Environmental adversity and uncertainty favour cooperation.

BACKGROUND: 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.
RESULTS: 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.
CONCLUSION: 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.

Background

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 [15], 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 [16]. Both adversity and uncertainty have been conceptualised as aspects of environmental 'risk' [17].

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 [18]; nematodes Caenorhabditis elegans aggregate in response to stressors [19]; 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 [24]; 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 [29], for communal sharing of hunted meat in various societies [30], and for sharing in laboratory experiments [31]. Examples of enhanced cooperation under adversity and uncertainty are discussed further by Andras & Lazarus [32].

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

We consider the influence of adversity on the minimal amount of a given resource that the individual finds acceptable for survival. We assume that the marginal fitness benefit of resource amounts decreases with the amount of resources the organism already has. For example, eating an extra food unit adds less to the fitness of a well fed animal than to the fitness of a hungry animal [32]. We also assume that the cost of acquiring resources increases monotonically with the amount of resources acquired. For example capturing a large prey takes more energy than capturing a small prey (see also Fig 1 legend for general argument). For the sake of simplicity we assume that the cost function is linear (although we note that in practice this may be depart from linearity in the sense that acquiring a certain biomass of resources in the form of five small prey items may be more expensive than acquiring the same biomass in the form of a single large prey item).

Figure 1

The minimal acceptable level of resources. The incremental fitness cost (assumed to be straight lines for simplicity) and benefit (curved line) are shown as a function of the resource amount gained, in a less adverse (continuous straight line) and a more adverse (segmented straight line) environment (the slope of the two lines is the same). Cost increases with resource amount since, optimally, more investment (cost) is made when the return (benefit) is greater. The resource amounts Rand Rare assumed to be the minimal acceptable levels of resources in the two environments.

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 Rand Rare 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 R

The minimum acceptable cut-off point means that all resources below that limit are considered by the organism to be equivalent to zero, accessing them being unprofitable. This allows us to derive a relationship between adversity and subjective resource uncertainty (i.e., the variance of the resource distribution after ignoring the resources below the minimum acceptable cut-off point – for example the variance of the distribution of sizes of acceptable food items, which are sufficiently big to be above the minimum acceptable cut-off point). Writing the formulae for the subjective variances of resources in the two environments we get:

where , are the respective means of the distributions of subjective acceptable resources. After algebraic manipulations we get

We assume that the minimum acceptable cut-off point Ris such that the acceptable part of the resource distribution includes more than half of the full distribution, i.e., . It can then be shown that

where is the mean value of the full (not truncated) distribution of resources. Consequently, if Rand Rare such that the minimum acceptable cut-off point is less than the mean value of the full resource distribution, and R

and consequently

if R≤ R ≤ R.

It follows from (3) and (7) that

V

Thus in a more adverse environment the individual experiences higher subjective variance (and therefore greater uncertainty) in its resources (Figure 2) (see also Appendix 1). The above discussion applies to the case when environmental adversity is measured in terms of an environmental quality (e.g., temperature, predation risk) different from the quality (usually a resource) in terms of which we measure the increased subjective environmental uncertainty. In this case the objective distributions of the second quality, resources, are the same in both environments. If the same environmental quality is used to measure both adversity and uncertainty we arrive at the same conclusion.

Figure 2

The distribution of resources in two environments having the same objective resource distribution. The resource amounts Rand Rare the minimal acceptable amounts of resources in the two environments. The shaded areas are the parts of the distributions ignored by animals living in the two environments. The larger the ignored area the higher is the subjective variance of the distribution, with the condition that the ignored area is smaller than half of the area below the curve of the distribution.

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 [40] 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, y) = (x, y) + (ξ, ξ), where ξ, ξare 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