QUANTITATIVE GENETICS AND POPULATION DYNAMICS

Rethinking the Prevalence and Relevance of Chaos in Ecology

Chaos was proposed in the 1970s as an alternative explanation for apparently noisy fluctuations in population size. Although readily demonstrated in models, the search for chaos in nature proved challenging and led many to conclude that chaos is either rare or nigh impossible to detect. However, in the intervening half-century, it has become clear that ecosystems are replete with the enabling conditions for chaos. Chaos has been repeatedly demonstrated under laboratory conditions and has been found in field data using updated detection methods. Together, these developments indicate that the apparent rarity of chaos was an artifact of data limitations and overreliance on low-dimensional population models. We invite readers to reevaluate the relevance of chaos in ecology, and we suggest that chaos is not as rare or undetectable as previously believed.

How does genetic architecture affect eco-evolutionary dynamics? A theoretical perspective

Recent studies have revealed the importance of feedbacks between contemporary rapid evolution (i.e. evolution that occurs through changes in allele frequencies) and ecological dynamics. Despite its inherent interdisciplinary nature, however, studies on eco-evolutionary feedbacks have been mostly ecological and tended to focus on adaptation at the phenotypic level without considering the genetic architecture of evolutionary processes. In empirical studies, researchers have often compared ecological dynamics when the focal species under selection has a single genotype with dynamics when it has multiple genotypes. In theoretical studies, common approaches are models of quantitative traits where mean trait values change adaptively along the fitness gradient and Mendelian traits with two alleles at a single locus. On the other hand, it is well known that genetic architecture can affect short-term evolutionary dynamics in population genetics. Indeed, recent theoretical studies have demonstrated that genetic architecture (e.g. the number of loci, linkage disequilibrium and ploidy) matters in eco-evolutionary dynamics (e.g. evolutionary rescue where rapid evolution prevents extinction and population cycles driven by (co)evolution). I propose that theoretical approaches will promote the synthesis of functional genomics and eco-evolutionary dynamics through models that combine population genetics and ecology as well as nonlinear time-series analyses using emerging big data.

This article is part of the theme issue ‘Genetic basis of adaptation and speciation: from loci to causative mutations’.

Coevolutionary theory of hosts and parasites

Host and parasite evolution are closely intertwined, with selection for adaptations and counter-adaptations forming a coevolutionary feedback loop. Coevolutionary dynamics are often difficult to intuit due to these feedbacks and are hard to demonstrate empirically in most systems. Theoretical models have therefore played a crucial role in shaping our understanding of host-parasite coevolution. Theoretical models vary widely in their assumptions, approaches and aims, and such variety makes it difficult, especially for non-theoreticians and those new to the field, to: (1) understand how model approaches relate to one another; (2) identify key modelling assumptions; (3) determine how model assumptions relate to biological systems; and (4) reconcile the results of different models with contrasting assumptions. In this review, we identify important model features, highlight key results and predictions and describe how these pertain to model assumptions. We carry out a literature survey of theoretical studies published since the 1950s (n = 219 papers) to support our analysis. We identify two particularly important features of models that tend to have a significant qualitative impact on the outcome of host-parasite coevolution: population dynamics and the genetic basis of infection. We also highlight the importance of other modelling features, such as stochasticity and whether time proceeds continuously or in discrete steps, that have received less attention but can drastically alter coevolutionary dynamics. We finish by summarizing recent developments in the field, specifically the trend towards greater model complexity, and discuss likely future directions for research.

A white noise approach to evolutionary ecology

Although the evolutionary response to random genetic drift is classically modelled as a sampling process for populations with fixed abundance, the abundances of populations in the wild fluctuate over time. Furthermore, since wild populations exhibit demographic stochasticity and since random genetic drift is in part due to demographic stochasticity, theoretical approaches are needed to understand the role of demographic stochasticity in eco-evolutionary dynamics. Here we close this gap for quantitative characters evolving in continuously reproducing populations by providing a framework to track the stochastic dynamics of abundance density across phenotypic space using stochastic partial differential equations. In the process we develop a set of heuristics to operationalize the powerful, but abstract theory of white noise and diffusion-limits of individual-based models. Applying these heuristics, we obtain stochastic ordinary differential equations that generalize classical expressions of ecological quantitative genetics. In particular, by supplying growth rate and reproductive variance as functions of abundance densities and trait values, these equations track population size, mean trait and additive genetic variance responding to mutation, demographic stochasticity, random genetic drift, deterministic selection and noise-induced selection. We demonstrate the utility of our approach by formulating a model of diffuse coevolution mediated by exploitative competition for a continuum of resources. In addition to trait and abundance distributions, this model predicts interaction networks defined by niche-overlap, competition coefficients, or selection gradients. Using a high-richness approximation, we find linear selection gradients and competition coefficients are uncorrelated, but magnitudes of linear selection gradients and quadratic selection gradients are both positively correlated with competition coefficients. Hence, competing species that strongly affect each other's abundance tend to also impose selection on one another, but the directionality is not predicted. This approach contributes to the development of a synthetic theory of evolutionary ecology by formalizing first principle derivations of stochastic models tracking feedbacks of biological processes and the patterns of diversity they produce.

Impact of herbivore preference on the benefit of plant trait variability

We explore the hypothesis that intraspecific trait variability can beper sebeneficial for the plant when the curvature of the herbivore response to this trait is concave downwards. This hypothesis is based on a mathematical relation for nonlinear averaging (Jensen’s inequality), leading to reduced herbivory when the trait distribution becomes broader. Our study introduces and investigates a model for plants and their insect herbivores that includes an unequal distribution of nutrient content between leaves. In contrast to earlier publications, we take into account the ability of herbivores to choose leaves, and the associated costs of this preference behavior. By performing computer simulations and analytic calculations, we find that this herbivore preference can considerably alter the conclusion cited above. In particular, we demonstrate that herbivore populations that show preference for leaves on which they grow well can benefit from large nutrient-level variability independently of the curvature of the herbivore response function, despite the cost for preference.

Resource diversity promotes among-individual diet variation, but not genomic diversity, in lake stickleback

Many generalist species consist of specialised individuals that use different resources. This within-population niche variation can stabilise population and community dynamics. Consequently, ecologists wish to identify environmental settings that promote such variation. Theory predicts that environments with greater resource diversity favour ecological diversity among consumers (via disruptive selection or plasticity). Alternatively, niche variation might be a side-effect of neutral genomic diversity in larger populations. We tested these alternatives in a metapopulation of threespine stickleback. Stickleback consume benthic and limnetic invertebrates, focusing on the former in small lakes, the latter in large lakes. Intermediate-sized lakes support generalist stickleback populations using an even mixture of the two prey types, and exhibit greater among-individual variation in diet and morphology. In contrast, genomic diversity increases with lake size. Thus, phenotypic diversity and neutral genetic polymorphism are decoupled: trophic diversity being greatest in intermediate-sized lakes with high resource diversity, whereas neutral genetic diversity is greatest in the largest lakes.

Host-parasite fluctuating selection in the absence of specificity

Fluctuating selection driven by coevolution between hosts and parasites is important for the generation of host and parasite diversity across space and time. Theory has focused primarily on infection genetics, with highly specific ‘matching-allele’ frameworks more likely to generate fluctuating selection dynamics (FSD) than ‘gene-for-gene’ (generalist–specialist) frameworks. However, the environment, ecological feedbacks and life-history characteristics may all play a role in determining when FSD occurs. Here, we develop eco-evolutionary models with explicit ecological dynamics to explore the ecological, epidemiological and host life-history drivers of FSD. Our key result is to demonstrate for the first time, to our knowledge, that specificity between hosts and parasites is not required to generate FSD. Furthermore, highly specific host–parasite interactions produce unstable, less robust stochastic fluctuations in contrast to interactions that lack specificity altogether or those that vary from generalist to specialist, which produce predictable limit cycles. Given the ubiquity of ecological feedbacks and the variation in the nature of specificity in host–parasite interactions, our work emphasizes the underestimated potential for host–parasite coevolution to generate fluctuating selection.

Florivory indirectly decreases the plant reproductive output through changes in pollinator attraction

Species often interact indirectly with each other via their traits. There is increasing appreciation of trait-mediated indirect effects linking multiple interactions. Flowers interact with both pollinators and floral herbivores, and the flower-pollinator interaction may be modified by indirect effects of floral herbivores (i.e., florivores) on flower traits such as flower size attracting pollinators. To explore whether flower size affects the flower-pollinator interaction, we used Eurya japonica flowers. We examined whether artificial florivory decreased fruit and seed production, and also whether flower size affected florivory and the number of floral visitors. The petal removal treatment (i.e., artificial florivory) showed approximately 50% reduction in both fruit and seed set in natural pollination but not in artificial pollination. Furthermore, flower size increased the number of floral visitors, although it did not affect the frequency of florivory. Our results demonstrate that petal removal indirectly decreased 75% of female reproductive output via decreased flower visits by pollinators and that flower size mediated indirect interactions between florivory and floral visitors.

Cryptic Biological Invasions: a General Model of Hybridization

The dispersal of non-native genes due to hybridization is a form of cryptic invasion with growing concern in evolution and conservation. This includes the spread of transgenic genes and antibiotic resistance. To investigate how genes and phenotypes are transmitted, we developed a general model that, for the first time, considers concurrently: multiple loci, quantitative and qualitative gene expression, assortative mating, dominance/recessivity inheritance and density-dependent demographic effects. Selection acting on alleles or genotypes can also be incorporated. Our results reveal that the conclusions about how hybridization threatens a species can be biased if they are based on single-gene models, while considering two or more genes can correct this bias. We also show that demography can amplify or balance the genetic effects, evidencing the need of jointly incorporating both processes. By implementing our model in a real case, we show that mallard ducks introduced in New Zealand benefit from hybridization to replace native grey-ducks. Total displacement can take a few generations and occurs by interspecific competition and by competition between hybrids and natives, demonstrating how hybridization may facilitate biological invasions. We argue that our general model represents a powerful tool for the study of a wide range of biological and societal questions.

Genomic plasticity and rapid host switching can promote the evolution of generalism: a case study in the zoonotic pathogen Campylobacter

Horizontal gene transfer accelerates bacterial adaptation to novel environments, allowing selection to act on genes that have evolved in multiple genetic backgrounds. This can lead to ecological specialization. However, little is known about how zoonotic bacteria maintain the ability to colonize multiple hosts whilst competing with specialists in the same niche. Here we develop a stochastic evolutionary model and show how genetic transfer of host segregating alleles, distributed as predicted for niche specifying genes, and the opportunity for host transition could interact to promote the emergence of host generalist lineages of the zoonotic bacterium Campylobacter. Using a modelling approach we show that increasing levels of homologous recombination enhance the efficiency with which selection can fix combinations of beneficial alleles, speeding adaptation. We then show how these predictions change in a multi-host system, with low levels of recombination, consistent with real r/m estimates, increasing the standing variation in the population, allowing a more effective response to changes in the selective landscape. Our analysis explains how observed gradients of host specialism and generalism can evolve in a multihost system through the transfer of ecologically important loci among coexisting strains.

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.

Multiple dimensions of biodiversity and ecosystem processes: Exploring the joint influence of intraspecific, specific and interspecific diversity

The positive influence of biodiversity on ecosystem processes was the focus of intense debate in ecology throughout the recent decades, becoming accepted and treated as a new paradigm in contemporary ecology. However, the available literature in this research field extensively explores species richness as an unidimensional measure for biodiversity. The present study explores how different components of biological diversity (number of genotypes, species, and functional groups) can influence an ecosystem process (biomass fixation). A mathematical model was employed and the simulation results showed that species richness per se does not affect the ecosystem productivity. Genotypic richness affected positively the ecosystem, but only if the genotypes are functionally complementary. The functional groups richness always affected positively the simulated ecosystem process. When together, richness at the different components of biological diversity showed stronger effect on ecosystem, and the scenarios with high species, genotypes and functional groups richness were the most productive ones. The results also allowed to observe that the ecosystems which are diverse in terms of functional groups and genotypes can be less susceptible to species loss. Finally, it is argued that a multiple dimension approach to biodiversity is relevant to advance the current knowledge on the relation between biodiversity and ecosystem functioning.

Diversity and the maintenance of sex by parasites

The Red Queen hypothesis (RQH) predicts that parasite-mediated selection will maintain sexual individuals in the face of competition from asexual lineages. The prediction is that sexual individuals will be difficult targets for coevolving parasites if they give rise to more genetically diverse offspring than asexual lineages. However, increasing host genetic diversity is known to suppress parasite spread, which could provide a short-term advantage to clonal lineages and lead to the extinction of sex. We test these ideas using a stochastic individual-based model. We find that if parasites are readily transmissible, then sex is most likely to be maintained when host diversity is high, in agreement with the RQH. If transmission rates are lower, however, we find that sexual populations are most likely to persist for intermediate levels of diversity. Our findings thus highlight the importance of genetic diversity and its impact on epidemiological dynamics for the maintenance of sex by parasites.

Individuals in food webs: the relationships between trophic position, omnivory and among-individual diet variation

Among-individual diet variation is common in natural populations and may occur at any trophic level within a food web. Yet, little is known about its variation among trophic levels and how such variation could affect phenotypic divergence within populations. In this study we investigate the relationships between trophic position (the population’s range and average) and among-individual diet variation. We test for diet variation among individuals and across size classes of Eurasian perch (Perca fluviatilis), a widespread predatory freshwater fish that undergoes ontogenetic niche shifts. Second, we investigate among-individual diet variation within fish and invertebrate populations in two different lake communities using stable isotopes. Third, we test potential evolutionary implications of population trophic position by assessing the relationship between the proportion of piscivorous perch (populations of higher trophic position) and the degree of phenotypic divergence between littoral and pelagic perch sub-populations. We show that among-individual diet variation is highest at intermediate trophic positions, and that this high degree of among-individual variation likely causes an increase in the range of trophic positions among individuals. We also found that phenotypic divergence was negatively related to trophic position in a population. This study thus shows that trophic position is related to and may be important for among-individual diet variation as well as to phenotypic divergence within populations.

Genetics, adaptation, and invasion in harsh environments

We analyze mathematical models to examine how the genetic basis of fitness affects the persistence of a population suddenly encountering a harsh environment where it would go extinct without evolution. The results are relevant for novel introductions and for an established population whose existence is threatened by a sudden change in the environment. The models span a range of genetic assumptions, including identical loci that contribute to absolute fitness, a two-locus quantitative genetic model with nonidentical loci, and a model with major and minor genes affecting a quantitative trait. We find as a general (though not universal) pattern that prospects for persistence narrow as more loci contribute to fitness, in effect because selection per locus is increasingly weakened with more loci, which can even overwhelm any initial enhancement of fitness that adding loci might provide. When loci contribute unequally to fitness, genes of small effect can significantly reduce extinction risk. Indeed, major and minor genes can interact synergistically to reduce the time needed to evolve growth. Such interactions can also increase vulnerability to extinction, depending not just on how genes interact but also on the initial genetic structure of the introduced, or newly invaded, population.

Does intraspecific size variation in a predator affect its diet diversity and top-down control of prey?

It has long been known that intraspecific variation impacts evolutionary processes, but only recently have its potential ecological effects received much attention. Theoretical models predict that genetic or phenotypic variance within species can alter interspecific interactions, and experiments have shown that genotypic diversity in clonal species can impact a wide range of ecological processes. To extend these studies to quantitative trait variation within populations, we experimentally manipulated the variance in body size of threespine stickleback in enclosures in a natural lake environment. We found that body size of stickleback in the lake is correlated with prey size and (to a lesser extent) composition, and that stickleback can exert top-down control on their benthic prey in enclosures. However, a six-fold contrast in body size variance had no effect on the degree of diet variation among individuals, or on the abundance or composition of benthic or pelagic prey. Interestingly, post-hoc analyses revealed suggestive correlations between the degree of diet variation and the strength of top-down control by stickleback. Our negative results indicate that, unless the correlation between morphology and diet is very strong, ecological variation among individuals may be largely decoupled from morphological variance. Consequently we should be cautious in our interpretation both of theoretical models that assume perfect correlations between morphology and diet, and of empirical studies that use morphological variation as a proxy for resource use diversity.

Why intraspecific trait variation matters in community ecology

Natural populations consist of phenotypically diverse individuals that exhibit variation in their demographic parameters and intra- and inter-specific interactions. Recent experimental work indicates that such variation can have significant ecological effects. However, ecological models typically disregard this variation and focus instead on trait means and total population density. Under what situations is this simplification appropriate? Why might intraspecific variation alter ecological dynamics? In this review we synthesize recent theory and identify six general mechanisms by which trait variation changes the outcome of ecological interactions. These mechanisms include several direct effects of trait variation per se and indirect effects arising from the role of genetic variation in trait evolution.

Sex and space destabilize intransitive competition within and between species

Organisms ranging from bacteria and corals to plants and vertebrates can form intransitive competitive networks, in which coexistence can be maintained because no one species or genotype is superior to all others. However, in the simplest case with three competing types, the long-term outcome may not be so clear if two of the three represent the ends of a continuous heritable trait distribution within one species, as has been recently demonstrated empirically in a short-term experiment with plants. Using simulation models of this scenario, results with asexual reproduction confirm previous studies which showed that local interactions promote coexistence. However, with sexual reproduction, genetic variance is reduced because selection fluctuates between favouring the two extremes during population cycles, while sex continually produces intermediates. Sex thus slows the response to selection when it is the strongest and therefore slows the recovery from extreme abundances, creating larger abundance fluctuations. Local interactions do not stabilize dynamics with sex because the resultant spatial patches of one species are genetically heterogeneous, such that particular phenotypes do not benefit from spatial refuges. In sharp contrast to previous models suggesting that sex or local interactions stabilize population dynamics, here sex and local interactions destabilize dynamics and increase extinction risk.

Explaining the explosion: modelling hybrid invasions

The emergence of hybrids between native and introduced species is an increasingly widespread problem which can alter entire ecosystems. We present a general model for the hybridization of two plant species to investigate the conditions under which hybrid invasions can occur, and the ecological and genetic consequences of such hybridizations. We find that parental compatibility and fecundity are important determinants of whether (and at what rate) hybrid genotypes emerge. Enhanced hybrid fitness traits affect both the population's genetic structure and total rate of increase, with rapid selection for the fittest genotype. Conversely, if different genotypes maximize different life-history characteristics, the ensuing population can be genetically very variable. The model provides a novel approach to evaluate the contributions of population dynamic and genetic processes in the study of hybrid invasions.

Frequency-dependent numerical dynamics in mosquitofish

Altering the genetic composition of a population can alter several aspects of its numerical dynamics. Whether natural populations routinely contain the genetic variation capable of affecting the stability of those dynamics is less clear. Here we report a study of experimental populations of mosquitofish (Gambusia holbrooki), designed to examine this issue. The experiment examined the numerical effects of varying the initial relative frequency of a rare male genotype. A higher relative frequency of the rare, melanic genotype produced higher mortality rates in melanic males, higher mortality rates in females, higher juvenile abundance, and fewer fluctuations in the numbers of females across time. This work demonstrates that a natural population can harbour genetic variants in a single gender that are capable of inducing qualitative differences in the numerical dynamics of the opposite gender, through the effects of negative frequency-dependent selection.

Host-parasite coevolution in a multilocus gene-for-gene system

This paper examines a mathematical model for the coevolution of parasite virulence and host resistance under a multilocus gene-for-gene interaction. The degrees of parasite virulence and host resistance show coevolutionary cycles for sufficiently small costs of virulence and resistance. Besides these coevolutionary cycles of a longer period, multilocus genotype frequencies show complex fluctuations over shorter periods. All multilocus genotypes are maintained within host and parasite classes having the same number of resistant/virulent alleles and their frequencies fluctuate with approximately equally displaced phases. If either the cost of virulence or the number of resistance loci is larger then a threshold, the host maintains the static polymorphism of singly (or doubly or more, depending on the cost of resistance) resistant genotypes and the parasite remains universally avirulent. In other words, host polymorphism can prevent the invasion of any virulent strain in the parasite. Thus, although assuming an empirically common type of asymmetrical gene-for-gene interaction, both host and parasite populations can maintain polymorphism in each locus and retain complex fluctuations. Implications for the red queen hypothesis of the evolution of sex and the control of multiple drug resistance are discussed.

A model for the coevolution of resistance and virulence in coupled host—parasitoid interactions

A coevolutionary model is developed of the interaction between a host and an internal parasitoid, where the outcome of parasitism depends upon the extent to which individual hosts invest in resistance mechanisms and individual parasitoids in countermeasures (virulence). The host and parasitoid are assumed to have coupled population dynamics (of Nicholson–Bailey form) and to be composed of a series of asexual clones with different levels of resistance and virulence. Investment in resistance and virulence mechanisms is assumed to be costly. The model has two main outcomes. First, if resistance is relatively costly compared to virulence, the host may be selected not to invest in resistance mechanisms despite parasitoid investment in virulence, in effect trading off the risks of parasitism against the savings in costs. A number of cases which appear to correspond to this result have been reported. Second, for most other feasible parameter values, an arms race occurs between host and parasitoid, until effective resistance becomes so costly that the host abandons defence. This abandonment is followed by a reduction in parasitoid virulence and the cycle begins again. These cycles may explain reports of persistent additive genetic variation in resistance and virulence, and may also contribute towards population dynamic stability.

Sexual reproduction and population dynamics: the role of polygyny and demographic sex differences

Most models of population dynamics do not take sexual reproduction into account (i.e., they do not consider the role of males). However, assumptions behind this practice--that no demographic sex differences exist and males are always abundant enough to fertilize all the females--are usually not justified in natural populations. On the contrary, demographic sex differences are common, especially in polygynous species. Previous models that consider sexual reproduction report a stabilizing effect through mixing of different genotypes, thus suggesting a decrease in the propensity for complex of dynamics in sexually reproducing populations. Here we show that considering the direct role of males in reproduction and density dependence leads to the conclusion that a two-sex model is not necessarily more stable compared with the corresponding one-sex model. Although solutions exist where sexual reproduction has a stabilizing effect even when no genotypic variability is included (primarily when associated with monogamy), factors like polygyny, sex differences in survival or density dependence, and possible alterations of the primary sex ratio (the Trivers-Willard mechanism), may enlarge the parametric region of complex dynamics. Sexual reproduction therefore does not necessarily increase the stability of population dynamics and can have destabilizing effects, at least in species with complicated mating systems and sexual dimorphism.