adverse. Plants at lower temperatures and higher altitudes, where abiotic stress is high, compete less and cooperate more with their neighbours ; nematodes Caenorhabditis elegans aggregate in response to stressors ; animals form more cohesive or larger groups, with consequent greater mutualistic benefits under greater predation risk [20–23]; mole-rats, a highly social species, delay dispersion more in arid than in mesic habitats ; human in-group solidarity is greatest when the group is under threat or in a harsh environment [25–28].
In humans there is also evidence for enhanced cooperation where the environment is more uncertain. This holds for common pool resource groups, such as fisheries , for communal sharing of hunted meat in various societies , and for sharing in laboratory experiments . Examples of enhanced cooperation under adversity and uncertainty are discussed further by Andras & Lazarus .
We present a model to explain this increase in cooperation under conditions of adversity and uncertainty. The model has two parts. First, we show that adversity increases the organism's uncertainty in its resource level, uncertainty being measured as subjectively perceived resource variance (sub-section 2.1). We then show that resource uncertainty increases cooperation, using a multi-agent simulation (sub-section 2.2).
Results and Discussion
Adversity and uncertainty: analytical results
The cost of foraging for resources is assumed to increase with adversity. For example, energy lost to foraging will be more costly in colder environments, and time spent foraging (and not available for anti-predator vigilance) will be more costly in environments with greater predation risk. We are interested in finding the minimal level of a particular resource that it is profitable to exploit, considering resource costs imposed by the environment (i.e. the minimal amount for which the benefits of acquiring the resource are larger than the costs of acquiring the resource). We term this level of resource the minimal acceptable level of resource. Note that we are not looking for the optimal level of resources, i.e., where the marginal benefit equals the marginal cost.
We denote by D(R) the probability density function of the distribution of resources (R – the amount of resources, R ≥ 0) in an individual's environment (i.e. is the probability that the amount of resources in a resource item or in a resource location is between the values R1 and R2). Let us assume that Rm 1and Rm 2are the minimum acceptable level of resource in a less adverse (1) and a more adverse (2) environment with the same resource distribution; we then get Rm 1<Rm 2(Figure 1). In other words, the minimum acceptable level of resources is greater in the more adverse environment. This prediction is supported by field studies of foraging in rodents, in which individuals select more profitable foods under environmental conditions – e.g. open habitat and moonlit nights – in which there is a greater risk from nocturnal predators [33–36]. (Animals under immediate predation risk, where anti-predator behaviour competes directly with foraging, trade-off the two concurrent demands and reduce selectivity in feeding in order to attend to the threat of predation [37–39], but this phenomenon is not relevant to the long-term response to adversity – and when prey are not under immediate threat of predation – with which we are concerned here. This distinction can explain the contrasting results of the two sets of studies.)
if Rm 1≤ R ≤ Rm 2.
It follows from (3) and (7) that
V2 – V1 > 0.
We have been dealing so far with subjective uncertainties that are naturally difficult to measure. For several reasons it would be preferable to deal with objective measures of uncertainty. First, it is objective measures that are employed in the following model. Second, as outlined above, we also wish to understand the possible direct effects of environmental uncertainty – as well as adversity – in enhancing cooperation. Last, if our conclusions are to be tested, objective measures of uncertainty will probably be required. Now, if the objective uncertainties of two environments differ, while the adversity (i.e., the mean value) of each is the same, then their consequent subjective uncertainties, as defined by a common minimal acceptable cut-off point, will differ in the same direction. This is because the proportion of the distribution that is unacceptable (and thus equated with zero) increases with objective variance. So, objectively more uncertain environments with the same mean expectations are also subjectively more uncertain, and objective uncertainty can stand proxy for subjective uncertainty in the model that follows.
Uncertainty and cooperation: an agent-based simulation
We have shown how increased adversity leads to increased subjective uncertainty, as measured by subjective variance. We have also shown that subjective and objective variance will be positively correlated. We now go on to show that an increase in objective variance in resources enhances cooperation. It will therefore follow that an increase in the subjective variance of resources will also enhance cooperation. Finally, since adversity causes an increase in subjective uncertainty we can conclude that adversity will favour cooperation.
Using a Prisoner's Dilemma type game theory model we built an agent-based simulation  to study the dynamics of the level of cooperation in relation to resource uncertainty. Our agents are generalised organisms that own resources (R) that they spend on living costs and use to generate new resources for the future. If the agent has less resource than the amount of living costs the agent dies. The agents live in a continuous two-dimensional world (i.e. unlimited flat continuous space, not a grid), each having a position (x, y) and change location by random movements, i.e. (x new , y new ) = (x, y) + (ξ x , ξ y ), where ξ x , ξ y are small random numbers. The agents have an inclination toward cooperation or competition, expressed as p the probability of cooperation of the agent with another agent. If p < 0.5 they are more likely to compete than to cooperate. They select their behaviour for each interaction in a probabilistic manner biased by their inclination. This is done by choosing a random number q from a uniform distribution over [0,1]; if q <p they cooperate, otherwise they compete.
The pay-off matrix for the cooperation/competition game
α · f(R1), f(R2) + Δ
f(R1) + Δ, α · f(R2)
where is the mean and σ R is the variance of the owned resources in the population of agents, and α, β, n0 are parameters. The offspring share equally the resources of their parent. The offspring start their life from their parent's last location with minor random changes, implying that the offspring of each agent will be closely packed at the beginning. The cluster of offspring diffuses with time, as the offspring make their random movements.
The results of our simulation study show that a high level of objective resource uncertainty induces a high level of cooperation in agent populations. We have no analytical results that would explain our simulation results unambiguously. One possibility is that the payoff matrices of games played deviate from the Prisoner's Dilemma matrix, and this causes more cooperation as environmental risk increases . Analysing our payoff matrix (see Table 1) we can exclude this possibility. Our payoff matrix is constructed such that in all cases the Prisoner's Dilemma inequalities are satisfied, i.e., payoff(cheater) > payoff (cooperation) > payoff(joint non-cooperation) > payoff (sucker), and payoff(cooperation) > [(payoff(cheater) + payoff(sucker)]/2, if Δ>0, and we have equalities instead of inequalities if Δ = 0, except the case of payoff(joint non-cooperation) > payoff (sucker), which is always satisfied. The payoff generating function f is set such that in most cases Δ>0, although the proportion of cases with Δ = 0 increases as environmental risk increases.
In our view the phenomenological explanation is that populations of agents survive in an uncertain environment only if the experienced individual uncertainties are around a steady-state level. At the steady-state level of experienced uncertainty the population maintains its size without major variations. By cooperation agents share individually perceived uncertainties, reducing their actual experienced uncertainty (similar to the reduction of risk on joining an insurance scheme). Higher environmental uncertainty implies that more cooperation is needed to reduce experienced individual uncertainties of agents in order to keep these uncertainties around the steady-state level. According to this argument, higher environmental uncertainty implies the presence of more cooperation in surviving populations, which is in good agreement with our simulation findings. Some research works suggest that above random level segregation of cooperating and non-cooperating agents is a key mechanism in the development of populations with high level of cooperation [14, 42–44]. In our case, as we noted above, the offspring of reproducing agents form originally a cluster around the earlier location of their parent, and later this cluster diffuses as the agent follow their random walk. This indicates that possibly the segregation mechanism contributes to some extent in our simulation to the emergence of agent populations that have sufficient level of cooperation that makes the experienced uncertainty of agents stay around the steady-state level.
The simulation study captures the essential features of the natural examples: the positive impact of resource adversity or uncertainty on cooperation. As our simulation is based on a very limited set of assumptions, the results are likely to be of broad applicability and may explain why cooperation flourishes in risky environments, whether risk is conceptualised as adversity, objective environmental variance or subjective environmental uncertainty . Elsewhere we demonstrate another way in which adversity and uncertainty may enhance cooperation .
Social psychological influences of perceived threat on group solidarity in humans [26–28] may seem removed from conclusions concerning cooperative behaviour, and outside the explanatory scope of models based on fitness considerations. However, human cooperative tendencies, and the associated prosocial cognitions and affective states, evolved in the small groups of early human societies [32, 45] – or earlier – where social responses to environmental adversity  and uncertainty  will have impacted directly on fitness. We should therefore expect to find our predicted relationships between perceived risk and behaviours broadly classifiable as cooperative in contemporary societies, as long as these contemporary perceptions and behaviours are recognized and mediated by the putative evolved cognitive mechanisms.
The methods are described in the main body of this paper (Results and discussion section).
where R m is the minimum acceptable cut-off point.
where δ0 is a Dirac-delta function centred on 0 such that .
This means that, given the condition (A1) being satisfied, the variance is an increasing function of the minimum cut-off point value, which increases with the adversity of the environment. This implies that the subjective resource variance of a more adverse environment is larger than the subjective variance of a less adverse environment, if the acceptable part of the resource distribution includes more than half of the full resource distribution.
We are grateful to Miles Hewstone and Ian Vine for discussion and for providing references on the social psychology of cooperation and risk.
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