Evolution of cooperation in spatial public goods games with common resource dynamics

Coevolutionary dynamics of genetic traits and their long-term extended effects under non-random interactions

Organisms continuously modify their living conditions via extended genetic effects on their environment, microbiome, and in some species culture. These effects can impact the fitness of current but also future conspecifics due to non-genetic transmission via ecological or cultural inheritance. In this case, selection on a gene with extended effects depends on the degree to which current and future genetic relatives are exposed to modified conditions. Here, we detail the selection gradient on a quantitative trait with extended effects in a patch-structured population, when gene flow between patches is limited and ecological inheritance within patches can be biased towards offspring. Such a situation is relevant to understand evolutionary driven changes in individual condition that can be preferentially transmitted from parent to offspring, such as cellular state, micro-environments (e.g., nests), pathogens, microbiome, or culture. Our analysis quantifies how the interaction between limited gene flow and biased ecological inheritance influences the joint evolutionary dynamics of traits together with the conditions they modify, helping understand adaptation via non-genetic modifications. As an illustration, we apply our analysis to a gene-culture coevolution scenario in which genetically-determined learning strategies coevolve with adaptive knowledge. In particular, we show that when social learning is synergistic, selection can favour strategies that generate remarkable levels of knowledge under intermediate levels of both vertical cultural transmission and limited dispersal. More broadly, our theory yields insights into the interplay between genetic and non-genetic inheritance, with implications for how organisms evolve to transform their environments.

Emergence of social inequality in the spatial harvesting of renewable public goods

Spatially extended ecological public goods, such as forests, grasslands, and fish stocks, are at risk of being overexploited by selfish consumers–a phenomenon widely recognized as the ‘tragedy of the commons.’ The interplay of spatial and ecological dimensions introduces new features absent in non-spatial ecological contexts, such as consumer mobility, local information availability, and strategy evolution through social learning in neighborhoods. It is unclear how these features interact to influence the harvesting and dispersal strategies of consumers. To answer these questions, we develop and analyze an individual-based, spatially structured, eco-evolutionary model with explicit resource dynamics. We report the following findings. (1) When harvesting efficiency is low, consumers evolve a sedentary consumption strategy, through which the resource is harvested sustainably, but with harvesting rates far below their maximum sustainable value. (2) As harvesting efficiency increases, consumers adopt a mobile ‘consume-and-disperse’ strategy, which is sustainable, equitable, and gives maximum sustainable yield. (3) A further increase in harvesting efficiency leads to large-scale overexploitation. (4) If costs of dispersal are significant, increased harvesting efficiency also leads to social inequality between frugal sedentary consumers and overexploitative mobile consumers. Whereas overexploitation can occur without social inequality, social inequality always leads to overexploitation. Thus, we identify four conditions that–while being characteristic of technological progress in modern societies–risk social inequality and overexploitation: high harvesting efficiency, moderately low costs of dispersal, high consumer density, and the tendency of consumers to adopt new strategies rapidly. We also show how access to global information–another feature widespread in modern societies–helps mitigate these risks.

Throughout history, humans have shaped ecological landscapes, which in turn have influenced human behavior. This mutual dependence is epitomized when human consumers harvest a spatially extended renewable resource. Simple models predict that, when multiple consumers harvest a shared resource, each is tempted to harvest faster than his/her peers, putting the resource at risk of overexploitation. It is unclear, however, how the interplay among resource productivity, consumer mobility, and social learning in spatial ecological public goods games influences evolved consumer behavior. Here, using an individual-based, spatially structured, eco-evolutionary model of consumers and a resource, we find that increasing resource productivity initially promotes efficient resource use by enabling mobile consumption strategies, but eventually leads to inequality and overexploitation, as overexploitative mobile consumers coexist with frugal sedentary consumers. When consumers are impatient (i.e., eager to imitate successful strategies) or myopic (i.e., unaware of conditions outside of their neighborhoods), inequality and overexploitation tend to aggravate.

Cyclic public goods games: Compensated coexistence among mutual cheaters stabilized by optimized penalty taxation

We study the problem of stabilized coexistence in a three-species public goods game in which each species simultaneously contributes to one public good while freeloading off another public good ("cheating"). The proportional population growth is governed by an appropriately modified replicator equation, depending on the returns from the public goods and the cost. We show that the replicator dynamic has at most one interior unstable fixed point and that the population becomes dominated by a single species. We then show that by applying an externally imposed penalty, or "tax" on success can stabilize the interior fixed point, allowing for the symbiotic coexistence of all species. We show that the interior fixed point is the point of globally minimal total population growth in both the taxed and untaxed cases. We then formulate an optimal taxation problem and show that it admits a quasilinearization, resulting in novel necessary conditions for the optimal control. In particular, the optimal control problem governing the tax rate must solve a certain second-order ordinary differential equation.

Fluctuations-induced coexistence in public goods dynamics

Cooperative interactions between individuals in a population and their stability properties are central to population dynamics and evolution. We introduce a generic class of nonlinear dynamical systems describing such interactions between producers and non-producers of a rapidly equilibrating common resource extracted from a finite environment. In the deterministic mean field approximation, fast-growing non-producers drive the entire population to extinction. However, the presence of arbitrarily small perturbations destabilizes this fixed point into a stochastic attractor where both phenotypes can survive. Phase space arguments and moment closure are used to characterize the attractor and show that its properties are not determined by the noise amplitude or boundary conditions, but rather it is stabilized by the stochastic nonlinear dynamics. Spatial Monte Carlo simulations with demographic fluctuations and diffusion illustrate a similar effect, supporting the validity of the two-dimensional stochastic differential equation as an approximation. The functional distribution of the noise emerges as the main factor determining the dynamical outcome. Noise resulting from diffusion between different regions, or additive noise, induce coexistence while multiplicative or local demographic noise do not alter the outcome of deterministic dynamics. The results are discussed in a general context of the effect of noise on phase space structure.

The soil microbial community predicts the importance of plant traits in plant-soil feedback

Reciprocal interaction between plant and soil (plant-soil feedback, PSF) can determine plant community structure. Understanding which traits control interspecific variation of PSF strength is crucial for plant ecology. Studies have highlighted either plant-mediated nutrient cycling (litter-mediated PSF) or plant-microbe interaction (microbial-mediated PSF) as important PSF mechanisms, each attributing PSF variation to different traits. However, this separation neglects the complex indirect interactions between the two mechanisms. We developed a model coupling litter- and microbial-mediated PSFs to identify the relative importance of traits in controlling PSF strength, and its dependency on the composition of root-associated microbes (i.e. pathogens and/or mycorrhizal fungi). Results showed that although plant carbon: nitrogen (C : N) ratio and microbial nutrient acquisition traits were consistently important, the importance of litter decomposability varied. Litter decomposability was not a major PSF determinant when pathogens are present. However, its importance increased with the relative abundance of mycorrhizal fungi as nutrient released from the mycorrhizal-enhanced litter production to the nutrient-depleted soils result in synergistic increase of soil nutrient and mycorrhizal abundance. Data compiled from empirical studies also supported our predictions. We propose that the importance of litter decomposability depends on the composition of root-associated microbes. Our results provide new perspectives in plant invasion and trait-based ecology.

Coexistence of productive and non-productive populations by fluctuation-driven spatio-temporal patterns

Cooperative interactions, their stability and evolution, provide an interesting context in which to study the interface between cellular and population levels of organization. Here we study a public goods model relevant to microorganism populations actively extracting a growth resource from their environment. Cells can display one of two phenotypes - a productive phenotype that extracts the resources at a cost, and a non-productive phenotype that only consumes the same resource. Both proliferate and are free to move by diffusion; growth rate and diffusion coefficient depend only weakly phenotype. We analyze the continuous differential equation model as well as simulate stochastically the full dynamics. We find that the two sub-populations, which cannot coexist in a well-mixed environment, develop spatio-temporal patterns that enable long-term coexistence in the shared environment. These patterns are purely fluctuation-driven, as the corresponding continuous spatial system does not display Turing instability. The average stability of coexistence patterns derives from a dynamic mechanism in which the producing sub-population equilibrates with the environmental resource and holds it close to an extinction transition of the other sub-population, causing it to constantly hover around this transition. Thus the ecological interactions support a mechanism reminiscent of self-organized criticality; power-law distributions and long-range correlations are found. The results are discussed in the context of general pattern formation and critical behavior in ecology as well as in an experimental context.

Evolutionary dynamics of group interactions on structured populations: a review

Interactions among living organisms, from bacteria colonies to human societies, are inherently more complex than interactions among particles and non-living matter. Group interactions are a particularly important and widespread class, representative of which is the public goods game. In addition, methods of statistical physics have proved valuable for studying pattern formation, equilibrium selection and self-organization in evolutionary games. Here, we review recent advances in the study of evolutionary dynamics of group interactions on top of structured populations, including lattices, complex networks and coevolutionary models. We also compare these results with those obtained on well-mixed populations. The review particularly highlights that the study of the dynamics of group interactions, like several other important equilibrium and non-equilibrium dynamical processes in biological, economical and social sciences, benefits from the synergy between statistical physics, network science and evolutionary game theory.

Scarcity may promote cooperation in populations of simple agents

In the study of the evolution of cooperation, resource limitations are usually assumed just to provide a finite population size. Recently, however, it has been pointed out that resource limitation may also generate dynamical payoffs able to modify the original structure of the games. Here we study analytically a phase transition from a homogeneous population of defectors when resources are abundant to the survival of unconditional cooperators when resources reduce below a threshold. To this end, we introduce a model of simple agents, with no memory or ability of recognition, interacting in well-mixed populations. The result might shed light on the role played by resource constraints on the origin of multicellularity.

Analytical models for well-mixed populations of cooperators and defectors under limiting resources

In the study of the evolution of cooperation, resource limitations are usually assumed just to provide a finite population size. Recently, however, agent-based models have pointed out that resource limitation may modify the original structure of the interactions and allow for the survival of unconditional cooperators in well-mixed populations. Here, we present analytical simplified versions of two types of agent-based models recently published: one in which the limiting resource constrains the ability of reproduction of individuals but not their survival, and a second one where the limiting resource is necessary for both reproduction and survival. One finds that the analytical models display, with a few differences, the same qualitative behavior of the more complex agent-based models. In addition, the analytical models allow us to expand the study and identify the dimensionless parameters governing the final fate of the system, such as coexistence of cooperators and defectors, or dominance of defectors or of cooperators. We provide a detailed analysis of the occurring phase transitions as these parameters are varied.

Adaptive and bounded investment returns promote cooperation in spatial public goods games

The public goods game is one of the most famous models for studying the evolution of cooperation in sizable groups. The multiplication factor in this game can characterize the investment return from the public good, which may be variable depending on the interactive environment in realistic situations. Instead of using the same universal value, here we consider that the multiplication factor in each group is updated based on the differences between the local and global interactive environments in the spatial public goods game, but meanwhile limited to within a certain range. We find that the adaptive and bounded investment returns can significantly promote cooperation. In particular, full cooperation can be achieved for high feedback strength when appropriate limitation is set for the investment return. Also, we show that the fraction of cooperators in the whole population can become larger if the lower and upper limits of the multiplication factor are increased. Furthermore, in comparison to the traditionally spatial public goods game where the multiplication factor in each group is identical and fixed, we find that cooperation can be better promoted if the multiplication factor is constrained to adjust between one and the group size in our model. Our results highlight the importance of the locally adaptive and bounded investment returns for the emergence and dominance of cooperative behavior in structured populations.

Coexistence of cooperators and defectors in well mixed populations mediated by limiting resources

Traditionally, resource limitation in evolutionary game theory is assumed just to impose a constant population size. Here we show that resource limitations may generate dynamical payoffs able to alter an original prisoner's dilemma, and to allow for the stable coexistence between unconditional cooperators and defectors in well-mixed populations. This is a consequence of a self-organizing process that turns the interaction payoff matrix into evolutionary neutral, and represents a resource-based control mechanism preventing the spread of defectors. To our knowledge, this is the first example of coexistence in well-mixed populations with a game structure different from a snowdrift game.

Noise driven evolutionary waves

Adaptation in spatially extended populations entails the propagation of evolutionary novelties across habitat ranges. Driven by natural selection, beneficial mutations sweep through the population in a "wave of advance". The standard model for these traveling waves, due to R. Fisher and A. Kolmogorov, plays an important role in many scientific areas besides evolution, such as ecology, epidemiology, chemical kinetics, and recently even in particle physics. Here, we extend the Fisher-Kolmogorov model to account for mutations that confer an increase in the density of the population, for instance as a result of an improved metabolic efficiency. We show that these mutations invade by the action of random genetic drift, even if the mutations are slightly deleterious. The ensuing class of noise-driven waves are characterized by a wave speed that decreases with increasing population sizes, contrary to conventional Fisher-Kolmogorov waves. When a trade-off exists between density and growth rate, an evolutionary optimal population density can be predicted. Our simulations and analytical results show that genetic drift in conjunction with spatial structure promotes the economical use of limited resources. The simplicity of our model, which lacks any complex interactions between individuals, suggests that noise-induced pattern formation may arise in many complex biological systems including evolution.

How life history and demography promote or inhibit the evolution of helping behaviours

In natural populations, dispersal tends to be limited so that individuals are in local competition with their neighbours. As a consequence, most behaviours tend to have a social component, e.g. they can be selfish, spiteful, cooperative or altruistic as usually considered in social evolutionary theory. How social behaviours translate into fitness costs and benefits depends considerably on life-history features, as well as on local demographic and ecological conditions. Over the last four decades, evolutionists have been able to explore many of the consequences of these factors for the evolution of social behaviours. In this paper, we first recall the main theoretical concepts required to understand social evolution. We then discuss how life history, demography and ecology promote or inhibit the evolution of helping behaviours, but the arguments developed for helping can be extended to essentially any social trait. The analysis suggests that, on a theoretical level, it is possible to contrast three critical benefit-to-cost ratios beyond which costly helping is selected for (three quantitative rules for the evolution of altruism). But comparison between theoretical results and empirical data has always been difficult in the literature, partly because of the perennial question of the scale at which relatedness should be measured under localized dispersal. We then provide three answers to this question.

Cultural transmission can inhibit the evolution of altruistic helping

The study of culturally inherited traits has led to the suggestion that the evolution of helping behaviors is more likely with cultural transmission than without. Here we evaluate this idea through a comparative analysis of selection on helping under both genetic and cultural inheritance. We develop two simple models for the evolution of helping through cultural group selection: one in which selection on the trait depends solely on Darwinian fitness effects and one in which selection is driven by nonreproductive factors, specifically imitation of strategies achieving higher payoffs. We show that when cultural variants affect Darwinian fitness, the selection pressure on helping can be markedly increased relative to that under genetic transmission. By contrast, when variants are driven by nonreproductive factors, the selection pressure on helping may be reduced relative to that under genetic inheritance. This occurs because, unlike biological offspring, the spread of cultural variants from one group to another through imitation does not reduce the number of these variants in the source group. As a consequence, there is increased within-group competition associated with traits increasing group productivity, which reduces the benefits of helping. In these cases, selection for harming behavior (decreasing the payoff to neighbors) may occur rather than selection for helping.

Population viscosity can promote the evolution of altruistic sterile helpers and eusociality

Because it increases relatedness between interacting individuals, population viscosity has been proposed to favour the evolution of altruistic helping. However, because it increases local competition between relatives, population viscosity may also act as a brake for the evolution of helping behaviours. In simple models, the kin selected fecundity benefits of helping are exactly cancelled out by the cost of increased competition between relatives when helping occurs after dispersal. This result has lead to the widespread view, especially among people working with social organisms, that special conditions are required for the evolution of altruism. Here, we re-examine this result by constructing a simple population genetic model where we analyse whether the evolution of a sterile worker caste (i.e. an extreme case of altruism) can be selected for by limited dispersal. We show that a sterile worker caste can be selected for even under the simplest life-cycle assumptions. This has relevant consequences for our understanding of the evolution of altruism in social organisms, as many social insects are characterized by limited dispersal and significant genetic population structure.

The adaptive dynamics of niche constructing traits in spatially subdivided populations: evolving posthumous extended phenotypes

Niche construction, by which organisms modify the environment in which they live, has been proposed to affect the evolution of many phenotypic traits. But what about the evolution of a niche constructing trait itself, whose expression changes the pattern of natural selection to which the trait is exposed in subsequent generations? This article provides an inclusive fitness analysis of selection on niche constructing phenotypes, which can affect their environment from local to global scales in arbitrarily spatially subdivided populations. The model shows that phenotypic effects of genes extending far beyond the life span of the actor can be affected by natural selection, provided they modify the fitness of those individuals living in the future that are likely to have inherited the niche construction lineage of the actor. Present benefits of behaviors are thus traded off against future indirect costs. The future costs will generally result from a complicated interplay of phenotypic effects, population demography and environmental dynamics. To illustrate these points, I derive the adaptive dynamics of a trait involved in the consumption of an abiotic resource, where resource abundance in future generations feeds back to the evolutionary dynamics of the trait.