The population genetics of adaptation on correlated fitness landscapes: the block model

Several recent theoretical studies of the genetics of adaptation have focused on the mutational landscape model, which considers evolution on rugged fitness landscapes (i.e., ones having many local optima). Adaptation in this model is characterized by several simple results. Here I ask whether these results also hold on correlated fitness landscapes, which are smoother than those considered in the mutational landscape model. In particular, I study the genetics of adaptation in the block model, a tunably rugged model of fitness landscapes. Considering the scenario in which adaptation begins from a high fitness wild-type DNA sequence, I use extreme value theory and computer simulations to study both single adaptive steps and entire adaptive walks. I show that all previous results characterizing single steps in adaptation in the mutational landscape model hold at least approximately on correlated landscapes in the block model; many entire-walk results, however, do not.     

AN ADAPTIVE WALK BY HUMAN IMMUNODEFICIENCY VIRUS TYPE 1 THROUGH A FLUCTUATING FITNESS LANDSCAPE

The mutational landscape model of adaptive sequence evolution has been used to explain an unexpected strong positive linear relationship between marginal fitness and mean site‐specific amino acid frequency in the functionally important HIV‐1 gp120 V3 protein region. The model predicts a positive linear relationship between the probability that a particular beneficial allele, among several, is the next to spread to fixation during an adaptive walk, its transition probability, and the allele's selection coefficient. Here, stochastic simulation is used to confirm the intuition that the linear relationship between transition probabilities and selection coefficients, predicted by the model, should, under fluctuating selection, produce a linear relationship between allele frequency, averaged across populations, and fitness. In addition, these relationships hold for the effective population size and mutation rate of HIV‐1 and for the moderately strong selection observed for V3. A survey of the strength of mutation for diverse organisms suggests that these relationships may be widely applicable.     

A Model for Damage Load and Its Implications for the Evolution of Bacterial Aging

Deleterious mutations appearing in a population increase in frequency until stopped by natural selection. The ensuing equilibrium creates a stable frequency of deleterious mutations or the mutational load. Here I develop the comparable concept of a damage load, which is caused by harmful non-heritable changes to the phenotype. A damage load also ensues when the increase of damage is opposed by selection. The presence of a damage load favors the evolution of asymmetrical transmission of damage by a mother to her daughters. The asymmetry is beneficial because it increases fitness variance, but it also leads to aging or senescence. A mathematical model based on microbes reveals that a cell lineage dividing symmetrically is immortal if lifetime damage rates do not exceed a threshold. The evolution of asymmetry allows the lineage to persist above the threshold, but the lineage becomes mortal. In microbes with low genomic mutation rates, it is likely that the damage load is much greater than the mutational load. In metazoans with higher genomic mutation rates, the damage and the mutational load could be of the same magnitude. A fit of the model to experimental data shows that Escherichia coli cells experience a damage rate that is below the threshold and are immortal under the conditions examined. The model estimates the asymmetry level of E. coli to be low but sufficient for persisting at higher damage rates. The model also predicts that increasing asymmetry results in diminishing fitness returns, which may explain why the bacterium has not evolved higher asymmetry.     

MUTATION AND EXTINCTION: THE ROLE OF VARIABLE MUTATIONAL EFFECTS,SYNERGISTIC EPISTASIS,BENEFICIAL MUTATIONS,AND DEGREE OF OUTCROSSING

Recent theoretical studies have illustrated the potential role of spontaneous deleterious mutation as a cause of extinction in small populations. However, these studies have not addressed several genetic issues, which can in principle have a substantial influence on the risk of extinction. These include the presence of synergistic epistasis, which can reduce the rate of mutation accumulation by progressively magnifying the selective effects of mutations, and the occurrence of beneficial mutations, which can offset the effects of previous deleterious mutations. In stochastic simulations of small populations (effective sizes on the order of 100 or less), we show that both synergistic epistasis and the rate of beneficial mutation must be unrealistically high to substantially reduce the risk of extinction due to random fixation of deleterious mutations. However, in analytical calculations based on diffusion theory, we show that in large, outcrossing populations (effective sizes greater than a few hundred), very low levels of beneficial mutation are sufficient to prevent mutational decay. Further simulation results indicate that in populations small enough to be highly vulnerable to mutational decay, variance in deleterious mutational effects reduces the risk of extinction, assuming that the mean deleterious mutational effect is on the order of a few percent or less. We also examine the magnitude of outcrossing that is necessary to liberate a predominantly selfing population from the threat of long-term mutational deterioration. The critical amount of outcrossing appears to be greater than is common in near-obligately selfing plant species, supporting the contention that such species are generally doomed to extinction via random drift of new mutations. Our results support the hypothesis that a long-term effective population size in the neighborhood of a few hundred individuals defines an approximate threshold, below which outcrossing populations are vulnerable to extinction via fixation of deleterious mutations, and above which immunity is acquired.     

Understanding the evolutionary fate of finite populations: the dynamics of mutational effects

The most consistent result in more than two decades of experimental evolution is that the fitness of populations adapting to a constant environment does not increase indefinitely, but reaches a plateau. Using experimental evolution with bacteriophage, we show here that the converse is also true. In populations small enough such that drift overwhelms selection and causes fitness to decrease, fitness declines down to a plateau. We demonstrate theoretically that both of these phenomena must be due either to changes in the ratio of beneficial to deleterious mutations, the size of mutational effects, or both. We use mutation accumulation experiments and molecular data from experimental evolution to show that the most significant change in mutational effects is a drastic increase in the rate of beneficial mutation as fitness decreases. In contrast, the size of mutational effects changes little even as organismal fitness changes over several orders of magnitude. These findings have significant implications for the dynamics of adaptation.     

Cancer in light of experimental evolution

Cancer initiation, progression, and the emergence of therapeutic resistance are evolutionary phenomena of clonal somatic cell populations. Studies in microbial experimental evolution and the theoretical work inspired by such studies are yielding deep insights into the evolutionary dynamics of clonal populations, yet there has been little explicit consideration of the relevance of this rapidly growing field to cancer biology. Here, we examine how the understanding of mutation, selection, and spatial structure in clonal populations that is emerging from experimental evolution may be applicable to cancer. Along the way, we discuss some significant ways in which cancer differs from the model systems used in experimental evolution. Despite these differences, we argue that enhanced prediction and control of cancer may be possible using ideas developed in the context of experimental evolution, and we point out some prospects for future research at the interface between these traditionally separate areas.     

Mutational Spectrum Drives the Rise of Mutator Bacteria

Understanding how mutator strains emerge in bacterial populations is relevant both to evolutionary theory and to reduce the threat they pose in clinical settings. The rise of mutator alleles is understood as a result of their hitchhiking with linked beneficial mutations, although the factors that govern this process remain unclear. A prominent but underappreciated fact is that each mutator allele increases only a specific spectrum of mutational changes. This spectrum has been speculated to alter the distribution of fitness effects of beneficial mutations, potentially affecting hitchhiking. To study this possibility, we analyzed the fitness distribution of beneficial mutations generated from different mutator and wild-type Escherichia coli strains. Using antibiotic resistance as a model system, we show that mutational spectra can alter these distributions substantially, ultimately determining the competitive ability of each strain across environments. Computer simulation showed that the effect of mutational spectrum on hitchhiking dynamics follows a non-linear function, implying that even slight spectrum-dependent fitness differences are sufficient to alter mutator success frequency by several orders of magnitude. These results indicate an unanticipated central role for the mutational spectrum in the evolution of bacterial mutation rates. At a practical level, this study indicates that knowledge of the molecular details of resistance determinants is crucial for minimizing mutator evolution during antibiotic therapy.     

The impact of population size on the evolution of asexual microbes on smooth versus rugged fitness landscapes

Background  

It is commonly thought that large asexual populations evolve more rapidly than smaller ones, due to their increased rate of beneficial mutations. Less clear is how population size influences the level of fitness an asexual population can attain. Here, we simulate the evolution of bacteria in repeated serial passage experiments to explore how features such as fitness landscape ruggedness, the size of the mutational target under selection, and the mutation supply rate, interact to affect the evolution of microbial populations of different sizes.     

Influences of Dominance and Evolution of Sex in Finite Diploid Populations

Most eukaryotes reproduce sexually. Although the benefits of sex in diploids mainly stem from recombination and segregation, the relative effects of recombination and segregation are relatively less known. In this study, we adopt an infinite loci model to illustrate how dominance coefficient of mutations affects the above-mentioned genetic events. However, we assume mutational effects to be independent and also ignore the effects of epistasis within loci. Our simulations show that with different levels of dominance, segregation and recombination may play different roles. In particular, recombination more commonly has a major impact on the evolution of sex when deleterious mutations are partially recessive. In contrast, when deleterious mutations are dominant, segregation becomes more important than recombination, a finding that is consistent with previous studies stating that segregation, rather than recombination, is more likely to drive the evolution of sex. Moreover, beneficial mutations alone remarkably increases the effects of recombination. We also note that populations favor sexual reproduction when deleterious mutations become more dominant or beneficial mutations become more recessive. Overall, these results illustrate that the existence of dominance is an important mechanism that affects the evolution of sex.     

Linking temperature dependence of fitness effects of mutations to thermal niche adaptation

Fitness effects of mutations may generally depend on temperature that influences all rate-limiting biophysical and biochemical processes. Earlier studies suggested that high temperatures may increase the availability of beneficial mutations (‘more beneficial mutations’), or allow beneficial mutations to show stronger fitness effects (‘stronger beneficial mutation effects’). The ‘more beneficial mutations’ scenario would inevitably be associated with increased proportion of conditionally beneficial mutations at higher temperatures. This in turn predicts that populations in warm environments show faster evolutionary adaptation but suffer fitness loss when faced with cold conditions, and those evolving in cold environments become thermal-niche generalists (‘hotter is narrower’). Under the ‘stronger beneficial mutation effects’ scenario, populations evolving in warm environments would show faster adaptation without fitness costs in cold environments, leading to a ‘hotter is (universally) better’ pattern in thermal niche adaptation. We tested predictions of the two competing hypotheses using an experimental evolution study in which populations of two model bacterial species, Escherichia coli and Pseudomonas fluorescens, evolved for 2400 generations at three experimental temperatures. Results of reciprocal transplant experiments with our P. fluorescens populations were largely consistent with the ‘hotter is narrower’ prediction. Results from the E. coli populations clearly suggested stronger beneficial mutation effects at higher assay temperatures, but failed to detect faster adaptation in populations evolving in warmer experimental environments (presumably because of limitation in the supply of genetic variation). Our results suggest that the influence of temperature on mutational effects may provide insight into the patterns of thermal niche adaptation and population diversification across thermal conditions.     

Microbial experiments on adaptive landscapes

The adaptive landscape is one of the most widely used metaphors in evolutionary biology. It is created by plotting fitness against phenotypes or genotypes in a given environment. The shape of the landscape is crucial in predicting the outcome of evolution: whether evolution will result in populations reaching predictable end points, or whether multiple evolutionary outcomes are more likely. In a more applied sense, the landscape will determine whether organisms will evolve to lose 'costly' resistance to antibiotics, herbicides or pesticides when the use of the control agent is stopped. Laboratory populations of microbes allow evolution to be observed in real time and, as such, provide key insights into the topology of adaptive landscapes.     

Clonal interference and the periodic selection of new beneficial mutations in Escherichia coli

The conventional model of adaptation in asexual populations implies sequential fixation of new beneficial mutations via rare selective sweeps that purge all variation and preserve the clonal genotype. However, in large populations multiple beneficial mutations may co-occur, causing competition among them, a phenomenon called "clonal interference." Clonal interference is thus expected to lead to longer fixation times and larger fitness effects of mutations that ultimately become fixed, as well as to a genetically more diverse population. Here, we study the significance of clonal interference in populations consisting of mixtures of differently marked wild-type and mutator strains of Escherichia coli that adapt to a minimal-glucose environment for 400 generations. We monitored marker frequencies during evolution and measured the competitive fitness of random clones from each marker state after evolution. The results demonstrate the presence of multiple beneficial mutations in these populations and slower and more erratic invasion of mutants than expected by the conventional model, showing the signature of clonal interference. We found that a consequence of clonal interference is that fitness estimates derived from invasion trajectories were less than half the magnitude of direct estimates from competition experiments, thus revealing fundamental problems with this fitness measure. These results force a reevaluation of the conventional model of periodic selection for asexual microbes.     

A general multivariate extension of Fisher's geometrical model and the distribution of mutation fitness effects across species

The evolution of complex organisms is a puzzle for evolutionary theory because beneficial mutations should be less frequent in complex organisms, an effect termed "cost of complexity." However, little is known about how the distribution of mutation fitness effects (f(s)) varies across genomes. The main theoretical framework to address this issue is Fisher's geometric model and related phenotypic landscape models. However, it suffers from several restrictive assumptions. In this paper, we intend to show how several of these limitations may be overcome. We then propose a model of f(s) that extends Fisher's model to account for arbitrary mutational and selective interactions among n traits. We show that these interactions result in f(s) that would be predicted by a much smaller number of independent traits. We test our predictions by comparing empirical f(s) across species of various gene numbers as a surrogate to complexity. This survey reveals, as predicted, that mutations tend to be more deleterious, less variable, and less skewed in higher organisms. However, only limited difference in the shape of f(s) is observed from Escherichia coli to nematodes or fruit flies, a pattern consistent with a model of random phenotypic interactions across many traits. Overall, these results suggest that there may be a cost to phenotypic complexity although much weaker than previously suggested by earlier theoretical works. More generally, the model seems to qualitatively capture and possibly explain the variation of f(s) from lower to higher organisms, which opens a large array of potential applications in evolutionary genetics.     

The spread of a beneficial mutation in experimental bacterial populations: the influence of the environment and genotype on the fixation of rpoS mutations

The spread of beneficial mutations through populations is at the core of evolutionary change. A long-standing hindrance to understanding mutational sweeps was that beneficial mutations have been slow to be identified, even in commonly studied experimental populations. The lack of information on what constitutes a beneficial mutation has led to many uncertainties about the frequency, fitness benefit and fixation of beneficial mutations. A more complete picture is currently emerging for a limited set of identified mutations in bacterial populations. In turn, this will allow quantitation of several features of mutational sweeps. Most importantly, the 'benefit' of beneficial mutations can now be explained in terms of physiological function and how variations in the environment change the selectability of mutations. Here, the sweep of rpoS mutations in Escherichia coli, in both experimental and natural populations, is described in detail. These studies reveal the subtleties of physiology and regulation that strongly influence the benefit of a mutation and explain differences in sweeps between strains and between various environments.     

How does adaptation sweep through the genome? Insights from long-term selection experiments

A major goal in evolutionary biology is to understand the origins and fates of adaptive mutations. Natural selection may act to increase the frequency of de novo beneficial mutations, or those already present in the population as standing genetic variation. These beneficial mutations may ultimately reach fixation in a population, or they may stop increasing in frequency once a particular phenotypic state has been achieved. It is not yet well understood how different features of population biology, and/or different environmental circumstances affect these adaptive processes. Experimental evolution is a promising technique for studying the dynamics of beneficial alleles, as populations evolving in the laboratory experience natural selection in a replicated, controlled manner. Whole-genome sequencing, regularly obtained over the course of sustained laboratory selection, could potentially reveal insights into the mutational dynamics that most likely occur in natural populations under similar circumstances. To date, only a few evolution experiments for which whole-genome data are available exist. This review describes results from these resequenced laboratory-selected populations, in systems with and without sexual recombination. In asexual systems, adaptation from new mutations can be studied, and results to date suggest that the complete, unimpeded fixation of these mutations is not always observed. In sexual systems, adaptation from standing genetic variation can be studied, and in the admittedly few examples we have, the complete fixation of standing variants is not always observed. To date, the relative frequency of adaptation from new mutations versus standing variation has not been tested using a single experimental system, but recent studies using Caenorhabditis elegans and Saccharomyces cerevisiae suggest that this a realistic future goal.     

FISHER'S MODEL AND THE GENOMICS OF ADAPTATION: RESTRICTED PLEIOTROPY,HETEROGENOUS MUTATION,AND PARALLEL EVOLUTION

Genetic theories of adaptation generally overlook the genes in which beneficial substitutions occur, and the likely variation in their mutational effects. We investigate the consequences of heterogeneous mutational effects among loci on the genetics of adaptation. We use a generalization of Fisher's geometrical model, which assumes multivariate Gaussian stabilizing selection on multiple characters. In our model, mutation has a distinct variance–covariance matrix of phenotypic effects for each locus. Consequently, the distribution of selection coefficients s varies across loci. We assume each locus can only affect a limited number of independent linear combinations of phenotypic traits (restricted pleiotropy), which differ among loci, an effect we term “orientation heterogeneity.” Restricted pleiotropy can sharply reduce the overall proportion of beneficial mutations. Orientation heterogeneity has little impact on the shape of the genomic distribution, but can substantially increase the probability of parallel evolution (the repeated fixation of beneficial mutations at the same gene in independent populations), which is highest with low pleiotropy. We also consider variation in the degree of pleiotropy and in the mean s across loci. The latter impacts the genomic distribution of s, but has a much milder effect on parallel evolution. We discuss these results in the light of evolution experiments.     

Unsupervised Inference of Protein Fitness Landscape from Deep Mutational Scan

The recent technological advances underlying the screening of large combinatorial libraries in high-throughput mutational scans deepen our understanding of adaptive protein evolution and boost its applications in protein design. Nevertheless, the large number of possible genotypes requires suitable computational methods for data analysis, the prediction of mutational effects, and the generation of optimized sequences. We describe a computational method that, trained on sequencing samples from multiple rounds of a screening experiment, provides a model of the genotype–fitness relationship. We tested the method on five large-scale mutational scans, yielding accurate predictions of the mutational effects on fitness. The inferred fitness landscape is robust to experimental and sampling noise and exhibits high generalization power in terms of broader sequence space exploration and higher fitness variant predictions. We investigate the role of epistasis and show that the inferred model provides structural information about the 3D contacts in the molecular fold.     

Self-structuring in spatial evolutionary ecology

Spatial self-structuring has been a focus of recent interest among evolutionary ecologists. We review recent developments in the study of the interplay between spatial self-structuring and evolution. We first discuss the relative merits of the various theoretical approaches to spatial modelling in ecology. Second, we synthesize the main theoretical studies of the evolution of cooperation in spatially structured populations. We show that population viscosity is generally beneficial to cooperation, because cooperators can reap additional benefits from being clustered. A similar mechanism can explain the evolution of honest communication and of reduced virulence in host–parasite interactions. We also discuss some recent innovative empirical results that test these theories. Third, we show the relevance of these results to the general field of evolutionary ecology. An important conclusion is that kin selection is the main process that drives evolution of cooperation in viscous populations. Many results of kin selection theory can be recovered as emergent properties of spatial ecological dynamics. We discuss the implications of these results for the study of multilevel selection and evolutionary transitions. We conclude by sketching some perspectives for future research, with a particular emphasis on the topics of evolutionary branching, criticality, spatial fluctuations and experimental tests of theoretical predictions.     

基于生命周期的乡村景观格局演变的预测方法——以湖南省金井镇为例

以洞庭湖区金井镇为案例,运用生命周期理论分析了乡村景观格局演变过程,模拟了乡村景观格局演变周期曲线,预测出乡村景观格局演变周期,并与CA-Markov模型相耦合,建立了一套符合乡村景观格局演变规律的预测模拟方法. 预测结果表明： 2020年金井镇乡村景观格局中聚落景观和水田景观变化最大,聚落景观将增加至1194.01 hm²,水田景观将减少至3090.24 hm²,模型预测结果的数量精度和空间精度分别达到99.3%和96.4%,明显优于单一的CA-Markov模型.本文提出的乡村景观格局演变周期的预测方法可以为未来乡村景观规划提供参考.     

Fly wing evolution explained by a neutral model with mutational pleiotropy

To what extent the speed of mutational production of phenotypic variation determines the rate of long-term phenotypic evolution is a central question. Houle et al. recently addressed this question by studying the mutational variances, additive genetic variances, and macroevolution of locations of vein intersections on fly wings, reporting very slow phenotypic evolution relative to the rates of mutational input, high phylogenetic signals, and a strong, linear relationship between the mutational variance of a trait and its rate of evolution. Houle et al. found no existing model of phenotypic evolution to be consistent with all these observations, and proposed the improbable scenario of equal influence of mutational pleiotropy on all traits. Here, we demonstrate that the purported linear relationship between mutational variance and evolutionary divergence is artifactual. We further show that the data are explainable by a simple model in which the wing traits are effectively neutral at least within a range of phenotypic values but their evolutionary rates are differentially reduced because mutations affecting these traits are purged owing to their different pleiotropic effects on other traits that are under stabilizing selection. Thus, the evolutionary patterns of fly wing morphologies are explainable under the existing theoretical framework of phenotypic evolution.