Fisher's geometric model with a moving optimum

Fisher's Geometric Model as a Tool to Study Speciation

Interactions between alleles and across environments play an important role in the fitness of hybrids and are at the heart of the speciation process. Fitness landscapes capture these interactions and can be used to model hybrid fitness, helping us to interpret empirical observations and clarify verbal models. Here, we review recent progress in understanding hybridization outcomes through Fisher's geometric model, an intuitive and analytically tractable fitness landscape that captures many fitness patterns observed across taxa. We use case studies to show how the model parameters can be estimated from different types of data and discuss how these estimates can be used to make inferences about the divergence history and genetic architecture. We also highlight some areas where the model's predictions differ from alternative incompatibility-based models, such as the snowball effect and outlier patterns in genome scans.

Evolutionary rescue on genotypic fitness landscapes

Populations facing adverse environments, novel pathogens or invasive competitors may be destined to extinction if they are unable to adapt rapidly. Quantitative predictions of the probability of survival through adaptation, evolutionary rescue, have been previously developed for one of the most natural and well-studied mappings from an organism's traits to its fitness, Fisher's geometric model (FGM). While FGM assumes that all possible trait values are accessible via mutation, in many applications only a finite set of rescue mutations will be available, such as mutations conferring resistance to a parasite, predator or toxin. We predict the probability of evolutionary rescue, via de novo mutation, when this underlying genetic structure is included. We find that rescue probability is always reduced when its genetic basis is taken into account. Unlike other known features of the genotypic FGM, however, the probability of rescue increases monotonically with the number of available mutations and approaches the behaviour of the classical FGM as the number of available mutations approaches infinity.

Phenotype Design Space Provides a Mechanistic Framework Relating Molecular Parameters to Phenotype Diversity Available for Selection

Two long-standing challenges in theoretical population genetics and evolution are predicting the distribution of phenotype diversity generated by mutation and available for selection, and determining the interaction of mutation, selection and drift to characterize evolutionary equilibria and dynamics. More fundamental for enabling such predictions is the current inability to causally link genotype to phenotype. There are three major mechanistic mappings required for such a linking - genetic sequence to kinetic parameters of the molecular processes, kinetic parameters to biochemical system phenotypes, and biochemical phenotypes to organismal phenotypes. This article introduces a theoretical framework, the Phenotype Design Space (PDS) framework, for addressing these challenges by focusing on the mapping of kinetic parameters to biochemical system phenotypes. It provides a quantitative theory whose key features include (1) a mathematically rigorous definition of phenotype based on biochemical kinetics, (2) enumeration of the full phenotypic repertoire, and (3) functional characterization of each phenotype independent of its context-dependent selection or fitness contributions. This framework is built on Design Space methods that relate system phenotypes to genetically determined parameters and environmentally determined variables. It also has the potential to automate prediction of phenotype-specific mutation rate constants and equilibrium distributions of phenotype diversity in microbial populations undergoing steady-state exponential growth, which provides an ideal reference to which more realistic cases can be compared. Although the framework is quite general and flexible, the details will undoubtedly differ for different functions, organisms and contexts. Here a hypothetical case study involving a small molecular system, a primordial circadian clock, is used to introduce this framework and to illustrate its use in a particular case. The framework is built on fundamental biochemical kinetics. Thus, the foundation is based on linear algebra and reasonable physical assumptions, which provide numerous opportunities for experimental testing and further elaboration to deal with complex multicellular organisms that are currently beyond its scope. The discussion provides a comparison of results from the PDS framework with those from other approaches in theoretical population genetics.

Genetic Architecture of Flowering Time Differs Between Populations With Contrasting Demographic and Selective Histories

Understanding the evolutionary factors that impact the genetic architecture of traits is a central goal of evolutionary genetics. Here, we investigate how quantitative trait variation accumulated over time in populations that colonized a novel environment. We compare the genetic architecture of flowering time in Arabidopsis populations from the drought-prone Cape Verde Islands and their closest outgroup population from North Africa. We find that trait polygenicity is severely reduced in the island populations compared to the continental North African population. Further, trait architectures and reconstructed allelic histories best fit a model of strong directional selection in the islands in accord with a Fisher-Orr adaptive walk. Consistent with this, we find that large-effect variants that disrupt major flowering time genes (FRI and FLC) arose first, followed by smaller effect variants, including ATX2 L125F, which is associated with a 4-day reduction in flowering time. The most recently arising flowering time-associated loci are not known to be directly involved in flowering time, consistent with an omnigenic signature developing as the population approaches its trait optimum. Surprisingly, we find no effect in the natural population of EDI-Cvi-0 (CRY2 V367M), an allele for which an effect was previously validated by introgression into a Eurasian line. Instead, our results suggest the previously observed effect of the EDI-Cvi-0 allele on flowering time likely depends on genetic background, due to an epistatic interaction. Altogether, our results provide an empirical example of the effects demographic history and selection has on trait architecture.

Evolutionary repeatability of emergent properties of ecological communities

Most species belong to ecological communities where their interactions give rise to emergent community-level properties, such as diversity and productivity. Understanding and predicting how these properties change over time has been a major goal in ecology, with important practical implications for sustainability and human health. Less attention has been paid to the fact that community-level properties can also change because member species evolve. Yet, our ability to predict long-term eco-evolutionary dynamics hinges on how repeatably community-level properties change as a result of species evolution. Here, we review studies of evolution of both natural and experimental communities and make the case that community-level properties at least sometimes evolve repeatably. We discuss challenges faced in investigations of evolutionary repeatability. In particular, only a handful of studies enable us to quantify repeatability. We argue that quantifying repeatability at the community level is critical for approaching what we see as three major open questions in the field: (i) Is the observed degree of repeatability surprising? (ii) How is evolutionary repeatability at the community level related to repeatability at the level of traits of member species? (iii) What factors affect repeatability? We outline some theoretical and empirical approaches to addressing these questions. Advances in these directions will not only enrich our basic understanding of evolution and ecology but will also help us predict eco-evolutionary dynamics. This article is part of the theme issue 'Interdisciplinary approaches to predicting evolutionary biology'.

Selective sweeps linked to the colonization of novel habitats and climatic changes in a wild tomato species

Positive selection is the driving force underpinning local adaptation and leaves footprints of selective sweeps on the underlying major genes. Quantifying the timing of selection and revealing the genetic bases of adaptation in plant species occurring in steep and varying environmental gradients are crucial to predict a species' ability to colonize new niches. We use whole-genome sequence data from six populations across three different habitats of the wild tomato species Solanum chilense to infer the past demographic history and search for genes under strong positive selection. We then correlate current and past climatic projections with the demographic history, allele frequencies, the age of selection events and distribution shifts. Several selective sweeps occur at regulatory networks involved in root-hair development in low altitude and response to photoperiod and vernalization in high-altitude populations. These sweeps appear to occur in a concerted fashion in a given regulatory gene network at particular periods of substantial climatic change. Using a unique combination of genome scans and modelling of past climatic data, we quantify the timing of selection at genes likely underpinning local adaptation to semiarid habitats.

The geometry of evolutionary conflict

Conflicts of interest abound not only in human affairs but also in the biological realm. Evolutionary conflict occurs over multiple scales of biological organization, from genetic outlawry within genomes, to sibling rivalry within nuclear families, to collective-action disputes within societies. However, achieving a general understanding of the dynamics and consequences of evolutionary conflict remains an outstanding challenge. Here, we show that a development of R. A. Fisher's classic 'geometric model' of adaptation yields novel and surprising insights into the dynamics of evolutionary conflict and resulting maladaptation, including the discoveries that: (i) conflict can drive evolving traits arbitrarily far away from all parties' optima and, indeed, if all mutations are equally likely then contested traits are more often than not driven outwith the zone of actual conflict (hyper-maladaptation); (ii) evolutionary conflicts drive persistent maladaptation of orthogonal, non-contested traits (para-maladaptation); and (iii) modular design greatly ameliorates conflict-driven maladaptation, thereby facilitating major transitions in individuality.

Using landscape genomics to delineate future adaptive potential for climate change in the Yosemite toad (Anaxyrus canorus)

An essential goal in conservation biology is delineating population units that maximize the probability of species persisting into the future and adapting to future environmental change. However, future-facing conservation concerns are often addressed using retrospective patterns that could be irrelevant. We recommend a novel landscape genomics framework for delineating future "Geminate Evolutionary Units" (GEUs) in a focal species: (1) identify loci under environmental selection, (2) model and map adaptive conservation units that may spawn future lineages, (3) forecast relative selection pressures on each future lineage, and (4) estimate their fitness and likelihood of persistence using geo-genomic simulations. Using this process, we delineated conservation units for the Yosemite toad (Anaxyrus canorus), a U.S. federally threatened species that is highly vulnerable to climate change. We used a genome-wide dataset, redundancy analysis, and Bayesian association methods to identify 24 candidate loci responding to climatic selection (R 2 ranging from 0.09 to 0.52), after controlling for demographic structure. Candidate loci included genes such as MAP3K5, involved in cellular response to environmental change. We then forecasted future genomic response to climate change using the multivariate machine learning algorithm Gradient Forests. Based on all available evidence, we found three GEUs in Yosemite National Park, reflecting contrasting adaptive optima: YF-North (high winter snowpack with moderate summer rainfall), YF-East (low to moderate snowpack with high summer rainfall), and YF-Low-Elevation (low snowpack and rainfall). Simulations under the RCP 8.5 climate change scenario suggest that the species will decline by 29% over 90 years, but the highly diverse YF-East lineage will be least impacted for two reasons: (1) geographically it will be sheltered from the largest climatic selection pressures, and (2) its standing genetic diversity will promote a faster adaptive response. Our approach provides a comprehensive strategy for protecting imperiled non-model species with genomic data alone and has wide applicability to other declining species.

Rate of environmental variation impacts the predictability in evolution

In the two last decades, we have improved our understanding of the adaptive evolution of natural populations under constant and stable environments. For instance, experimental methods from evolutionary biology have allowed us to explore the structure of fitness landscapes and survey how the landscape properties can constrain the adaptation process. However, understanding how environmental changes can affect adaptation remains challenging. Very little progress has been made with respect to time-varying fitness landscapes. Using the adaptive-walk approximation, we survey the evolutionary process of populations under a scenario of environmental variation. In particular, we investigate how the rate of environmental variation influences the predictability in evolution. We observe that the rate of environmental variation not only changes the duration of adaptive walks towards fitness peaks of the fitness landscape, but also affects the degree of repeatability of both outcomes and evolutionary paths. In general, slower environmental variation increases the predictability in evolution. The accessibility of endpoints is greatly influenced by the ecological dynamics. The dependence of these quantities on the genome size and number of traits is also addressed. To our knowledge, this contribution is the first to use the predictive approach to quantify and understand the impact of the speed of environmental variation on the degree of parallelism of the evolutionary process.

The diverse effects of phenotypic dominance on hybrid fitness

When divergent populations interbreed, their alleles are brought together in hybrids. In the initial F1 cross, most divergent loci are heterozygous. Therefore, F1 fitness can be influenced by dominance effects that could not have been selected to function well together. We present a systematic study of these F1 dominance effects by introducing variable phenotypic dominance into Fisher's geometric model. We show that dominance often reduces hybrid fitness, which can generate optimal outbreeding followed by a steady decline in F1 fitness, as is often observed. We also show that "lucky" beneficial effects sometimes arise by chance, which might be important when hybrids can access novel environments. We then show that dominance can lead to violations of Haldane's Rule (reduced fitness of the heterogametic F1) but strengthens Darwin's Corollary (F1 fitness differences between cross directions). Taken together, results show that the effects of dominance on hybrid fitness can be surprisingly difficult to isolate, because they often resemble the effects of uniparental inheritance or expression. Nevertheless, we identify a pattern of environment-dependent heterosis that only dominance can explain, and for which there is some suggestive evidence. Our results also show how existing data set upper bounds on the size of dominance effects. These bounds could explain why additive models often provide good predictions for later-generation recombinant hybrids, even when dominance qualitatively changes outcomes for the F1.

Variation in shape and consistency of selection between populations of the threatened Hihi (Notiomystis cincta)

The shape and intensity of natural selection can vary between years, potentially resulting in a chronic reduction of fitness as individuals need to track a continually changing optimum of fitness (i.e., a "lag load"). In endangered species, often characterized by small population size, the lack of genetic diversity is expected to limit the response to this constant need to adjust to fluctuating selection, increasing the fitness burden and thus the risk of extinction. Here, we use long-term monitoring data to assess whether the type of selection for a key fitness trait (i.e., lay date) differs between two reintroduced populations of a threatened passerine bird, the hihi (Notiomystis cincta). We apply recent statistical developments to test for the presence or absence of fluctuation in selection in both the Tiritiri Mātangi Island and the Kārori sanctuary populations. Our results support the presence of stabilizing selection in Tiritiri Mātangi with a potential moving optimum for lay date. In Kārori our results favour a regime of directional selection. Although the shape of selection may differ, for both populations an earlier lay date generally increases fitness in both environments. Further, the moving optimum models of lay date on Tiritiri Mātangi, suggesting that selection varies between years, imply a substantial lag load in addition to the fitness burden caused by the population laying too late. Our results highlight the importance of characterizing the form and temporal variation of selection for each population to predict the effects of environmental change and to inform management.

Biological adaptation in light of the Lewontin-Williams (a)symmetry

Neo-Darwinism characterizes biological adaptation as a one-sided process, in which organisms adapt to their environment but not vice versa. This asymmetric relationship-here called Williams' asymmetry-is called into question by Niche Construction Theory, which emphasizes that organisms and their environments often mutually affect each other. Here, we clarify that Williams' asymmetry is specifically concerned with (quasi)-directed modifications toward phenotypes that increase individual fitness. This directedness-which drives the adaptive fit between organism and environment-entails far more than the mere presence of cause-effect relationships. We argue that difficulties with invoking fitness as the guiding principle of adaptive evolution are resolved with an appropriate definition of fitness and that objections against Williams' asymmetry reflect confusions about the nature of biological adaptation.

Evolution in small steps and giant leaps

The first Editor of Evolution was Ernst Mayr. His foreword to the first issue of Evolution published in 1947 framed evolution as a "problem of interaction" that was just beginning to be studied in this broad context. First, I explore progress and prospects on understanding the subsidiary interactions identified by Mayr, including interactions between parts of organisms, between individuals and populations, between species, and between the organism and its abiotic environment. Mayr's overall "problem of interaction" framework is examined in the context of coevolution within and among levels of biological organization. This leads to a comparison in the relative roles of biotic versus abiotic agents of selection and fluctuating versus directional selection, followed by stabilizing selection in shaping the genomic architecture of adaptation. Oligogenic architectures may be typical for traits shaped more by fluctuating selection and biotic selection. Conversely, polygenic architectures may be typical for traits shaped more by directional followed by stabilizing selection and abiotic selection. The distribution of effect sizes and turnover dynamics of adaptive alleles in these scenarios deserves further study. Second, I review two case studies on the evolution of acquired toxicity in animals, one involving cardiac glycosides obtained from plants and one involving bacterial virulence factors horizontally transferred to animals. The approaches used in these studies and the results gained directly flow from Mayr's vision of an evolutionary biology that revolves around the "problem of interaction."

Allen Orr and the genetics of adaptation

Over most of the 20th century, evolutionary biologists predominantly subscribed to a strong form of "micro-mutationism," in which adaptive phenotypic divergence arises from allele frequency changes at many loci, each with a small effect on the phenotype. To be sure, there were well-known examples of large-effect alleles contributing to adaptation, yet such cases were generally regarded as atypical and unrepresentative of evolutionary change in general. In 1998, Allen Orr published a landmark theoretical paper in Evolution, which showed that both small- and large-effect mutations are likely to contribute to "adaptive walks" of a population to an optimum. Coupled with a growing set of empirical examples of large-effect alleles contributing to divergence (e.g., from QTL studies), Orr's paper provided a mathematical formalism that converted many evolutionary biologists from micro-mutationism to a more pluralistic perspective on the genetic basis of evolutionary change. We revisit the theoretical insights emerging from Orr's paper within the historical context leading up to 1998, and track the influence of this paper on the field of evolutionary biology through an examination of its citations over the last two decades and an analysis of the extensive body of theoretical and empirical research that Orr's pioneering paper inspired.

Multidimensional divergent selection, local adaptation, and speciation

Divergent selection applied to one or more traits drives local adaptation and may lead to ecological speciation. Divergent selection on many traits might be termed "multidimensional" divergent selection. There is a commonly held view that multidimensional divergent selection is likely to promote local adaptation and speciation to a greater extent than unidimensional divergent selection. We disentangle the core concepts underlying dimensionality as a property of the environment, phenotypes, and genome. In particular, we identify a need to separate the overall strength of selection and the number of loci affected from dimensionality per se, and to distinguish divergence dimensionality from dimensionality of stabilizing selection. We then critically scrutinize this commonly held view that multidimensional selection promotes speciation, re-examining the evidence base from theory, experiments, and nature. We conclude that the evidence base is currently weak and generally suffers from confounding of possible causal effects. Finally, we propose several mechanisms by which multidimensional divergent selection and related processes might influence divergence, both as a driver and as a barrier.

The geometry and genetics of hybridization

When divergent populations form hybrids, hybrid fitness can vary with genome composition, current environmental conditions, and the divergence history of the populations. We develop analytical predictions for hybrid fitness, which incorporate all three factors. The predictions are based on Fisher's geometric model, and apply to a wide range of population genetic parameter regimes and divergence conditions, including allopatry and parapatry, local adaptation, and drift. Results show that hybrid fitness can be decomposed into intrinsic effects of admixture and heterozygosity, and extrinsic effects of the (local) adaptedness of the parental lines. Effect sizes are determined by a handful of geometric distances, which have a simple biological interpretation. These distances also reflect the mode and amount of divergence, such that there is convergence toward a characteristic pattern of intrinsic isolation. We next connect our results to the quantitative genetics of line crosses in variable or patchy environments. This means that the geometrical distances can be estimated from cross data, and provides a simple interpretation of the "composite effects." Finally, we develop extensions to the model, involving selectively induced disequilibria, and variable phenotypic dominance. The geometry of fitness landscapes provides a unifying framework for understanding speciation, and wider patterns of hybrid fitness.

Evolutionary adaptation of high-diversity communities to changing environments

We use adaptive dynamics models to study how changes in the abiotic environment affect patterns of evolutionary dynamics and diversity in evolving communities of organisms with complex phenotypes. The models are based on the logistic competition model, and environmental changes are implemented as a temporal change of the carrying capacity as a function of phenotype. In general, we observe that environmental changes cause a reduction in the number of species, in total population size, and in phenotypic diversity. The rate of environmental change is crucial for determining whether a community survives or undergoes extinction. Until some critical rate of environmental changes, species are able to follow evolutionarily the shifting phenotypic optimum of the carrying capacity, and many communities adapt to the changing conditions and converge to new stationary states. When environmental changes stop, such communities gradually restore their initial phenotypic diversity.

Adapt or Perish: Evolutionary Rescue in a Gradually Deteriorating Environment

We investigate the evolutionary rescue of a microbial population in a gradually deteriorating environment, through a combination of analytical calculations and stochastic simulations. We consider a population destined for extinction in the absence of mutants, which can survive only if mutants sufficiently adapted to the new environment arise and fix. We show that mutants that appear later during the environment deterioration have a higher probability to fix. The rescue probability of the population increases with a sigmoidal shape when the product of the carrying capacity and of the mutation probability increases. Furthermore, we find that rescue becomes more likely for smaller population sizes and/or mutation probabilities if the environment degradation is slower, which illustrates the key impact of the rapidity of environment degradation on the fate of a population. We also show that our main conclusions are robust across various types of adaptive mutants, including specialist and generalist ones, as well as mutants modeling antimicrobial resistance evolution. We further express the average time of appearance of the mutants that do rescue the population and the average extinction time of those that do not. Our methods can be applied to other situations with continuously variable fitnesses and population sizes, and our analytical predictions are valid in the weak-to-moderate mutation regime.

Experimental Hybridization Studies Suggest That Pleiotropic Alleles Commonly Underlie Adaptive Divergence between Natural Populations

The alleles used for adaptation can pleiotropically affect traits under stabilizing selection. The fixation of alleles with deleterious pleiotropic side effects causes compensatory alleles to be favored by selection. Such compensatory alleles might segregate in interpopulation hybrids, resulting in segregation variance for traits where parents have indistinguishable phenotypes. If adaptation typically involves pleiotropy and compensation, then the segregation variance for traits under stabilizing selection is expected to increase with the magnitude of adaptive phenotypic divergence between parents. This prediction has not been tested empirically, and I gathered data from experimental hybridization studies to evaluate it. I found that pairs of parents that are more phenotypically divergent beget hybrids with more segregation variance in traits for which the parents are statistically indistinguishable. This result suggests that adaptive divergence between pairs of natural populations proceeds via pleiotropy and compensation and that deleterious transgressive segregation variance accumulates systematically as populations diverge.

Why is cancer not more common? A changing microenvironment may help to explain why, and suggests strategies for anti-cancer therapy

One of the great unsolved puzzles in cancer biology is not why cancers occur, but rather explaining why so few cancers occur compared with the theoretical number that could occur, given the number of progenitor cells in the body and the normal mutation rate. We hypothesized that a contributory explanation is that the tumour microenvironment (TME) is not fixed due to factors such as immune cell infiltration, and that this could impair the ability of neoplastic cells to retain a high enough fitness to become a cancer. The TME has implicitly been assumed to be static in most cancer evolution models, and we therefore developed a mathematical model of spatial cancer evolution assuming that the TME, and thus the optimum cancer phenotype, changes over time. Based on simulations, we show how cancer cell populations adapt to diverse changing TME conditions and fitness landscapes. Compared with static TMEs, which generate neutral dynamics, changing TMEs lead to complex adaptations with characteristic spatio-temporal heterogeneity involving variable fitness effects of driver mutations, subclonal mixing, subclonal competition and phylogeny patterns. In many cases, cancer cell populations fail to grow or undergo spontaneous regression, and even extinction. Our analyses predict that cancer evolution in a changing TME is challenging, and can help to explain why cancer is neither inevitable nor as common as expected. Should cancer driver mutations with effects dependent of the TME exist, they are likely to be selected. Anti-cancer prevention and treatment strategies based on changing the TME are feasible and potentially effective.

Long-term evolutionary conflict, Sisyphean arms races, and power in Fisher's geometric model

Evolutionary conflict and arms races are important drivers of evolution in nature. During arms races, new abilities in one party select for counterabilities in the second party. This process can repeat and lead to successive fixations of novel mutations, without a long-term increase in fitness. Models of co-evolution rarely address successive fixations, and one of the main models that use successive fixations-Fisher's geometric model-does not address co-evolution. We address this gap by expanding Fisher's geometric model to the evolution of joint phenotypes that are affected by two parties, such as probability of infection of a host by a pathogen. The model confirms important intuitions and offers some new insights. Conflict can lead to long-term Sisyphean arms races, where parties continue to climb toward their fitness peaks, but are dragged back down by their opponents. This results in far more adaptive evolution compared to the standard geometric model. It also results in fixation of mutations of larger effect, with the important implication that the common modeling assumption of small mutations will apply less often under conflict. Even in comparison with random abiotic change of the same magnitude, evolution under conflict results in greater distances from the optimum, lower fitness, and more fixations, but surprisingly, not larger fixed mutations. We also show how asymmetries in selection strength, mutation size, and mutation input allow one party to win over another. However, winning abilities come with diminishing returns, helping to keep weaker parties in the game.

Thinking About the Evolution of Complex Traits in the Era of Genome-Wide Association Studies

Many traits of interest are highly heritable and genetically complex, meaning that much of the variation they exhibit arises from differences at numerous loci in the genome. Complex traits and their evolution have been studied for more than a century, but only in the last decade have genome-wide association studies (GWASs) in humans begun to reveal their genetic basis. Here, we bring these threads of research together to ask how findings from GWASs can further our understanding of the processes that give rise to heritable variation in complex traits and of the genetic basis of complex trait evolution in response to changing selection pressures (i.e., of polygenic adaptation). Conversely, we ask how evolutionary thinking helps us to interpret findings from GWASs and informs related efforts of practical importance.

Surfing on the seascape: Adaptation in a changing environment

The environment changes constantly at various time scales and, in order to survive, species need to keep adapting. Whether these species succeed in avoiding extinction is a major evolutionary question. Using a multilocus evolutionary model of a mutation-limited population adapting under strong selection, we investigate the effects of the frequency of environmental fluctuations on adaptation. Our results rely on an "adaptive-walk" approximation and use mathematical methods from evolutionary computation theory to investigate the interplay between fluctuation frequency, the similarity of environments, and the number of loci contributing to adaptation. First, we assume a linear additive fitness function, but later generalize our results to include several types of epistasis. We show that frequent environmental changes prevent populations from reaching a fitness peak, but they may also prevent the large fitness loss that occurs after a single environmental change. Thus, the population can survive, although not thrive, in a wide range of conditions. Furthermore, we show that in a frequently changing environment, the similarity of threats that a population faces affects the level of adaptation that it is able to achieve. We check and supplement our analytical results with simulations.

Does Adaptive Protein Evolution Proceed by Large or Small Steps at the Amino Acid Level?

A long-standing question in evolutionary biology is the relative contribution of large and small effect mutations to the adaptive process. We have investigated this question in proteins by estimating the rate of adaptive evolution between all pairs of amino acids separated by one mutational step using a McDonald-Kreitman type approach and genome-wide data from several Drosophila species. We find that the rate of adaptive evolution is highest among amino acids that are more similar. This is partly due to the fact that the proportion of mutations that are adaptive is higher among more similar amino acids. We also find that the rate of neutral evolution between amino acids is higher among more similar amino acids. Overall our results suggest that both the adaptive and nonadaptive evolution of proteins are dominated by substitutions between similar amino acids.

Symbiont evolution during the free-living phase can improve host colonization

For micro-organisms cycling between free-living and host-associated stages, where reproduction occurs in both of these lifestyles, an interesting inquiry is whether evolution during the free-living stage can be positively pleiotropic to microbial fitness in a host environment. To address this topic, the squid host Euprymna tasmanica and the marine bioluminescent bacterium Vibrio fischeri were utilized. Microbial ecological diversification in static liquid microcosms was used to simulate symbiont evolution during the free-living stage. Thirteen genetically distinct V. fischeri strains from a broad diversity of ecological sources (e.g. squid light organs, fish light organs and seawater) were examined to see if the results were reproducible in many different genetic settings. Genetic backgrounds that are closely related can be predisposed to considerable differences in how they respond to similar selection pressures. For all strains examined, new mutations with striking and facilitating effects on host colonization arose quickly during microbial evolution in the free-living stage, regardless of the ecological context under consideration for a strain’s genetic background. Microbial evolution outside a host environment promoted host range expansion, improved host colonization for a micro-organism, and diminished the negative correlation between biofilm formation and motility.

Slower environmental change hinders adaptation from standing genetic variation

Evolutionary responses to environmental change depend on the time available for adaptation before environmental degradation leads to extinction. Explicit tests of this relationship are limited to microbes where adaptation usually depends on the sequential fixation of de novo mutations, excluding standing variation for genotype-by-environment fitness interactions that should be key for most natural species. For natural species evolving from standing genetic variation, adaptation at slower rates of environmental change may be impeded since the best genotypes at the most extreme environments can be lost during evolution due to genetic drift or founder effects. To address this hypothesis, we perform experimental evolution with self-fertilizing populations of the nematode Caenorhabditis elegans and develop an inference model to describe natural selection on extant genotypes under environmental change. Under a sudden environmental change, we find that selection rapidly increases the frequency of genotypes with high fitness in the most extreme environment. In contrast, under a gradual environmental change selection first favors genotypes that are worse at the most extreme environment. We demonstrate with a second set of evolution experiments that, as a consequence of slower environmental change and thus longer periods to reach the most extreme environments, genetic drift and founder effects can lead to the loss of the most beneficial genotypes. We further find that maintenance of standing genetic variation can retard the fixation of the best genotypes in the most extreme environment because of interference between them. Taken together, these results show that slower environmental change can hamper adaptation from standing genetic variation and they support theoretical models indicating that standing variation for genotype-by-environment fitness interactions critically alters the pace and outcome of adaptation under environmental change.

Phenotypic lag and population extinction in the moving-optimum model: insights from a small-jumps limit

Continuous environmental change-such as slowly rising temperatures-may create permanent maladaptation of natural populations: Even if a population adapts evolutionarily, its mean phenotype will usually lag behind the phenotype favored in the current environment, and if the resulting phenotypic lag becomes too large, the population risks extinction. We analyze this scenario using a moving-optimum model, in which one or more quantitative traits are under stabilizing selection towards an optimal value that increases at a constant rate. We have recently shown that, in the limit of infinitely small mutations and high mutation rate, the evolution of the phenotypic lag converges to an Ornstein-Uhlenbeck process around a long-term equilibrium value. Both the mean and the variance of this equilibrium lag have simple analytical formulas. Here, we study the properties of this limit and compare it to simulations of an evolving population with finite mutational effects. We find that the "small-jumps limit" provides a reasonable approximation, provided the mean lag is so large that the optimum cannot be reached by a single mutation. This is the case for fast environmental change and/or weak selection. Our analysis also provides insights into population extinction: Even if the mean lag is small enough to allow a positive growth rate, stochastic fluctuations of the lag will eventually cause extinction. We show that the time until this event follows an exponential distribution, whose mean depends strongly on a composite parameter that relates the speed of environmental change to the adaptive potential of the population.

Robustness and evolvability of heterogeneous cell populations

Biological systems are endowed with two fundamental but seemingly contradictory properties: robustness, the ability to withstand environmental fluctuations and genetic variability; and evolvability, the ability to acquire selectable and heritable phenotypic changes. Cell populations with heterogeneous genetic makeup, such as those of infectious microbial organisms or cancer, rely on their inherent robustness to maintain viability and fitness, but when encountering environmental insults, such as drug treatment, these populations are also poised for rapid adaptation through evolutionary selection. In this study, we develop a general mathematical model that allows us to explain and quantify this fundamental relationship between robustness and evolvability of heterogeneous cell populations. Our model predicts that robustness is, in fact, essential for evolvability, especially for more adverse environments, a trend we observe in aneuploid budding yeast and breast cancer cells. Robustness also compensates for the negative impact of the systems' complexity on their evolvability. Our model also provides a mathematical means to estimate the number of independent processes underlying a system's performance and identify the most generally adapted subpopulation, which may resemble the multi-drug-resistant "persister" cells observed in cancer.

Genomics of Adaptation Depends on the Rate of Environmental Change in Experimental Yeast Populations

The rate of directional environmental change may have profound consequences for evolutionary dynamics and outcomes. Yet, most evolution experiments impose a sudden large change in the environment, after which the environment is kept constant. We previously cultured replicate Saccharomyces cerevisiae populations for 500 generations in the presence of either gradually increasing or constant high concentrations of the heavy metals cadmium, nickel, and zinc. Here, we investigate how each of these treatments affected genomic evolution. Whole-genome sequencing of evolved clones revealed that adaptation occurred via a combination of SNPs, small indels, and whole-genome duplications and other large-scale structural changes. In contrast to some theoretical predictions, gradual and abrupt environmental change caused similar numbers of genomic changes. For cadmium, which is toxic already at comparatively low concentrations, mutations in the same genes were used for adaptation to both gradual and abrupt increase in concentration. Conversely, for nickel and zinc, which are toxic at high concentrations only, mutations in different genes were used for adaptation depending on the rate of change. Moreover, evolution was more repeatable following a sudden change in the environment, particularly for nickel and zinc. Our results show that the rate of environmental change and the nature of the selection pressure are important drivers of evolutionary dynamics and outcomes, which has implications for a better understanding of societal problems such as climate change and pollution.

Effect of Host Species on Topography of the Fitness Landscape for a Plant RNA Virus

Adaptive fitness landscapes are a fundamental concept in evolutionary biology that relate the genotypes of individuals to their fitness. In the end, the evolutionary fate of evolving populations depends on the topography of the landscape, that is, the numbers of accessible mutational pathways and possible fitness peaks (i.e., adaptive solutions). For a long time, fitness landscapes were only theoretical constructions due to a lack of precise information on the mapping between genotypes and phenotypes. In recent years, however, efforts have been devoted to characterizing the properties of empirical fitness landscapes for individual proteins or for microbes adapting to artificial environments. In a previous study, we characterized the properties of the empirical fitness landscape defined by the first five mutations fixed during adaptation of tobacco etch potyvirus (TEV) to a new experimental host, Arabidopsis thaliana Here we evaluate the topography of this landscape in the ancestral host Nicotiana tabacum By comparing the topographies of the landscapes for the two hosts, we found that some features remained similar, such as the existence of fitness holes and the prevalence of epistasis, including cases of sign and reciprocal sign epistasis that created rugged, uncorrelated, and highly random topographies. However, we also observed significant differences in the fine-grained details between the two landscapes due to changes in the fitness and epistatic interactions of some genotypes. Our results support the idea that not only fitness tradeoffs between hosts but also topographical incongruences among fitness landscapes in alternative hosts may contribute to virus specialization. IMPORTANCE Despite its importance for understanding virus evolutionary dynamics, very little is known about the topography of virus adaptive fitness landscapes, and even less is known about the effects that different host species and environmental conditions may have on this topography. To bridge this gap, we evaluated the topography of a small fitness landscape formed by all genotypes that result from every possible combination of the first five mutations fixed during adaptation of TEV to the novel host A. thaliana To assess the effect that host species may have on this topography, we evaluated the fitness of every genotype in both the ancestral and novel hosts. We found that both landscapes share some macroscopic properties, such as the existence of holes and being highly rugged and uncorrelated, yet they differ in microscopic details due to changes in the magnitude and sign of fitness and epistatic effects.

The genetics of speciation: Insights from Fisher's geometric model

Research in speciation genetics has uncovered many robust patterns in intrinsic reproductive isolation, and fitness landscape models have been useful in interpreting these patterns. Here, we examine fitness landscapes based on Fisher's geometric model. Such landscapes are analogous to models of optimizing selection acting on quantitative traits, and have been widely used to study adaptation and the distribution of mutational effects. We show that, with a few modifications, Fisher's model can generate all of the major findings of introgression studies (including "speciation genes" with strong deleterious effects, complex epistasis and asymmetry), and the major patterns in overall hybrid fitnesses (including Haldane's Rule, the speciation clock, heterosis, hybrid breakdown, and male-female asymmetry in the F1). We compare our approach to alternative modeling frameworks that assign fitnesses to genotypes by identifying combinations of incompatible alleles. In some cases, the predictions are importantly different. For example, Fisher's model can explain conflicting empirical results about the rate at which incompatibilities accumulate with genetic divergence. In other cases, the predictions are identical. For example, the quality of reproductive isolation is little affected by the manner in which populations diverge.

Limits to Adaptation in Partially Selfing Species

In outcrossing populations, "Haldane's sieve" states that recessive beneficial alleles are less likely to fix than dominant ones, because they are less exposed to selection when rare. In contrast, selfing organisms are not subject to Haldane's sieve and are more likely to fix recessive types than outcrossers, as selfing rapidly creates homozygotes, increasing overall selection acting on mutations. However, longer homozygous tracts in selfers also reduce the ability of recombination to create new genotypes. It is unclear how these two effects influence overall adaptation rates in partially selfing organisms. Here, we calculate the fixation probability of beneficial alleles if there is an existing selective sweep in the population. We consider both the potential loss of the second beneficial mutation if it has a weaker advantage than the first one, and the possible replacement of the initial allele if the second mutant is fitter. Overall, loss of weaker adaptive alleles during a first selective sweep has a larger impact on preventing fixation of both mutations in highly selfing organisms. Furthermore, the presence of linked mutations has two opposing effects on Haldane's sieve. First, recessive mutants are disproportionally likely to be lost in outcrossers, so it is likelier that dominant mutations will fix. Second, with elevated rates of adaptive mutation, selective interference annuls the advantage in selfing organisms of not suffering from Haldane's sieve; outcrossing organisms are more able to fix weak beneficial mutations of any dominance value. Overall, weakened recombination effects can greatly limit adaptation in selfing organisms.

Factors influencing the effect size distribution of adaptive substitutions

The distribution of effect sizes of adaptive substitutions has been central to evolutionary biology since the modern synthesis. Early theory proposed that because large-effect mutations have negative pleiotropic consequences, only small-effect mutations contribute to adaptation. More recent theory suggested instead that large-effect mutations could be favoured when populations are far from their adaptive peak. Here we suggest that the distributions of effect sizes are expected to differ among study systems, reflecting the wide variation in evolutionary forces and ecological conditions experienced in nature. These include selection, mutation, genetic drift, gene flow, and other factors such as the degree of pleiotropy, the distance to the phenotypic optimum, whether the optimum is stable or moving, and whether new mutation or standing genetic variation provides the source of adaptive alleles. Our goal is to review how these factors might affect the distribution of effect sizes and to identify new research directions. Until more theory and empirical work is available, we feel that it is premature to make broad generalizations about the effect size distribution of adaptive substitutions important in nature.

Diverse phenotypic and genetic responses to short-term selection in evolving Escherichia coli populations

Beneficial mutations fuel adaptation by altering phenotypes that enhance the fit of organisms to their environment. However, the phenotypic effects of mutations often depend on ecological context, making the distribution of effects across multiple environments essential to understanding the true nature of beneficial mutations. Studies that address both the genetic basis and ecological consequences of adaptive mutations remain rare. Here, we characterize the direct and pleiotropic fitness effects of a collection of 21 first-step beneficial mutants derived from naïve and adapted genotypes used in a long-term experimental evolution of Escherichia coli. Whole-genome sequencing was able to identify the majority of beneficial mutations. In contrast to previous studies, we find diverse fitness effects of mutations selected in a simple environment and few cases of genetic parallelism. The pleiotropic effects of these mutations were predominantly positive but some mutants were highly antagonistic in alternative environments. Further, the fitness effects of mutations derived from the adapted genotypes were dramatically reduced in nearly all environments. These findings suggest that many beneficial variants are accessible from a single point on the fitness landscape, and the fixation of alternative beneficial mutations may have dramatic consequences for niche breadth reduction via metabolic erosion.

Local Adaptation by Alleles of Small Effect

Population genetic models predict that alleles with small selection coefficients may be swamped by migration and will not contribute to local adaptation. But if most alleles contributing to standing variation are of small effect, how does local adaptation proceed? Here I review predictions of population and quantitative genetic models and use individual-based simulations to illustrate how the architecture of local adaptation depends on the genetic redundancy of the trait, the maintenance of standing genetic variation (V(G)), and the susceptibility of alleles to swamping. Even when population genetic models predict swamping for individual alleles, considerable local adaptation can evolve at the phenotypic level if there is sufficient V(G). However, in such cases the underlying architecture of divergence is transient: F(ST) is low across all loci, and no locus makes an important contribution for very long. Because this kind of local adaptation is mainly due to transient frequency changes and allelic covariances, these architectures will be difficult--if not impossible--to detect using current approaches to studying the genomic basis of adaptation. Even when alleles are large and resistant to swamping, architectures can be highly transient if genetic redundancy and mutation rates are high. These results suggest that drift can play a critical role in shaping the architecture of local adaptation, both through eroding V(G) and affecting the rate of turnover of polymorphisms with redundant phenotypic effects.

Catch Me if You Can: Adaptation from Standing Genetic Variation to a Moving Phenotypic Optimum

Adaptation lies at the heart of Darwinian evolution. Accordingly, numerous studies have tried to provide a formal framework for the description of the adaptive process. Of these, two complementary modeling approaches have emerged: While so-called adaptive-walk models consider adaptation from the successive fixation of de novo mutations only, quantitative genetic models assume that adaptation proceeds exclusively from preexisting standing genetic variation. The latter approach, however, has focused on short-term evolution of population means and variances rather than on the statistical properties of adaptive substitutions. Our aim is to combine these two approaches by describing the ecological and genetic factors that determine the genetic basis of adaptation from standing genetic variation in terms of the effect-size distribution of individual alleles. Specifically, we consider the evolution of a quantitative trait to a gradually changing environment. By means of analytical approximations, we derive the distribution of adaptive substitutions from standing genetic variation, that is, the distribution of the phenotypic effects of those alleles from the standing variation that become fixed during adaptation. Our results are checked against individual-based simulations. We find that, compared to adaptation from de novo mutations, (i) adaptation from standing variation proceeds by the fixation of more alleles of small effect and (ii) populations that adapt from standing genetic variation can traverse larger distances in phenotype space and, thus, have a higher potential for adaptation if the rate of environmental change is fast rather than slow.

The distribution of fitness effects in an uncertain world

The distribution of fitness effects (DFE) among new mutations plays a critical role in adaptive evolution and the maintenance of genetic variation. Although fitness landscape models predict several key features of the DFE, most theory to date focuses on predictable environmental conditions, while ignoring stochastic environmental fluctuations that feature prominently in the ecology of many organisms. Here, we derive an extension of Fisher's geometric model that incorporates two common effects of environmental variation: (1) nonadaptive genotype-by-environment interactions (G × E), in which the phenotype of a given genotype varies across environmental contexts; and (2) random fluctuation of the fitness optimum, which generates fluctuating selection. We show that both factors cause a mismatch between the DFE within single generations and the distribution of geometric mean fitness effects (averaged over multiple generations) that governs long-term evolutionary change. Such mismatches permit strong evolutionary constraints-despite an abundance of beneficial fitness variation within single environmental contexts-and to conflicting DFE estimates from direct versus indirect inference methods. Finally, our results suggest an intriguing parallel between the genetics and ecology of evolutionary constraints, with environmental fluctuations and pleiotropy placing qualitatively similar limits on the availability of adaptive genetic variation.

The rule of declining adaptability in microbial evolution experiments

One of the most recurrent observations after two decades of microbial evolution experiments regards the dynamics of fitness change. In a given environment, low-fitness genotypes are recurrently observed to adapt faster than their more fit counterparts. Since adaptation is the main macroscopic outcome of Darwinian evolution, studying its patterns of change could potentially provide insight into key issues of evolutionary theory, from fixation dynamics to the genetic architecture of organisms. Here, we re-analyze several published datasets from experimental evolution with microbes and show that, despite large differences in the origin of the data, a pattern of inverse dependence of adaptability with fitness clearly emerges. In quantitative terms, it is remarkable to observe little if any degree of idiosyncrasy across systems as diverse as virus, bacteria and yeast. The universality of this phenomenon suggests that its emergence might be understood from general principles, giving rise to the exciting prospect that evolution might be statistically predictable at the macroscopic level. We discuss these possibilities in the light of the various theories of adaptation that have been proposed and delineate future directions of research.

The genetic architecture of traits associated with the evolution of self-pollination in Mimulus

Quantitative trait locus (QTL) mapping is a first step toward understanding the genetic basis of adaptive evolution and may also reveal reproductive incompatibilities unique to hybrids. In plants, the shift from outcrossing to self-pollination is common, providing the opportunity for comparisons of QTL architecture among parallel evolutionary transitions. We used QTL mapping in hybrids between the bee-pollinated monkeyflower Mimulus lewisii and the closely related selfer Mimulus parishii to determine the genetic basis of divergence in floral traits and flowering time associated with mating-system evolution, and to characterize hybrid anther sterility. We found a moderately polygenic and highly directional basis for floral size evolution, suggesting adaptation from standing variation or in pursuit of a moving optimum, whereas only a few major loci accounted for substantial flowering-time divergence. Cytonuclear incompatibilities caused hybrid anther sterility, confounding estimation of reproductive organ QTLs. The genetic architecture of floral traits associated with selfing in M. parishii was primarily polygenic, as in other QTL studies of this transition, but in contrast to the previously characterized oligogenic basis of a pollinator shift in close relatives. Hybrid anther sterility appeared parallel at the molecular level to previously characterized incompatibilities, but also raised new questions about cytonuclear co-evolution in plants.

The probability of improvement in Fisher's geometric model: a probabilistic approach

Fisher developed his geometric model to support the micro-mutationalism hypothesis which claims that small mutations are more likely to be beneficial and therefore to contribute to evolution and adaptation. While others have provided a general solution to the model using geometric approaches, we derive an equivalent general solution using a probabilistic approach. Our approach to Fisher's geometric model provides alternative intuition and interpretation of the solution in terms of the model's parameters: for mutation to improve a phenotype, its relative beneficial effect must be larger than the ratio of its total effect and twice the difference between the current phenotype and the optimal one. Our approach provides new insight into this classical model of adaptive evolution.

On the effect of phenotypic dimensionality on adaptation and optimality

What proportion of the traits of individuals has been optimally shaped by natural selection and what has not? Here, we estimate the maximal number of those traits using a mathematical model for natural selection in multitrait organisms. The model represents the most ideal conditions for natural selection: a simple genotype-phenotype map and independent variation between traits. The model is also used to disentangle the influence of fitness functions and the number of traits, n, per se on the efficiency of natural selection. We also allow n to evolve. Our simulations show that, for all fitness functions and even in the best conditions optimal phenotypes are rarely encountered, only for n = 1, and that a large proportion of traits are always far from their optimum, specially for large n. This happens to different degrees depending on the fitness functions (additive linear, additive nonlinear, Gaussian and multiplicative). The traits that arise earlier in evolution account for a larger proportion of the absolute fitness of individuals. Thus, complex phenotypes have, in proportion, more traits that are far from optimal and the closeness to the optimum correlates with the age of the trait. Based on estimated population sizes, mutation rates and selection coefficients, we provide an upper estimation of the number of traits that can become and remain adapted by direct natural selection.