Bet hedging based cooperation can limit kin selection and form a basis for mutualism

The ergodicity solution of the cooperation puzzle

When two entities cooperate by sharing resources, one relinquishes something of value to the other. This apparent altruism is frequently observed in nature. Why? Classical treatments assume circumstances where combining resources creates an immediate benefit, e.g. through complementarity or thresholds. Here we ask whether cooperation is predictable without such circumstances. We study a model in which resources self-multiply with fluctuations, a null model of a range of phenomena from viral spread to financial investment. Two fundamental growth rates exist: the ensemble-average growth rate, achieved by the average resources of a large population; and the time-average growth rate, achieved by individual resources over a long time. As a consequence of non-ergodicity, the latter is lower than the former by a term which depends on fluctuation size. Repeated pooling and sharing of resources reduces the effective size of fluctuations and increases the time-average growth rate, which approaches the ensemble-average growth rate in the many-cooperator limit. Therefore, cooperation is advantageous in our model for the simple reason that those who do it grow faster than those who do not. We offer this as a candidate explanation for observed cooperation in rudimentary environments, and as a behavioural baseline for cooperation more generally. This article is part of the theme issue 'Emergent phenomena in complex physical and socio-technical systems: from cells to societies'.

The ergodicity solution of the cooperation puzzle

When two entities cooperate by sharing resources, one relinquishes something of value to the other. This apparent altruism is frequently observed in nature. Why? Classical treatments assume circumstances where combining resources creates an immediate benefit, e.g. through complementarity or thresholds. Here we ask whether cooperation is predictable without such circumstances. We study a model in which resources self-multiply with fluctuations, a null model of a range of phenomena from viral spread to financial investment. Two fundamental growth rates exist: the ensemble-average growth rate, achieved by the average resources of a large population; and the time-average growth rate, achieved by individual resources over a long time. As a consequence of non-ergodicity, the latter is lower than the former by a term which depends on fluctuation size. Repeated pooling and sharing of resources reduces the effective size of fluctuations and increases the time-average growth rate, which approaches the ensemble-average growth rate in the many-cooperator limit. Therefore, cooperation is advantageous in our model for the simple reason that those who do it grow faster than those who do not. We offer this as a candidate explanation for observed cooperation in rudimentary environments, and as a behavioural baseline for cooperation more generally. This article is part of the theme issue 'Emergent phenomena in complex physical and socio-technical systems: from cells to societies'.

Altruism in a volatile world

The evolution of altruism-costly self-sacrifice in the service of others-has puzzled biologists since The Origin of Species. For half a century, attempts to understand altruism have developed around the concept that altruists may help relatives to have extra offspring in order to spread shared genes. This theory-known as inclusive fitness-is founded on a simple inequality termed Hamilton's rule. However, explanations of altruism have typically not considered the stochasticity of natural environments, which will not necessarily favour genotypes that produce the greatest average reproductive success. Moreover, empirical data across many taxa reveal associations between altruism and environmental stochasticity, a pattern not predicted by standard interpretations of Hamilton's rule. Here we derive Hamilton's rule with explicit stochasticity, leading to new predictions about the evolution of altruism. We show that altruists can increase the long-term success of their genotype by reducing the temporal variability in the number of offspring produced by their relatives. Consequently, costly altruism can evolve even if it has a net negative effect on the average reproductive success of related recipients. The selective pressure on volatility-suppressing altruism is proportional to the coefficient of variation in population fitness, and is therefore diminished by its own success. Our results formalize the hitherto elusive link between bet-hedging and altruism, and reveal missing fitness effects in the evolution of animal societies.

Facilitation as a ubiquitous driver of biodiversity

Models describing the biotic drivers that create and maintain biological diversity within trophic levels have focused primarily on negative interactions (i.e. competition), leaving marginal room for positive interactions (i.e. facilitation). We show facilitation to be a ubiquitous driver of biodiversity by first noting that all species use resources and thus change the local biotic or abiotic conditions, altering the available multidimensional niches. This can cause a shift in local species composition, which can cause an increase in beta, and sometimes alpha, diversity. We show that these increases are ubiquitous across ecosystems. These positive effects on diversity occur via a broad host of disparate direct and indirect mechanisms. We identify and unify several of these facilitative mechanisms and discuss why it has been easy to underappreciate the importance of facilitation. We show that net positive effects have a long history of being considered ecologically or evolutionarily unstable, and we present recent evidence of its potential stability. Facilitation goes well beyond the common case of stress amelioration and it probably gains importance as community complexity increases. While biodiversity is, in part, created by species exploiting many niches, many niches are available to exploit only because species create them.

Monogamy has a fixation advantage based on fitness variance in an ideal promiscuity group

We consider an ideal promiscuity group of females, which implies that all males have the same average mating success. If females have concealed ovulation, then the males' paternity chances are equal. We find that male-based monogamy will be fixed in females' promiscuity group when the stochastic Darwinian selection is described by a Markov chain.We point out that in huge populations the relative advantage (difference between average fitness of different strategies) determines primarily the end of evolution; in the case of neutrality (means are equal) the smallest variance guarantees fixation (absorption) advantage; when the means and variances are the same, then the higher third moment determines which types will be fixed in the Markov chains.