The dynamics of strangling among forest trees

Strangler trees germinate and grow on other trees, eventually enveloping and potentially even girdling their hosts. This allows them to mitigate fitness costs otherwise incurred by germinating and competing with other trees on the forest floor, as well as minimize risks associated with host tree-fall. If stranglers can themselves host other strangler trees, they may not even seem to need non-stranglers to persist. Yet despite their high fitness potential, strangler trees neither dominate the communities in which they occur nor is the strategy particularly common outside of figs (genus Ficus). Here we analyze how dynamic interactions between strangling and non-strangling trees can shape the adaptive landscape for strangling mutants and mutant trees that have lost the ability to strangle. We find a threshold which strangler germination rates must exceed for selection to favor the evolution of strangling, regardless of how effectively hemiepiphytic stranglers may subsequently replace their hosts. This condition describes the magnitude of the phenotypic displacement in the ability to germinate on other trees necessary for invasion by a mutant tree that could potentially strangle its host following establishment as an epiphyte. We show how the relative abilities of strangling and non-strangling trees to occupy empty sites can govern whether strangling is an evolutionarily stable strategy, and obtain the conditions for strangler coexistence with non-stranglers. We then elucidate when the evolution of strangling can disrupt stable coexistence between commensal epiphytic ancestors and their non-strangling host trees. This allows us to highlight parallels between the invasion fitness of strangler trees arising from commensalist ancestors, and cases where strangling can arise in concert with the evolution of hemiepiphytism among free-standing ancestors. Finally, we discuss how our results can inform the evolutionary ecology of antagonistic interactions more generally.

Evolutionary Stability of Minimal Mutation Rates in an Evo-epidemiological Model

We consider the evolution of mutation rate in a seasonally forced, deterministic, compartmental epidemiological model with a transmission-virulence trade-off. We model virulence as a quantitative genetic trait in a haploid population and mutation as continuous diffusion in the trait space. There is a mutation rate threshold above which the pathogen cannot invade a wholly susceptible population. The evolutionarily stable (ESS) mutation rate is the one which drives the lowest average density, over the course of one forcing period, of susceptible individuals at steady state. In contrast with earlier eco-evolutionary models in which higher mutation rates allow for better evolutionary tracking of a dynamic environment, numerical calculations suggest that in our model the minimum average susceptible population, and hence the ESS, is achieved by a pathogen strain with zero mutation. We discuss how this result arises within our model and how the model might be modified to obtain a nonzero optimum.

Indirect evolutionary rescue: prey adapts, predator avoids extinction

Recent studies have increasingly recognized evolutionary rescue (adaptive evolution that prevents extinction following environmental change) as an important process in evolutionary biology and conservation science. Researchers have concentrated on single species living in isolation, but populations in nature exist within communities of interacting species, so evolutionary rescue should also be investigated in a multispecies context. We argue that the persistence or extinction of a focal species can be determined solely by evolutionary change in an interacting species. We demonstrate that prey adaptive evolution can prevent predator extinction in two-species predator–prey models, and we derive the conditions under which this indirect evolutionary interaction is essential to prevent extinction following environmental change. A nonevolving predator can be rescued from extinction by adaptive evolution of its prey due to a trade-off for the prey between defense against predation and population growth rate. As prey typically have larger populations and shorter generations than their predators, prey evolution can be rapid and have profound effects on predator population dynamics. We suggest that this process, which we term ‘indirect evolutionary rescue’, has the potential to be critically important to the ecological and evolutionary responses of populations and communities to dramatic environmental change.

The evolutionary dynamics of a population model with a strong Allee effect

An evolutionary game theoretic model for a population subject to predation and a strong Allee threshold of extinction is analyzed using, among other methods, Poincaré-Bendixson theory. The model is a nonlinear, plane autonomous system whose state variables are population density and the mean of a phenotypic trait, which is subject to Darwinian evolution, that determines the population's inherent (low density) growth rate (fitness). A trade-off is assumed in that an increase in the inherent growth rate results in a proportional increase in the predator's attack rate. The main results are that orbits equilibrate (there are no cycles or cycle chains of saddles), that the extinction set (or Allee basin) shrinks when evolution occurs, and that the meant trait component of survival equilibria occur at maxima of the inherent growth rate (as a function of the trait).

The role of biotic forces in driving macroevolution: beyond the Red Queen

A multitude of hypotheses claim that abiotic factors are the main drivers of macroevolutionary change. By contrast, Van Valen's Red Queen hypothesis is often put forward as the sole representative of the view that biotic forcing is the main evolutionary driver. This imbalance of hypotheses does not reflect our current knowledge: theoretical work demonstrates the plausibility of biotically driven long-term evolution, whereas empirical work suggests a central role for biotic forcing in macroevolution. We call for a more pluralistic view of how biotic forces may drive long-term evolution that is compatible with both phenotypic stasis in the fossil record and with non-constant extinction rates. Promising avenues of research include contrasting predictions from relevant theories within ecology and macroevolution, as well as embracing both abiotic and biotic proxies while modelling long-term evolutionary data. By fitting models describing hypotheses of biotically driven macroevolution to data, we could dissect their predictions and transcend beyond pattern description, possibly narrowing the divide between our current understanding of micro- and macroevolution.

Size-selective fishing gear and life history evolution in the Northeast Arctic cod

Industrial fishing has been identified as a cause for life history changes in many harvested stocks, mainly because of the intense fishing mortality and its size-selectivity. Because these changes are potentially evolutionary, we investigate evolutionarily stable life-histories and yield in an energy-allocation state-dependent model for Northeast Arctic cod Gadus morhua. We focus on the evolutionary effects of size-selective fishing because regulation of gear selectivity may be an efficient management tool. Trawling, which harvests fish above a certain size, leads to early maturation except when fishing is low and confined to mature fish. Gillnets, where small and large fish escape, lead to late maturation for low to moderate harvest rates, but when harvest rates increase maturation age suddenly drops. This is because bell-shaped selectivity has two size-refuges, for fish that are below and above the harvestable size-classes. Depending on the harvest rate it either pays to grow through the harvestable slot and mature above it, or mature small below it. Sustainable yield on the evolutionary time-scale is highest when fishing is done by trawling, but only for a small parameter region. Fishing with gillnets is better able to withstand life-history evolution, and maintains yield over a wider range of fishing intensities.

Applying evolutionary biology to address global challenges

Two categories of evolutionary challenges result from escalating human impacts on the planet. The first arises from cancers, pathogens, and pests that evolve too quickly and the second, from the inability of many valued species to adapt quickly enough. Applied evolutionary biology provides a suite of strategies to address these global challenges that threaten human health, food security, and biodiversity. This Review highlights both progress and gaps in genetic, developmental, and environmental manipulations across the life sciences that either target the rate and direction of evolution or reduce the mismatch between organisms and human-altered environments. Increased development and application of these underused tools will be vital in meeting current and future targets for sustainable development.

Multidimensional (co)evolutionary stability

The complexity of biotic and abiotic environmental conditions is such that the fitness of individuals is likely to depend on multiple traits. Using a synthetic framework of phenotypic evolution that draws from adaptive dynamics and quantitative genetics approaches, we explore how the number of traits under selection influences convergence stability and evolutionary stability in models for coevolution in multidimensional phenotype spaces. Our results allow us to identify three different effects of trait dimensionality on stability. First are (i) a "combinatorial effect": without epistasis and genetic correlations, a higher number of trait dimensions offers more opportunities for equilibria to be unstable; and (ii) epistatic interactions, that is, fitness interactions between traits, which tend to destabilize evolutionary equilibria; this effect increases with the dimension of phenotype space. These first two effects influence both convergence stability and evolutionary stability, while (iii) genetic correlations (due, e.g., to pleiotropy or linkage disequilibrium) can affect only convergence stability. We illustrate the general prediction that increased dimensionality destabilizes evolutionary equilibria using examples drawn from well-studied classical models of frequency-dependent competition for resources, adaptation to a spatially heterogeneous environment, and antagonistic coevolution. In addition, our analyses show that increased dimensionality can favor diversification, for example, in the form of local adaptation, as well as evolutionary escape.

Adaptive foraging behaviour of individual pollinators and the coexistence of co-flowering plants

Although pollinators can play a central role in determining the structure and stability of plant communities, little is known about how their adaptive foraging behaviours at the individual level, e.g. flower constancy, structure these interactions. Here, we construct a mathematical model that integrates individual adaptive foraging behaviour and population dynamics of a community consisting of two plant species and a pollinator species. We find that adaptive foraging at the individual level, as a complementary mechanism to adaptive foraging at the species level, can further enhance the coexistence of plant species through niche partitioning between conspecific pollinators. The stabilizing effect is stronger than that of unbiased generalists when there is also strong competition between plant species over other resources, but less so than that of multiple specialist species. This suggests that adaptive foraging in mutualistic interactions can have a very different impact on the plant community structure from that in predator-prey interactions. In addition, the adaptive behaviour of individual pollinators may cause a sharp regime shift for invading plant species. These results indicate the importance of integrating individual adaptive behaviour and population dynamics for the conservation of native plant communities.

Coevolution and the effects of climate change on interacting species

BACKGROUND

Recent studies suggest that environmental changes may tip the balance between interacting species, leading to the extinction of one or more species. While it is recognized that evolution will play a role in determining how environmental changes directly affect species, the interactions among species force us to consider the coevolutionary responses of species to environmental changes.

METHODOLOGY/PRINCIPLE FINDINGS

We use simple models of competition, predation, and mutualism to organize and synthesize the ways coevolution modifies species interactions when climatic changes favor one species over another. In cases where species have conflicting interests (i.e., selection for increased interspecific interaction strength on one species is detrimental to the other), we show that coevolution reduces the effects of climate change, leading to smaller changes in abundances and reduced chances of extinction. Conversely, when species have nonconflicting interests (i.e., selection for increased interspecific interaction strength on one species benefits the other), coevolution increases the effects of climate change.

CONCLUSIONS/SIGNIFICANCE

Coevolution sets up feedback loops that either dampen or amplify the effect of environmental change on species abundances depending on whether coevolution has conflicting or nonconflicting effects on species interactions. Thus, gaining a better understanding of the coevolutionary processes between interacting species is critical for understanding how communities respond to a changing climate. We suggest experimental methods to determine which types of coevolution (conflicting or nonconflicting) drive species interactions, which should lead to better understanding of the effects of coevolution on species adaptation. Conducting these experiments across environmental gradients will test our predictions of the effects of environmental change and coevolution on ecological communities.

Integrating evolution into ecological modelling: accommodating phenotypic changes in agent based models

Evolutionary change is a characteristic of living organisms and forms one of the ways in which species adapt to changed conditions. However, most ecological models do not incorporate this ubiquitous phenomenon. We have developed a model that takes a 'phenotypic gambit' approach and focuses on changes in the frequency of phenotypes (which differ in timing of breeding and fecundity) within a population, using, as an example, seasonal breeding. Fitness per phenotype calculated as the individual's contribution to population growth on an annual basis coincide with the population dynamics per phenotype. Simplified model variants were explored to examine whether the complexity included in the model is justified. Outputs from the spatially implicit model underestimated the number of individuals across all phenotypes. When no phenotype transitions are included (i.e. offspring always inherit their parent's phenotype) numbers of all individuals are always underestimated. We conclude that by using a phenotypic gambit approach evolutionary dynamics can be incorporated into individual based models, and that all that is required is an understanding of the probability of offspring inheriting the parental phenotype.

Coexistence in a variable environment: eco-evolutionary perspectives

A central question in community ecology is the means by which species coexist. Models of coexistence often assume that species have fixed trait values and consider questions such as how tradeoffs and environmental variation influence coexistence and diversity. However, species traits can be dynamic, varying between populations and individuals and changing over time as species adapt and evolve, at rates that are relevant to ecological processes. Consequently, adding evolution to ecological coexistence models may modify their predictions and stability in complex or unexpected ways. We extend a well-studied coexistence mechanism depending on resource fluctuations by allowing evolution along a tradeoff between maximum growth rate and competitive ability. Interactions between favorable season length and the period of fluctuations constrain coexistence, with two species coexistence favored by intermediate season length and arising through evolutionary branching or non-local invasion. However, these results depend on the relative rates of ecological and evolutionary processes: rapid evolution leads to a complete breakdown of otherwise stable coexistence. Other coexistence mechanisms should be evaluated from an evolutionary perspective to examine how evolutionary forces may alter predicted ecological dynamics.

Navigating the devious course of evolution: the importance of mechanistic models for identifying eco-evolutionary dynamics in nature

In proposing his genetic feedback mechanism, David Pimentel was one of the first biologists to argue that the reciprocal interplay of ecological and evolutionary dynamics is an important process regulating population dynamics and ultimately affecting community composition. Although the past decade has seen an increase in research activity on these so-called eco-evolutionary dynamics, there remains a conspicuous lack of compelling natural examples of such feedback. Here we argue that this lack may be due to an inherent difficulty in detecting eco-evolutionary dynamics in nature. By examining models of virulence evolution, host resistance evolution, and antigenic evolution, we show that the influence of evolution on ecological dynamics can often be obscured by other ecological processes that yield similar dynamics. We then show, however, that mechanistic models can be used to navigate this, in Pimentel's words, "devious" course of evolution when effectively combined with empirical data. We argue that these models, improving upon Pimentel's original mathematical models, will therefore play an increasingly important role in identifying more subtle, but possibly ubiquitous, eco-evolutionary dynamics in nature. To highlight the importance of identifying these potentially subtle dynamics in nature, we end by considering our ability to anticipate the effect of population control strategies in the presence of these eco-evolutionary feedbacks.

The evolutionary dynamics of receptor binding avidity in influenza A: a mathematical model for a new antigenic drift hypothesis

The most salient feature of influenza evolution in humans is its antigenic drift. This process is characterized by structural changes in the virus's B-cell epitopes and ultimately results in the ability of the virus to evade immune recognition and thereby reinfect previously infected hosts. Until recently, amino acid substitutions in epitope regions of the viral haemagglutinin were thought to be positively selected for their ability to reduce antibody binding and therefore were thought to be responsible for driving antigenic drift. However, a recent hypothesis put forward by Hensley and co-workers posits that cellular receptor binding avidity is the dominant phenotype under selection, with antigenic drift being a side effect of these binding avidity changes. Here, we present a mathematical formulation of this new antigenic drift model and use it to show how rates of antigenic drift depend on epidemiological parameters. We further use the model to evaluate how two different vaccination strategies can impact antigenic drift rates and ultimately disease incidence levels. Finally, we discuss the assumptions present in the model formulation, predictions of the model, and future work that needs to be done to determine the consistency of this hypothesis with known patterns of influenza's genetic and antigenic evolution.

The evolution of optimal female mating rate changes the coevolutionary dynamics of female resistance and male persistence

Mating decisions usually involve conflict of interests between sexes. Accordingly, males benefit from increased number of matings, whereas costs of mating favour a lower mating rate for females. The resulting sexual conflict underlies the coevolution of male traits that affect male mating success ('persistence') and female traits that affect female mating patterns ('resistance'). Theoretical studies on the coevolutionary dynamics of male persistence and female resistance assumed that costs of mating and, consequently, the optimal female mating rate are evolutionarily constant. Costs of mating, however, are often caused by male 'persistence' traits that determine mating success. Here, we present a model where the magnitude of costs of mating depend on, and evolve with, male persistence. We find that allowing costs of mating to depend on male persistence results in qualitatively different coevolutionary dynamics. Specifically, we find that male traits such as penis spikes that harm females are not predicted to exhibit runaway selection with female resistance, in contrast to previous theory that predicts indefinite escalation. We argue that it is essential to determine when and to what extent costs of mating are caused by male persistence in order to understand and accurately predict coevolutionary dynamics of traits involved in mating decisions.

A global pattern of thermal adaptation in marine phytoplankton

Rising ocean temperatures will alter the productivity and composition of marine phytoplankton communities, thereby affecting global biogeochemical cycles. Predicting the effects of future ocean warming on biogeochemical cycles depends critically on understanding how existing global temperature variation affects phytoplankton. Here we show that variation in phytoplankton temperature optima over 150 degrees of latitude is well explained by a gradient in mean ocean temperature. An eco-evolutionary model predicts a similar relationship, suggesting that this pattern is the result of evolutionary adaptation. Using mechanistic species distribution models, we find that rising temperatures this century will cause poleward shifts in species' thermal niches and a sharp decline in tropical phytoplankton diversity in the absence of an evolutionary response.

Quantitative genetic analysis of subspecific differences in body shape in the snail-feeding carabid beetle Damaster blaptoides

A dimorphic pattern of macrocephalic (wide, short) and stenocephalic (narrow, long) body shapes is observed in snail-feeding carabid beetles globally. The former exhibits high performance in crushing snail shells with powerful jaws, whereas the latter specializes in eating snails' soft body directly by inserting the head into the shell. In the snail-feeding species Damaster blaptoides, the subspecies D. b. capito has a wide, short forebody, and D. b. fortunei has a narrow, long forebody. They exhibit distinct morphologies despite their geographic and phylogenetic proximity. To examine the genetic basis of the morphological differences between these two subspecies, we conducted quantitative genetic analyses by crossing these subspecies and producing F(1) and backcross hybrids. The hybrids had body shapes intermediate between the parental subspecies. The variation between wide, short and narrow, long forebodies was based on negative genetic correlations between width and length of the head and thorax. Between one and eight genetic factors were involved in the morphological differences between subspecies. We suggest that the morphological integration of forebody parts in a small number of loci has facilitated the marked morphological diversification between subspecies of D. blaptoides.

When does pathogen evolution maximize the basic reproductive number in well-mixed host-pathogen systems?

Pathogen evolution towards the largest basic reproductive number, R0, has been observed in many theoretical models, but this conclusion does not hold universally. Previous studies of host-pathogen systems have defined general conditions under which R0 maximization occurs in terms of R0 itself. However, it is unclear what constraints these conditions impose on the functional forms of pathogen related processes (e.g. transmission, recover, or mortality) and how those constraints relate to the characteristics of natural systems. Here we focus on well-mixed SIR-type host-pathogen systems and, via a synthesis of results from the literature, we present a set of sufficient mathematical conditions under which evolution maximizes R0. Our conditions are in terms of the functional responses of the system and yield three general biological constraints on when R0 maximization will occur. First, there are no genotype-by-environment interactions. Second, the pathogen utilizes a single transmission pathway (i.e. either horizontal, vertical, or vector transmission). Third, when mortality is density dependent: (i) there is a single infectious class that individuals cannot recover from, (ii) mortality in the infectious class is entirely density dependent, and (iii) the rates of recovery, infection progression, and mortality in the exposed classes are independent of the pathogen trait. We discuss how this approach identifies the biological mechanisms that increase the dimension of the environmental feedback and prevent R0 maximization.

Origins of altruism diversity II: Runaway coevolution of altruistic strategies via "reciprocal niche construction"

Understanding the evolution of altruism requires knowledge of both its constraints and its drivers. Here we show that, paradoxically, ecological constraints on altruism may ultimately be its strongest driver. We construct a two-trait, coevolutionary adaptive dynamics model of social evolution in a genetically structured population with local resource competition. The intensity of local resource competition, which influences the direction and strength of social selection and which is typically treated as a static parameter, is here allowed to be an evolvable trait. Evolution of survival/fecundity altruism, which requires weak local competition, increases local competition as it evolves, creating negative environmental feedback that ultimately inhibits its further evolutionary advance. Alternatively, evolution of resource-based altruism, which requires strong local competition, weakens local competition as it evolves, also ultimately causing its own evolution to stall. When evolving independently, these altruistic strategies are intrinsically self-limiting. However, the coexistence of these two altruism types transforms the negative ecoevolutionary feedback generated by each strategy on itself into positive feedback on the other, allowing the presence of one trait to drive the evolution of the other. We call this feedback conversion "reciprocal niche construction." In the absence of constraints, this process leads to runaway coevolution of altruism types. We discuss applications to the origins and evolution of eusociality, division of labor, the inordinate ecological success of eusocial species, and the interaction between technology and demography in human evolution. Our theory suggests that the evolution of extreme sociality may often be an autocatalytic process.

Integrating mechanistic organism–environment interactions into the basic theory of community and evolutionary ecology

This paper presents an overview of how mechanistic knowledge of organism–environment interactions, including biomechanical interactions of heat, mass and momentum transfer, can be integrated into basic theoretical population biology through mechanistic functional responses that quantitatively describe how organisms respond to their physical environment. Integrating such functional responses into simple community and microevolutionary models allows scaling up of the organism-level understanding from biomechanics both ecologically and temporally. For community models, Holling-type functional responses for predator–prey interactions provide a classic example of the functional response affecting qualitative model dynamics, and recent efforts are expanding analogous models to incorporate environmental influences such as temperature. For evolutionary models, mechanistic functional responses dependent on the environment can serve as fitness functions in both quantitative genetic and game theoretic frameworks, especially those concerning function-valued traits. I present a novel comparison of a mechanistic fitness function based on thermal performance curves to a commonly used generic fitness function, which quantitatively differ in their predictions for response to environmental change. A variety of examples illustrate how mechanistic functional responses enhance model connections to biologically relevant traits and processes as well as environmental conditions and therefore have the potential to link theoretical and empirical studies. Sensitivity analysis of such models can provide biologically relevant insight into which parameters and processes are important to community and evolutionary responses to environmental change such as climate change, which can inform conservation management aimed at protecting response capacity. Overall, the distillation of detailed knowledge or organism–environment interactions into mechanistic functional responses in simple population biology models provides a framework for integrating biomechanics and ecology that allows both tractability and generality.

Evolutionarily labile species interactions and spatial spread of invasive species

Both exotic and native species have been shown to evolve in response to invasions, yet the impacts of rapidly evolving interactions between novel species pairs have been largely ignored in studies of invasive species spread. Here, I use a mathematical model of an interacting invasive predator and its native prey to determine when and how evolutionary lability in one or both species might impact the dynamics of the invader's spatial advance. The model shows that evolutionarily labile invaders continually evolve better adapted phenotypes along the moving invasion front, offering an explanation for accelerating spread and spatial phenotype clines following invasion. I then analytically derive a formula to estimate the relative change in spread rate due to evolution. Using parameter estimates from the literature, this formula shows that moderate heritabilities and selection strengths are sufficient to account for changes in spread rates observed in historical and ongoing invasions. Evolutionarily labile native species can slow invader spread when genes flow from native populations with exposure to the invader into native populations ahead of the invasion front. This outcome is more likely in systems with highly diffuse native dispersal, net directional movement of natives toward the invasion front, or human inoculation of uninvaded native populations.

Adaptive behaviour, tri-trophic food-web stability and damping of chaos

We examine the effect of adaptive foraging behaviour within a tri-trophic food web with intra-guild predation. The intra-guild prey is allowed to adjust its foraging effort so as to achieve an optimal per capita growth rate in the face of realized feeding, predation risk and foraging cost. Adaptive fitness-seeking behaviour of the intra-guild prey has a stabilizing effect on the tri-trophic food-web dynamics provided that (i) a finite optimal foraging effort exists and (ii) the trophic transfer efficiency from resource to predator via the intra-guild prey is greater than that from the resource directly. The latter condition is a general criterion for the feasibility of intra-guild predation as a trophic mode. Under these conditions, we demonstrate rigorously that adaptive behaviour will always promote stability of community dynamics in the sense that the region of parameter space in which stability is achieved is larger than for the non-adaptive counterpart of the system.

Impact of environmental covariation in growth and mortality on evolving maturation reaction norms

Maturation age and size have important fitness consequences through their effects on survival probabilities and body sizes. The evolution of maturation reaction norms in response to environmental covariation in growth and mortality is therefore a key subject of life-history theory. The eco-evolutionary model we present and analyze here incorporates critical features that earlier studies of evolving maturation reaction norms have often neglected: the trade-off between growth and reproduction, source-sink population structure, and population regulation through density-dependent growth and fecundity. We report the following findings. First, the evolutionarily optimal age at maturation can be decomposed into the sum of a density-dependent and a density-independent component. These components measure, respectively, the hypothetical negative age at which an individual's length would be 0 and the delay in maturation relative to this offset. Second, along any growth trajectory, individuals mature earlier when mortality is higher. This allows us to deduce, third, how the shapes of evolutionarily optimal maturation reaction norms depend on the covariation between growth and mortality (positive or negative, linear or curvilinear, and deterministic or probabilistic). Providing eco-evolutionary explanations for many alternative reaction-norm shapes, our results appear to be in good agreement with current empirical knowledge on maturation dynamics.

Evolutionary game theory as a framework for studying biological invasions

Although biological invasions pose serious threats to biodiversity, they also provide the opportunity to better understand interactions between the ecological and evolutionary processes structuring populations and communities. However, ecoevolutionary frameworks for studying species invasions are lacking. We propose using game theory and the concept of an evolutionarily stable strategy (ESS) as a conceptual framework for integrating the ecological and evolutionary dynamics of invasions. We suggest that the pathways by which a recipient community may have no ESS provide mechanistic hypotheses for how such communities may be vulnerable to invasion and how invaders can exploit these vulnerabilities. We distinguish among these pathways by formalizing the evolutionary contexts of the invader relative to the recipient community. We model both the ecological and the adaptive dynamics of the interacting species. We show how the ESS concept provides new mechanistic hypotheses for when invasions result in long- or short-term increases in biodiversity, species replacement, and subsequent evolutionary changes.

Understanding rapid evolution in predator‐prey interactions using the theory of fast‐slow dynamical systems

The accumulation of evidence that ecologically important traits often evolve at the same time and rate as ecological dynamics (e.g., changes in species' abundances or spatial distributions) has outpaced theory describing the interplay between ecological and evolutionary processes with comparable timescales. The disparity between experiment and theory is partially due to the high dimensionality of models that include both evolutionary and ecological dynamics. Here we show how the theory of fast-slow dynamical systems can be used to reduce model dimension, and we use that body of theory to study a general predator-prey system exhibiting fast evolution in either the predator or the prey. Our approach yields graphical methods with predictive power about when new and unique dynamics (e.g., completely out-of-phase oscillations and cryptic dynamics) can arise in ecological systems exhibiting fast evolution. In addition, we derive analytical expressions for determining when such behavior arises and how evolution affects qualitative properties of the ecological dynamics. Finally, while the theory requires a separation of timescales between the ecological and evolutionary processes, our approach yields insight into systems where the rates of those processes are comparable and thus is a step toward creating a general ecoevolutionary theory.

Influence of evolution on the stability of ecological communities

In randomly assembled communities, diversity is known to have a destabilizing effect. Evolution may affect this result, but our theoretical knowledge of its role is mostly limited to models of small food webs. In the present article, I introduce evolution in a two-species Lotka-Volterra model in which I vary the interaction type and the cost constraining evolution. Regardless of the cost type, evolution tends to stabilize the dynamics more often in trophic interactions than for mutualism or competition. I then use simulations to study the effect of evolution in larger communities that contain all interaction types. Results suggest that evolution usually stabilizes the dynamics. This stabilizing effect is stronger when evolution affects trophic interactions, but happens for all interaction types. Stabilization decreases with diversity and evolution becomes destabilizing in very diverse communities. This suggests that evolution may not counteract the destabilizing effect of diversity observed in random communities.

Rapid exploiter-victim coevolution: the race is not always to the swift

The modeling of coevolutionary races has traditionally been dominated by methods invoking a timescale separation between ecological and evolutionary dynamics, the latter assumed to be much slower than the former. Yet it is becoming increasingly clear that in many cases the two processes occur on similar timescales and that such "rapid" evolution can have profound implications for the dynamics of communities and ecosystems. After briefly reviewing the timescale separations most common in coevolution theory, we use a general model of exploiter-victim coevolution to confront predictions from slow-evolution analysis with Monte Carlo simulations. We show how rapid evolution radically alters the dynamics and outcome of coevolutionary arms races. In particular, a fast-evolving exploiter can enable victim diversification and thereby lose a race it is expected to win. We explain simulation results, using mathematical analysis with relaxed timescale separations. Unusual mutation parameters are not required, since rapid evolution naturally emerges from slow competitive exclusion. Our results point to interesting consequences of exploiter rapid evolution and experimentally testable patterns, while indicating that more attention should be paid to rapid evolution in evolutionary theory.

Next-generation tools for evolutionary invasion analyses

Evolutionary invasion analysis is a powerful technique for modelling in evolutionary biology. The general approach is to derive an expression for the growth rate of a mutant allele encoding some novel phenotype, and then to use this expression to predict long-term evolutionary outcomes. Mathematically, such 'invasion fitness' expressions are most often derived using standard linear stability analyses from dynamical systems theory. Interestingly, there is a mathematically equivalent approach to such stability analyses that is often employed in mathematical epidemiology, and that is based on so-called 'next-generation' matrices. Although this next-generation matrix approach has sometimes also been used in evolutionary invasion analyses, it is not yet common in this area despite the fact that it can sometimes greatly simplify calculations. The aim of this article is to bring the approach to a wider evolutionary audience in two ways. First, we review the next-generation matrix approach and provide a novel, and easily intuited, interpretation of how this approach relates to more standard techniques. Second, we illustrate next-generation methods in evolutionary invasion analysis through a series of informative examples. Although focusing primarily on evolutionary invasion analysis, we provide several insights that apply to biological modelling in general.

Transient virulence of emerging pathogens

Should emerging pathogens be unusually virulent? If so, why? Existing theories of virulence evolution based on a tradeoff between high transmission rates and long infectious periods imply that epidemic growth conditions will select for higher virulence, possibly leading to a transient peak in virulence near the beginning of an epidemic. This transient selection could lead to high virulence in emerging pathogens. Using a simple model of the epidemiological and evolutionary dynamics of emerging pathogens, along with rough estimates of parameters for pathogens such as severe acute respiratory syndrome, West Nile virus and myxomatosis, we estimated the potential magnitude and timing of such transient virulence peaks. Pathogens that are moderately evolvable, highly transmissible, and highly virulent at equilibrium could briefly double their virulence during an epidemic; thus, epidemic-phase selection could contribute significantly to the virulence of emerging pathogens. In order to further assess the potential significance of this mechanism, we bring together data from the literature for the shapes of tradeoff curves for several pathogens (myxomatosis, HIV, and a parasite of Daphnia) and the level of genetic variation for virulence for one (myxomatosis). We discuss the need for better data on tradeoff curves and genetic variance in order to evaluate the plausibility of various scenarios of virulence evolution.

Adaptive changes in prey vulnerability shape the response of predator populations to mortality

Simple models are used to explore how adaptive changes in prey vulnerability alter the population response of their predator to increased mortality. If the mortality is an imposed harvest, the change in prey vulnerability also influences the relationship between harvest effort and yield of the predator. The models assume that different prey phenotypes share a single resource, but have different vulnerabilities to the predator. Decreased vulnerability is assumed to decrease resource consumption rate. Adaptive change may occur by phenotypic changes in the traits of a single species or by shifts in the abundances of a pair of coexisting species or morphs. The response of the predator population is influenced by the shape of the predator's functional response, the shape of resource density dependence, and the shape of the tradeoff between vulnerability and food intake in the prey. Given a linear predator functional response, adaptive prey defense tends to produce a decelerating decline in predator population size with increased mortality. Prey defense may also greatly increase the range of mortality rates that allow predator persistence. If the predator has a type-2 response with a significant handling time, adaptive prey defense may have a greater variety of effects on the predator's response to mortality, sometimes producing alternative attractors, population cycles, or increased mean predator density. Situations in which there is disruptive selection on prey defense often imply a bimodal change in yield as a function of harvesting effort, with a minimum at intermediate effort. These results argue against using single-species models of density dependent growth to manage predatory species, and illustrate the importance of incorporating anti-predator behavior into models in applied population ecology.

Contrasting size evolution in marine and freshwater diatoms

Diatoms are key players in the global carbon cycle and most aquatic ecosystems. Their cell sizes impact carbon sequestration and energy transfer to higher trophic levels. We report fundamental differences in size distributions of marine and freshwater diatoms, with marine diatoms significantly larger than freshwater species. An evolutionary game theoretical model with empirical allometries of growth and nutrient uptake shows that these differences can be explained by nitrogen versus phosphorus limitation, nutrient fluctuations and mixed layer depth differences. Constant and pulsed phosphorus supply select for small sizes, as does constant nitrogen supply. In contrast, intermediate frequency nitrogen pulses common in the ocean select for large sizes or the evolutionarily stable coexistence of large and small sizes. Size-dependent sinking interacts with mixed layer depth (MLD) to further modulate optimal sizes, with smaller sizes selected for by strong sinking and shallow MLD. In freshwaters, widespread phosphorus limitation, together with strong sinking and shallow MLD produce size distributions with smaller range, means and upper values, compared with the ocean. Shifting patterns of nutrient limitation and mixing may alter diatom size distributions, affecting global carbon cycle and the structure and functioning of aquatic ecosystems.

The role of ecological feedbacks in the evolution of host defence: what does theory tell us?

Hosts have evolved a diverse range of defence mechanisms in response to challenge by infectious organisms (parasites and pathogens). Whether defence is through avoidance of infection, control of the growth of the parasite once infected, clearance of the infection, tolerance to the disease caused by infection or innate and/or acquired immunity, it will have important implications for the population ecology (epidemiology) of the host-parasite interaction. As a consequence, it is important to understand the evolutionary dynamics of defence in the light of the ecological feedbacks that are intrinsic to the interaction. Here, we review the theoretical models that examine how these feedbacks influence the nature and extent of the defence that will evolve. We begin by briefly comparing different evolutionary modelling approaches and discuss in detail the modern game theoretical approach (adaptive dynamics) that allows ecological feedbacks to be taken into account. Next, we discuss a number of models of host defence in detail and, in particular, make a distinction between 'resistance' and 'tolerance'. Finally, we discuss coevolutionary models and the potential use of models that include genetic and game theoretical approaches. Our aim is to review theoretical approaches that investigate the evolution of defence and to explain how the type of defence and the costs associated with its acquisition are important in determining the level of defence that evolves.

Evolution of specialization in resource utilization in structured metapopulations

We study the evolution of resource utilization in a structured discrete-time metapopulation model with an infinite number of patches, prone to local catastrophes. The consumer faces a trade-off in the abilities to consume two resources available in different amounts in each patch. We analyse how the evolution of specialization in the utilization of the resources is affected by different ecological factors: migration, local growth, local catastrophes, forms of the trade-off and distribution of the resources in the patches. Our modelling approach offers a natural way to include more than two patch types into the models. This has not been usually possible in the previous spatially heterogeneous models focusing on the evolution of specialization.