Microbial evolution-An under-appreciated driver of soil carbon cycling

Although substantial advances in predicting the ecological impacts of global change have been made, predictions of the evolutionary impacts have lagged behind. In soil ecosystems, microbes act as the primary energetic drivers of carbon cycling; however, microbes are also capable of evolving on timescales comparable to rates of global change. Given the importance of soil ecosystems in global carbon cycling, we assess the potential impact of microbial evolution on carbon-climate feedbacks in this system. We begin by reviewing the current state of knowledge concerning microbial evolution in response to global change and its specific effect on soil carbon dynamics. Through this integration, we synthesize a roadmap detailing how to integrate microbial evolution into ecosystem biogeochemical models. Specifically, we highlight the importance of microscale mechanistic soil carbon models, including choosing an appropriate evolutionary model (e.g., adaptive dynamics, quantitative genetics), validating model predictions with 'omics' and experimental data, scaling microbial adaptations to ecosystem level processes, and validating with ecosystem-scale measurements. The proposed steps will require significant investment of scientific resources and might require 10-20 years to be fully implemented. However, through the application of multi-scale integrated approaches, we will advance the integration of microbial evolution into predictive understanding of ecosystems, providing clarity on its role and impact within the broader context of environmental change.

Treatment outcome in an SI model with evolutionary resistance: a Darwinian model for the evolution of resistance

We consider a Darwinian (evolutionary game theoretic) version of a standard susceptible-infectious SI model in which the resistance of the disease causing pathogen to a treatment that prevents death to infected individuals is subject to evolutionary adaptation. We determine the existence and stability of all equilibria, both disease-free and endemic, and use the results to determine conditions under which the treatment will succeed or fail. Of particular interest are conditions under which a successful treatment in the absence of resistance adaptation (i.e. one that leads to a stable disease-free equilibrium) will succeed or fail when pathogen resistance is adaptive. These conditions are determined by the relative breadths of treatment effectiveness and infection transmission rate distributions as functions of pathogen resistance.

High importance of indirect evolutionary rescue in a small food web

Evolutionary rescue may allow species to survive environmental change, but how this mechanism operates in food webs is poorly understood. Here, the evolutionary rescue was investigated in a small model food web, systematically allowing the evolution of each single species in order to reveal how its adaptation affects the persistence of itself and others. The impact of evolution was highly species-specific and not necessarily positive: only one species, the specialist predator, consistently had a positive impact on overall persistence. Most strikingly, evolution overwhelmingly affected other species: rescue of others (indirect rescue) was far more frequent than self-rescue, and negative effects were nearly always indirect. This demonstrates that evolutionary rescue in food webs is inextricably bound up with species interactions, as the effects of evolution in one species ripple through the entire community. It is therefore critically important to consider the food web context in efforts to understand how species may survive global change.

Beyond classical theories: An integrative mathematical model of mating dynamics and parental care

Classical theories, such as Bateman's principle and Trivers' parental investment theory, attempted to explain the coevolution of sexual selection and parental care through simple verbal arguments. Since then, quantitative models have demonstrated that it is rarely that simple because many non-intuitive structures and non-linear relationships are actually at play. In this study, we propose a new standard for models of mating dynamics and parental care, emphasizing the clarity and use of mathematical and probabilistic arguments, the meaning of consistency conditions, and the key role of spatial densities and the law of mass action. We used adaptive dynamics to calculate the evolutionary trajectory of the total care duration. Our results clearly show how the outcomes of parental care evolution can be diverse, depending on the quantitative balance between a set of dynamical forces arising from relevant differences and conditions in the male and female populations. The intensity of sexual selection, synergy of care, care quality, and relative mortality rates during mating interactions and caring activities act as forces driving evolutionary transitions between uniparental and biparental care. Sexual selection reduces the care duration of the selected sex, uniparental care evolves in the sex that offers the higher care quality, higher mortality during mating interactions of one sex leads to more care by that sex, and higher mortality during caring activities of one sex favours the evolution of uniparental care in the other sex. Both synergy and higher overall mortality during mating interactions can stabilize biparental care when sexual selection reduces the care duration of the selected sex. We discuss how the interaction between these forces influences the evolution of care patterns, and how sex ratios can vary and be interpreted in these contexts. We also propose new directions for future developments of our integrative model, creating new comparable analyses that share the same underlying assumptions and dynamical frameworks.

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.

Integrating eco-evolutionary dynamics and modern coexistence theory

Community ecology typically assumes that competitive exclusion and species coexistence are unaffected by evolution on the time scale of ecological dynamics. However, recent studies suggest that rapid evolution operating concurrently with competition may enable species coexistence. Such findings necessitate general theory that incorporates the coexistence contributions of eco-evolutionary processes in parallel with purely ecological mechanisms and provides metrics for quantifying the role of evolution in shaping competitive outcomes in both modelling and empirical contexts. To foster the development of such theory, here we extend the interpretation of the two principal metrics of modern coexistence theory-niche and competitive ability differences-to systems where competitors evolve. We define eco-evolutionary versions of these metrics by considering how invading and resident species adapt to conspecific and heterospecific competitors. We show that the eco-evolutionary niche and competitive ability differences are sums of ecological and evolutionary processes, and that they accurately predict the potential for stable coexistence in previous theoretical studies of eco-evolutionary dynamics. Finally, we show how this theory frames recent empirical assessments of rapid evolution effects on species coexistence, and how empirical work and theory on species coexistence and eco-evolutionary dynamics can be further integrated.

Frequency dependence and the predictability of evolution in a changing environment

Frequency‐dependent (FD) selection, whereby fitness and selection depend on the genetic or phenotypic composition of the population, arises in numerous ecological contexts (competition, mate choice, crypsis, mimicry, etc.) and can strongly impact evolutionary dynamics. In particular, negative frequency‐dependent selection (NFDS) is well known for its ability to potentially maintain stable polymorphisms, but it has also been invoked as a source of persistent, predictable frequency fluctuations. However, the conditions under which such fluctuations persist are not entirely clear. In particular, previous work rarely considered that FD is unlikely to be the sole driver of evolutionary dynamics when it occurs, because most environments are not static but instead change dynamically over time. Here, we investigate how FD interacts with a temporally fluctuating environment to shape the dynamics of population genetic change. We show that a simple metric introduced by Lewontin, the slope of frequency change against frequency near equilibrium, works as a key criterion for distinguishing microevolutionary outcomes, even in a changing environment. When this slope D is between 0 and –2 (consistent with the empirical examples we review), substantial fluctuations would not persist on their own in a large population occupying a constant environment, but they can still be maintained indefinitely as quasi‐cycles fueled by environmental noise or genetic drift. However, such moderate NFDS buffers and temporally shifts evolutionary responses to periodic environments (e.g., seasonality). Stronger FD, with slope D < –2, can produce self‐sustained cycles that may overwhelm responses to a changing environment, or even chaos that fundamentally limits predictability. This diversity of expected outcomes, together with the empirical evidence for both FD and environment‐dependent selection, suggests that the interplay of internal dynamics with external forcing should be investigated more systematically to reach a better understanding and prediction of evolution.

Character displacement in the presence of multiple trait differences: Evolution of the storage effect in germination and growth

Ecological character displacement is a prominent hypothesis for the maintenance of ecological differences between species that are critical to stable coexistence. Models of character displacement often ascribe interspecific competitive interactions to a single character, but multiple characters contribute to competition, and their effects on selection can be nonadditive. Focusing on one character, we ask if other characters that affect competition alter evolutionary outcomes for the focal character. We address this question using the variable environment seed bank model for two species with two traits. The focal trait is the temporal pattern of germination, which is evolutionary labile. The other trait is the temporal pattern of plant growth, which is assumed fixed. We ask whether evolutionary divergence of germination patterns between species depends on species differences in plant growth. Patterns of growth can affect selection on germination patterns in two ways. First, cues present at germination can provide information about future growth. Second, germination and growth jointly determine the biomass of plants, which determines demand for resources. Germination and growth contribute to the selection gradient in distinct components, one density-independent and the other density-dependent. Importantly, the relative strengths of the components are key. When the density-dependent component is stronger, displacement in germination patterns between species is larger. Stronger cues at germination strengthen the density-independent component by increasing the benefits of germinating in years of favorable growth. But cues also affect the density-dependent component by boosting a species' biomass, and hence its competitive effect, in good years. Consequently, cues weaken character displacement when growth patterns are similar for two competitors, but favor displacement when growth patterns are species-specific. Understanding how these selection components change between contexts can help understand the origin and maintenance of species differences in germination patterns in temporally fluctuating environments.

Rapid evolution promotes fluctuation-dependent species coexistence

Recent studies have demonstrated that rapid contemporary evolution can play a significant role in regulating population dynamics on ecological timescales. Here we identify a previously unrecognised mode by which rapid evolution can promote species coexistence via temporal fluctuations and a trade-off between competitive ability and the speed of adaptive evolution. We show that this interaction between rapid evolution and temporal fluctuations not only increases the range of coexistence conditions under a gleaner-opportunist trade-off (i.e. low minimum resource requirement [R^* ] vs. high maximum growth rate) but also yields stable coexistence in the absence of a classical gleaner-opportunist trade-off. Given the propensity for both oscillatory dynamics and different rates of adaptation between species (including rapid evolution and phenotypic plasticity) in the real world, we argue that this expansion of fluctuation-dependent coexistence theory provides an important overlooked solution to the so-called 'paradox of the plankton'.

Positive interactions within and between populations decrease the likelihood of evolutionary rescue

Positive interactions, including intraspecies cooperation and interspecies mutualisms, play crucial roles in shaping the structure and function of many ecosystems, ranging from plant communities to the human microbiome. While the evolutionary forces that form and maintain positive interactions have been investigated extensively, the influence of positive interactions on the ability of species to adapt to new environments is still poorly understood. Here, we use numerical simulations and theoretical analyses to study how positive interactions impact the likelihood that populations survive after an environment deteriorates, such that survival in the new environment requires quick adaptation via the rise of new mutants-a scenario known as evolutionary rescue. We find that the probability of evolutionary rescue in populations engaged in positive interactions is reduced significantly. In cooperating populations, this reduction is largely due to the fact that survival may require at least a minimal number of individuals, meaning that adapted mutants must arise and spread before the population declines below this threshold. In mutualistic populations, the rescue probability is decreased further due to two additional effects-the need for both mutualistic partners to adapt to the new environment, and competition between the two species. Finally, we show that the presence of cheaters reduces the likelihood of evolutionary rescue even further, making it extremely unlikely. These results indicate that while positive interactions may be beneficial in stable environments, they can hinder adaptation to changing environments and thereby elevate the risk of population collapse. Furthermore, these results may hint at the selective pressures that drove co-dependent unicellular species to form more adaptable organisms able to differentiate into multiple phenotypes, including multicellular life.

Evolutionarily stable strategies in stable and periodically fluctuating populations: The Rosenzweig-MacArthur predator-prey model

An evolutionarily stable strategy (ESS) is an evolutionary strategy that, if adapted by a population, cannot be invaded by any deviating (mutant) strategy. The concept of ESS has been extensively studied and widely applied in ecology and evolutionary biology [M. Smith, On Evolution (1972)] but typically on the assumption that the system is ecologically stable. With reference to a Rosenzweig-MacArthur predator-prey model [M. Rosenzweig, R. MacArthur, Am. Nat. 97, 209-223 (1963)], we derive the mathematical conditions for the existence of an ESS when the ecological dynamics have asymptotically stable limit points as well as limit cycles. By extending the framework of Reed and Stenseth [J. Reed, N. C. Stenseth, J. Theoret. Biol. 108, 491-508 (1984)], we find that ESSs occur at values of the evolutionary strategies that are local optima of certain functions of the model parameters. These functions are identified and shown to have a similar form for both stable and fluctuating populations. We illustrate these results with a concrete example.

Surprising spatiotemporal stability of a multi-peak fitness landscape revealed by independent field experiments measuring hybrid fitness

The effect of the environment on fitness in natural populations is a fundamental question in evolutionary biology. However, experimental manipulations of both environment and phenotype at the same time are rare. Thus, the relative importance of the competitive environment versus intrinsic organismal performance in shaping the location, height, and fluidity of fitness peaks and valleys remains largely unknown. Here, we experimentally tested the effect of competitor frequency on the complex fitness landscape driving adaptive radiation of a generalist and two trophic specialist pupfishes, a scale-eater and molluscivore, endemic to hypersaline lakes on San Salvador Island (SSI), Bahamas. We manipulated phenotypes, by generating 3407 F4/F5 lab-reared hybrids, and competitive environment, by altering the frequency of rare transgressive hybrids between field enclosures in two independent lake populations. We then tracked hybrid survival and growth rates across these four field enclosures for 3-11 months. In contrast to competitive speciation theory, we found no evidence that the frequency of hybrid phenotypes affected their survival. Instead, we observed a strikingly similar fitness landscape to a previous independent field experiment, each supporting multiple fitness peaks for generalist and molluscivore phenotypes and a large fitness valley isolating the divergent scale-eater phenotype. These features of the fitness landscape were stable across manipulated competitive environments, multivariate trait axes, and spatiotemporal heterogeneity. We suggest that absolute performance constraints and divergent gene regulatory networks shape macroevolutionary (interspecific) fitness landscapes in addition to microevolutionary (intraspecific) competitive dynamics. This interplay between organism and environment underlies static and dynamic features of the adaptive landscape.

Coevolution, diversification and alternative states in two-trophic communities

Single-trait eco-evolutionary models of arms races between consumers and their resource species often show inhibition rather than promotion of community diversification. In contrast, modelling arms races involving multiple traits, we found that arms races can promote diversification when trade-off costs among traits make simultaneous investment in multiple traits either more beneficial or more costly. Coevolution between resource and consumer species generates an adaptive landscape for each, with the configuration giving predictable suites of consumer and resource species. Nonetheless, the adaptive landscape contains multiple alternative stable states, and which stable community is reached depends on small stochastic differences occurring along evolutionary pathways. Our results may solve a puzzling conflict between eco-evolutionary theory that predicts community diversification via consumer-resource interactions will be rare, and empirical research that has uncovered real cases. Furthermore, our results suggest that these real cases might be just a subset of alternative stable communities.

The target of selection matters: An established resistance-development-time negative genetic trade-off is not found when selecting on development time

Trade-offs are fundamental to evolutionary outcomes and play a central role in eco-evolutionary theory. They are often examined by experimentally selecting on one life-history trait and looking for negative correlations in other traits. For example, populations of the moth Plodia interpunctella selected to resist viral infection show a life-history cost with longer development times. However, we rarely examine whether the detection of such negative genetic correlations depends on the trait on which we select. Here, we examine a well-characterized negative genotypic trade-off between development time and resistance to viral infection in the moth Plodia interpunctella and test whether selection on a phenotype known to be a cost of resistance (longer development time) leads to the predicted correlated increase in resistance. If there is tight pleiotropic relationship between genes that determine development time and resistance underpinning this trade-off, we might expect increased resistance when we select on longer development time. However, we show that selecting for longer development time in this system selects for reduced resistance when compared to selection for shorter development time. This shows how phenotypes typically characterized by a trade-off can deviate from that trade-off relationship, and suggests little genetic linkage between the genes governing viral resistance and those that determine response to selection on the key life-history trait. Our results are important for both selection strategies in applied biological systems and for evolutionary modelling of host-parasite interactions.

Intraspecific Adaptation Load: A Mechanism for Species Coexistence

Evolutionary ecological theory suggests that selection arising from interactions with conspecifics, such as sexual and kin selection, may result in evolution of intraspecific conflicts and evolutionary 'tragedy of the commons'. Here, we propose that such an evolution of conspecific conflicts may affect population dynamics in a way that enhances species coexistence. Empirical evidence and theoretical models suggest that more abundant species is more susceptible to invasion of 'selfish' individuals that increase their own reproductive success at the expense of population growth (intraspecific adaptation load). The density-dependent intraspecific adaptation load gives rise to a self-regulation mechanism at the population level, and stabilizes species coexistence at the community level by negative frequency-dependence.

Plant evolution can mediate negative effects from honey bees on wild pollinators

Pollinators are introduced to agroecosystems to provide pollination services. Introductions of managed pollinators often promote ecosystem services, but it remains largely unknown whether they also affect evolutionary mutualisms between wild pollinators and plants.Here, we developed a model to assess effects of managed honey bees on mutualisms between plants and wild pollinators. Our model tracked how interactions among wild pollinators and honey bees affected pollinator and plant populations.We show that when managed honey bees have a competitive advantage over wild pollinators, or a greater carrying capacity, the honey bees displace the wild pollinator. This leads to reduced plant density because plants benefit less by visits from honey bees than wild pollinators that coevolved with the plants.As wild pollinators are displaced, plants evolve by increasing investment in traits that are attractive for honey bees but not wild pollinators. This evolutionary switch promotes wild pollinator displacement. However, higher mutualism investment costs by the plant to the honey bee can promote pollinator coexistence.Our results show plant evolution can promote displacement of wild pollinators by managed honey bees, while limited plant evolution may lead to pollinator coexistence. More broadly, effects of honey bees on wild pollinators in agroecosystems, and effects on ecosystem services, may depend on the capacity of plant populations to evolve.

Intraindividual variability in behavior shapes fitness landscapes

Although intraindividual variability (IIV) in behavior is fundamental to ecological dynamics, the factors that contribute to the expression of IIV are poorly understood. Using an individual-based model, this study examined the effects of stochasticity on the evolution of IIV represented by the residual variability of behavior. The model describes a population of prey with nonoverlapping generations, in which prey take refuge upon encountering a predator. The strategy of a prey is characterized by the mean and IIV (i.e., standard deviation) of hiding duration. Prey with no IIV will spend the same duration hiding in a refuge at each predator encounter, while prey with IIV will have variable hiding durations among encounters. For the sources of stochasticity, within-generation stochasticity (represented by random predator encounters) and between-generation stochasticity (represented by random resource availability) were considered. Analysis of the model indicates that individuals with high levels of IIV are maintained in a population in the presence of between-generation stochasticity even though the optimal strategy in each generation is a strategy with no IIV, regardless of the presence or absence of within-generation stochasticity. This contradictory pattern emerges because the mean behavioral trait and IIV do not independently influence fitness (e.g., the sign of the selection gradient with respect to IIV depends on the mean trait). Consequently, even when evolution eventually leads toward a strategy with no IIV (i.e., the optimal strategy), greater IIV may be transiently selected. Between-generation stochasticity consistently imposes such transient selection and maintain high levels of IIV in a population.

Predator coexistence through emergent fitness equalization

The competitive exclusion principle is one of the oldest ideas in ecology and states that without additional self-limitation two predators cannot coexist on a single prey. The search for mechanisms allowing coexistence despite this has identified niche differentiation between predators as crucial: without this, coexistence requires the predators to have exactly the same R* values, which is considered impossible. However, this reasoning misses a critical point: predators' R* values are not static properties, but affected by defensive traits of their prey, which in turn can adapt in response to changes in predator densities. Here I show that this feedback between defense and predator dynamics enables stable predator coexistence without ecological niche differentiation. Instead, the mechanism driving coexistence is that prey adaptation causes defense to converge to the value where both predators have equal R* values ("fitness equalization"). This result is highly general, independent of specific model details, and applies to both rapid defense evolution and inducible defenses. It demonstrates the importance of considering long-standing ecological questions from an eco-evolutionary viewpoint, and showcases how the effects of adaptation can cascade through communities, driving diversity on higher trophic levels. These insights offer an important new perspective on coexistence theory.

Host-virus-predator coexistence in a grey-box model with dynamic optimization of host fitness

Lytic viruses are believed to affect both flow patterns and host diversity in microbial food webs. Models resolving host and virus communities into subgroups can represent both aspects. However, when flow pattern is the prime interest, such models may seem unnecessary complex. This has led to proposals of black-box models using only total community sizes as state variables. This simplification creates a coexistence problem, however, since predator and virus communities then compete for the same, shared, prey = host community. Mathematically, this problem can be solved by introducing feedbacks allowing community-level properties to adapt. The different mathematical alternatives for such feedback represent different ecological assumptions and thus different hypotheses for how the balance between predators and viruses is controlled in nature. We here explore a model where the feedback works through an increase in host community resistance in response to high virus abundances, thereby reducing virus production. We use a dynamic "strategy" index S to describe the balance between defensive and competitive abilities in the host community, and assume the rate of change in S to be proportional to the local slope of the per capita fitness gradient for the host. We explore how such a "grey-box" model can allow stable coexistence of viruses and predators, and how equilibrium food web structure, virus-to-host ratio, and partitioning of host production varies; both as functions of host community traits, and as functions of external bottom-up and top-down drivers.

Difference equations as models of evolutionary population dynamics

We describe the evolutionary game theoretic methodology for extending a difference equation population dynamic model in a way so as to account for the Darwinian evolution of model coefficients. We give a general theorem that describes the familiar transcritical bifurcation that occurs in non-evolutionary models when theextinction equilibrium destabilizes. This bifurcation results in survival (positive) equilibria whose stability depends on the direction of bifurcation. We give several applications based on evolutionary versions of some classic equations, such as the discrete logistic (Beverton-Holt) and Ricker equations. In addition to illustrating our theorems, these examples also illustrate other biological phenomena, such as strong Allee effects, time-dependent adaptive landscapes, and evolutionary stable strategies.

An evolutionary quantitative genetics model for phenotypic (co)variances under limited dispersal, with an application to socially synergistic traits

Darwinian evolution consists of the gradual transformation of heritable traits due to natural selection and the input of random variation by mutation. Here, we use a quantitative genetics approach to investigate the coevolution of multiple quantitative traits under selection, mutation, and limited dispersal. We track the dynamics of trait means and of variance-covariances between traits that experience frequency-dependent selection. Assuming a multivariate-normal trait distribution, we recover classical dynamics of quantitative genetics, as well as stability and evolutionary branching conditions of invasion analyses, except that due to limited dispersal, selection depends on indirect fitness effects and relatedness. In particular, correlational selection that associates different traits within-individuals depends on the fitness effects of such associations between-individuals. We find that these kin selection effects can be as relevant as pleiotropy for the evolution of correlation between traits. We illustrate this with an example of the coevolution of two social traits whose association within-individuals is costly but synergistically beneficial between-individuals. As dispersal becomes limited and relatedness increases, associations between-traits between-individuals become increasingly targeted by correlational selection. Consequently, the trait distribution goes from being bimodal with a negative correlation under panmixia to unimodal with a positive correlation under limited dispersal.

How (co)evolution alters predator responses to increased mortality: extinction thresholds and hydra effects

Population responses to environmental change depend on both the ecological interactions between species and the evolutionary responses of all species. In this study, we explore how evolution in prey, predators, or both species affect the responses of predator populations to a sustained increase in mortality. We use an eco-evolutionary predator-prey model to explore how evolution alters the predator extinction threshold (defined as the minimum mortality rate that prevents population growth at low predator densities) and predator hydra effects (increased predator abundance in response to increased mortality). Our analysis identifies how evolutionary responses of prey and predators individually affect the predator extinction threshold and hydra effects, and how those effects are altered by interactions between the evolutionary responses. Based on our theoretical results, we predict that it is common in natural systems for evolutionary responses in one or both species to allow predators to persist at higher mortality rates than would be possible in the absence of evolution (i.e., evolution increases the predator mortality extinction threshold). We also predict that evolution-driven hydra effects occur in a minority of natural systems, but are not rare. We revisited published eco-evolutionary models and found that evolution causes hydra effects and increases the predator extinction threshold in many studies, but those effects have been overlooked. We discuss the implications of these results for species conservation, predicting population responses to environmental change, and the possibility of evolutionary rescue.

Evolutionarily stable communities: a framework for understanding the role of trait evolution in the maintenance of diversity

Biological diversity depends on the interplay between evolutionary diversification and ecological mechanisms allowing species to coexist. Current research increasingly integrates ecology and evolution over a range of timescales, but our common conceptual framework for understanding species coexistence requires better incorporation of evolutionary processes. Here, we focus on the idea of evolutionarily stable communities (ESCs), which are theoretical endpoints of evolution in a community context. We use ESCs as a unifying framework to highlight some important but under-appreciated theoretical results, and we review empirical research relevant to these theoretical predictions. We explain how, in addition to generating diversity, evolution can also limit diversity by reducing the effectiveness of coexistence mechanisms. The coevolving traits of competing species may either diverge or converge, depending on whether the number of species in the community is low (undersaturated) or high (oversaturated) relative to the ESC. Competition in oversaturated communities can lead to extinction or neutrally coexisting, ecologically equivalent species. It is critical to consider trait evolution when investigating fundamental ecological questions like the strength of different coexistence mechanisms, the feasibility of ecologically equivalent species, and the interpretation of different patterns of trait dispersion.

From the Price equation to the selection gradient in class-structured populations: a quasi-equilibrium route

Recent studies in theoretical evolutionary ecology have emphasised two approaches to modelling evolution. On the one hand, models based on a separation of time scales rely on the concept of invasion fitness. On the other hand, models based on the Price equation track the dynamics of a trait average, coupled with a description of ecological dynamics. The aim of this article is to show that, in class-structured populations, both approaches yield the same expression for the selection gradient under weak selection. Although the result is not new, I propose an alternative route to its derivation using the dynamics of scaled measures of between-class phenotypic differentiation. Under weak selection, these measures of phenotypic differentiation can be treated as fast variables compared to the trait mean, which allows for a quasi-equilibrium approximation. This suggests a different approach to calculating weak selection approximations of evolutionary dynamics, and clarifies the links between short- and long-term perspectives on evolution in structured populations.

Reversed predator-prey cycles are driven by the amplitude of prey oscillations

Ecoevolutionary feedbacks in predator-prey systems have been shown to qualitatively alter predator-prey dynamics. As a striking example, defense-offense coevolution can reverse predator-prey cycles, so predator peaks precede prey peaks rather than vice versa. However, this has only rarely been shown in either model studies or empirical systems. Here, we investigate whether this rarity is a fundamental feature of reversed cycles by exploring under which conditions they should be found. For this, we first identify potential conditions and parameter ranges most likely to result in reversed cycles by developing a new measure, the effective prey biomass, which combines prey biomass with prey and predator traits, and represents the prey biomass as perceived by the predator. We show that predator dynamics always follow the dynamics of the effective prey biomass with a classic ¼-phase lag. From this key insight, it follows that in reversed cycles (i.e., ¾-lag), the dynamics of the actual and the effective prey biomass must be in antiphase with each other, that is, the effective prey biomass must be highest when actual prey biomass is lowest, and vice versa. Based on this, we predict that reversed cycles should be found mainly when oscillations in actual prey biomass are small and thus have limited impact on the dynamics of the effective prey biomass, which are mainly driven by trait changes. We then confirm this prediction using numerical simulations of a coevolutionary predator-prey system, varying the amplitude of the oscillations in prey biomass: Reversed cycles are consistently associated with regions of parameter space leading to small-amplitude prey oscillations, offering a specific and highly testable prediction for conditions under which reversed cycles should occur in natural systems.

Theoretical Approaches in Evolutionary Ecology: Environmental Feedback as a Unifying Perspective

Evolutionary biology and ecology have a strong theoretical underpinning, and this has fostered a variety of modeling approaches. A major challenge of this theoretical work has been to unravel the tangled feedback loop between ecology and evolution. This has prompted the development of two main classes of models. While quantitative genetics models jointly consider the ecological and evolutionary dynamics of a focal population, a separation of timescales between ecology and evolution is assumed by evolutionary game theory, adaptive dynamics, and inclusive fitness theory. As a result, theoretical evolutionary ecology tends to be divided among different schools of thought, with different toolboxes and motivations. My aim in this synthesis is to highlight the connections between these different approaches and clarify the current state of theory in evolutionary ecology. Central to this approach is to make explicit the dependence on environmental dynamics of the population and evolutionary dynamics, thereby materializing the eco-evolutionary feedback loop. This perspective sheds light on the interplay between environmental feedback and the timescales of ecological and evolutionary processes. I conclude by discussing some potential extensions and challenges to our current theoretical understanding of eco-evolutionary dynamics.

Disentangling eco-evolutionary dynamics of predator-prey coevolution: the case of antiphase cycles

The impact of rapid predator-prey coevolution on predator-prey dynamics remains poorly understood, as previous modelling studies have given rise to contradictory conclusions and predictions. Interpreting and reconciling these contradictions has been challenging due to the inherent complexity of model dynamics, defying mathematical analysis and mechanistic understanding. We develop a new approach here, based on the Geber method for deconstructing eco-evolutionary dynamics, for gaining such understanding. We apply this approach to a co-evolutionary predator-prey model to disentangle the processes leading to either antiphase or ¼-lag cycles. Our analysis reveals how the predator-prey phase relationship is driven by the temporal synchronization between prey biomass and defense dynamics. We further show when and how prey biomass and trait dynamics become synchronized, resulting in antiphase cycles, allowing us to explain and reconcile previous modelling and empirical predictions. The successful application of our proposed approach provides an important step towards a comprehensive theory on eco-evolutionary feedbacks in predator-prey systems.

The evolution of toxicant resistance in daphniids and its role on surrogate species

Prolonged exposure to a disturbance such as a toxicant has the potential to result in rapid evolution to toxicant resistance in many short-lived species such as daphniids. This evolution may allow a population to persist at higher levels of the toxicant than is possible without evolution. Here we apply evolutionary game theory to a Leslie matrix model for a daphniid population to obtain a Darwinian model that couples population dynamics with the dynamics of an evolving trait. We use the Darwinian model to consider how the evolution of resistance to the lethal or sublethal effects of a disturbance may change the population dynamics. In particular, we determine the conditions under which a daphniid population can persist by evolving toxicant resistance. We then consider the implications of this evolution in terms of the use of daphniids as surrogate species. We show for three species of daphniids that evolution of toxicant resistance means that one species may persist while another does not. These results suggest that toxicant studies that do not consider the potential of a species (or its surrogate) to develop toxicant resistance may not accurately predict the long term persistence of the species.

The Price Equation, Gradient Dynamics, and Continuous Trait Game Theory

A recent article convincingly nominated the Price equation as the fundamental theorem of evolution and used it as a foundation to derive several other theorems. A major section of evolutionary theory that was not addressed is that of game theory and gradient dynamics of continuous traits with frequency-dependent fitness. Deriving fundamental results in these fields under the unifying framework of the Price equation illuminates similarities and differences between approaches and allows a simple, unified view of game-theoretical and dynamic concepts. Using Taylor polynomials and the Price equation, I derive a dynamic measure of evolutionary change, a condition for singular points, the convergence stability criterion, and an alternative interpretation of evolutionary stability. Furthermore, by applying the Price equation to a multivariable Taylor polynomial, the direct fitness approach to kin selection emerges. Finally, I compare these results to the mean gradient equation of quantitative genetics and the canonical equation of adaptive dynamics.

The Ecological Dynamics of Natural Selection: Traits and the Coevolution of Community Structure

Natural selection has both genetic and ecological dynamics. The fitnesses of individuals change with their ecological context, and so the form and strength of selective agents change with abiotic factors and the phenotypes and abundances of interacting species. I use standard models of consumer-resource interactions to explore the ecological dynamics of natural selection and how various trait types influence these dynamics and the resulting structure of a community of coevolving species. Evolutionary optima favored by natural selection depend critically on the abundances of interacting species, and the traits of species can undergo dynamic cycling in limited areas of parameter space. The ecological dynamics of natural selection can also drive shifts from one adaptive peak to another, and these ecologically driven adaptive peak shifts are fundamental to the dynamics of niche differentiation. Moreover, this ecological differentiation is fostered in more productive and more benign environments where species interactions are stronger and where the selection gradients generated by species interactions are stronger. Finally, community structure resulting from coevolution depends fundamentally on the types of traits that underlie species interactions. The ecological dynamics of the process cannot be simplified, neglected, or ignored if we are to build a predictive theory of natural selection.

Antagonistic coevolution between quantitative and Mendelian traits

Coevolution is relentlessly creating and maintaining biodiversity and therefore has been a central topic in evolutionary biology. Previous theoretical studies have mostly considered coevolution between genetically symmetric traits (i.e. coevolution between two continuous quantitative traits or two discrete Mendelian traits). However, recent empirical evidence indicates that coevolution can occur between genetically asymmetric traits (e.g. between quantitative and Mendelian traits). We examine consequences of antagonistic coevolution mediated by a quantitative predator trait and a Mendelian prey trait, such that predation is more intense with decreased phenotypic distance between their traits (phenotype matching). This antagonistic coevolution produces a complex pattern of bifurcations with bistability (initial state dependence) in a two-dimensional model for trait coevolution. Furthermore, with eco-evolutionary dynamics (so that the trait evolution affects predator-prey population dynamics), we find that coevolution can cause rich dynamics including anti-phase cycles, in-phase cycles, chaotic dynamics and deterministic predator extinction. Predator extinction is more likely to occur when the prey trait exhibits complete dominance rather than semidominance and when the predator trait evolves very rapidly. Our study illustrates how recognizing the genetic architectures of interacting ecological traits can be essential for understanding the population and evolutionary dynamics of coevolving species.

Evolutionary dynamics of a quantitative trait in a finite asexual population

In finite populations, mutation limitation and genetic drift can hinder evolutionary diversification. We consider the evolution of a quantitative trait in an asexual population whose size can vary and depends explicitly on the trait. Previous work showed that evolutionary branching is certain ("deterministic branching") above a threshold population size, but uncertain ("stochastic branching") below it. Using the stationary distribution of the population's trait variance, we identify three qualitatively different sub-domains of "stochastic branching" and illustrate our results using a model of social evolution. We find that in very small populations, branching will almost never be observed; in intermediate populations, branching is intermittent, arising and disappearing over time; in larger populations, finally, branching is expected to occur and persist for substantial periods of time. Our study provides a clearer picture of the ecological conditions that facilitate the appearance and persistence of novel evolutionary lineages in the face of genetic drift.