Evolutionary dynamics in structured populations

Evolutionary dynamics shape the living world around us. At the centre of every evolutionary process is a population of reproducing individuals. The structure of that population affects evolutionary dynamics. The individuals can be molecules, cells, viruses, multicellular organisms or humans. Whenever the fitness of individuals depends on the relative abundance of phenotypes in the population, we are in the realm of evolutionary game theory. Evolutionary game theory is a general approach that can describe the competition of species in an ecosystem, the interaction between hosts and parasites, between viruses and cells, and also the spread of ideas and behaviours in the human population. In this perspective, we review the recent advances in evolutionary game dynamics with a particular emphasis on stochastic approaches in finite sized and structured populations. We give simple, fundamental laws that determine how natural selection chooses between competing strategies. We study the well-mixed population, evolutionary graph theory, games in phenotype space and evolutionary set theory. We apply these results to the evolution of cooperation. The mechanism that leads to the evolution of cooperation in these settings could be called ‘spatial selection’: cooperators prevail against defectors by clustering in physical or other spaces

Demographic noise can reverse the direction of deterministic selection

Deterministic evolutionary theory robustly predicts that populations displaying altruistic behaviours will be driven to extinction by mutant cheats that absorb common benefits but do not themselves contribute. Here we show that when demographic stochasticity is accounted for, selection can in fact act in the reverse direction to that predicted deterministically, instead favouring cooperative behaviors that appreciably increase the carrying capacity of the population. Populations that exist in larger numbers experience a selective advantage by being more stochastically robust to invasions than smaller populations, and this advantage can persist even in the presence of reproductive costs. We investigate this general effect in the specific context of public goods production and find conditions for stochastic selection reversal leading to the success of public good producers. This insight, developed here analytically, is missed by both the deterministic analysis as well as standard game theoretic models that enforce a fixed population size. The effect is found to be amplified by space; in this scenario we find that selection reversal occurs within biologically reasonable parameter regimes for microbial populations. Beyond the public good problem, we formulate a general mathematical framework for models that may exhibit stochastic selection reversal. In this context, we describe a stochastic analogue to r-K theory, by which small populations can evolve to higher densities in the absence of disturbance.Comment: 25 pages, 12 figure

On the origin of biological construction, with a focus on multicellularity

Biology is marked by a hierarchical organization: all life consists of cells; in some cases, these cells assemble into groups, such as endosymbionts or multicellular organisms; in turn, multicellular organisms sometimes assemble into yet other groups, such as primate societies or ant colonies. The construction of new organizational layers results from hierarchical evolutionary transitions, in which biological units (e.g., cells) form groups that evolve into new units of biological organization (e.g., multicellular organisms). Despite considerable advances, there is no bottom-up, dynamical account of how, starting from the solitary ancestor, the first groups originate and subsequently evolve the organizing principles that qualify them as new units. Guided by six central questions, we propose an integrative bottom-up approach for studying the dynamics underlying hierarchical evolutionary transitions, which builds on and synthesizes existing knowledge. This approach highlights the crucial role of the ecology and development of the solitary ancestor in the emergence and subsequent evolution of groups, and it stresses the paramount importance of the life cycle: only by evaluating groups in the context of their life cycle can we unravel the evolutionary trajectory of hierarchical transitions. These insights also provide a starting point for understanding the types of subsequent organizational complexity. The central research questions outlined here naturally link existing research programs on biological construction (e.g., on cooperation, multilevel selection, self-organization, and development) and thereby help integrate knowledge stemming from diverse fields of biology

Calculating Evolutionary Dynamics in Structured Populations

Evolution is shaping the world around us. At the core of every evolutionary process is a population of reproducing individuals. The outcome of an evolutionary process depends on population structure. Here we provide a general formula for calculating evolutionary dynamics in a wide class of structured populations. This class includes the recently introduced “games in phenotype space” and “evolutionary set theory.” There can be local interactions for determining the relative fitness of individuals, but we require global updating, which means all individuals compete uniformly for reproduction. We study the competition of two strategies in the context of an evolutionary game and determine which strategy is favored in the limit of weak selection. We derive an intuitive formula for the structure coefficient, σ, and provide a method for efficient numerical calculation

Mutation-selection equilibrium in games with multiple strategies

In evolutionary games the fitness of individuals is not constant but depends on the relative abundance of the various strategies in the population. Here we study general games among n strategies in populations of large but finite size. We explore stochastic evolutionary dynamics under weak selection, but for any mutation rate. We analyze the frequency dependent Moran process in well-mixed populations, but almost identical results are found for the Wright-Fisher and Pairwise Comparison processes. Surprisingly simple conditions specify whether a strategy is more abundant on average than 1/n, or than another strategy, in the mutation-selection equilibrium. We find one condition that holds for low mutation rate and another condition that holds for high mutation rate. A linear combination of these two conditions holds for any mutation rate. Our results allow a complete characterization of n*n games in the limit of weak selection.Comment: version 2 is the final published versio

A theoretical foundation for multi-scale regular vegetation patterns

Self-organized regular vegetation patterns are widespread and thought to mediate ecosystem functions such as productivity and robustness, but the mechanisms underlying their origin and maintenance remain disputed. Particularly controversial are landscapes of overdispersed (evenly spaced) elements, such as North American Mima mounds, Brazilian murundus, South African heuweltjies, and, famously, Namibian fairy circles. Two competing hypotheses are currently debated. On the one hand, models of scale-dependent feedbacks, whereby plants facilitate neighbours while competing with distant individuals, can reproduce various regular patterns identified in satellite imagery. Owing to deep theoretical roots and apparent generality, scale-dependent feedbacks are widely viewed as a unifying and near-universal principle of regular-pattern formation despite scant empirical evidence. On the other hand, many overdispersed vegetation patterns worldwide have been attributed to subterranean ecosystem engineers such as termites, ants, and rodents. Although potentially consistent with territorial competition, this interpretation has been challenged theoretically and empirically and (unlike scale-dependent feedbacks) lacks a unifying dynamical theory, fuelling scepticism about its plausibility and generality. Here we provide a general theoretical foundation for self-organization of social-insect colonies, validated using data from four continents, which demonstrates that intraspecific competition between territorial animals can generate the large-scale hexagonal regularity of these patterns. However, this mechanism is not mutually exclusive with scale-dependent feedbacks. Using Namib Desert fairy circles as a case study, we present field data showing that these landscapes exhibit multi-scale patterning-previously undocumented in this system-that cannot be explained by either mechanism in isolation. These multi-scale patterns and other emergent properties, such as enhanced resistance to and recovery from drought, instead arise from dynamic interactions in our theoretical framework, which couples both mechanisms. The potentially global extent of animal-induced regularity in vegetation-which can modulate other patterning processes in functionally important ways-emphasizes the need to integrate multiple mechanisms of ecological self-organization

The ecology and evolution of social behavior in microbes

Cooperation has been studied extensively across the tree of life, from eusociality in insects to social behavior in humans, but it is only recently that a social dimension has been recognized and extensively explored for microbes. Research into microbial cooperation has accelerated dramatically and microbes have become a favorite system because of their fast evolution, their convenience as lab study systems and the opportunity for molecular investigations. However, the study of microbes also poses significant challenges, such as a lack of knowledge and an inaccessibility of the ecological context (used here to include both the abiotic and the biotic environment) under which the trait deemed cooperative has evolved and is maintained. I review the experimental and theoretical evidence in support of the limitations of the study of social behavior in microbes in the absence of an ecological context. I discuss both the need and the opportunities for experimental investigations that can inform a theoretical framework able to reframe the general questions of social behavior in a clear ecological context and to account for eco-evolutionary feedback

Emergence of diverse life cycles and life histories at the origin of multicellularity

The evolution of multicellularity has given rise to a remarkable diversity of multicellular life cycles and life histories. Whereas some multicellular organisms are long-lived, grow through cell division, and repeatedly release single-celled propagules (for example, animals), others are short-lived, form by aggregation, and propagate only once, by generating large numbers of solitary cells (for example, cellular slime moulds). There are no systematic studies that explore how diverse multicellular life cycles can come about. Here, we focus on the origin of multicellularity and develop a mechanistic model to examine the primitive life cycles that emerge from a unicellular ancestor when an ancestral gene is co-opted for cell adhesion. Diverse life cycles readily emerge, depending on ecological conditions, group-forming mechanism, and ancestral constraints. Among these life cycles, we recapitulate both extremes of long-lived groups that propagate continuously and short-lived groups that propagate only once, with the latter type of life cycle being particularly favoured when groups can form by aggregation. Our results show how diverse life cycles and life histories can easily emerge at the origin of multicellularity, shaped by ancestral constraints and ecological conditions. Beyond multicellularity, this finding has similar implications for other major transitions, such as the evolution of sociality

Social influence and interaction bias can drive emergent behavioural specialization and modular social networks across systems

In social systems ranging from ant colonies to human society, behavioural specialization—consistent individual differences in behaviour—is commonplace: individuals can specialize in the tasks they perform (division of labour (DOL)), the political behaviour they exhibit ( political polarization) or the non-task behaviours they exhibit (personalities). Across these contexts, behavioural specialization often co-occurs with modular and assortative social networks, such that individuals tend to associate with others that have the same behavioural specialization. This raises the question of whether a common mechanism could drive co-emergent behavioural specialization and social network structure across contexts. To investigate this question, here we extend a model of self-organized DOL to account for social influence and interaction bias among individuals—social dynamics that have been shown to drive political polarization. We find that these same social dynamics can also drive emergent DOL by forming a feedback loop that reinforces behavioural differences between individuals, a feedback loop that is impacted by group size. Moreover, this feedback loop also results in modular and assortative social network structure, whereby individuals associate strongly with those performing the same task. Our findings suggest that DOL and political polarization—two social phenomena not typically considered together—may actually share a common social mechanism. This mechanism may result in social organization in many contexts beyond task performance and political behaviour