Towards a mechanistic foundation of evolutionary theory

Frequency-dependent returns in nonlinear public goods games

When individuals interact in groups, the evolution of cooperation is traditionally modelled using the framework of public goods games. These models often assume that the return of the public goods depends linearly on the fraction of contributors. In contrast, in real-life public goods interactions, the return can depend on the size of the investor pool as well. Here, we consider a model in which the multiplication factor (marginal per capita return) for the public goods depends linearly on how many contribute, which results in a nonlinear model of public goods. This simple model breaks the curse of dominant defection found in linear public goods interactions and gives rise to richer dynamical outcomes in evolutionary settings. We provide an in-depth analysis of the more varied decisions by the classical rational player in nonlinear public goods interactions as well as a mechanistic, microscopic derivation of the evolutionary outcomes for the stochastic dynamics in finite populations and in the deterministic limit of infinite populations. This kind of nonlinearity provides a natural way to model public goods with diminishing returns as well as economies of scale.

Fission as a source of variation for group selection

Without heritable variation natural selection cannot effect evolutionary change. In the case of group selection, there must be variation in the population of groups. Where does this variation come from? One source of variation is from the stochastic birth-death processes that occur within groups. This is where variation between groups comes from in most mathematical models of group selection. Here, we argue that another important source of variation between groups is fission, the (generally random) group-level reproduction where parent groups split into two or more offspring groups. We construct a simple model of the fissioning process with a parameter that controls how much variation is produced among the offspring groups. We then illustrate the effect of that parameter with some examples. In most models of group selection in the literature, no variation is produced during group reproduction events; that is, groups "clone" themselves when they reproduce. Fission is often a more biologically realistic method of group reproduction, and it can significantly increase the efficacy of group selection.

Fitness as the organismal performance measure guiding adaptive evolution

A long-standing problem in evolutionary theory is to clarify in what sense (if any) natural selection cumulatively improves the design of organisms. Various concepts, such as fitness and inclusive fitness, have been proposed to resolve this problem. In addition, there have been attempts to replace the original problem with more tractable questions, such as whether a given gene or trait is favored by selection. Here, we ask what theoretical properties the concept fitness should possess to encapsulate the improvement criterion required to talk meaningfully about adaptive evolution. We argue that natural selection tends to shape phenotypes based on the causal properties of individuals and that this tendency is, therefore, best captured by a fitness concept that focuses on these properties. We highlight a fitness concept that meets this role under broad conditions but requires adjustments in our conceptual understanding of adaptive evolution. These adjustments combine elements of Dawkinsian gene selectionism and Egbert Leigh's "parliament of genes."

Emergence and maintenance of stable coexistence during a long-term multicellular evolution experiment

The evolution of multicellular life spurred evolutionary radiations, fundamentally changing many of Earth's ecosystems. Yet little is known about how early steps in the evolution of multicellularity affect eco-evolutionary dynamics. Through long-term experimental evolution, we observed niche partitioning and the adaptive divergence of two specialized lineages from a single multicellular ancestor. Over 715 daily transfers, snowflake yeast were subjected to selection for rapid growth, followed by selection favouring larger group size. Small and large cluster-forming lineages evolved from a monomorphic ancestor, coexisting for over ~4,300 generations, specializing on divergent aspects of a trade-off between growth rate and survival. Through modelling and experimentation, we demonstrate that coexistence is maintained by a trade-off between organismal size and competitiveness for dissolved oxygen. Taken together, this work shows how the evolution of a new level of biological individuality can rapidly drive adaptive diversification and the expansion of a nascent multicellular niche, one of the most historically impactful emergent properties of this evolutionary transition.

Putting theory to the test: An integrated computational/experimental chemostat model of the tragedy of the commons

Cooperation via shared public goods is ubiquitous in nature, however, noncontributing social cheaters can exploit the public goods provided by cooperating individuals to gain a fitness advantage. Theory predicts that this dynamic can cause a Tragedy of the Commons, and in particular, a 'Collapsing' Tragedy defined as the extinction of the entire population if the public good is essential. However, there is little empirical evidence of the Collapsing Tragedy in evolutionary biology. Here, we experimentally demonstrate this outcome in a microbial model system, the public good-producing bacterium Pseudomonas aeruginosa grown in a continuous-culture chemostat. In a growth medium that requires extracellular protein digestion, we find that P. aeruginosa populations maintain a high density when entirely composed of cooperating, protease-producing cells but completely collapse when non-producing cheater cells are introduced. We formulate a mechanistic mathematical model that recapitulates experimental observations and suggests key parameters, such as the dilution rate and the cost of public good production, that define the stability of cooperative behavior. We combine model prediction with experimental validation to explain striking differences in the long-term cheater trajectories of replicate cocultures through mutational events that increase cheater fitness. Taken together, our integrated empirical and theoretical approach validates and parametrizes the Collapsing Tragedy in a microbial population, and provides a quantitative, mechanistic framework for generating testable predictions of social behavior.

Transforming yeast into a facultative photoheterotroph via expression of vacuolar rhodopsin

Phototrophic metabolism, the capture of light for energy, was a pivotal biological innovation that greatly increased the total energy available to the biosphere. Chlorophyll-based photosynthesis is the most familiar phototrophic metabolism, but retinal-based microbial rhodopsins transduce nearly as much light energy as chlorophyll does,1 via a simpler mechanism, and are found in far more taxonomic groups. Although this system has apparently spread widely via horizontal gene transfer,2,3,4 little is known about how rhodopsin genes (with phylogenetic origins within prokaryotes5,6) are horizontally acquired by eukaryotic cells with complex internal membrane architectures or the conditions under which they provide a fitness advantage. To address this knowledge gap, we sought to determine whether Saccharomyces cerevisiae, a heterotrophic yeast with no known evolutionary history of phototrophy, can function as a facultative photoheterotroph after acquiring a single rhodopsin gene. We inserted a rhodopsin gene from Ustilago maydis,7 which encodes a proton pump localized to the vacuole, an organelle normally acidified via a V-type rotary ATPase, allowing the rhodopsin to supplement heterotrophic metabolism. Probes of the physiology of modified cells show that they can deacidify the cytoplasm using light energy, demonstrating the ability of rhodopsins to ameliorate the effects of starvation and quiescence. Further, we show that yeast-bearing rhodopsins gain a selective advantage when illuminated, proliferating more rapidly than their non-phototrophic ancestor or rhodopsin-bearing yeast cultured in the dark. These results underscore the ease with which rhodopsins may be horizontally transferred even in eukaryotes, providing novel biological function without first requiring evolutionary optimization.

Extinction scenarios in evolutionary processes: a multinomial Wright-Fisher approach

We study a discrete-time multi-type Wright-Fisher population process. The mean-field dynamics of the stochastic process is induced by a general replicator difference equation. We prove several results regarding the asymptotic behavior of the model, focusing on the impact of the mean-field dynamics on it. One of the results is a limit theorem that describes sufficient conditions for an almost certain path to extinction, first eliminating the type which is the least fit at the mean-field equilibrium. The effect is explained by the metastability of the stochastic system, which under the conditions of the theorem spends almost all time before the extinction event in a neighborhood of the equilibrium. In addition to the limit theorems, we propose a maximization principle for a general deterministic replicator dynamics and study its implications for the stochastic model.

Ghosts of the past: Elemental composition, biosynthesis reactions and thermodynamic properties of Zeta P.2, Eta B.1.525, Theta P.3, Kappa B.1.617.1, Iota B.1.526, Lambda C.37 and Mu B.1.621 variants of SARS-CoV-2

From the perspectives of molecular biology, genetics and biothermodynamics, SARS-CoV-2 is the among the best characterized viruses. Research on SARS-CoV-2 has shed a new light onto driving forces and molecular mechanisms of viral evolution. This paper reports results on empirical formulas, biosynthesis reactions and thermodynamic properties of biosynthesis (multiplication) for the Zeta P.2, Eta B.1.525, Theta P.3, Kappa B.1.617.1, Iota B.1.526, Lambda C.37 and Mu B.1.621 variants of SARS-CoV-2. Thermodynamic analysis has shown that the physical driving forces for evolution of SARS-CoV-2 are Gibbs energy of biosynthesis and Gibbs energy of binding. The driving forces have led SARS-CoV-2 through the evolution process from the original Hu-1 to the newest variants in accordance with the expectations of the evolution theory.

Predation drives complex eco-evolutionary dynamics in sexually selected traits

Predation plays a role in preventing the evolution of ever more complicated sexual displays, because such displays often increase an individual's predation risk. Sexual selection theory, however, omits a key feature of predation in modeling costs to sexually selected traits: Predation is density dependent. As a result of this density dependence, predator-prey dynamics should feed back into the evolution of sexual displays, which, in turn, feeds back into predator-prey dynamics. Here, we develop both population and quantitative genetic models of sexual selection that explicitly link the evolution of sexual displays with predator-prey dynamics. Our primary result is that predation can drive eco-evolutionary cycles in sexually selected traits. We also show that mechanistically modeling the cost to sexual displays as predation leads to novel outcomes such as the maintenance of polymorphism in sexual displays and alters ecological dynamics by muting prey cycles. These results suggest predation as a potential mechanism to maintain variation in sexual displays and underscore that short-term studies of sexual display evolution may not accurately predict long-run dynamics. Further, they demonstrate that a common verbal model (that predation limits sexual displays) with widespread empirical support can result in unappreciated, complex dynamics due to the density-dependent nature of predation.

Inferring density-dependent population dynamics mechanisms through rate disambiguation for logistic birth-death processes

Density dependence is important in the ecology and evolution of microbial and cancer cells. Typically, we can only measure net growth rates, but the underlying density-dependent mechanisms that give rise to the observed dynamics can manifest in birth processes, death processes, or both. Therefore, we utilize the mean and variance of cell number fluctuations to separately identify birth and death rates from time series that follow stochastic birth-death processes with logistic growth. Our nonparametric method provides a novel perspective on stochastic parameter identifiability, which we validate by analyzing the accuracy in terms of the discretization bin size. We apply our method to the scenario where a homogeneous cell population goes through three stages: (1) grows naturally to its carrying capacity, (2) is treated with a drug that reduces its carrying capacity, and (3) overcomes the drug effect to restore its original carrying capacity. In each stage, we disambiguate whether the dynamics occur through the birth process, death process, or some combination of the two, which contributes to understanding drug resistance mechanisms. In the case of limited sample sizes, we provide an alternative method based on maximum likelihood and solve a constrained nonlinear optimization problem to identify the most likely density dependence parameter for a given cell number time series. Our methods can be applied to other biological systems at different scales to disambiguate density-dependent mechanisms underlying the same net growth rate.

Maximal ecological diversity exceeds evolutionary diversity in model ecosystems

Understanding community saturation is fundamental to ecological theory. While investigations of the diversity of evolutionary stable states (ESSs) are widespread, the diversity of communities that have yet to reach an evolutionary endpoint is poorly understood. We use Lotka-Volterra dynamics and trait-based competition to compare the diversity of randomly assembled communities to the diversity of the ESS. We show that, with a large enough founding diversity (whether assembled at once or through sequential invasions), the number of long-time surviving species exceeds that of the ESS. However, the excessive founding diversity required to assemble a saturated community increases rapidly with the dimension of phenotype space. Additionally, traits present in communities resulting from random assembly are more clustered in phenotype space compared to random, although still markedly less ordered than the ESS. By combining theories of random assembly and ESSs we bring a new viewpoint to both the saturation and random assembly literature.

Emergence and maintenance of stable coexistence during a long-term multicellular evolution experiment

The evolution of multicellular life spurred evolutionary radiations, fundamentally changing many of Earth’s ecosystems. Yet little is known about how early steps in the evolution of multicellularity transform eco-evolutionary dynamics, e.g., via niche expansion processes that may facilitate coexistence. Using long-term experimental evolution in the snowflake yeast model system, we show that the evolution of multicellularity drove niche partitioning and the adaptive divergence of two distinct, specialized lineages from a single multicellular ancestor. Over 715 daily transfers, snowflake yeast were subject to selection for rapid growth in rich media, followed by selection favoring larger group size. Both small and large cluster-forming lineages evolved from a monomorphic ancestor, coexisting for over ~4,300 generations. These small and large sized snowflake yeast lineages specialized on divergent aspects of a trade-off between growth rate and survival, mirroring predictions from ecological theory. Through modeling and experimentation, we demonstrate that coexistence is maintained by a trade-off between organismal size and competitiveness for dissolved oxygen. Taken together, this work shows how the evolution of a new level of biological individuality can rapidly drive adaptive diversification and the expansion of a nascent multicellular niche, one of the most historically-impactful emergent properties of this evolutionary transition.

Stochasticity directs adaptive evolution toward nonequilibrium evolutionary attractors

Stochastic processes such as genetic drift may hinder adaptation, but the effect of such stochasticity on evolution via its effect on ecological dynamics is poorly understood. Here we evaluate patterns of adaptation in a population subject to variation in demographic stochasticity. We show that stochasticity can alter population dynamics and lead to evolutionary outcomes that are not predicted by classic eco-evolutionary modeling approaches. We also show, however, that these outcomes are governed by nonequilibrium evolutionary attractors-these are maxima in lifetime reproductive success when stochasticity keeps the ecological system away from the deterministic equilibrium. These NEEAs alter the path of evolution but are not visible through the equilibrium lens that underlies much evolutionary theory. Our results reveal that considering population processes during transient periods can greatly improve our understanding of the path and pace of evolution.

Tradeoff breaking as model of evolutionary transitions in individuality and the limits of the fitness-decoupling metaphor

Evolutionary transitions in individuality (ETIs) involve the formation of Darwinian collectives from Darwinian particles. The transition from cells to multicellular life is a prime example. During an ETI, collectives become units of selection in their own right. However, the underlying processes are poorly understood. One observation used to identify the completion of an ETI is an increase in collective-level performance accompanied by a decrease in particle-level performance, for example measured by growth rate. This seemingly counterintuitive dynamic has been referred to as fitness decoupling and has been used to interpret both models and experimental data. Extending and unifying results from the literature, we show that fitness of particles and collectives can never decouple because calculations of fitness performed over appropriate and equivalent time intervals are necessarily the same provided the population reaches a stable collective size distribution. By way of solution, we draw attention to the value of mechanistic approaches that emphasise traits, and tradeoffs among traits, as opposed to fitness. This trait-based approach is sufficient to capture dynamics that underpin evolutionary transitions. In addition, drawing upon both experimental and theoretical studies, we show that while early stages of transitions might often involve tradeoffs among particle traits, later—and critical—stages are likely to involve the rupture of such tradeoffs. Thus, when observed in the context of ETIs, tradeoff-breaking events stand as a useful marker of these transitions.

Seed banks alter the molecular evolutionary dynamics of Bacillus subtilis

Fluctuations in the availability of resources constrain the growth and reproduction of individuals, which subsequently affects the evolution of their respective populations. Many organisms contend with such fluctuations by entering a reversible state of reduced metabolic activity, a phenomenon known as dormancy. This pool of dormant individuals (i.e. a seed bank) does not reproduce and is expected to act as an evolutionary buffer, though it is difficult to observe this effect directly over an extended evolutionary timescale. Through genetic manipulation, we analyze the molecular evolutionary dynamics of Bacillus subtilis populations in the presence and absence of a seed bank over 700 days. The ability of these bacteria to enter a dormant state increased the accumulation of genetic diversity over time and altered the trajectory of mutations, findings that were recapitulated using simulations based on a mathematical model of evolutionary dynamics. While the ability to form a seed bank did not alter the degree of negative selection, we found that it consistently altered the direction of molecular evolution across genes. Together, these results show that the ability to form a seed bank can affect the direction and rate of molecular evolution over an extended evolutionary timescale.

A general calculus of fitness landscapes finds genes under selection in cancers

Genetic variants drive the evolution of traits and diseases. We previously modeled these variants as small displacements in fitness landscapes and estimated their functional impact by differentiating the evolutionary relationship between genotype and phenotype. Conversely, here we integrate these derivatives to identify genes steering specific traits. Over cancer cohorts, integration identified 460 likely tumor-driving genes. Many have literature and experimental support but had eluded prior genomic searches for positive selection in tumors. Beyond providing cancer insights, these results introduce a general calculus of evolution to quantify the genotype-phenotype relationship and discover genes associated with complex traits and diseases.

Evolution of innate behavioral strategies through competitive population dynamics

Many organism behaviors are innate or instinctual and have been "hard-coded" through evolution. Current approaches to understanding these behaviors model evolution as an optimization problem in which the traits of organisms are assumed to optimize an objective function representing evolutionary fitness. Here, we use a mechanistic birth-death dynamics approach to study the evolution of innate behavioral strategies in a simulated population of organisms. In particular, we performed agent-based stochastic simulations and mean-field analyses of organisms exploring random environments and competing with each other to find locations with plentiful resources. We find that when organism density is low, the mean-field model allows us to derive an effective objective function, predicting how the most competitive phenotypes depend on the exploration-exploitation trade-off between the scarcity of high-resource sites and the increase in birth rate those sites offer organisms. However, increasing organism density alters the most competitive behavioral strategies and precludes the derivation of a well-defined objective function. Moreover, there exists a range of densities for which the coexistence of many phenotypes persists for evolutionarily long times.

Modeling host-associating microbes under selection

The concept of fitness is often reduced to a single component, such as the replication rate in a given habitat. For species with multi-step life cycles, this can be an unjustified oversimplification, as every step of the life cycle can contribute to the overall reproductive success in a specific way. In particular, this applies to microbes that spend part of their life cycles associated to a host. In this case, there is a selection pressure not only on the replication rates, but also on the phenotypic traits associated to migrating from the external environment to the host and vice-versa (i.e., the migration rates). Here, we investigate a simple model of a microbial lineage living, replicating, migrating and competing in and between two compartments: a host and an environment. We perform a sensitivity analysis on the overall growth rate to determine the selection gradient experienced by the microbial lineage. We focus on the direction of selection at each point of the phenotypic space, defining an optimal way for the microbial lineage to increase its fitness. We show that microbes can adapt to the two-compartment life cycle through either changes in replication or migration rates, depending on the initial values of the traits, the initial distribution across the two compartments, the intensity of competition, and the time scales involved in the life cycle versus the time scale of adaptation (which determines the adequate probing time to measure fitness). Overall, our model provides a conceptual framework to study the selection on microbes experiencing a host-associated life cycle.

Intriguing effects of selection intensity on the evolution of prosocial behaviors

In many models of evolving populations, genetic drift has an outsized role relative to natural selection, or vice versa. While there are many scenarios in which one of these two assumptions is reasonable, intermediate balances between these forces are also biologically relevant. In this study, we consider some natural axioms for modeling intermediate selection intensities, and we explore how to quantify the long-term evolutionary dynamics of such a process. To illustrate the sensitivity of evolutionary dynamics to drift and selection, we show that there can be a “sweet spot” for the balance of these two forces, with sufficient noise for rare mutants to become established and sufficient selection to spread. This balance allows prosocial traits to evolve in evolutionary models that were previously thought to be unconducive to the emergence and spread of altruistic behaviors. Furthermore, the effects of selection intensity on long-run evolutionary outcomes in these settings, such as when there is global competition for reproduction, can be highly non-monotonic. Although intermediate selection intensities (neither weak nor strong) are notoriously difficult to study analytically, they are often biologically relevant; and the results we report suggest that they can elicit novel and rich dynamics in the evolution of prosocial behaviors.

Theoretical models of populations have been useful for assessing when and how traits spread, in large part because they are simple. Rather than being used to reproduce empirical data, these idealized models involve relatively few parameters and are utilized to gain a qualitative understanding of what promotes or suppresses a trait. For prosocial traits, which entail a cost to self to help another, one thing that mathematical models often suggest is that competition to reproduce must be localized, meaning an individual must be fitter than just a small subset of the population in order to produce an offspring. We show here that this finding is not robust. Such traits can indeed proliferate when there is global competition for reproduction, which we demonstrate by increasing the degree to which payoffs from games affect birth rates. Since this kind of “stronger selection” has also been observed empirically, we discuss how it is incorporated into theoretical models more broadly.

The Macroevolutionary Consequences of Niche Construction in Microbial Metabolism

Microorganisms display a stunning metabolic diversity. Understanding the origin of this diversity requires understanding how macroevolutionary processes such as innovation and diversification play out in the microbial world. Metabolic networks, which govern microbial resource use, can evolve through different mechanisms, e.g., horizontal gene transfer or de novo evolution of enzymes and pathways. This process is governed by a combination of environmental factors, selective pressures, and the constraints imposed by the genetic architecture of metabolic networks. In addition, many independent results hint that the process of niche construction, by which organisms actively modify their own and each other’s niches and selective pressures, could play a major role in microbial innovation and diversification. Yet, the general principles by which niche construction shapes microbial macroevolutionary patterns remain largely unexplored. Here, we discuss several new hypotheses and directions, and suggest metabolic modeling methods that could allow us to explore large-scale empirical genotype-phenotype-(G-P)-environment spaces in order to study the macroevolutionary effects of niche construction. We hope that this short piece will further stimulate a systematic and quantitative characterization of macroevolutionary patterns and processes in microbial metabolism.

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.

Molecular Evolutionary Dynamics of Energy Limited Microorganisms

Microorganisms have the unique ability to survive extended periods of time in environments with extremely low levels of exploitable energy. To determine the extent that energy limitation affects microbial evolution, we examined the molecular evolutionary dynamics of a phylogenetically diverse set of taxa over the course of 1,000 days. We found that periodic exposure to energy limitation affected the rate of molecular evolution, the accumulation of genetic diversity, and the rate of extinction. We then determined the degree that energy limitation affected the spectrum of mutations as well as the direction of evolution at the gene level. Our results suggest that the initial depletion of energy altered the direction and rate of molecular evolution within each taxon, though after the initial depletion the rate and direction did not substantially change. However, this consistent pattern became diminished when comparisons were performed across phylogenetically distant taxa, suggesting that while the dynamics of molecular evolution under energy limitation are highly generalizable across the microbial tree of life, the targets of adaptation are specific to a given taxon.

Towards a replicator dynamics model of age structured populations

We present a new modelling framework combining replicator dynamics, the standard model of frequency dependent selection, with an age-structured population model. The new framework allows for the modelling of populations consisting of competing strategies carried by individuals who change across their life cycle. Firstly the discretization of the McKendrick von Foerster model is derived. We show that the Euler–Lotka equation is satisfied when the new model reaches a steady state (i.e. stable frequencies between the age classes). This discretization consists of unit age classes where the timescale is chosen so that only a fraction of individuals play a single game round. This implies a linear dynamics and individuals not killed during the round are moved to the next age class; linearity means that the system is equivalent to a large Bernadelli–Lewis–Leslie matrix. Then we use the methodology of multipopulation games to derive two, mutually equivalent systems of equations. The first contains equations describing the evolution of the strategy frequencies in the whole population, completed by subsystems of equations describing the evolution of the age structure for each strategy. The second contains equations describing the changes of the general population’s age structure, completed with subsystems of equations describing the selection of the strategies within each age class. We then present the obtained system of replicator dynamics in the form of the mixed ODE-PDE system which is independent of the chosen timescale, and much simpler. The obtained results are illustrated by the example of the sex ratio model which shows that when different mortalities of the sexes are assumed, the sex ratio of 0.5 is obtained but that Fisher’s mechanism, driven by the reproductive value of the different sexes, is not in equilibrium.

Replicator dynamics for the game theoretic selection models based on state

The paper presents an attempt to integrate the classical evolutionary game theory based on replicator dynamics and the state-based approach of Houston and McNamara. In the new approach, individuals have different heritable strategies; however, individuals carrying the same strategy can differ in terms of state, role or the situation in which they act. Thus, the classical replicator dynamics is completed by the additional subsystem of differential equations describing the dynamics of transitions between different states. In effect, the interactions described by game structure, in addition to the demographic payoffs (constituted by births and deaths), can lead to the change in state of the competing individuals. Special cases of reversible and irreversible incremental stage-structured models, where the state changes can describeenergy accumulation, developmental steps or aging, are derived for discrete and continuous versions. The new approach is illustrated using the example of the Owner-Intruder game with explicit dynamics of the role changes. The new model presents a generalization of the demographic version of the Hawk-Dove game,with the difference being that the opponents in the game are drawn from two separate subpopulations consisting of Owners and Intruders. Here, the Intruders check random nest sites and play the Hawk-Dove game with the Owner if they are occupied. Meanwhile, the Owners produce newborns that become Intruders, since they must find a free nest site to reproduce. An interesting feedback mechanism is produced via the fluxes of individuals between the different subpopulations. In addition, the population growth suppression mechanism resulting from the fixation Bourgeois strategy is analyzed.

Trophic cascades alter eco-evolutionary dynamics and body size evolution

Trait evolution in predator-prey systems can feed back to the dynamics of interacting species as well as cascade to impact the dynamics of indirectly linked species (eco-evolutionary trophic cascades; EETCs). A key mediator of trophic cascades is body mass, as it both strongly influences and evolves in response to predator-prey interactions. Here, we use Gillespie eco-evolutionary models to explore EETCs resulting from top predator loss and mediated by body mass evolution. Our four-trophic-level food chain model uses allometric scaling to link body mass to different functions (ecological pleiotropy) and is realistically parameterized from the FORAGE database to mimic the parameter space of a typical freshwater system. To track real-time changes in selective pressures, we also calculated fitness gradients for each trophic level. As predicted, top predator loss generated alternating shifts in abundance across trophic levels, and, depending on the nature and strength in changes to fitness gradients, also altered trajectories of body mass evolution. Although more distantly linked, changes in the abundance of top predators still affected the eco-evolutionary dynamics of the basal producers, in part because of their relatively short generation times. Overall, our results suggest that impacts on top predators can set off transient EETCs with the potential for widespread indirect impacts on food webs.

Same-sex sexual behaviour and selection for indiscriminate mating

The widespread presence of same-sex sexual behaviour (SSB) has long been thought to pose an evolutionary conundrum, as participants in SSB suffer the cost of failing to reproduce after expending the time and energy to find a mate. The potential for SSB to occur as part of an optimal strategy has received less attention, although indiscriminate sexual behaviour may be the ancestral mode of sexual reproduction. Here, we build a simple model of sexual reproduction and create a theoretical framework for the evolution of indiscriminate sexual behaviour. We provide strong support for the hypothesis that SSB can be maintained by selection for indiscriminate sexual behaviour, by showing that indiscriminate mating is the optimal strategy under a wide range of conditions. Further, our model suggests that the conditions that most strongly favour indiscriminate mating were probably present at the origin of sexual behaviour. These findings have implications not only for the evolutionary origins of SSB, but also for the evolution of discriminate sexual behaviour across the animal kingdom.

Eco-evolutionary dynamics of nested Darwinian populations and the emergence of community-level heredity

Interactions among microbial cells can generate new chemistries and functions, but exploitation requires establishment of communities that reliably recapitulate community-level phenotypes. Using mechanistic mathematical models, we show how simple manipulations to population structure can exogenously impose Darwinian-like properties on communities. Such scaffolding causes communities to participate directly in the process of evolution by natural selection and drives the evolution of cell-level interactions to the point where, despite underlying stochasticity, derived communities give rise to offspring communities that faithfully re-establish parental phenotype. The mechanism is akin to a developmental process (developmental correction) that arises from density-dependent interactions among cells. Knowledge of ecological factors affecting evolution of developmental correction has implications for understanding the evolutionary origin of major egalitarian transitions, symbioses, and for top-down engineering of microbial communities.

Evolutionary dynamics from deterministic microscopic ecological processes

The central goal of a dynamical theory of evolution is to abstract the mean evolutionary trajectory in the trait space by considering ecological processes at the level of the individual. In this work we develop such a theory for a class of deterministic individual-based models describing individual births and deaths, which captures the essential features of standard stochastic individual-based models and becomes identical to the latter under maximal competition. The key motivation is to derive the canonical equation of adaptive dynamics from this microscopic ecological model, which can be regarded as a paradigm to study evolution in a simple way and give it an intuitive geometric interpretation. Another goal is to study evolution and sympatric speciation under maximal competition. We show that these models, in the deterministic limit of adaptive dynamics, lead to the same equations that describe the unraveling of the mean evolutionary trajectory as those obtained from the standard stochastic models. We further study conditions under which these models lead to evolutionary branching and find them to be similar to those obtained from the standard stochastic models. We find that, although deterministic models result in a strong competition that leads to a speedup in the temporal dynamics of a population cloud in the phenotypic space as well as an increase in the rate of generation of biodiversity, they do not seem to result in an absolute increase in biodiversity as far as the total number of species is concerned. Hence, they essentially capture all the features of the standard stochastic model. Interestingly, the notion of a fitness function does not explicitly enter in our derivation of the canonical equation, thereby advocating a mechanistic view of evolution based on fundamental birth-death events where fitness is a derived quantity rather than a fundamental ingredient. We illustrate our work with the help of several examples and qualitatively compare the rate of unraveling of evolutionary trajectory and generation of biodiversity for the deterministic and standard individual-based models by showing the motion of population clouds in the trait space.

Ecological scaffolding and the evolution of individuality

Evolutionary transitions in individuality are central to the emergence of biological complexity. Recent experiments provide glimpses of processes underpinning the transition from single cells to multicellular life and draw attention to the critical role of ecology. Here, we emphasize this ecological dimension and argue that its current absence from theoretical frameworks hampers development of general explanatory solutions. Using mechanistic mathematical models, we show how a minimal ecological structure comprising patchily distributed resources and between-patch dispersal can scaffold Darwinian-like properties on collectives of cells. This scaffolding causes cells to participate directly in the process of evolution by natural selection as if they were members of multicellular collectives, with collectives participating in a death-birth process arising from the interplay between the timing of dispersal events and the rate of resource use by cells. When this timescale is sufficiently long and new collectives are founded by single cells, collectives experience conditions that favour evolution of a reproductive division of labour. Together our simple model makes explicit key events in the major evolutionary transition to multicellularity. It also makes predictions concerning the life history of certain pathogens and serves as an ecological recipe for experimental realization of evolutionary transitions.

Division of labor in bacterial populations

Cooperating behaviors abound across all domains of life, but are vulnerable to invasion by cheaters. An important evolutionary question is to determine mechanisms that stabilize and maintain cooperation levels and prevent population collapse. Policing is one strategy populations may employ to achieve this goal, and it has been observed in many natural populations including microbes. Here we present and analyze a division of labor model to investigate if, when and how policing can be a cooperation-stabilizing mediator. The model represents a chemostat where cooperators produce a public good that benefits all individuals, and where toxin-producers produce a toxin that harms both cooperators and cheaters. We show that in many cases, the mere presence of toxin-producers is not enough to avoid a Tragedy of the Commons in which all individuals go extinct. The main focus of our work is to identify conditions on various model parameters which ensure that a mixed population of cooperators and toxin-producers can stably coexist and can avoid invasion by a cheater population. This happens when all of the following conditions hold: (i) The cost of policing must exceed the cost of cooperation. (ii) There is enough "collateral damage" caused by policing, i.e. the toxicity rate experienced by cooperators is sufficiently high, and (iii) The toxin affects cheaters even more than cooperators, and we provide a precise mathematical condition of how much stronger this effect should be.

Simulations reveal challenges to artificial community selection and possible strategies for success

Multispecies microbial communities often display "community functions" arising from interactions of member species. Interactions are often difficult to decipher, making it challenging to design communities with desired functions. Alternatively, similar to artificial selection for individuals in agriculture and industry, one could repeatedly choose communities with the highest community functions to reproduce by randomly partitioning each into multiple "Newborn" communities for the next cycle. However, previous efforts in selecting complex communities have generated mixed outcomes that are difficult to interpret. To understand how to effectively enact community selection, we simulated community selection to improve a community function that requires 2 species and imposes a fitness cost on one or both species. Our simulations predict that improvement could be easily stalled unless various aspects of selection are carefully considered. These aspects include promoting species coexistence, suppressing noncontributors, choosing additional communities besides the highest functioning ones to reproduce, and reducing stochastic fluctuations in the biomass of each member species in Newborn communities. These considerations can be addressed experimentally. When executed effectively, community selection is predicted to improve costly community function, and may even force species to evolve slow growth to achieve species coexistence. Our conclusions hold under various alternative model assumptions and are therefore applicable to a variety of communities.

Computation and Simulation of Evolutionary Game Dynamics in Finite Populations

The study of evolutionary dynamics increasingly relies on computational methods, as more and more cases outside the range of analytical tractability are explored. The computational methods for simulation and numerical approximation of the relevant quantities are diverging without being compared for accuracy and performance. We thoroughly investigate these algorithms in order to propose a reliable standard. For expositional clarity we focus on symmetric 2 × 2 games leading to one-dimensional processes, noting that extensions can be straightforward and lessons will often carry over to more complex cases. We provide time-complexity analysis and systematically compare three families of methods to compute fixation probabilities, fixation times and long-term stationary distributions for the popular Moran process. We provide efficient implementations that substantially improve wall times over naive or immediate implementations. Implications are also discussed for the Wright-Fisher process, as well as structured populations and multiple types.

A multi-model framework for the Arabidopsis life cycle

Linking our understanding of biological processes at different scales is a major conceptual challenge in biology and aggravated by differences in research methods. Modelling can be a useful approach to consolidating our understanding across traditional research domains. The laboratory model species Arabidopsis is very widely used to study plant growth processes and has also been tested more recently in ecophysiology and population genetics. However, approaches from crop modelling that might link these domains are rarely applied to Arabidopsis. Here, we combine plant growth models with phenology models from ecophysiology, using the agent-based modelling language Chromar. We introduce a simpler Framework Model of vegetative growth for Arabidopsis, FM-lite. By extending this model to include inflorescence and fruit growth and seed dormancy, we present a whole-life-cycle, multi-model FM-life, which allows us to simulate at the population level in various genotype × environment scenarios. Environmental effects on plant growth distinguish between the simulated life history strategies that were compatible with previously described Arabidopsis phenology. Our results simulate reproductive success that is founded on the broad range of physiological processes familiar from crop models and suggest an approach to simulating evolution directly in future.

Social evolution under demographic stochasticity

How social traits such as altruism and spite evolve remains an open question in evolutionary biology. One factor thought to be potentially important is demographic stochasticity. Here we provide a general theoretical analysis of the role of demographic stochasticity in social evolution. We show that the evolutionary impact of stochasticity depends on how the social action alters the recipient’s life cycle. If the action alters the recipient’s death rate, then demographic stochasticity always favours altruism and disfavours spite. On the other hand, if the action alters the recipient’s birth rate, then stochasticity can either favour or disfavour both altruism and spite depending on the ratio of the rate of population turnover to the population size. Finally, we also show that this ratio is critical to determining if demographic stochasticity can reverse the direction of selection upon social traits. Our analysis thus provides a general understanding of the role of demographic stochasticity in social evolution.

Explaining the evolution of social traits such as altruism and spite remains a key outstanding problem in evolutionary biology. Here we develop a simple theory for the effect of demographic stochasticity (random variation in an individual’s birth and death rates) on the evolution of social traits. Our results provide a clear set of predictions: whether a social trait is favoured or disfavoured is determined by how the social action alters the recipient’s life cycle. If the social action alters the recipient’s death rate, then altruism is favoured and spite disfavoured. If instead the social action alters the recipient’s birth rate, then both altruism and spite can be either favoured or disfavoured—the precise outcome depends upon the ratio of the population turnover rate to the population size.

Available energy fluxes drive a transition in the diversity, stability, and functional structure of microbial communities

A fundamental goal of microbial ecology is to understand what determines the diversity, stability, and structure of microbial ecosystems. The microbial context poses special conceptual challenges because of the strong mutual influences between the microbes and their chemical environment through the consumption and production of metabolites. By analyzing a generalized consumer resource model that explicitly includes cross-feeding, stochastic colonization, and thermodynamics, we show that complex microbial communities generically exhibit a transition as a function of available energy fluxes from a "resource-limited" regime where community structure and stability is shaped by energetic and metabolic considerations to a diverse regime where the dominant force shaping microbial communities is the overlap between species' consumption preferences. These two regimes have distinct species abundance patterns, different functional profiles, and respond differently to environmental perturbations. Our model reproduces large-scale ecological patterns observed across multiple experimental settings such as nestedness and differential beta diversity patterns along energy gradients. We discuss the experimental implications of our results and possible connections with disorder-induced phase transitions in statistical physics.

A mathematical formalism for natural selection with arbitrary spatial and genetic structure

We define a general class of models representing natural selection between two alleles. The population size and spatial structure are arbitrary, but fixed. Genetics can be haploid, diploid, or otherwise; reproduction can be asexual or sexual. Biological events (e.g. births, deaths, mating, dispersal) depend in arbitrary fashion on the current population state. Our formalism is based on the idea of genetic sites. Each genetic site resides at a particular locus and houses a single allele. Each individual contains a number of sites equal to its ploidy (one for haploids, two for diploids, etc.). Selection occurs via replacement events, in which alleles in some sites are replaced by copies of others. Replacement events depend stochastically on the population state, leading to a Markov chain representation of natural selection. Within this formalism, we define reproductive value, fitness, neutral drift, and fixation probability, and prove relationships among them. We identify four criteria for evaluating which allele is selected and show that these become equivalent in the limit of low mutation. We then formalize the method of weak selection. The power of our formalism is illustrated with applications to evolutionary games on graphs and to selection in a haplodiploid population.

On the deformability of an empirical fitness landscape by microbial evolution

A fitness landscape is a map between the genotype and its reproductive success in a given environment. The topography of fitness landscapes largely governs adaptive dynamics, constraining evolutionary trajectories and the predictability of evolution. Theory suggests that this topography can be deformed by mutations that produce substantial changes to the environment. Despite its importance, the deformability of fitness landscapes has not been systematically studied beyond abstract models, and little is known about its reach and consequences in empirical systems. Here we have systematically characterized the deformability of the genome-wide metabolic fitness landscape of the bacterium Escherichia coli Deformability is quantified by the noncommutativity of epistatic interactions, which we experimentally demonstrate in mutant strains on the path to an evolutionary innovation. Our analysis shows that the deformation of fitness landscapes by metabolic mutations rarely affects evolutionary trajectories in the short range. However, mutations with large environmental effects produce long-range landscape deformations in distant regions of the genotype space that affect the fitness of later descendants. Our results therefore suggest that, even in situations in which mutations have strong environmental effects, fitness landscapes may retain their power to forecast evolution over small mutational distances despite the potential attenuation of that power over longer evolutionary trajectories. Our methods and results provide an avenue for integrating adaptive and eco-evolutionary dynamics with complex genetics and genomics.

Disentangling eco-evolutionary effects on trait fixation

In population genetics, fixation of traits in a demographically changing population under frequency-independent selection has been extensively analysed. In evolutionary game theory, models of fixation have typically focused on fixed population sizes and frequency-dependent selection. A combination of demographic fluctuations with frequency-dependent interactions such as Lotka-Volterra dynamics has received comparatively little attention. We consider a stochastic, competitive Lotka-Volterra model with higher order interactions between two traits. The emerging individual-based model allows for stochastic fluctuations in the frequencies of the two traits and the total population size. We calculate the fixation probability of a trait under differing competition coefficients. This fixation probability resembles, qualitatively, the deterministic evolutionary dynamics. Furthermore, we partially disentangle the selection effects into their ecological and evolutionary components. We find that changing the evolutionary selection strength also changes the population dynamics and vice versa. Thus, a clean separation of the ecological and evolutionary effects is not possible. Instead, our results imply a nested interaction of the evolutionary and ecological effects. The entangled eco-evolutionary processes thus cannot be ignored when determining fixation properties in a co-evolutionary system.

Pathogen evolution in finite populations: slow and steady spreads the best

The theory of life-history evolution provides a powerful framework to understand the evolutionary dynamics of pathogens. It assumes, however, that host populations are large and that one can neglect the effects of demographic stochasticity. Here, we expand the theory to account for the effects of finite population size on the evolution of pathogen virulence. We show that demographic stochasticity introduces additional evolutionary forces that can qualitatively affect the dynamics and the evolutionary outcome. We discuss the importance of the shape of the pathogen fitness landscape on the balance between mutation, selection and genetic drift. This analysis reconciles Adaptive Dynamics with population genetics in finite populations and provides a new theoretical toolbox to study life-history evolution in realistic ecological scenarios.

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.

Synergy from reproductive division of labor and genetic complexity drive the evolution of sex

Computer experiments that mirror the evolutionary dynamics of sexual and asexual organisms as they occur in nature were used to test features proposed to explain the evolution of sexual recombination. Results show that this evolution is better described as a network of interactions between possible sexual forms, including diploidy, thelytoky, facultative sex, assortation, bisexuality, and division of labor between the sexes, rather than a simple transition from parthenogenesis to sexual recombination. Diploidy was shown to be fundamental for the evolution of sex; bisexual reproduction emerged only among anisogamic diploids with a synergistic division of reproductive labor; and facultative sex was more likely to evolve among haploids practicing assortative mating. Looking at the evolution of sex as a complex system through individual-based simulations explains better the diversity of sexual strategies known to exist in nature, compared to classical analytical models.