The fitness effect of mutations across environments: Fisher's geometrical model with multiple optima

Data-driven discovery of the interplay between genetic and environmental factors in bacterial growth

A complex interplay of genetic and environmental factors influences bacterial growth. Understanding these interactions is crucial for insights into complex living systems. This study employs a data-driven approach to uncover the principles governing bacterial growth changes due to genetic and environmental variation. A pilot survey is conducted across 115 Escherichia coli strains and 135 synthetic media comprising 45 chemicals, generating 13,944 growth profiles. Machine learning analyzes this dataset to predict the chemicals' priorities for bacterial growth. The primary gene-chemical networks are structured hierarchically, with glucose playing a pivotal role. Offset in bacterial growth changes is frequently observed across 1,445,840 combinations of strains and media, with its magnitude correlating to individual alterations in strains or media. This counterbalance in the gene-chemical interplay is supposed to be a general feature beneficial for bacterial population growth.

Evolution in microbial microcosms is highly parallel, regardless of the presence of interacting species

Evolution often follows similar trajectories in replicate populations, suggesting that it may be predictable. However, populations are naturally embedded in multispecies communities, and the extent to which evolution is contingent on the specific species interacting with the focal population is still largely unexplored. Here, we study adaptations in strains of 11 different species, experimentally evolved both in isolation and in various pairwise co-cultures. Although partner-specific effects are detectable, evolution was mostly shared between strains evolved with different partners; similar changes occurred in strains' growth abilities, in community properties, and in about half of the repeatedly mutated genes. This pattern persisted even in species pre-adapted to the abiotic conditions. These findings indicate that evolution may not always depend strongly on the biotic environment, making predictions regarding coevolutionary dynamics less challenging than previously thought. A record of this paper's transparent peer review process is included in the supplemental information.

Correlated responses to selection across diverse environments during experimental evolution of Tetrahymena thermophila

Correlated responses to selection have long been observed and studied; however, it remains unclear when they will arise, and in what direction. To contribute to a growing understanding of correlated responses to selection, we used experimental evolution of the ciliate Tetrahymena thermophila to study direct and correlated responses in a variety of different environmental conditions. One experiment focused on adaptation to two different temperatures and the correlated responses across temperatures. Another experiment used inhibitory concentrations of a variety of compounds to test direct and correlated responses to selection. We found that all populations adapted to the environments in which they evolved. We also found many cases of correlated evolution across environments; few conditions resulted in trade-offs and many resulted in a positive correlated response. Surprisingly, in many instances, the correlated response was of a larger magnitude than the direct response. We find that ancestral fitness predicts the extent of adaptation, consistent with diminishing returns epistasis. Unexpectedly, we also find that this pattern of diminishing returns holds across environments regardless of the environment in which evolution occurs. We also found that the correlated response is asymmetric across environments, that is, the fitness of a population evolved in one environment and assayed in a second was inversely related to the fitness of a population evolved in the second environment and assayed in the first. These results support the notion that positive correlated responses to selection across environments are frequent, and worth further study.

Mutations in yeast are deleterious on average regardless of the degree of adaptation to the testing environment

The role of spontaneous mutations in evolution depends on the distribution of their effects on fitness. Despite a general consensus that new mutations are deleterious on average, a handful of mutation accumulation experiments in diverse organisms instead suggest that beneficial and deleterious mutations can have comparable fitness impacts, i.e. the product of their respective rates and effects can be roughly equal. We currently lack a general framework for predicting when such a pattern will occur. One idea is that beneficial mutations will be more evident in genotypes that are not well adapted to the testing environment. We tested this prediction experimentally in the laboratory yeast Saccharomyces cerevisiae by allowing nine replicate populations to adapt to novel environments with complex sets of stressors. After >1000 asexual generations interspersed with 41 rounds of sexual reproduction, we assessed the mean effect of induced mutations on yeast growth in both the environment to which they had been adapting and the alternative novel environment. The mutations were deleterious on average, with the severity depending on the testing environment. However, we found no evidence that the adaptive match between genotype and environment is predictive of mutational fitness effects.

Genotype-by-environment interactions govern fitness changes associated with adaptive mutations in two-component response systems

Introduction: Two-component response systems (TCRS) are the main mechanism by which prokaryotes acclimate to changing environments. These systems are composed of a membrane bound histidine kinase (HK) that senses external signals and a response regulator (RR) that activates transcription of response genes. Despite their known role in acclimation, little is known about the role TCRS play in environmental adaptation. Several experimental evolution studies have shown the acquisition of mutations in TCRS during adaptation, therefore here we set out to characterize the adaptive mechanism resulting from these mutations and evaluate whether single nucleotide changes in one gene could induce variable genotype-by-environment (GxE) interactions. Methods: To do this, we assessed fitness changes and differential gene expression for four adaptive mutations in cusS, the gene that encodes the HK CusS, acquired by Escherichia coli during silver adaptation. Results: Fitness assays showed that as the environment changed, each mutant displayed a unique fitness profile with greatest fitness in the original selection environment. RNAseq then indicated that, in ± silver nitrate, each mutant induces a primary response that upregulates cusS, its RR cusR, and constitutively expresses the target response genes cusCFBA. This then induces a secondary response via differential expression of genes regulated by the CusR through TCRS crosstalk. Finally, each mutant undergoes fitness tuning through unique tertiary responses that result in gene expression patterns specific for the genotype, the environment and optimized for the original selection conditions. Discussion: This three-step response shows that different mutations in a single gene leads to individualized phenotypes governed by unique GxE interactions that not only contribute to transcriptional divergence but also to phenotypic plasticity.

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.

Adaptation in a heterogeneous environment II: to be three or not to be

We propose a model to describe the adaptation of a phenotypically structured population in a H-patch environment connected by migration, with each patch associated with a different phenotypic optimum, and we perform a rigorous mathematical analysis of this model. We show that the large-time behaviour of the solution (persistence or extinction) depends on the sign of a principal eigenvalue, [Formula: see text], and we study the dependency of [Formula: see text] with respect to H. This analysis sheds new light on the effect of increasing the number of patches on the persistence of a population, which has implications in agroecology and for understanding zoonoses; in such cases we consider a pathogenic population and the patches correspond to different host species. The occurrence of a springboard effect, where the addition of a patch contributes to persistence, or on the contrary the emergence of a detrimental effect by increasing the number of patches on the persistence, depends in a rather complex way on the respective positions in the phenotypic space of the optimal phenotypes associated with each patch. From a mathematical point of view, an important part of the difficulty in dealing with [Formula: see text], compared to [Formula: see text] or [Formula: see text], comes from the lack of symmetry. Our results, which are based on a fixed point theorem, comparison principles, integral estimates, variational arguments, rearrangement techniques, and numerical simulations, provide a better understanding of these dependencies. In particular, we propose a precise characterisation of the situations where the addition of a third patch increases or decreases the chances of persistence, compared to a situation with only two patches.

Pervasive genotype-by-environment interactions shape the fitness effects of antibiotic resistance mutations

The fitness effects of antibiotic resistance mutations are a major driver of resistance evolution. While the nutrient environment affects bacterial fitness, experimental studies of resistance typically measure fitness of mutants in a single environment only. We explored how the nutrient environment affected the fitness effects of rifampicin-resistant rpoB mutations in Escherichia coli under several conditions critical for the emergence and spread of resistance-the presence of primary or secondary antibiotic, or the absence of any antibiotic. Pervasive genotype-by-environment (GxE) interactions determined fitness in all experimental conditions, with rank order of fitness in the presence and absence of antibiotics being strongly dependent on the nutrient environment. GxE interactions also affected the magnitude and direction of collateral effects of secondary antibiotics, in some cases so drastically that a mutant that was highly sensitive in one nutrient environment exhibited cross-resistance to the same antibiotic in another. It is likely that the mutant-specific impact of rpoB mutations on the global transcriptome underpins the observed GxE interactions. The pervasive, mutant-specific GxE interactions highlight the importance of doing what is rarely done when studying the evolution and spread of resistance in experimental and clinical work: assessing fitness of antibiotic-resistant mutants across a range of relevant environments.

Hypermutator emergence in experimental Escherichia coli populations is stress-type dependent

Genotypes exhibiting an increased mutation rate, called hypermutators, can propagate in microbial populations because they can have an advantage due to the higher supply of beneficial mutations needed for adaptation. Although this is a frequently observed phenomenon in natural and laboratory populations, little is known about the influence of parameters such as the degree of maladaptation, stress intensity, and the genetic architecture for adaptation on the emergence of hypermutators. To address this knowledge gap, we measured the emergence of hypermutators over ~1,000 generations in experimental Escherichia coli populations exposed to different levels of osmotic or antibiotic stress. Our stress types were chosen based on the assumption that the genetic architecture for adaptation differs between them. Indeed, we show that the size of the genetic basis for adaptation is larger for osmotic stress compared to antibiotic stress. During our experiment, we observed an increased emergence of hypermutators in populations exposed to osmotic stress but not in those exposed to antibiotic stress, indicating that hypermutator emergence rates are stress type dependent. These results support our hypothesis that hypermutator emergence is linked to the size of the genetic basis for adaptation. In addition, we identified other parameters that covaried with stress type (stress level and IS transposition rates) that might have contributed to an increased hypermutator provision and selection. Our results provide a first comparison of hypermutator emergence rates under varying stress conditions and point towards complex interactions of multiple stress-related factors on the evolution of mutation rates.

Epistasis decreases with increasing antibiotic pressure but not temperature

Predicting mutational effects is essential for the control of antibiotic resistance (ABR). Predictions are difficult when there are strong genotype-by-environment (G × E), gene-by-gene (G × G or epistatic) or gene-by-gene-by-environment (G × G × E) interactions. We quantified G × G × E effects in Escherichia coli across environmental gradients. We created intergenic fitness landscapes using gene knock-outs and single-nucleotide ABR mutations previously identified to vary in the extent of G × E effects in our environments of interest. Then, we measured competitive fitness across a complete combinatorial set of temperature and antibiotic dosage gradients. In this way, we assessed the predictability of 15 fitness landscapes across 12 different but related environments. We found G × G interactions and rugged fitness landscapes in the absence of antibiotic, but as antibiotic concentration increased, the fitness effects of ABR genotypes quickly overshadowed those of gene knock-outs, and the landscapes became smoother. Our work reiterates that some single mutants, like those conferring resistance or susceptibility to antibiotics, have consistent effects across genetic backgrounds in stressful environments. Thus, although epistasis may reduce the predictability of evolution in benign environments, evolution may be more predictable in adverse environments. This article is part of the theme issue 'Interdisciplinary approaches to predicting evolutionary biology'.

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'.

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.

Carry-over effects and fitness trade-offs in marine life histories: The costs of complexity for adaptation

Most marine organisms have complex life histories, where the individual stages of a life cycle are often morphologically and ecologically distinct. Nevertheless, life-history stages share a single genome and are linked phenotypically (by "carry-over effects"). These commonalities across the life history couple the evolutionary dynamics of different stages and provide an arena for evolutionary constraints. The degree to which genetic and phenotypic links among stages hamper adaptation in any one stage remains unclear and yet adaptation is essential if marine organisms will adapt to future climates. Here, we use an extension of Fisher's geometric model to explore how both carry-over effects and genetic links among life-history stages affect the emergence of pleiotropic trade-offs between fitness components of different stages. We subsequently explore the evolutionary trajectories of adaptation of each stage to its optimum using a simple model of stage-specific viability selection with nonoverlapping generations. We show that fitness trade-offs between stages are likely to be common and that such trade-offs naturally emerge through either divergent selection or mutation. We also find that evolutionary conflicts among stages should escalate during adaptation, but carry-over effects can ameliorate this conflict. Carry-over effects also tip the evolutionary balance in favor of better survival in earlier life-history stages at the expense of poorer survival in later stages. This effect arises in our discrete-generation framework and is, therefore, unrelated to age-related declines in the efficacy of selection that arise in models with overlapping generations. Our results imply a vast scope for conflicting selection between life-history stages, with pervasive evolutionary constraints emerging from initially modest selection differences between stages. Organisms with complex life histories should also be more constrained in their capacity to adapt to global change than those with simple life histories.

Strong selective environments determine evolutionary outcome in time‐dependent fitness seascapes

The impact of fitness landscape features on evolutionary outcomes has attracted considerable interest in recent decades. However, evolution often occurs under time‐dependent selection in so‐called fitness seascapes where the landscape is under flux. Fitness seascapes are an inherent feature of natural environments, where the landscape changes owing both to the intrinsic fitness consequences of previous adaptations and extrinsic changes in selected traits caused by new environments. The complexity of such seascapes may curb the predictability of evolution. However, empirical efforts to test this question using a comprehensive set of regimes are lacking. Here, we employed an in vitro microbial model system to investigate differences in evolutionary outcomes between time‐invariant and time‐dependent environments, including all possible temporal permutations, with three subinhibitory antimicrobials and a viral parasite (phage) as selective agents. Expectedly, time‐invariant environments caused stronger directional selection for resistances compared to time‐dependent environments. Intriguingly, however, multidrug resistance outcomes in both cases were largely driven by two strong selective agents (rifampicin and phage) out of four agents in total. These agents either caused cross‐resistance or obscured the phenotypic effect of other resistance mutations, modulating the evolutionary outcome overall in time‐invariant environments and as a function of exposure epoch in time‐dependent environments. This suggests that identifying strong selective agents and their pleiotropic effects is critical for predicting evolution in fitness seascapes, with ramifications for evolutionarily informed strategies to mitigate drug resistance evolution.

Multivariate selection mediated by aridity predicts divergence of drought-resistant traits along natural aridity gradients of an invasive weed

Geographical variation in the environment underpins selection for local adaptation and evolutionary divergence among populations. Because many environmental conditions vary across species' ranges, identifying the specific environmental variables underlying local adaptation is profoundly challenging. We tested whether natural selection mediated by aridity predicts clinal divergence among invasive populations of capeweed (Arctotheca calendula) that established and spread across southern Australia during the last two centuries. Using common garden experiments with two environmental treatments (wet and dry) that mimic aridity conditions across capeweed's invasive range, we estimated clinal divergence and effects of aridity on fitness and multivariate phenotypic selection in populations sampled along aridity gradients in Australia. We show that: (1) capeweed populations have relatively high fitness in aridity environments similar to their sampling locations; (2) the magnitude and direction of selection strongly differs between wet and dry treatments, with drought stress increasing the strength of selection; and (3) differences in directional selection between wet and dry treatments predict patterns of clinal divergence across the aridity gradient, particularly for traits affecting biomass, flowering phenology and putative antioxidant expression. Our results suggest that aridity-mediated selection contributes to trait diversification among invasive capeweed populations, possibly facilitating the expansion of capeweed across southern Australia.

Experimental Evolution Expands the Breadth of Adaptation to an Environmental Gradient Correlated With Genome Reduction

Whether and how adaptive evolution adjusts the breadth of adaptation in coordination with the genome are essential issues for connecting evolution with ecology. To address these questions, experimental evolution in five Escherichia coli strains carrying either the wild-type genome or a reduced genome was performed in a defined minimal medium (C0). The ancestral and evolved populations were subsequently subjected to fitness and chemical niche analyses across an environmental gradient with 29 combinations of eight chemical components of the minimal medium. The results showed that adaptation was achieved not only specific to the evolutionary condition (C0), but also generally, to the environmental gradient; that is, the breadth of adaptation to the eight chemical niches was expanded. The magnitudes of the adaptive improvement and the breadth increase were both correlated with genome reduction and were highly significant in two out of eight niches (i.e., glucose and sulfate). The direct adaptation-induced correlated adaptation to the environmental gradient was determined by only a few genome mutations. An additive increase in fitness associated with the stepwise fixation of mutations was consistently observed in the reduced genomes. In summary, this preliminary survey demonstrated that evolution finely tuned the breadth of adaptation correlated with genome reduction.

Selection bias in mutation accumulation

Mutation accumulation (MA) experiments, in which de novo mutations are sampled and subsequently characterized, are an essential tool in understanding the processes underlying evolution. In microbial populations, MA protocols typically involve a period of population growth between severe bottlenecks, such that a single individual can form a visible colony. While it has long been appreciated that the action of positive selection during this growth phase cannot be eliminated, it is typically assumed to be negligible. Here, we quantify the effect of both positive and negative selection in MA studies, demonstrating that selective effects can substantially bias the distribution of fitness effects (DFE) and mutation rates estimated from typical MA protocols in microbes. We then present a simple correction for this bias which applies to both beneficial and deleterious mutations, and can be used to correct the observed DFE in multiple environments. We use simulated MA experiments to illustrate the extent to which the MA-inferred DFE differs from the underlying true DFE, and demonstrate that the proposed correction accurately reconstructs the true DFE over a wide range of scenarios; we also provide an example of these corrections applied to experimental data. These results highlight that positive selection during microbial MA experiments is in fact not negligible, but can be corrected to gain a more accurate understanding of fundamental evolutionary parameters. This article is protected by copyright. All rights reserved.

The population genetics of collateral resistance and sensitivity

Resistance mutations against one drug can elicit collateral sensitivity against other drugs. Multi-drug treatments exploiting such trade-offs can help slow down the evolution of resistance. However, if mutations with diverse collateral effects are available, a treated population may evolve either collateral sensitivity or collateral resistance. How to design treatments robust to such uncertainty is unclear. We show that many resistance mutations in Escherichia coli against various antibiotics indeed have diverse collateral effects. We propose to characterize such diversity with a joint distribution of fitness effects (JDFE) and develop a theory for describing and predicting collateral evolution based on simple statistics of the JDFE. We show how to robustly rank drug pairs to minimize the risk of collateral resistance and how to estimate JDFEs. In addition to practical applications, these results have implications for our understanding of evolution in variable environments.

Drugs known as antibiotics are the main treatment for most serious infections caused by bacteria. However, many bacteria are acquiring genetic mutations that make them resistant to the effects of one or more types of antibiotics, making them harder to eliminate.

One way to tackle drug-resistant bacteria is to develop new types of antibiotics; however, in recent years, the rate at which new antibiotics have become available has been dwindling. Using two or more existing drugs, one after another, can also be an effective way to eliminate resistant bacteria. The success of any such ‘multi-drug’ treatment lies in being able to predict whether mutations that make the bacteria resistant to one drug simultaneously make it sensitive to another, a phenomenon known as collateral sensitivity.

Different resistance mutations may have different collateral effects: some may increase the bacteria’s sensitivity to the second drug, while others might make the bacteria more resistant. However, it is currently unclear how to design robust multi-drug treatments that take this diversity of collateral effects into account.

Here, Ardell and Kryazhimskiy used a concept called JDFE (short for the joint distribution of fitness effects) to describe the diversity of collateral effects in a population of bacteria exposed to a single drug. This information was then used to mathematically model how collateral effects evolved in the population over time.

Ardell and Kryazhimskiy showed that this approach can predict how likely a population is to become collaterally sensitive or collaterally resistant to a second antibiotic. Drug pairs can then be ranked according to the risk of collateral resistance emerging, so long as information on the variety of resistance mutations available to the bacteria are included in the model.

Each year, more than 700,000 people die from infections caused by bacteria that are resistant to one or more antibiotics. The findings of Ardell and Kryazhimskiy may eventually help clinicians design multi-drug treatments that effectively eliminate bacterial infections and help to prevent more bacteria from evolving resistance to antibiotics. However, to achieve this goal, more research is needed to fully understand the range collateral effects caused by resistance mutations.

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.

The cost of evolved constitutive lac gene expression is usually, but not always, maintained during evolution of generalist populations

Beneficial mutations can become costly following an environmental change. Compensatory mutations can relieve these costs, while not affecting the selected function, so that the benefits are retained if the environment shifts back to be similar to the one in which the beneficial mutation was originally selected. Compensatory mutations have been extensively studied in the context of antibiotic resistance, responses to specific genetic perturbations, and in the determination of interacting gene network components. Few studies have focused on the role of compensatory mutations during more general adaptation, especially as the result of selection in fluctuating environments where adaptations to different environment components may often involve trade-offs. We examine whether costs of a mutation in lacI, which deregulated the expression of the lac operon in evolving populations of Escherichia coli bacteria, were compensated. This mutation occurred in multiple replicate populations selected in environments that fluctuated between growth on lactose, where the mutation was beneficial, and on glucose, where it was deleterious. We found that compensation for the cost of the lacI mutation was rare, but, when it did occur, it did not negatively affect the selected benefit. Compensation was not more likely to occur in a particular evolution environment. Compensation has the potential to remove pleiotropic costs of adaptation, but its rarity indicates that the circumstances to bring about the phenomenon may be peculiar to each individual or impeded by other selected mutations.

Adaptation in a heterogeneous environment I: persistence versus extinction

Understanding how a diversity of plants in agroecosystems affects the adaptation of pathogens is a key issue in agroecology. We analyze PDE systems describing the dynamics of adaptation of two phenotypically structured populations, under the effects of mutation, selection and migration in a two-patch environment, each patch being associated with a different phenotypic optimum. We consider two types of growth functions that depend on the n-dimensional phenotypic trait: either local and linear or nonlocal nonlinear. In both cases, we obtain existence and uniqueness results as well as a characterization of the large-time behaviour of the solution (persistence or extinction) based on the sign of a principal eigenvalue. We show that migration between the two environments decreases the chances of persistence, with in some cases a 'lethal migration threshold' above which persistence is not possible. Comparison with stochastic individual-based simulations shows that the PDE approach accurately captures this threshold. Our results illustrate the importance of cultivar mixtures for disease prevention and control.

Adaptation and correlated fitness responses over two time scales in Drosophila suzukii populations evolving in different environments

The process of local adaptation involves differential changes in fitness over time across different environments. Although experimental evolution studies have extensively tested for patterns of local adaptation at a single time point, there is relatively little research that examines fitness more than once during the time course of adaptation. We allowed replicate populations of the fruit pest Drosophila suzukii to evolve in one of eight different fruit media. After five generations, populations with the highest initial levels of maladaptation had mostly gone extinct, whereas experimental populations evolving on cherry, strawberry and cranberry media had survived. We measured the fitness of each surviving population in each of the three fruit media after five and after 26 generations of evolution. After five generations, adaptation to each medium was associated with increased fitness in the two other media. This was also true after 26 generations, except when populations that evolved on cranberry medium developed on cherry medium. These results suggest that, in the theoretical framework of a fitness landscape, the fitness optima of cherry and cranberry media are the furthest apart. Our results show that studying how fitness changes across several environments and across multiple generations provides insights into the dynamics of local adaptation that would not be evident if fitness were analysed at a single point in time. By allowing a qualitative mapping of an experimental fitness landscape, our approach will improve our understanding of the ecological factors that drive the evolution of local adaptation in D. suzukii.

The evolution of trait correlations constrains phenotypic adaptation to high CO2 in a eukaryotic alga

Microbes form the base of food webs and drive biogeochemical cycling. Predicting the effects of microbial evolution on global elemental cycles remains a significant challenge due to the sheer number of interacting environmental and trait combinations. Here, we present an approach for integrating multivariate trait data into a predictive model of trait evolution. We investigated the outcome of thousands of possible adaptive walks parameterized using empirical evolution data from the alga Chlamydomonas exposed to high CO₂. We found that the direction of historical bias (existing trait correlations) influenced both the rate of adaptation and the evolved phenotypes (trait combinations). Critically, we use fitness landscapes derived directly from empirical trait values to capture known evolutionary phenomena. This work demonstrates that ecological models need to represent both changes in traits and changes in the correlation between traits in order to accurately capture phytoplankton evolution and predict future shifts in elemental cycling.

Inferring genome-wide correlations of mutation fitness effects between populations

The effect of a mutation on fitness may differ between populations depending on environmental and genetic context, but little is known about the factors that underlie such differences. To quantify genome-wide correlations in mutation fitness effects, we developed a novel concept called a joint distribution of fitness effects (DFE) between populations. We then proposed a new statistic w to measure the DFE correlation between populations. Using simulation, we showed that inferring the DFE correlation from the joint allele frequency spectrum is statistically precise and robust. Using population genomic data, we inferred DFE correlations of populations in humans, Drosophila melanogaster, and wild tomatoes. In these species, we found that the overall correlation of the joint DFE was inversely related to genetic differentiation. In humans and D. melanogaster, deleterious mutations had a lower DFE correlation than tolerated mutations, indicating a complex joint DFE. Altogether, the DFE correlation can be reliably inferred, and it offers extensive insight into the genetics of population divergence.

Fitness effects of mutation in natural populations of Arabidopsis thaliana reveal a complex influence of local adaptation

Little is empirically known about the contribution of mutations to fitness in natural environments. However, Fisher's Geometric Model (FGM) provides a conceptual foundation to consider the influence of the environment on mutational effects. To quantify mutational properties in the field, we established eight sets of MA lines (7-10 generations) derived from eight founders collected from natural populations of Arabidopsis thaliana from French and Swedish sites, representing the range margins of the species in Europe. We reciprocally planted the MA lines and their founders at French and Swedish sites, allowing us to test predictions of FGM under naturally occurring environmental conditions. The performance of the MA lines relative to each other and to their respective founders confirmed some and contradicted other predictions of the FGM: the contribution of mutation to fitness variance increased when the genotype was in an environment where its fitness was low, that is, in the away environment, but mutations were more likely to be beneficial when the genotype was in its home environment. Consequently, environmental context plays a large role in the contribution of mutations to the evolutionary process and local adaptation does not guarantee that a genotype is at or close to its optimum.

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.

Pleiotropy facilitates local adaptation to distant optima in common ragweed (Ambrosia artemisiifolia)

Pleiotropy, the control of multiple phenotypes by a single locus, is expected to slow the rate of adaptation by increasing the chance that beneficial alleles also have deleterious effects. However, a prediction arising from classical theory of quantitative trait evolution states that pleiotropic alleles may have a selective advantage when phenotypes are distant from their selective optima. We examine the role of pleiotropy in regulating adaptive differentiation among populations of common ragweed (Ambrosia artemisiifolia); a species that has recently expanded its North American range due to human-mediated habitat change. We employ a phenotype-free approach by using connectivity in gene networks as a proxy for pleiotropy. First, we identify loci bearing footprints of local adaptation, and then use genotype-expression mapping and co-expression networks to infer the connectivity of the genes. Our results indicate that the putatively adaptive loci are highly pleiotropic, as they are more likely than expected to affect the expression of other genes, and they reside in central positions within the gene networks. We propose that the conditionally advantageous alleles at these loci avoid the cost of pleiotropy by having large phenotypic effects that are beneficial when populations are far from their selective optima. We further use evolutionary simulations to show that these patterns are in agreement with a model where populations face novel selective pressures, as expected during a range expansion. Overall, our results suggest that highly connected genes may be targets of positive selection during environmental change, even though they likely experience strong purifying selection in stable selective environments.

Genetic Paths to Evolutionary Rescue and the Distribution of Fitness Effects Along Them

The past century has seen substantial theoretical and empirical progress on the genetic basis of adaptation. Over this same period, a pressing need to prevent the evolution of drug resistance has uncovered much about the potential genetic basis of persistence in declining populations. However, we have little theory to predict and generalize how persistence-by sufficiently rapid adaptation-might be realized in this explicitly demographic scenario. Here, we use Fisher's geometric model with absolute fitness to begin a line of theoretical inquiry into the genetic basis of evolutionary rescue, focusing here on asexual populations that adapt through de novo mutations. We show how the dominant genetic path to rescue switches from a single mutation to multiple as mutation rates and the severity of the environmental change increase. In multi-step rescue, intermediate genotypes that themselves go extinct provide a "springboard" to rescue genotypes. Comparing to a scenario where persistence is assured, our approach allows us to quantify how a race between evolution and extinction leads to a genetic basis of adaptation that is composed of fewer loci of larger effect. We hope this work brings awareness to the impact of demography on the genetic basis of adaptation.

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.

Genomic Patterns of Local Adaptation under Gene Flow in Arabidopsis lyrata

Short-scale local adaptation is a complex process involving selection, migration, and drift. The expected effects on the genome are well grounded in theory but examining these on an empirical level has proven difficult, as it requires information about local selection, demographic history, and recombination rate variation. Here, we use locally adapted and phenotypically differentiated Arabidopsis lyrata populations from two altitudinal gradients in Norway to test these expectations at the whole-genome level. Demography modeling indicates that populations within the gradients diverged <2 kya and that the sites are connected by gene flow. The gene flow estimates are, however, highly asymmetric with migration from high to low altitudes being several times more frequent than vice versa. To detect signatures of selection for local adaptation, we estimate patterns of lineage-specific differentiation among these populations. Theory predicts that gene flow leads to concentration of adaptive loci in areas of low recombination; a pattern we observe in both lowland-alpine comparisons. Although most selected loci display patterns of conditional neutrality, we found indications of genetic trade-offs, with one locus particularly showing high differentiation and signs of selection in both populations. Our results further suggest that resistance to solar radiation is an important adaptation to alpine environments, while vegetative growth and bacterial defense are indicated as selected traits in the lowland habitats. These results provide insights into genetic architectures and evolutionary processes driving local adaptation under gene flow. We also contribute to understanding of traits and biological processes underlying alpine adaptation in northern latitudes.

The evolution of hybrid fitness during speciation

The evolution of postzygotic reproductive isolation is an important component of speciation. But before isolation is complete there is sometimes a phase of heterosis in which hybrid fitness exceeds that of the two parental species. The genetics and evolution of heterosis and postzygotic isolation have typically been studied in isolation, precluding the development of a unified theory of speciation. Here, we develop a model that incorporates both positive and negative gene interactions, and accounts for the evolution of both heterosis and postzygotic isolation. We parameterize the model with recent data on the fitness effects of 10,000 mutations in yeast, singly and in pairwise epistatic combinations. The model makes novel predictions about the types of interactions that contribute to declining hybrid fitness. We reproduce patterns familiar from earlier models of speciation (e.g. Haldane's Rule and Darwin's Corollary) and identify new mechanisms that may underlie these patterns. Our approach provides a general framework for integrating experimental data from gene interaction networks into speciation theory and makes new predictions about the genetic mechanisms of speciation.

Parallel genetic evolution and speciation from standing variation

Adaptation often proceeds from standing variation, and natural selection acting on pairs of populations is a quantitative continuum ranging from parallel to divergent. Yet, it is unclear how the extent of parallel genetic evolution during adaptation from standing variation is affected by the difference in the direction of selection between populations. Nor is it clear whether the availability of standing variation for adaptation affects progress toward speciation in a manner that depends on the difference in the direction of selection. We conducted a theoretical study investigating these questions and have two primary findings. First, the extent of parallel genetic evolution between two populations rapidly declines as selection changes from fully parallel toward divergent, and this decline is steeper in organisms with more traits (i.e., greater dimensionality). This rapid decline happens because small differences in the direction of selection greatly reduce the fraction of alleles that are beneficial in both populations. For example, populations adapting to optima separated by an angle of 33° might have only 50% of potentially beneficial alleles in common. Second, relative to when adaptation is from only new mutation, adaptation from standing variation improves hybrid fitness under parallel selection and reduces hybrid fitness under divergent selection. Under parallel selection, genetic parallelism from standing variation reduces the phenotypic segregation variance in hybrids, thereby increasing mean fitness in the parental environment. Under divergent selection, larger pleiotropic effects of alleles fixed from standing variation cause maladaptive transgressive phenotypes when combined in hybrids. Adaptation from standing genetic variation therefore slows progress toward speciation under parallel selection and facilitates progress toward speciation under divergent selection.

Dominance reversals and the maintenance of genetic variation for fitness

Antagonistic selection between different fitness components (e.g., survival versus fertility) or different types of individuals in a population (e.g., females versus males) can potentially maintain genetic diversity and thereby account for the high levels of fitness variation observed in natural populations. However, the degree to which antagonistic selection can maintain genetic variation critically depends on the dominance relations between antagonistically selected alleles in diploid individuals. Conditions for stable polymorphism of antagonistically selected alleles are narrow, particularly when selection is weak, unless the alleles exhibit "dominance reversals"-in which each allele is partially or completely dominant in selective contexts in which it is favored and recessive in contexts in which it is harmful. Although theory predicts that dominance reversals should emerge under biologically plausible conditions, evidence for dominance reversals is sparse. In this primer, we review theoretical arguments and data supporting a role for dominance reversals in the maintenance of genetic variation. We then highlight an illuminating new study by Grieshop and Arnqvist, which reports a genome-wide signal of dominance reversals between male and female fitness in seed beetles.

Adaptive Evolution under Extreme Genetic Drift in Oxidatively Stressed Caenorhabditis elegans

A mutation-accumulation (MA) experiment with Caenorhabditis elegans nematodes was conducted in which replicate, independently evolving lines were initiated from a low-fitness mitochondrial electron transport chain mutant, gas-1. The original intent of the study was to assess the effect of electron transport chain dysfunction involving elevated reactive oxygen species production on patterns of spontaneous germline mutation. In contrast to results of standard MA experiments, gas-1 MA lines evolved slightly higher mean fitness alongside reduced among-line genetic variance compared with their ancestor. Likewise, the gas-1 MA lines experienced partial recovery to wildtype reactive oxygen species levels. Whole-genome sequencing and analysis revealed that the molecular spectrum but not the overall rate of nuclear DNA mutation differed from wildtype patterns. Further analysis revealed an enrichment of mutations in loci that occur in a gas-1-centric region of the C. elegans interactome, and could be classified into a small number of functional-genomic categories. Characterization of a backcrossed four-mutation set isolated from one gas-1 MA line revealed this combination to be beneficial on both gas-1 mutant and wildtype genetic backgrounds. Our combined results suggest that selection favoring beneficial mutations can be powerful even under unfavorable population genetic conditions, and agree with fitness landscape theory predicting an inverse relationship between population fitness and the likelihood of adaptation.

Information Theory, Developmental Psychology, and the Baldwin Effect

As part of the extended evolutionary synthesis, there has recently been a new emphasis on the effects of biological development on genetic inheritance and variation. The exciting new directions taken by those in the community have by a pre-history filled with related ideas that were never given a rigorous foundation or combined coherently. Part of the historical background of the extended synthesis is the work of James Mark Baldwin on his so-called “Baldwin Effect.” Many variant re-interpretations of his work obscure the original meaning of the Baldwin Effect. This paper emphasizes a new approach to the Baldwin Effect, focusing on his work in developmental psychology and how that would impact evolution. We propose a novel population genetics model of the Baldwin Effect. First, the impact of a kind of learning process motivated by motor babbling, in the developmental psychology literature, on evolution; second, that Information-theoretic phenotype reshaping speeds up evolution compared to populations without this kind of learning. The basic idea behind the model is to allow the organism to apply abstraction to his initial phenotype to situate it within one of a few different classes of phenotypes in the local neighborhood of a fitness maximum. The reshaping of the phenotype space thereby allows the organism to reach a nearby fitness maximum. By so doing, valleys in the fitness landscape are leveled out, making a rugged fitness landscape into a set of mesas and plateaus with increasing height. Using this model we can show the first sizeable speed-up for the Baldwin Effect compared to ordinary population genetics. We also introduce an information-theoretic foundation for the Baldwin Effect, which may be of independent interest.

Parallel genetic adaptation across environments differing in mode of growth or resource availability

Evolution experiments have demonstrated high levels of genetic parallelism between populations evolving in identical environments. However, natural populations evolve in complex environments that can vary in many ways, likely sharing some characteristics but not others. Here, we ask whether shared selection pressures drive parallel evolution across distinct environments. We addressed this question in experimentally evolved populations founded from a clone of the bacterium Burkholderia cenocepacia. These populations evolved for 90 days (approximately 600 generations) under all combinations of high or low carbon availability and selection for either planktonic or biofilm modes of growth. Populations that evolved in environments with shared selection pressures (either level of carbon availability or mode of growth) were more genetically similar to each other than populations from environments that shared neither characteristic. However, not all shared selection pressures led to parallel evolution. Genetic parallelism between low-carbon biofilm and low-carbon planktonic populations was very low despite shared selection for growth under low-carbon conditions, suggesting that evolution in low-carbon environments may generate stronger trade-offs between biofilm and planktonic modes of growth. For all environments, a population's fitness in a particular environment was positively correlated with the genetic similarity between that population and the populations that evolved in that particular environment. Although genetic similarity was low between low-carbon environments, overall, evolution in similar environments led to higher levels of genetic parallelism and that genetic parallelism, in turn, was correlated with fitness in a particular environment.

Evolution of bacteria specialization along an antibiotic dose gradient

Antibiotic and pesticide resistance of pathogens are major and pressing worldwide issues. Resistance evolution is often considered in simplified ecological contexts: treated versus nontreated environments. In contrast, antibiotic usually present important dose gradients: from ecosystems to hospitals to polluted soils, in treated patients across tissues. However, we do not know whether adaptation to low or high doses involves different phenotypic traits, and whether these traits trade‐off with each other. In this study, we investigated the occurrence of such fitness trade‐offs along a dose gradient by evolving experimentally resistant lines of Escherichia coli at different antibiotic concentrations for ∼400 generations. Our results reveal fast evolution toward specialization following the first mutational step toward resistance, along with pervasive trade‐offs among different evolution doses. We found clear and regular fitness patterns of specialization, which converged rapidly from different initial starting points. These findings are consistent with a simple fitness peak shift model as described by the classical evolutionary ecology theory of adaptation across environmental gradients. We also found that the fitness costs of resistance tend to be compensated through time at low doses whereas they increase through time at higher doses. This cost evolution follows a linear trend with the log‐dose of antibiotic along the gradient. These results suggest a general explanation for the variability of the fitness costs of resistance and their evolution. Overall, these findings call for more realistic models of resistance management incorporating dose‐specialization.

Quantifying natural seasonal variation in mutation parameters with mutation accumulation lines

Mutations create novel genetic variants, but their contribution to variation in fitness and other phenotypes may depend on environmental conditions. Furthermore, natural environments may be highly heterogeneous. We assessed phenotypes associated with survival and reproductive success in over 30,000 plants representing 100 mutation accumulation lines of Arabidopsis thaliana across four temporal environments at a single field site. In each of the four assays, environmental variance was substantially larger than mutational variance. For some traits, whether mutational variance was significantly varied between seasons. The founder genotype had mean trait values near the mean of the distribution of the mutation accumulation lines in all field experiments. New mutations also contributed more phenotypic variation than would be predicted, given phenotypic and sequence‐level divergence among natural populations of A. thaliana. The combination of large environmental variance with a mean effect of mutation near zero suggests that mutations could contribute substantially to standing genetic variation.

Evolutionary Rescue over a Fitness Landscape

Evolutionary rescue describes a situation where adaptive evolution prevents the extinction of a population facing a stressing environment. Models of evolutionary rescue could in principle be used to predict the level of stress beyond which extinction becomes likely for species of conservation concern, or, conversely, the treatment levels most likely to limit the emergence of resistant pests or pathogens. Stress levels are known to affect both the rate of population decline (demographic effect) and the speed of adaptation (evolutionary effect), but the latter aspect has received less attention. Here, we address this issue using Fisher's geometric model of adaptation. In this model, the fitness effects of mutations depend both on the genotype and the environment in which they arise. In particular, the model introduces a dependence between the level of stress, the proportion of rescue mutants, and their costs before the onset of stress. We obtain analytic results under a strong-selection-weak-mutation regime, which we compare to simulations. We show that the effect of the environment on evolutionary rescue can be summarized into a single composite parameter quantifying the effective stress level, which is amenable to empirical measurement. We describe a narrow characteristic stress window over which the rescue probability drops from very likely to very unlikely as the level of stress increases. This drop is sharper than in previous models, as a result of the decreasing proportion of stress-resistant mutations as stress increases. We discuss how to test these predictions with rescue experiments across gradients of stress.

Genetic constraints on adaptation: a theoretical primer for the genomics era

Genetic constraints are features of inheritance systems that slow or prohibit adaptation. Several population genetic mechanisms of constraint have received sustained attention within the field since they were first articulated in the early 20th century. This attention is now reflected in a rich, and still growing, theoretical literature on the genetic limits to adaptive change. In turn, empirical research on constraints has seen a rapid expansion over the last two decades in response to changing interests of evolutionary biologists, along with new technologies, expanding data sets, and creative analytical approaches that blend mathematical modeling with genomics. Indeed, one of the most notable and exciting features of recent progress in genetic constraints is the close connection between theoretical and empirical research. In this review, we discuss five major population genetic contexts of genetic constraint: genetic dominance, pleiotropy, fitness trade-offs between types of individuals of a population, sign epistasis, and genetic linkage between loci. For each, we outline historical antecedents of the theory, specific contexts where constraints manifest, and their quantitative consequences for adaptation. From each of these theoretical foundations, we discuss recent empirical approaches for identifying and characterizing genetic constraints, each grounded and motivated by this theory, and outline promising areas for future work.

Effects of mutation and selection on plasticity of a promoter activity in Saccharomyces cerevisiae

Phenotypic plasticity is an evolvable property of biological systems that can arise from environment-specific regulation of gene expression. To better understand the evolutionary and molecular mechanisms that give rise to plasticity in gene expression, we quantified the effects of 235 single-nucleotide mutations in the Saccharomyces cerevisiae TDH3 promoter (P_TDH3 ) on the activity of this promoter in media containing glucose, galactose, or glycerol as a carbon source. We found that the distributions of mutational effects differed among environments because many mutations altered the plastic response exhibited by the wild-type allele. Comparing the effects of these mutations with the effects of 30 P_TDH3 polymorphisms on expression plasticity in the same environments provided evidence of natural selection acting to prevent the plastic response in P_TDH3 activity between glucose and galactose from becoming larger. The largest changes in expression plasticity were observed between fermentable (glucose or galactose) and nonfermentable (glycerol) carbon sources and were caused by mutations located in the RAP1 and GCR1 transcription factor binding sites. Mutations altered expression plasticity most frequently between the two fermentable environments, with mutations causing significant changes in plasticity between glucose and galactose distributed throughout the promoter, suggesting they might affect chromatin structure. Taken together, these results provide insight into the molecular mechanisms underlying gene-by-environment interactions affecting gene expression as well as the evolutionary dynamics affecting natural variation in plasticity of gene expression.

Fitness effects of mutation: testing genetic redundancy in Arabidopsis thaliana

Screens of organisms with disruptive mutations in a single gene often fail to detect phenotypic consequences for the majority of mutants. One explanation for this phenomenon is that the presence of paralogous loci provides genetic redundancy. However, it is also possible that the assayed traits are affected by few loci, that effects could be subtle or that phenotypic effects are restricted to certain environments. We assayed a set of T-DNA insertion mutant lines of Arabidopsis thaliana to determine the frequency with which mutation affected fitness-related phenotypes. We found that between 8% and 42% of the assayed lines had altered fitness from the wild type. Furthermore, many of these lines exhibited fitness greater than the wild type. In a second experiment, we grew a subset of the lines in multiple environments and found whether a T-DNA insert increased or decreased fitness traits depended on the assay environment. Overall, our evidence contradicts the hypothesis that genetic redundancy is a common phenomenon in A. thaliana for fitness traits. Evidence for redundancy from prior screens of knockout mutants may often be an artefact of the design of the phenotypic assays which have focused on less complex phenotypes than fitness and have used single environments. Finally, our study adds to evidence that beneficial mutations may represent a significant component of the mutational spectrum of A. thaliana.

The Relative Contributions of the X Chromosome and Autosomes to Local Adaptation

Models of sex chromosome and autosome evolution yield key predictions about the genomic basis of adaptive divergence, and such models have been important in guiding empirical research in comparative genomics and studies of speciation. In addition to the adaptive differentiation that occurs between species over time, selection also favors genetic divergence across geographic space, with subpopulations of single species evolving conspicuous differences in traits involved in adaptation to local environmental conditions. The potential contribution of sex chromosomes (the X or Z) to local adaptation remains unclear, as we currently lack theory that directly links spatial variation in selection to local adaptation of X-linked and autosomal genes. Here, we develop population genetic models that explicitly consider the effects of genetic dominance, effective population size, and sex-specific migration and selection on the relative contributions of X-linked and autosomal genes to local adaptation. We show that X-linked genes should nearly always disproportionately contribute to local adaptation in the presence of gene flow. We also show that considerations of dominance and effective population size-which play pivotal roles in the theory of faster-X adaptation between species-have surprisingly little influence on the relative contribution of the X chromosome to local adaptation. Instead, sex-biased migration is the primary mediator of the strength of spatial large-X effects. Our results yield novel predictions about the role of sex chromosomes in local adaptation. We outline empirical approaches in evolutionary quantitative genetics and genomics that could build upon this new theory.

Fisher's geometrical model and the mutational patterns of antibiotic resistance across dose gradients

Fisher's geometrical model (FGM) has been widely used to depict the fitness effects of mutations. It is a general model with few underlying assumptions that gives a large and comprehensive view of adaptive processes. It is thus attractive in several situations, for example adaptation to antibiotics, but comes with limitations, so that more mechanistic approaches are often preferred to interpret experimental data. It might be possible however to extend FGM assumptions to better account for mutational data. This is theoretically challenging in the context of antibiotic resistance because resistance mutations are assumed to be rare. In this article, we show with Escherichia coli how the fitness effects of resistance mutations screened at different doses of nalidixic acid vary across a dose-gradient. We found experimental patterns qualitatively consistent with the basic FGM (rate of resistance across doses, gamma distributed costs) but also unexpected patterns such as a decreasing mean cost of resistance with increasing screen dose. We show how different extensions involving mutational modules and variations in trait covariance across environments, can be discriminated based on these data. Overall, simple extensions of the FGM accounted well for complex mutational effects of resistance mutations across antibiotic doses.