Evolutionary and population dynamics: a coupled approach

Hypochaos prevents tragedy of the commons in discrete-time eco-evolutionary game dynamics

While quite a few recent papers have explored game-resource feedback using the framework of evolutionary game theory, almost all the studies are confined to using time-continuous dynamical equations. Moreover, in such literature, the effect of ubiquitous chaos in the resulting eco-evolutionary dynamics is rather missing. Here, we present a deterministic eco-evolutionary discrete-time dynamics in generation-wise non-overlapping population of two types of harvesters-one harvesting at a faster rate than the other-consuming a self-renewing resource capable of showing chaotic dynamics. In the light of our finding that sometimes chaos is confined exclusively to either the dynamics of the resource or that of the consumer fractions, an interesting scenario is realized: The resource state can keep oscillating chaotically, and hence, it does not vanish to result in the tragedy of the commons-extinction of the resource due to selfish indiscriminate exploitation-and yet the consumer population, whose dynamics depends directly on the state of the resource, may end up being composed exclusively of defectors, i.e., high harvesters. This appears non-intuitive because it is well known that prevention of tragedy of the commons usually requires substantial cooperation to be present.

Coupled environmental and demographic fluctuations shape the evolution of cooperative antimicrobial resistance

There is a pressing need to better understand how microbial populations respond to antimicrobial drugs, and to find mechanisms to possibly eradicate antimicrobial-resistant cells. The inactivation of antimicrobials by resistant microbes can often be viewed as a cooperative behaviour leading to the coexistence of resistant and sensitive cells in large populations and static environments. This picture is, however, greatly altered by the fluctuations arising in volatile environments, in which microbial communities commonly evolve. Here, we study the eco-evolutionary dynamics of a population consisting of an antimicrobial-resistant strain and microbes sensitive to antimicrobial drugs in a time-fluctuating environment, modelled by a carrying capacity randomly switching between states of abundance and scarcity. We assume that antimicrobial resistance (AMR) is a shared public good when the number of resistant cells exceeds a certain threshold. Eco-evolutionary dynamics is thus characterised by demographic noise (birth and death events) coupled to environmental fluctuations which can cause population bottlenecks. By combining analytical and computational means, we determine the environmental conditions for the long-lived coexistence and fixation of both strains, and characterise a fluctuation-driven AMR eradication mechanism, where resistant microbes experience bottlenecks leading to extinction. We also discuss the possible applications of our findings to laboratory-controlled experiments.

Game-environment feedback dynamics in growing population: Effect of finite carrying capacity

The tragedy of the commons (TOC) is an unfortunate situation where a shared resource is exhausted due to uncontrolled exploitation by the selfish individuals of a population. Recently, the paradigmatic replicator equation has been used in conjunction with a phenomenological equation for the state of the shared resource to gain insight into the influence of the games on the TOC. The replicator equation, by construction, models a fixed infinite population undergoing microevolution. Thus, it is unable to capture any effect of the population growth and the carrying capacity of the population although the TOC is expected to be dependent on the size of the population. Therefore, in this paper, we present a mathematical framework that incorporates the density dependent payoffs and the logistic growth of the population in the eco-evolutionary dynamics modeling the game-resource feedback. We discover a bistability in the dynamics: a finite carrying capacity can either avert or cause the TOC depending on the initial states of the resource and the initial fraction of cooperators. In fact, depending on the type of strategic game-theoretic interaction, a finite carrying capacity can either avert or cause the TOC when it is exactly the opposite for the corresponding case with infinite carrying capacity.

Phenotypic-dependent variability and the emergence of tolerance in bacterial populations

Ecological and evolutionary dynamics have been historically regarded as unfolding at broadly separated timescales. However, these two types of processes are nowadays well-documented to intersperse much more tightly than traditionally assumed, especially in communities of microorganisms. Advancing the development of mathematical and computational approaches to shed novel light onto eco-evolutionary problems is a challenge of utmost relevance. With this motivation in mind, here we scrutinize recent experimental results showing evidence of rapid evolution of tolerance by lag in bacterial populations that are periodically exposed to antibiotic stress in laboratory conditions. In particular, the distribution of single-cell lag times-i.e., the times that individual bacteria from the community remain in a dormant state to cope with stress-evolves its average value to approximately fit the antibiotic-exposure time. Moreover, the distribution develops right-skewed heavy tails, revealing the presence of individuals with anomalously large lag times. Here, we develop a parsimonious individual-based model mimicking the actual demographic processes of the experimental setup. Individuals are characterized by a single phenotypic trait: their intrinsic lag time, which is transmitted with variation to the progeny. The model-in a version in which the amplitude of phenotypic variations grows with the parent's lag time-is able to reproduce quite well the key empirical observations. Furthermore, we develop a general mathematical framework allowing us to describe with good accuracy the properties of the stochastic model by means of a macroscopic equation, which generalizes the Crow-Kimura equation in population genetics. Even if the model does not account for all the biological mechanisms (e.g., genetic changes) in a detailed way-i.e., it is a phenomenological one-it sheds light onto the eco-evolutionary dynamics of the problem and can be helpful to design strategies to hinder the emergence of tolerance in bacterial communities. From a broader perspective, this work represents a benchmark for the mathematical framework designed to tackle much more general eco-evolutionary problems, thus paving the road to further research avenues.

Evolutionary graph theory derived from eco-evolutionary dynamics

A biologically motivated individual-based framework for evolution in network-structured populations is developed that can accommodate eco-evolutionary dynamics. This framework is used to construct a network birth and death model. The evolutionary graph theory model, which considers evolutionary dynamics only, is derived as a special case, highlighting additional assumptions that diverge from real biological processes. This is achieved by introducing a negative ecological feedback loop that suppresses ecological dynamics by forcing births and deaths to be coupled. We also investigate how fitness, a measure of reproductive success used in evolutionary graph theory, is related to the life-history of individuals in terms of their birth and death rates. In simple networks, these ecologically motivated dynamics are used to provide new insight into the spread of adaptive mutations, both with and without clonal interference. For example, the star network, which is known to be an amplifier of selection in evolutionary graph theory, can inhibit the spread of adaptive mutations when individuals can die naturally.

Population Dynamics in a Changing Environment: Random versus Periodic Switching

Environmental changes greatly influence the evolution of populations. Here, we study the dynamics of a population of two strains, one growing slightly faster than the other, competing for resources in a time-varying binary environment modeled by a carrying capacity switching either randomly or periodically between states of abundance and scarcity. The population dynamics is characterized by demographic noise (birth and death events) coupled to a varying environment. We elucidate the similarities and differences of the evolution subject to a stochastically and periodically varying environment. Importantly, the population size distribution is generally found to be broader under intermediate and fast random switching than under periodic variations, which results in markedly different asymptotic behaviors between the fixation probability of random and periodic switching. We also determine the detailed conditions under which the fixation probability of the slow strain is maximal.

Coexistence and cooperation in structured habitats

Background

Natural habitats are typically structured, imposing constraints on inhabiting populations and their interactions. Which conditions are important for coexistence of diverse communities, and how cooperative interaction stabilizes in such populations, have been important ecological and evolutionary questions.

Results

We investigate a minimal ecological framework of microbial population dynamics that exhibits crucial features to show coexistence: Populations repeatedly undergo cycles of separation into compartmentalized habitats and mixing with new resources. The characteristic time-scale is longer than that typical of individual growth. Using analytic approximations, averaging techniques and phase-plane methods of dynamical systems, we provide a framework for analyzing various types of microbial interactions. Population composition and population size are both dynamic variables of the model; they are found to be decoupled both in terms of time-scale and parameter dependence. We present specific results for two examples of cooperative interaction by public goods: collective antibiotics resistance, and enhanced iron-availability by pyoverdine. We find stable coexistence to be a likely outcome.

Conclusions

The two simple features of a long mixing time-scale and spatial compartmentalization are enough to enable coexisting strains. In particular, costly social traits are often stabilized in such an environment—and thus cooperation established.

Steering eco-evolutionary game dynamics with manifold control

Feedback loops between population dynamics of individuals and their ecological environment are ubiquitously found in nature and have shown profound effects on the resulting eco-evolutionary dynamics. By incorporating linear environmental feedback law into the replicator dynamics of two-player games, recent theoretical studies have shed light on understanding the oscillating dynamics of the social dilemma. However, the detailed effects of more general nonlinear feedback loops in multi-player games, which are more common especially in microbial systems, remain unclear. Here, we focus on ecological public goods games with environmental feedbacks driven by a nonlinear selection gradient. Unlike previous models, multiple segments of stable and unstable equilibrium manifolds can emerge from the population dynamical systems. We find that a larger relative asymmetrical feedback speed for group interactions centred on cooperators not only accelerates the convergence of stable manifolds but also increases the attraction basin of these stable manifolds. Furthermore, our work offers an innovative manifold control approach: by designing appropriate switching control laws, we are able to steer the eco-evolutionary dynamics to any desired population state. Our mathematical framework is an important generalization and complement to coevolutionary game dynamics, and also fills the theoretical gap in guiding the widespread problem of population state control in microbial experiments.

Cooperation in Microbial Populations: Theory and Experimental Model Systems

Cooperative behavior, the costly provision of benefits to others, is common across all domains of life. This review article discusses cooperative behavior in the microbial world, mediated by the exchange of extracellular products called public goods. We focus on model species for which the production of a public good and the related growth disadvantage for the producing cells are well described. To unveil the biological and ecological factors promoting the emergence and stability of cooperative traits we take an interdisciplinary perspective and review insights gained from both mathematical models and well-controlled experimental model systems. Ecologically, we include crucial aspects of the microbial life cycle into our analysis and particularly consider population structures where ensembles of local communities (subpopulations) continuously emerge, grow, and disappear again. Biologically, we explicitly consider the synthesis and regulation of public good production. The discussion of the theoretical approaches includes general evolutionary concepts, population dynamics, and evolutionary game theory. As a specific but generic biological example, we consider populations of Pseudomonas putida and its regulation and use of pyoverdines, iron scavenging molecules, as public goods. The review closes with an overview on cooperation in spatially extended systems and also provides a critical assessment of the insights gained from the experimental and theoretical studies discussed. Current challenges and important new research opportunities are discussed, including the biochemical regulation of public goods, more realistic ecological scenarios resembling native environments, cell-to-cell signaling, and multispecies communities.

Population size changes and extinction risk of populations driven by mutant interactors

Spontaneous random mutations are an important source of variation in populations. Many evolutionary models consider mutants with a fixed fitness, chosen from a fitness distribution without considering microscopic interactions among the residents and mutants. Here, we go beyond this and consider "mutant interactors," which lead to new interactions between the residents and invading mutants that can affect the population size and the extinction risk of populations. We model microscopic interactions between individuals by using a dynamic interaction matrix, the dimension of which increases with the emergence of a new mutant and decreases with extinction. The new interaction parameters of the mutant follow a probability distribution around the payoff entries of its ancestor. These new interactions can drive the population away from the previous equilibrium and lead to changes in the population size. Thus, the population size is an evolving property rather than an externally controlled variable. We calculate the average population size of our stochastic system over time and quantify the extinction risk of the population by the mean time to extinction.

Fixation probabilities in populations under demographic fluctuations

We study the fixation probability of a mutant type when introduced into a resident population. We implement a stochastic competitive Lotka-Volterra model with two types and intra- and interspecific competition. The model further allows for stochastically varying population sizes. The competition coefficients are interpreted in terms of inverse payoffs emerging from an evolutionary game. Since our study focuses on the impact of the competition values, we assume the same net growth rate for both types. In this general framework, we derive a formula for the fixation probability [Formula: see text] of the mutant type under weak selection. We find that the most important parameter deciding over the invasion success of the mutant is its death rate due to competition with the resident. Furthermore, we compare our approximation to results obtained by implementing population size changes deterministically in order to explore the parameter regime of validity of our method. Finally, we put our formula in the context of classical evolutionary game theory and observe similarities and differences to the results obtained in that constant population size setting.

Eco-evolutionary dynamics of a population with randomly switching carrying capacity

Environmental variability greatly influences the eco-evolutionary dynamics of a population, i.e. it affects how its size and composition evolve. Here, we study a well-mixed population of finite and fluctuating size whose growth is limited by a randomly switching carrying capacity. This models the environmental fluctuations between states of resources abundance and scarcity. The population consists of two strains, one growing slightly faster than the other, competing under two scenarios: one in which competition is solely for resources, and one in which the slow (cooperating) strain produces a public good (PG) that benefits also the fast (free-riding) strain. We investigate how the coupling of demographic and environmental (external) noise affects the population's eco-evolutionary dynamics. By analytical and computational means, we study the correlations between the population size and its composition, and discuss the social-dilemma-like 'eco-evolutionary game' characterizing the PG production. We determine in what conditions it is best to produce a PG; when cooperating is beneficial but outcompeted by free riding, and when the PG production is detrimental for cooperators. Within a linear noise approximation to populations of varying size, we also accurately analyse the coupled effects of demographic and environmental noise on the size distribution.

Interactions mediated by a public good transiently increase cooperativity in growing Pseudomonas putida metapopulations

Bacterial communities have rich social lives. A well-established interaction involves the exchange of a public good in Pseudomonas populations, where the iron-scavenging compound pyoverdine, synthesized by some cells, is shared with the rest. Pyoverdine thus mediates interactions between producers and non-producers and can constitute a public good. This interaction is often used to test game theoretical predictions on the "social dilemma" of producers. Such an approach, however, underestimates the impact of specific properties of the public good, for example consequences of its accumulation in the environment. Here, we experimentally quantify costs and benefits of pyoverdine production in a specific environment, and build a model of population dynamics that explicitly accounts for the changing significance of accumulating pyoverdine as chemical mediator of social interactions. The model predicts that, in an ensemble of growing populations (metapopulation) with different initial producer fractions (and consequently pyoverdine contents), the global producer fraction initially increases. Because the benefit of pyoverdine declines at saturating concentrations, the increase need only be transient. Confirmed by experiments on metapopulations, our results show how a changing benefit of a public good can shape social interactions in a bacterial population.

A phenomenological analysis of eco-evolutionary coupling under dilution

Evolutionary dynamics experienced by mixed microbial populations of cooperators and cheaters has been examined in experiments in the literature using a protocol of periodic dilution to investigate the properties of resilience and adaptability to environmental changes. Data depicted on an appropriate phase diagram indicate, among other features, a stable equilibrium point at which cooperators and cheaters coexist (Sanchez and Gore, 2013). We present here a phenomenological analysis of these data focusing on an eco-evolutionary-game perspective. To that end, we work on an extension of the model proposed in Tao and Cressman (2007). It's original version takes into account changes of the total population density while the individuals experience a pairwise Prisoners Dilemma game. The extension devised here contains a dilution parameter to conform with the experimental procedure, in addition to a term accounting for Allee effects. In contrast to other descriptions proposed in similar contexts, however, the model here does not account for assortative encounters, group or kin selection. Nonetheless, it describes surprisingly well both qualitatively and quantitatively the features of the observed phase diagram. We discuss these results in terms of the behavior of an effective payoff matrix defined accordingly.

Extinction dynamics from metastable coexistences in an evolutionary game

Deterministic evolutionary game dynamics can lead to stable coexistences of different types. Stochasticity, however, drives the loss of such coexistences. This extinction is usually accompanied by population size fluctuations. We investigate the most probable extinction trajectory under such fluctuations by mapping a stochastic evolutionary model to a problem of classical mechanics using the Wentzel-Kramers-Brillouin (WKB) approximation. Our results show that more abundant types in a coexistence may be more likely to go extinct first, in good agreement with previous results. The distance between the coexistence and extinction points is not a good predictor of extinction either. Instead, the WKB method correctly predicts the type going extinct first.

Evolution of a Fluctuating Population in a Randomly Switching Environment

Environment plays a fundamental role in the competition for resources, and hence in the evolution of populations. Here, we study a well-mixed, finite population consisting of two strains competing for the limited resources provided by an environment that randomly switches between states of abundance and scarcity. Assuming that one strain grows slightly faster than the other, we consider two scenarios-one of pure resource competition, and one in which one strain provides a public good-and investigate how environmental randomness (external noise) coupled to demographic (internal) noise determines the population's fixation properties and size distribution. By analytical means and simulations, we show that these coupled sources of noise can significantly enhance the fixation probability of the slower-growing species. We also show that the population size distribution can be unimodal, bimodal, or multimodal and undergoes noise-induced transitions between these regimes when the rate of switching matches the population's growth rate.

Master equations and the theory of stochastic path integrals

This review provides a pedagogic and self-contained introduction to master equations and to their representation by path integrals. Since the 1930s, master equations have served as a fundamental tool to understand the role of fluctuations in complex biological, chemical, and physical systems. Despite their simple appearance, analyses of master equations most often rely on low-noise approximations such as the Kramers-Moyal or the system size expansion, or require ad-hoc closure schemes for the derivation of low-order moment equations. We focus on numerical and analytical methods going beyond the low-noise limit and provide a unified framework for the study of master equations. After deriving the forward and backward master equations from the Chapman-Kolmogorov equation, we show how the two master equations can be cast into either of four linear partial differential equations (PDEs). Three of these PDEs are discussed in detail. The first PDE governs the time evolution of a generalized probability generating function whose basis depends on the stochastic process under consideration. Spectral methods, WKB approximations, and a variational approach have been proposed for the analysis of the PDE. The second PDE is novel and is obeyed by a distribution that is marginalized over an initial state. It proves useful for the computation of mean extinction times. The third PDE describes the time evolution of a 'generating functional', which generalizes the so-called Poisson representation. Subsequently, the solutions of the PDEs are expressed in terms of two path integrals: a 'forward' and a 'backward' path integral. Combined with inverse transformations, one obtains two distinct path integral representations of the conditional probability distribution solving the master equations. We exemplify both path integrals in analysing elementary chemical reactions. Moreover, we show how a well-known path integral representation of averaged observables can be recovered from them. Upon expanding the forward and the backward path integrals around stationary paths, we then discuss and extend a recent method for the computation of rare event probabilities. Besides, we also derive path integral representations for processes with continuous state spaces whose forward and backward master equations admit Kramers-Moyal expansions. A truncation of the backward expansion at the level of a diffusion approximation recovers a classic path integral representation of the (backward) Fokker-Planck equation. One can rewrite this path integral in terms of an Onsager-Machlup function and, for purely diffusive Brownian motion, it simplifies to the path integral of Wiener. To make this review accessible to a broad community, we have used the language of probability theory rather than quantum (field) theory and do not assume any knowledge of the latter. The probabilistic structures underpinning various technical concepts, such as coherent states, the Doi-shift, and normal-ordered observables, are thereby made explicit.

Eco-evolutionary Model of Rapid Phenotypic Diversification in Species-Rich Communities

Evolutionary and ecosystem dynamics are often treated as different processes –operating at separate timescales– even if evidence reveals that rapid evolutionary changes can feed back into ecological interactions. A recent long-term field experiment has explicitly shown that communities of competing plant species can experience very fast phenotypic diversification, and that this gives rise to enhanced complementarity in resource exploitation and to enlarged ecosystem-level productivity. Here, we build on progress made in recent years in the integration of eco-evolutionary dynamics, and present a computational approach aimed at describing these empirical findings in detail. In particular we model a community of organisms of different but similar species evolving in time through mechanisms of birth, competition, sexual reproduction, descent with modification, and death. Based on simple rules, this model provides a rationalization for the emergence of rapid phenotypic diversification in species-rich communities. Furthermore, it also leads to non-trivial predictions about long-term phenotypic change and ecological interactions. Our results illustrate that the presence of highly specialized, non-competing species leads to very stable communities and reveals that phenotypically equivalent species occupying the same niche may emerge and coexist for very long times. Thus, the framework presented here provides a simple approach –complementing existing theories, but specifically devised to account for the specificities of the recent empirical findings for plant communities– to explain the collective emergence of diversification at a community level, and paves the way to further scrutinize the intimate entanglement of ecological and evolutionary processes, especially in species-rich communities.

Population ecology and evolutionary biology have been traditionally studied as separate disciplines, even if feedbacks between community and evolutionary processes are known to exist, having been empirically characterized in recent years in different types of communities (from microbes to plants and vertebrates), and theoretically analyzed with novel and powerful mathematical tools. Recent long-term field experiments with plants have proven that rapid co-evolution and diversification of species traits results in an overall enhancement of the ecosystem productivity, with important consequences for agriculture and conservation. Here, we propose a relatively simple computational eco-evolutionary model specifically devised to describe rapid phenotypic diversification in this type of species-rich communities. Our model captures the main phenomenology observed experimentally, and it also makes non-trivial predictions for long term phenotypic change and ecological interactions, such as the stable coexistence of highly specialized species or the possible emergence of phenotypically equivalent species occupying the same niche. Finally, the model is easily generalizable to analyze different eco-evolutionary problems within a relatively simple and unified computational framework.

Eco-evolutionary dynamics of social dilemmas

Social dilemmas are an integral part of social interactions. Cooperative actions, ranging from secreting extra-cellular products in microbial populations to donating blood in humans, are costly to the actor and hence create an incentive to shirk and avoid the costs. Nevertheless, cooperation is ubiquitous in nature. Both costs and benefits often depend non-linearly on the number and types of individuals involved-as captured by idioms such as 'too many cooks spoil the broth' where additional contributions are discounted, or 'two heads are better than one' where cooperators synergistically enhance the group benefit. Interaction group sizes may depend on the size of the population and hence on ecological processes. This results in feedback mechanisms between ecological and evolutionary processes, which jointly affect and determine the evolutionary trajectory. Only recently combined eco-evolutionary processes became experimentally tractable in microbial social dilemmas. Here we analyse the evolutionary dynamics of non-linear social dilemmas in settings where the population fluctuates in size and the environment changes over time. In particular, cooperation is often supported and maintained at high densities through ecological fluctuations. Moreover, we find that the combination of the two processes routinely reveals highly complex dynamics, which suggests common occurrence in nature.

The Impact of Environmental Fluctuations on Evolutionary Fitness Functions

The concept of fitness as a measure for a species' success in natural selection is central to the theory of evolution. We here investigate how reproduction rates which are not constant but vary in response to environmental fluctuations, influence a species' prosperity and thereby its fitness. Interestingly, we find that not only larger growth rates but also reduced sensitivities to environmental changes substantially increase the fitness. Thereby, depending on the noise level of the environment, it might be an evolutionary successful strategy to minimize this sensitivity rather than to optimize the reproduction speed. Also for neutral evolution, where species with exactly the same properties compete, variability in the growth rates plays a crucial role. The time for one species to fixate is strongly reduced in the presence of environmental noise. Hence, environmental fluctuations constitute a possible explanation for effective population sizes inferred from genetic data that often are much smaller than the census population size.

Non-Selective Evolution of Growing Populations

Non-selective effects, like genetic drift, are an important factor in modern conceptions of evolution, and have been extensively studied for constant population sizes (Kimura, 1955; Otto and Whitlock, 1997). Here, we consider non-selective evolution in the case of growing populations that are of small size and have varying trait compositions (e.g. after a population bottleneck). We find that, in these conditions, populations never fixate to a trait, but tend to a random limit composition, and that the distribution of compositions “freezes” to a steady state. This final state is crucially influenced by the initial conditions. We obtain these findings from a combined theoretical and experimental approach, using multiple mixed subpopulations of two Pseudomonas putida strains in non-selective growth conditions (Matthijs et al, 2009) as model system. The experimental results for the population dynamics match the theoretical predictions based on the Pólya urn model (Eggenberger and Pólya, 1923) for all analyzed parameter regimes. In summary, we show that exponential growth stops genetic drift. This result contrasts with previous theoretical analyses of non-selective evolution (e.g. genetic drift), which investigated how traits spread and eventually take over populations (fixate) (Kimura, 1955; Otto and Whitlock, 1997). Moreover, our work highlights how deeply growth influences non-selective evolution, and how it plays a key role in maintaining genetic variability. Consequently, it is of particular importance in life-cycles models (Melbinger et al, 2010; Cremer et al, 2011; Cremer et al, 2012) of periodically shrinking and expanding populations.

Evolutionary dynamics with fluctuating population sizes and strong mutualism

Game theory ideas provide a useful framework for studying evolutionary dynamics in a well-mixed environment. This approach, however, typically enforces a strictly fixed overall population size, deemphasizing natural growth processes. We study a competitive Lotka-Volterra model, with number fluctuations, that accounts for natural population growth and encompasses interaction scenarios typical of evolutionary games. We show that, in an appropriate limit, the model describes standard evolutionary games with both genetic drift and overall population size fluctuations. However, there are also regimes where a varying population size can strongly influence the evolutionary dynamics. We focus on the strong mutualism scenario and demonstrate that standard evolutionary game theory fails to describe our simulation results. We then analytically and numerically determine fixation probabilities as well as mean fixation times using matched asymptotic expansions, taking into account the population size degree of freedom. These results elucidate the interplay between population dynamics and evolutionary dynamics in well-mixed systems.

The emergence of cooperation from a single mutant during microbial life cycles

Cooperative behaviour is widespread in nature, even though cooperating individuals always run the risk of being exploited by free-riders. Population structure effectively promotes cooperation given that a threshold in the level of cooperation was already reached. However, the question how cooperation can emerge from a single mutant, which cannot rely on a benefit provided by other cooperators, is still puzzling. Here, we investigate this question for a well-defined but generic situation based on typical life cycles of microbial populations where individuals regularly form new colonies followed by growth phases. We analyse two evolutionary mechanisms favouring cooperative behaviour and study their strength depending on the inoculation size and the length of a life cycle. In particular, we find that population bottlenecks followed by exponential growth phases strongly increase the survival and fixation probabilities of a single cooperator in a free-riding population.

feedback between population and evolutionary dynamics determines the fate of social microbial populations

A new study finds that the evolution of social genes may be coupled with population dynamics, and may dramatically affect ecological resilience, particularly in the face of rapidly deteriorating environments.

The evolutionary spread of cheater strategies can destabilize populations engaging in social cooperative behaviors, thus demonstrating that evolutionary changes can have profound implications for population dynamics. At the same time, the relative fitness of cooperative traits often depends upon population density, thus leading to the potential for bi-directional coupling between population density and the evolution of a cooperative trait. Despite the potential importance of these eco-evolutionary feedback loops in social species, they have not yet been demonstrated experimentally and their ecological implications are poorly understood. Here, we demonstrate the presence of a strong feedback loop between population dynamics and the evolutionary dynamics of a social microbial gene, SUC2, in laboratory yeast populations whose cooperative growth is mediated by the SUC2 gene. We directly visualize eco-evolutionary trajectories of hundreds of populations over 50–100 generations, allowing us to characterize the phase space describing the interplay of evolution and ecology in this system. Small populations collapse despite continual evolution towards increased cooperative allele frequencies; large populations with a sufficient number of cooperators “spiral” to a stable state of coexistence between cooperator and cheater strategies. The presence of cheaters does not significantly affect the equilibrium population density, but it does reduce the resilience of the population as well as its ability to adapt to a rapidly deteriorating environment. Our results demonstrate the potential ecological importance of coupling between evolutionary dynamics and the population dynamics of cooperatively growing organisms, particularly in microbes. Our study suggests that this interaction may need to be considered in order to explain intraspecific variability in cooperative behaviors, and also that this feedback between evolution and ecology can critically affect the demographic fate of those species that rely on cooperation for their survival.

The fact that rapid evolution within a species can cause dramatic ecological changes has only recently begun to be appreciated. In particular, it has often been assumed that population dynamics, controlled by ecological circumstances such as the presence of predators or disease, occur at such different timescales compared with evolutionary dynamics that they are effectively de-coupled. Recent studies, however, have found that evolution can occur over ecological timescales and thus may have important effects on ecological dynamics. Here, we demonstrate the presence of a tight coupling between population dynamics and the evolutionary dynamics of a “social” microbial gene, which allows a laboratory population of budding yeast to cooperatively break down sucrose and grow on the simpler sugars released from it. In such cooperative populations, evolution may favor non-cooperative, or “cheater” individuals that do not contribute to the public good (in this case, the products of sucrose break down), but still use that public good to grow at the expense of the individuals that do cooperate. Our study shows that a population of cooperators that is invaded by cheaters does not collapse as a result of cheater proliferation but can evolve to a viable equilibrium. However, the coexisting population is less resilient to perturbations.

Range expansion promotes cooperation in an experimental microbial metapopulation

Natural populations throughout the tree of life undergo range expansions in response to changes in the environment. Recent theoretical work suggests that range expansions can have a strong effect on evolution, even leading to the fixation of deleterious alleles that would normally be outcompeted in the absence of migration. However, little is known about how range expansions might influence alleles under frequency- or density-dependent selection. Moreover, there is very little experimental evidence to complement existing theory, since expanding populations are difficult to study in the natural environment. In this study, we have used a yeast experimental system to explore the effect of range expansions on the maintenance of cooperative behaviors, which commonly display frequency- and density-dependent selection and are widespread in nature. We found that range expansions favor the maintenance of cooperation in two ways: (i) through the enrichment of cooperators at the front of the expanding population and (ii) by allowing cooperators to "outrun" an invading wave of defectors. In this system, cooperation is enhanced through the coupling of population ecology and evolutionary dynamics in expanding populations, thus providing experimental evidence for a unique mechanism through which cooperative behaviors could be maintained in nature.

Mobility, fitness collection, and the breakdown of cooperation

The spatial arrangement of individuals is thought to overcome the dilemma of cooperation: When cooperators engage in clusters, they might share the benefit of cooperation while being more protected against noncooperating individuals, who benefit from cooperation but save the cost of cooperation. This is paradigmatically shown by the spatial prisoner's dilemma model. Here, we study this model in one and two spatial dimensions, but explicitly take into account that in biological setups, fitness collection and selection are separated processes occurring mostly on vastly different time scales. This separation is particularly important to understand the impact of mobility on the evolution of cooperation. We find that even small diffusive mobility strongly restricts cooperation since it enables noncooperative individuals to invade cooperative clusters. Thus, in most biological scenarios, where the mobility of competing individuals is an irrefutable fact, the spatial prisoner's dilemma alone cannot explain stable cooperation, but additional mechanisms are necessary for spatial structure to promote the evolution of cooperation. The breakdown of cooperation is analyzed in detail. We confirm the existence of a phase transition, here controlled by mobility and costs, which distinguishes between purely cooperative and noncooperative absorbing states. While in one dimension the model is in the class of the voter model, it belongs to the directed percolation universality class in two dimensions.

Growth dynamics and the evolution of cooperation in microbial populations

Microbes providing public goods are widespread in nature despite running the risk of being exploited by free-riders. However, the precise ecological factors supporting cooperation are still puzzling. Following recent experiments, we consider the role of population growth and the repetitive fragmentation of populations into new colonies mimicking simple microbial life-cycles. Individual-based modeling reveals that demographic fluctuations, which lead to a large variance in the composition of colonies, promote cooperation. Biased by population dynamics these fluctuations result in two qualitatively distinct regimes of robust cooperation under repetitive fragmentation into groups. First, if the level of cooperation exceeds a threshold, cooperators will take over the whole population. Second, cooperators can also emerge from a single mutant leading to a robust coexistence between cooperators and free-riders. We find frequency and size of population bottlenecks, and growth dynamics to be the major ecological factors determining the regimes and thereby the evolutionary pathway towards cooperation.