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

When are mutations beneficial in one environment and deleterious in another? More generally, what is the relationship between mutation effects across environments? These questions are crucial to predict adaptation in heterogeneous conditions in a broad sense. Empirical evidence documents various patterns of fitness effects across environments but we still lack a framework to analyze these multivariate data. In this article, we extend Fisher's geometrical model to multiple environments determining distinct peaks. We derive the fitness distribution, in one environment, among mutants with a given fitness in another and the bivariate distribution of random mutants’ fitnesses across two or more environments. The geometry of the phenotype‐fitness landscape is naturally interpreted in terms of fitness trade‐offs between environments. These results may be used to fit/predict empirical distributions or to predict the pattern of adaptation across heterogeneous conditions. As an example, we derive the genomic rate of substitution and of adaptation in a metapopulation divided into two distinct habitats in a high migration regime and show that they depend critically on the geometry of the phenotype‐fitness landscape.     

The fitness effects of spontaneous mutations in Caenorhabditis elegans

Abstract. Spontaneous mutation to mildly deleterious alleles has emerged as a potentially unifying component of a variety of observations in evolutionary genetics and molecular evolution. However, the biological significance of hypotheses based on mildly deleterious mutation depends critically on the rate at which new mutations arise and on their average effects. A long-term mutation-accumulation experiment with replicate lines of the nematode Caenorhabditis elegans maintained by single-progeny descent indicates that recurrent spontaneous mutation causes approximately 0.1% decline in fitness per generation, which is about an order of magnitude less than that suggested by previous studies with Drosophila . Two rather different approaches, Bateman-Mukai and maximum likelihood, suggest that this observation, along with the observed rate of increase in the variance of fitness among lines, is consistent with a genomic deleterious mutation rate for fitness of approximately 0.03 per generation and with an average homozygous effect of approximately 12%. The distribution of mutational effects for fitness appears to have a relatively low coefficient of variation, being no more extreme than expected for a negative exponential, and for one composite fitness measure (total progeny production) approaches constancy of effects. These results are derived from assays in a benign environment. At stressful temperatures, estimates of the genomic deleterious mutation rate (for genes expressed at such temperatures) is sixfold lower, whereas those for the average homozygous effect is approximately eightfold higher. Our results are reasonably compatible with existing estimates for flies, when one considers the differences between these species in the number of germ-line cell divisions per generation and the magnitude of transposable element activity.     

Fisher'S geometrical model of fitness landscape and variance in fitness within a changing environment

The fitness of an individual can be simply defined as the number of its offspring in the next generation. However, it is not well understood how selection on the phenotype determines fitness. In accordance with Fisher's fundamental theorem, fitness should have no or very little genetic variance, whereas empirical data suggest that is not the case. To bridge these knowledge gaps, we follow Fisher's geometrical model and assume that fitness is determined by multivariate stabilizing selection toward an optimum that may vary among generations. We assume random mating, free recombination, additive genes, and uncorrelated stabilizing selection and mutational effects on traits. In a constant environment, we find that genetic variance in fitness under mutation-selection balance is a U-shaped function of the number of traits (i.e., of the so-called "organismal complexity"). Because the variance can be high if the organism is of either low or high complexity, this suggests that complexity has little direct costs. Under a temporally varying optimum, genetic variance increases relative to a constant optimum and increasingly so when the mutation rate is small. Therefore, mutation and changing environment together can maintain high genetic variance. These results therefore lend support to Fisher's geometric model of a fitness landscape.     

Riding across the selection landscape: fitness consequences of annual variation in reproductive characteristics

Evolutionary models estimating phenotypic selection in character size usually assume that the character is invariant across reproductive bouts. We show that variation in the size of reproductive traits may be large over multiple events and can influence fitness in organisms where these traits are produced anew each season. With data from populations of two orchid species, Caladenia valida and Tolumnia variegata, we used Bayesian statistics to investigate the effect on the distribution in fitness of individuals when the fitness landscape is not flat and when characters vary across reproductive bouts. Inconsistency in character size across reproductive periods within an individual increases the uncertainty of mean fitness and, consequently, the uncertainty in individual fitness. The trajectory of selection is likely to be muddled as a consequence of variation in morphology of individuals across reproductive bouts. The frequency and amplitude of such changes will certainly affect the dynamics between selection and genetic drift.     

Fitness effects of new mutations in Chlamydomonas reinhardtii across two stress gradients

Most spontaneous mutations affecting fitness are likely to be deleterious, but the strength of selection acting on them might be impacted by environmental stress. Such stress‐dependent selection could expose hidden genetic variation, which in turn might increase the adaptive potential of stressed populations. On the other hand, this variation might represent a genetic load and thus lead to population extinction under stress. Previous studies to determine the link between stress and mutational effects on fitness, however, have produced inconsistent results. Here, we determined the net change in fitness in 29 genotypes of the green algae Chlamydomonas reinhardtii that accumulated mutations in the near absence of selection for approximately 1000 generations across two stress gradients, increasing NaCl and decreasing phosphate. We found mutational effects to be magnified under extremely stressful conditions, but such effects were specific both to the type of stress and to the genetic background. The detection of stress‐dependent fitness effects of mutations depended on accurately scaling relative fitness measures by generation times, thus offering an explanation for the inconsistencies among previous studies.     

Synthetic shuffling and in vitro selection reveal the rugged adaptive fitness landscape of a kinase ribozyme

The relationship between genotype and phenotype is often described as an adaptive fitness landscape. In this study, we used a combination of recombination, in vitro selection, and comparative sequence analysis to characterize the fitness landscape of a previously isolated kinase ribozyme. Point mutations present in improved variants of this ribozyme were recombined in vitro in more than 10¹⁴ different arrangements using synthetic shuffling, and active variants were isolated by in vitro selection. Mutual information analysis of 65 recombinant ribozymes isolated in the selection revealed a rugged fitness landscape in which approximately one-third of the 91 pairs of positions analyzed showed evidence of correlation. Pairs of correlated positions overlapped to form densely connected networks, and groups of maximally connected nucleotides occurred significantly more often in these networks than they did in randomized control networks with the same number of links. The activity of the most efficient recombinant ribozyme isolated from the synthetically shuffled pool was 30-fold greater than that of any of the ribozymes used to build it, which indicates that synthetic shuffling can be a rich source of ribozyme variants with improved properties.     

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.     

Statistical convenience vs biological insight: consequences of data transformation for the analysis of fitness variation in heterogeneous environments

In plants, more favourable environmental conditions can lead to dramatic increases in both mean fitness and variance in fitness. This results in data that violate the equality-of-variance assumption of anova, a problem that most empiricists would address by log-transforming fitness values. Using heuristic data sets and simple simulations, we show that anova on log-transformed fitness consistently fails to match the outcome of selection in a heterogeneous environment or its sensitivity to environmental frequency. Only anova based on relative fitness within environments accurately predicts the sensitivity of genotype selection to the frequency of alternative environments. Parallel analyses of variance based on absolute fitness and relative fitness can bracket the expected success of alternative genotypes under hard and soft selection, respectively. For example, for Sinapis arvensis growing in full sun and partial shade treatments, families achieving high fitness in the best environment are favoured under hard selection, whereas soft selection favours different families that achieve consistently good performance across environments. Based on these findings, we recommend that log-transformation of fitness should no longer be standard practice in ecological genetics studies. Weighted anova is a preferable method for dealing with unequal variances, and investigators should also make greater use of techniques such as quantile regression or resampling to describe and evaluate fitness variation across heterogeneous environments.     

The effect of spontaneous mutations on competitive ability

Understanding the impact of spontaneous mutations on fitness has many theoretical and practical applications in biology. Although mutational effects on individual morphological or life‐history characters have been measured in several classic genetic model systems, there are few estimates of the rate of decline due to mutation for complex fitness traits. Here, we estimate the effects of mutation on competitive ability, an important complex fitness trait, in a model system for ecological and evolutionary genomics, Daphnia. Competition assays were performed to compare fitness between mutation‐accumulation (MA) lines and control lines from eight different genotypes from two populations of Daphnia pulicaria after 30 and 65 generations of mutation accumulation. Our results show a fitness decline among MA lines relative to controls as expected, but highlight the influence of genomic background on this effect. In addition, in some assays, MA lines outperform controls providing insight into the frequency of beneficial mutations.     

The ecology and genetics of fitness in Chlamydomonas. IX. The rate of accumulation of variation of fitness under selection

Populations of Chlamydomonas founded by single cells were cultured in chemostats for 50 days, representing about 125 generations. The mean and variance of division rate was measured daily by withdrawing cells from the effluent and culturing them for 24 h on filtered effluent medium solidified with agar. Mean fitness did not change during the period of culture, and the behavior of neutral markers indicated that no substitutions of novel beneficial mutations occurred. However, the variance of fitness increased markedly at about the same rate in two replicate populations. The standardized rate, or mutational heritability, was Vm/VE = 4-5 x 10(-3) per generation. This is substantially greater than most other estimates for characters closely correlated with fitness. Moreover, it seems difficult to reconcile with the absence of any change in mean fitness. We investigated the possibility that frequency-dependent selection was created by spatial heterogeneity within the culture vessel by testing cell populations with different phenotypes from the top, bottom, and surface of the chemostats. However, the differentiation of these populations seemed to be attributable to phenotypic plasticity, with no evidence that their characteristics were heritable. Finally, we report an experiment in which lines were selected for about 100 generations on solid or liquid medium. These lines became specifically adapted to the medium on which they were cultured, showing that liquid and solid media, even when chemically identical, provide different conditions of growth for Chlamydomonas. The genetic variance appearing in the cultures was therefore attributed to conditionally neutral mutations that were not expressed in the chemostat. This implies that rates of accumulation of mutational variance measured in the culture environment itself (where this can be done) may greatly underestimate the variation available for a response through selection to environmental change. Moreover, it suggests that chemostat populations may be more dynamic and more diverse than is usually thought.     

The ecology and genetics of fitness in Chlamydomonas. X. The relationship between genetic correlation and genetic distance

Abstract.— A necessary condition for the maintenance of genetic variation in heterogenous environments is that the relative fitnesses of a collection of genotypes vary as conditions of growth change. This can be detected by estimating the amount of gene-by-environment interaction (G X E) when a range of types are tested across a range of conditions. However it is the sign and magnitude of the genetic correlation, which is a component of G X E, that governs the ultimate fate of variation. Whether genetic variation will be preserved, then, depends on how the genetic correlation changes as a function of the ecological differences among environments and the genetic differences among genotypes. To evaluate this, we assayed the performance of 15 chlorophyte species of known genetic relation in 20 environments. We found that the quantity of G X E increased as both the environmental variance across environments and the genetic distance increased. Moreover the genetic correlation declined as the environmental variance between pairs of environments and the genetic distance between pairs of genotypes increased. These results suggest that divergent selection will be more likely to maintain genetic variation when environments are strongly contrasted and genotypes widely divergent.     

The effect of phenotypic plasticity on evolution in multipeaked fitness landscapes

When facing the challenge of developing an individual that best fits its environment, nature demonstrates an interesting combination of two fundamentally different adaptive mechanisms: genetic evolution and phenotypic plasticity. Following numerous computational models, it has become the accepted wisdom that lifetime acclimation (e.g. via learning) smooths the fitness landscape and consequently accelerates evolution. However, analytical studies, focusing on the effect of phenotypic plasticity on evolution in simple unimodal landscapes, have often found that learning hinders the evolutionary process rather than accelerating it. Here, we provide a general framework for studying the effect of plasticity on evolution in multipeaked landscapes and introduce a rigorous mathematical analysis of these dynamics. We show that the convergence rate of the evolutionary process in a given arbitrary one-dimensional fitness landscape is dominated by the largest descent (drawdown) in the landscape and provide numerical evidence to support an analogous dominance also in multidimensional landscapes. We consider several schemes of phenotypic plasticity and examine their effect on the landscape drawdown, identifying the conditions under which phenotypic plasticity is advantageous. The lack of such a drawdown in unimodal landscapes vs. its dominance in multipeaked landscapes accounts for the seemingly contradictory findings of previous studies.     

The distribution of fitness effects of new beneficial mutations in Pseudomonas fluorescens

Theoretical studies of adaptation emphasize the importance of understanding the distribution of fitness effects (DFE) of new mutations. We report the isolation of 100 adaptive mutants—without the biasing influence of natural selection—from an ancestral genotype whose fitness in the niche occupied by the derived type is extremely low. The fitness of each derived genotype was determined relative to a single reference type and the fitness effects found to conform to a normal distribution. When fitness was measured in a different environment, the rank order changed, but not the shape of the distribution. We argue that, even with detailed knowledge of the genetic architecture underpinning the adaptive types (as is the case here), the DFEs remain unpredictable, and we discuss the possibility that general explanations for the shape of the DFE might not be possible in the absence of organism-specific biological details.     

基于景观连接度的土地整理生态效应评价

近年来,土地整理区的生物多样性保护和景观功能的维持受到广泛关注。本文选取贵州省道真县洛龙镇国家重点土地整理项目区,运用基于结构与功能相结合景观连接度模型(综合连接度(IIC)和连接度概率(PC)),计算了500、1000、2000、3000和4000m种群迁移扩散距离阈值情景下,土地整理前后各生境斑块对景观连接度的重要程度,识别重要斑块变化范围,从功能角度评价整理后的生态效应。结果表明:连接度指数能较好地识别土地整理前后各生境斑块的重要类别及其改变;其中,巨型斑块所占面积最大,分别占总面积的57.0%和57.2%;小型斑块数目整理前后分别占斑块总数的48.0%和48.9%;空间上,斑块的重要性分布也产生一定的变化。整理后生境斑块的连通性较整理前也有所下降,IIC和PC平均值分别为0.434和0.680,且随着距离阈值的增大,连接度逐渐增大。巨型斑块对生境斑块景观连通性的相对重要值最大,中型斑块和大型斑块次之,小型斑块最低。研究表明,土地整理过程中,大面积生境斑块和"踏脚石"斑块对维持土地整理生态效益具有重要作用。     

地形因子对森林景观格局多尺度效应分析

以TM影像和野外调查为数据源,3S技术为研究手段,分析了泰山的森林景观结构动态变化以及景观格局沿高程的分异。选择相对高差较大的区域设计了8个地形方位,采用3种由连续样方组成的辐射状样带,在遥感影像上进行信息采集,研究地形对森林景观格局的多尺度效应,分析了不同地形因子对森林景观分异的影响。结果表明,在景观尺度上,地形方位、海拔、山地类型是影响森林景观镶嵌格局的控制因素,坡向、坡度是重要因素,坡形、坡位是不明显因素。以TM影像为信息源,从森林景观分异和梯度分析上,首先要考虑海拔坡向指数、坡形坡位指数和海拔,并立足于地形方位。地形主要因子间存在着稳定的显著正相关,为森林分异多尺度格局提供了较强的综合解释能力。     

The use and misuse of regression models in landscape genetic analyses

The field of landscape genetics has been rapidly evolving, adopting and adapting analytical frameworks to address research questions. Current studies are increasingly using regression‐based frameworks to infer the individual contributions of landscape and habitat variables on genetic differentiation. This paper outlines appropriate and inappropriate uses of multiple regression for these purposes, and demonstrates through simulation the limitations of different analytical frameworks for making correct inference. Of particular concern are recent studies seeking to explain genetic differences by fitting regression models with effective distance variables calculated independently on separate landscape resistance surfaces. When moving across the landscape, organisms cannot respond independently and uniquely to habitat and landscape features. Analyses seeking to understand how landscape features affect gene flow should model a single conductance or resistance surface as a parameterized function of relevant spatial covariates, and estimate the values of these parameters by linking a single set of resistance distances to observed genetic dissimilarity via a loss function. While this loss function may involve a regression‐like step, the associated nuisance parameters are not interpretable in terms of organismal movement and should not be conflated with what is actually of interest: the mapping between spatial covariates and conductance/resistance. The growth and evolution of landscape genetics as a field has been rapid and exciting. It is the goal of this paper to highlight past missteps and demonstrate limitations of current approaches to ensure that future use of regression models will appropriately consider the process being modeled, which will provide clarity to model interpretation.     

No evidence for accumulation of deleterious mutations and fitness degradation in clonal fish hybrids: Abandoning sex without regrets

Despite its inherent costs, sexual reproduction is ubiquitous in nature, and the mechanisms to protect it from a competitive displacement by asexuality remain unclear. Popular mutation‐based explanations, like the Muller's ratchet and the Kondrashov's hatchet, assume that purifying selection may not halt the accumulation of deleterious mutations in the nonrecombining genomes, ultimately leading to their degeneration. However, empirical evidence is scarce and it remains particularly unclear whether mutational degradation proceeds fast enough to ensure the decay of clonal organisms and to prevent them from outcompeting their sexual counterparts. To test this hypothesis, we jointly analysed the exome sequences and the fitness‐related phenotypic traits of the sexually reproducing fish species and their clonal hybrids, whose evolutionary ages ranged from F1 generations to 300 ky. As expected, mutations tended to accumulate in the clonal genomes in a time‐dependent manner. However, contrary to the predictions, we found no trend towards increased nonsynonymity of mutations acquired by clones, nor higher radicality of their amino acid substitutions. Moreover, there was no evidence for fitness degeneration in the old clones compared with that in the younger ones. In summary, although an efficacy of purifying selection may still be reduced in the asexual genomes, our data indicate that its efficiency is not drastically decreased. Even the oldest investigated clone was found to be too young to suffer fitness consequences from a mutation accumulation. This suggests that mechanisms other than mutation accumulation may be needed to explain the competitive advantage of sex in the short term.     

Fitness effects of mutation accumulation in a natural outbred population of wild radish (Raphanus raphanistrum): comparison of field and greenhouse environments

Spontaneous deleterious mutation has been measured in a handful of organisms, always under laboratory conditions and usually employing inbred species or genotypes. We report the results of a mutation accumulation experiment with an outbred annual plant, Raphanus raphanistrum, with lifetime fitness measured in both the field and the greenhouse. This is the first study to report the effects of spontaneous mutation measured under field conditions. Two large replicate populations (N(e) approximately 600) were maintained with random mating in the greenhouse under relaxed selection for nine generations before the field assay was performed and ten generations before the greenhouse assay. Each generation, every individual was mated twice, once as a pollen donor and once as a pollen recipient, and a single seed from each plant was chosen randomly to create the next generation. The ancestral population was maintained as seeds at 4 degrees C. Declines in lifetime fitness were observed in both the field (1.7% per generation; P= 0.27) and the greenhouse (0.6% per generation; P= 0.07). Significant increases in additive genetic variance for fitness were found for stems per day, flowers per stem, fruits per flower and seeds per fruit in the field as well as for fruits per flower in the greenhouse. Lack of significance of the fitness decline may be due to the short period of mutation accumulation, the use of outbred populations, or both. The percent declines in fitness are at the high end of the range observed in other mutation accumulation experiments and give some support to the idea that mutational effects may be magnified under harsher field conditions. Thus, measurement of mutational parameters under laboratory conditions may underestimate the effects of mutations in natural populations.     

The contribution of spontaneous mutation to variation in environmental responses of Arabidopsis thaliana: responses to light

It has been hypothesized that new, spontaneous mutations tend to reduce fitness more severely in more stressful environments. To address this hypothesis, we grew plants representing 20 Arabidopsis thaliana mutation-accumulation (M-A) lines, advanced to generation 17, and their progenitor, in differing light conditions. The experiment was conducted in a greenhouse, and two treatments were used: full sun and shade, in which influx of red light was reduced relative to far-red. The shade treatment was considered the more stressful because mean absolute fitness was lower in that treatment, though not significantly so. Plants from generation 17 of M-A developed significantly faster than those from generation 0 in both treatments. A significant interaction between generation and treatment revealed that, counter to the hypothesis, M-A lines tended to have higher fitness on average relative to the progenitor in the shaded conditions, whereas, in full sun, the two generations were similar in fitness. A secondary objective of this experiment was to characterize the contribution of new mutations to genotype x environment interaction. We did not, however, detect a significant interaction between M-A line and treatment. Plots of the line-specific environmental responses indicate no tendency of new mutations to contribute to fitness trade-offs, between environments. They also do not support a model of conditionally deleterious mutation, in which a mutant reduces fitness only in a particular environment. These results suggest that interactions between genotype and light environment previously documented for A. thaliana are not explicable primarily as a consequence of steady input of spontaneous mutations having environment-specific effects.