SOLVING THE PARADOX OF STASIS: SQUASHED STABILIZING SELECTION AND THE LIMITS OF DETECTION

Despite the potential for rapid evolution, stasis is commonly observed over geological timescales—the so‐called “paradox of stasis.” This paradox would be resolved if stabilizing selection were common, but stabilizing selection is infrequently detected in natural populations. We hypothesize a simple solution to this apparent disconnect: stabilizing selection is hard to detect empirically once populations have adapted to a fitness peak. To test this hypothesis, we developed an individual‐based model of a population evolving under an invariant stabilizing fitness function. Stabilizing selection on the population was infrequently detected in an “empirical” sampling protocol, because (1) trait variation was low relative to the fitness peak breadth; (2) nonselective deaths masked selection; (3) populations wandered around the fitness peak; and (4) sample sizes were typically too small. Moreover, the addition of negative frequency‐dependent selection further hindered detection by flattening or even dimpling the fitness peak, a phenomenon we term “squashed stabilizing selection.” Our model demonstrates that stabilizing selection provides a plausible resolution to the paradox of stasis despite its infrequent detection in nature. The key reason is that selection “erases its traces”: once populations have adapted to a fitness peak, they are no longer expected to exhibit detectable stabilizing selection.     

适合度的相对性与路径依赖的自然选择

自然选择理论认为生物个体或者种群在进化的过程中, 其基因或者性状、行为策略的选择一定是能够提高其适合度或者达到某个可期的“目标”。然而, 随着某个突变基因或者性状特征、行为策略在种群中扩散, 其期望收益将随着其在种群中分布的密度变化或环境改变而发生改变, 这就是适合度景观的悖论, 即静态的、固定可期望的收益可能因此而不存在。基于动态而非静态适合度景观的概念, 我们提出路径依赖的自然选择概念。路径依赖的自然选择过程中, 一个突变的基因或表型在某种环境下随机产生, 但是该基因或表型在某些特定环境下会产生正反馈。尤其是在正反馈与随机漂变的共同作用下, 多条路径的演化就可能发生, 并且其路径的形成将同时受到其种群进化历史过程和空间特征分布等因素的强烈影响。而在不同路径下, 由于观测维度、角度和尺度的不同, 适合度意义将因此而存在不同。在此意义下, 自然选择更可能选择路径频率而不是适合度大小。基于上述概念, 我们借鉴现代物理学中复函数的方法, 来描述多重动力对物种形成或者生物特征、种群进化等路径依赖的演化过程, 以期为同域物种、隐存种形成以及生物多样性演化提供解释机制。     

The impact of random frequency-dependent mutations on the average population fitness

ABSTRACT: BACKGROUND: In addition to selection, the process of evolution is accompanied by stochastic effects, such as changing environmental conditions, genetic drift and mutations. Commonly it is believed that without genetic drift, advantageous mutations quickly fixate in a halpoid population due to strong selection and lead to a continuous increase of the average fitness. This conclusion is based on the assumption of constant fitness. However, for frequency dependent fitness, where the fitness of an individual depends on the interactions with other individuals in the population, this does not hold. RESULTS: We propose a mathematical model that allows to understand the consequences of random frequency dependent mutations on the dynamics of an infinite large population. The frequencies of different types change according to the replicator equations and the fitness of a mutant is random and frequency dependent. To capture the interactions of different types, we employ a payoff matrix of variable size and thus are able to accommodate an arbitrary number of mutations. We assume that at most one mutant type arises at a time. The payoff entries to describe the mutant type are random variables obeying a probability distribution which is related to the fitness of the parent type. CONCLUSIONS: We show that a random mutant can decrease the average fitness under frequency dependent selection, based on analytical results for two types, and on simulations for n types. Interestingly, in the case of at most two types the probabilities to increase or decrease the average fitness are independent of the concrete probability density function. Instead, they only depend on the probability that the payoff entries of the mutant are larger than the payoff entries of the parent type.     

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.     

Deleterious Mutations, Apparent Stabilizing Selection and the Maintenance of Quantitative Variation

Apparent stabilizing selection on a quantitative trait that is not causally connected to fitness can result from the pleiotropic effects of unconditionally deleterious mutations, because as N. Barton noted, "...individuals with extreme values of the trait will tend to carry more deleterious alleles...." We use a simple model to investigate the dependence of this apparent selection on the genomic deleterious mutation rate, U; the equilibrium distribution of K, the number of deleterious mutations per genome; and the parameters describing directional selection against deleterious mutations. Unlike previous analyses, we allow for epistatic selection against deleterious alleles. For various selection functions and realistic parameter values, the distribution of K, the distribution of breeding values for a pleiotropically affected trait, and the apparent stabilizing selection function are all nearly Gaussian. The additive genetic variance for the quantitative trait is kQa2, where k is the average number of deleterious mutations per genome, Q is the proportion of deleterious mutations that affect the trait, and a2 is the variance of pleiotropic effects for individual mutations that do affect the trait. In contrast, when the trait is measured in units of its additive standard deviation, the apparent fitness function is essentially independent of Q and a2; and beta, the intensity of selection, measured as the ratio of additive genetic variance to the "variance" of the fitness curve, is very close to s = U/k, the selection coefficient against individual deleterious mutations at equilibrium. Therefore, this model predicts appreciable apparent stabilizing selection if s exceeds about 0.03, which is consistent with various data. However, the model also predicts that beta must equal Vm/VG, the ratio of new additive variance for the trait introduced each generation by mutation to the standing additive variance. Most, although not all, estimates of this ratio imply apparent stabilizing selection weaker than generally observed. A qualitative argument suggests that even when direct selection is responsible for most of the selection observed on a character, it may be essentially irrelevant to the maintenance of variation for the character by mutation-selection balance. Simple experiments can indicate the fraction of observed stabilizing selection attributable to the pleiotropic effects of deleterious mutations.     

Genetic Diversity in the Interference Selection Limit

Pervasive natural selection can strongly influence observed patterns of genetic variation, but these effects remain poorly understood when multiple selected variants segregate in nearby regions of the genome. Classical population genetics fails to account for interference between linked mutations, which grows increasingly severe as the density of selected polymorphisms increases. Here, we describe a simple limit that emerges when interference is common, in which the fitness effects of individual mutations play a relatively minor role. Instead, similar to models of quantitative genetics, molecular evolution is determined by the variance in fitness within the population, defined over an effectively asexual segment of the genome (a “linkage block”). We exploit this insensitivity in a new “coarse-grained” coalescent framework, which approximates the effects of many weakly selected mutations with a smaller number of strongly selected mutations that create the same variance in fitness. This approximation generates accurate and efficient predictions for silent site variability when interference is common. However, these results suggest that there is reduced power to resolve individual selection pressures when interference is sufficiently widespread, since a broad range of parameters possess nearly identical patterns of silent site variability.     

Competition strategies and correlated selection on responses to polyandry in the seed beetle Callosobruchus maculatus

Abstract Polyandry reflected in multiple mating with different mates is regarded as favoured by natural selection in males but not necessarily in females, where conflicting effects on fitness components can occur. The present study aims to provide empirical evidence to predict which fitness components may be affected in this sexual conflict using a species that demonstrates potential between‐population variation in their resolution: the cowpea weevil Callosobruchus maculatus. Two strains showing contrasting competition outcomes (scramble × contest) and contrasting life‐history strategies based on trade‐offs between longevity and fecundity are crossed for subsequent selection based on larval‐competition strategy, expecting the production of a correlated response to multiple (polyandrous) mating. Such a response is expected because the scramble strain shows high fecundity (and lower longevity) and would benefit from multiple mating, in contrast with the contest strain, which shows high juvenile mortality. The scramble‐selected lines would evolve a response of increased fecundity and reduced longevity under multiple and potentially polyandrous mating but the contest‐selected lines would not respond to multiple (polyandrous) mating. Instead, both scramble‐ and contest‐selected lines show increased fecundity and reduced longevity with multiple (polyandrous) matings, which did not affect egg weight. Indirect benefits of multiple (polyandrous) mating appear to be relevant for lines showing contest competition among juveniles.     

The nature of nurture in a wild mammal's fitness

Genetic variation in fitness is required for the adaptive evolution of any trait but natural selection is thought to erode genetic variance in fitness. This paradox has motivated the search for mechanisms that might maintain a population''s adaptive potential. Mothers make many contributions to the attributes of their developing offspring and these maternal effects can influence responses to natural selection if maternal effects are themselves heritable. Maternal genetic effects (MGEs) on fitness might, therefore, represent an underappreciated source of adaptive potential in wild populations. Here we used two decades of data from a pedigreed wild population of North American red squirrels to show that MGEs on offspring fitness increased the population''s evolvability by over two orders of magnitude relative to expectations from direct genetic effects alone. MGEs are predicted to maintain more variation than direct genetic effects in the face of selection, but we also found evidence of maternal effect trade-offs. Mothers that raised high-fitness offspring in one environment raised low-fitness offspring in another environment. Such a fitness trade-off is expected to maintain maternal genetic variation in fitness, which provided additional capacity for adaptive evolution beyond that provided by direct genetic effects on fitness.     

The effect of pathogens on selection against deleterious mutations in Drosophila melanogaster

In natural populations, fitness is reduced by both deleterious mutations and parasites. Few studies have examined interactions between these two factors, particularly at the level of individual genes. We examined how the presence of a bacterial pathogen, Pseudomonas aeruginosa, affected the selection against each of eight deleterious mutations in Drosophila melanogaster. We found that mutations tended to become more deleterious in the presence of disease. This increase in the average selection was primarily due to three genes with the remainder showing little evidence of change.     

GENOTYPE-BY-ENVIRONMENT INTERACTIONS FOR FITNESS OF ERIGERON ANNUUS SHOW FINE-SCALE SELECTIVE HETEROGENEITY

The results of natural selection depend critically on whether variation in fitness is finegrained or coarse-grained with respect to dispersal, but little is known of the spatial scale of fitness variation in natural populations. For most evolutionary questions, environmental heterogeneity must be defined by reversals in the relative fitness of genotypes; absolute fitness may vary, but if genotypes respond in parallel then selection is uniform. Thus, measurements of genotype-by-environment (G × E) interactions for fitness are necessary to understand patterns of variation in natural selection.     

Characterizing selection in black‐throated blue warblers using a sexual network approach

Our understanding of trait evolution is built upon studies that examine the correlation between traits and fitness, most of which implicitly assume all individuals experience similar selective environments. However, accounting for differences in selective pressures, such as variation in the social environment, can advance our understanding of how selection shapes individual traits and subsequent fitness. In this study, we test whether variation in the social environment affects selection on individual phenotype. We apply a new sexual network framework to quantify each male's social environment as the mean body size of his primary competitors. We test for direct and social selection on male body size using a 10‐year data set on black‐throated blue warblers (Setophaga caerulescens), a territorial species for which body size is hypothesized to mediate competition for mates. We found that direct selection on body size was weak and nonsignificant, as was social selection via the body size of the males' competitors. Analysing both types of selection simultaneously allows us to firmly reject a role for body size in competitive interactions between males and subsequent male fitness in this population. We evaluate the application of the sexual network approach to empirical data and suggest that other phenotypic traits such as song characteristics and plumage may be more relevant than body size for male–male competition in this small passerine bird.     

The Environment Affects Epistatic Interactions to Alter the Topology of an Empirical Fitness Landscape

The fitness effect of mutations can be influenced by their interactions with the environment, other mutations, or both. Previously, we constructed 32 ( = 2⁵) genotypes that comprise all possible combinations of the first five beneficial mutations to fix in a laboratory-evolved population of Escherichia coli. We found that (i) all five mutations were beneficial for the background on which they occurred; (ii) interactions between mutations drove a diminishing returns type epistasis, whereby epistasis became increasingly antagonistic as the expected fitness of a genotype increased; and (iii) the adaptive landscape revealed by the mutation combinations was smooth, having a single global fitness peak. Here we examine how the environment influences epistasis by determining the interactions between the same mutations in two alternative environments, selected from among 1,920 screened environments, that produced the largest increase or decrease in fitness of the most derived genotype. Some general features of the interactions were consistent: mutations tended to remain beneficial and the overall pattern of epistasis was of diminishing returns. Other features depended on the environment; in particular, several mutations were deleterious when added to specific genotypes, indicating the presence of antagonistic interactions that were absent in the original selection environment. Antagonism was not caused by consistent pleiotropic effects of individual mutations but rather by changing interactions between mutations. Our results demonstrate that understanding adaptation in changing environments will require consideration of the combined effect of epistasis and pleiotropy across environments.     

The Distribution of Fitness Effects of Beneficial Mutations in Pseudomonas aeruginosa

Understanding how beneficial mutations affect fitness is crucial to our understanding of adaptation by natural selection. Here, using adaptation to the antibiotic rifampicin in the opportunistic pathogen Pseudomonas aeruginosa as a model system, we investigate the underlying distribution of fitness effects of beneficial mutations on which natural selection acts. Consistent with theory, the effects of beneficial mutations are exponentially distributed where the fitness of the wild type is moderate to high. However, when the fitness of the wild type is low, the data no longer follow an exponential distribution, because many beneficial mutations have large effects on fitness. There is no existing population genetic theory to explain this bias towards mutations of large effects, but it can be readily explained by the underlying biochemistry of rifampicin–RNA polymerase interactions. These results demonstrate the limitations of current population genetic theory for predicting adaptation to severe sources of stress, such as antibiotics, and they highlight the utility of integrating statistical and biophysical approaches to adaptation.     

Antagonistic pleiotropy in species with separate sexes,and the maintenance of genetic variation in life‐history traits and fitness

Antagonistic pleiotropy (AP)—where alleles of a gene increase some components of fitness at a cost to others—can generate balancing selection, and contribute to the maintenance of genetic variation in fitness traits, such as survival, fecundity, fertility, and mate competition. Previous theory suggests that AP is unlikely to maintain variation unless antagonistic selection is strong, or AP alleles exhibit pronounced differences in genetic dominance between the affected traits. We show that conditions for balancing selection under AP expand under the likely scenario that the strength of selection on each fitness component differs between the sexes. Our model also predicts that the vast majority of balanced polymorphisms have sexually antagonistic effects on total fitness, despite the absence of sexual antagonism for individual fitness components. We conclude that AP polymorphisms are less difficult to maintain than predicted by prior theory, even under our conservative assumption that selection on components of fitness is universally sexually concordant. We discuss implications for the maintenance of genetic variation, and for inferences of sexual antagonism that are based on sex‐specific phenotypic selection estimates—many of which are based on single fitness components.     

Mate choice for non-additive genetic benefits: a resolution to the lek paradox

In promiscuous mating systems, females often show a consistent preference to mate with one or a few males, presumably to acquire heritable genetic benefits for their offspring. However, strong directional selection should deplete additive genetic variation in fitness and consequently any benefit to expressing the preference by females (referred to as the lek paradox). Here, we provide a novel resolution that examines non-additive genetic benefits, such as overdominance or inbreeding, as a source of genetic variation. Focusing on the inbreeding coefficient f and overdominance effects, we use dynamic models to show that (1) f can be inherited from sire to offspring, (2) populations with females that express a mating preferences for outbred males (low f) maintain higher genetic variation than populations with females that mate randomly, and (3) preference alleles for outbred males can invade populations even when the alleles are associated with a fecundity cost. We show that non-additive genetic variation due to overdominance can be converted to additive genetic variation and becomes “heritable” when the frequencies of alternative homozygous genotypes at fitness loci deviate from equality. Unlike previous models that assume an infinite population size, we now show that genetic drift in finite populations can lead to the necessary deviations in the frequencies of homozygous genotypes. We also show that the “heritability of f,” and hence the benefit to a mating preference for non-additive genetic benefits, is highest in small populations and populations in which a smaller number of loci contribute to fitness via overdominance. Our model contributes to the solution of the lek paradox.     

Inclusive fitness,asymmetric competition and kin selection in plants

The findings that some plants alter their competitive phenotype in response to genetic relatedness of its conspecific neighbour (and presumed competitor) has spurred an increasing interest in plant kin‐interactions. This phenotypic response suggests the ability to assess the genetic relatedness of conspecific competitors, proposing kin selection as a process that can influence plant competitive interactions. Kin selection can favour restrained competitive growth towards kin, if the fitness loss from reducing own growth is compensated by increased fitness in the related neighbour. This may lead to positive frequency dependency among related conspecifics with important ecological consequences for species assemblage and coexistence. However, kin selection in plants is still controversial. First, many studies documenting a plastic response to neighbour relatedness do not estimate fitness consequences of the individual that responds, and when estimated, fitness of individuals grown in competition with kin did not necessarily exceed that of individuals grown in non‐kin groups. Although higher fitness in kin groups could be consistent with kin selection, this could also arise from mechanisms like asymmetric competition in the non‐kin groups. Here we outline the main challenges for studying kin selection in plants taking genetic variation for competitive ability into account. We emphasize the need to measure inclusive fitness in order to assess whether kin selection occurs, and show under which circumstances kin selected responses can be expected. We also illustrate why direct fitness estimates of a focal plant, and group fitness estimates are not suitable for documenting kin selection. Importantly, natural selection occurs at the individual level and it is the inclusive fitness of an individual plant – not the mean fitness of the group – that can capture if a differential response to neighbour relatedness is favoured by kin selection.     

Invasion of cooperators in lattice populations: Linear and non-linear public good games

A generalized version of the N-person volunteer's dilemma (NVD) Game has been suggested recently for illustrating the problem of N-person social dilemmas. Using standard replicator dynamics it can be shown that coexistence of cooperators and defectors is typical in this model. However, the question of how a rare mutant cooperator could invade a population of defectors is still open.     

Fitness effects of mutations in bacteria

Mutation is the primary source of variation in any organism. Without it, natural selection cannot operate and organisms cannot adapt to novel environments. Mutation is also generally a source of defect: many mutations are not neutral but cause fitness decreases in the organisms where they arise. In bacteria, another important source of variation is horizontal gene transfer. This source of variation can also cause beneficial or deleterious effects. Determining the distribution of fitness effects of mutations in different environments and genetic backgrounds is an active research field. In bacteria, knowledge of these distributions is key for understanding important traits. For example, for determining the dynamics of microorganisms with a high genomic mutation rate (mutators), and for understanding the evolution of antibiotic resistance, and the emergence of pathogenic traits. All of these characteristics are extremely relevant for human health both at the individual and population levels. Experimental evolution has been a valuable tool to address these questions. Here, we review some of the important findings of mutation effects in bacteria revealed through laboratory experiments.     

Phenotypic selection and covariation in the life‐history traits of elephant seals: heavier offspring gain a double selective advantage

Early developmental conditions contribute to individual heterogeneity of both phenotypic traits and fitness components, ultimately affecting population dynamics. Although the demographic consequences of ontogenic growth are best quantified using an integrated measure of fitness, most analyses to date have instead studied individual fitness components in isolation. Here, we estimated phenotypic selection on weaning mass in female southern elephant seals Mirounga leonina by analyzing individual‐based data collected between 1986 and 2016 with capture–recapture and matrix projection models. In support of a hypothesis predicting a gradual decrease of weaning mass effects with time since weaning (the replacement hypothesis), we found that the estimated effects of weaning mass on future survival and recruitment probability was of intermediate duration (rather than transient or permanent). Heavier female offspring had improved odds of survival in early life and a higher probability to recruit at an early age. The positive link between weaning mass and recruitment age is noteworthy, considering that pre‐recruitment mortality already imposed a strong selective filter on the population, leaving only the most ‘robust’ individuals to reproduce. The selection gradient on asymptotic population growth rate, a measure of mean absolute fitness, was weaker than selection on first‐year survival and recruitment probabilities. Weaker selection on mean fitness occurs because weaning mass has little impact on adult survival, the fitness component to which the population growth of long‐lived species is most sensitive. These results highlight the need to interpret individual variation in phenotypic traits in a context that considers the demographic pathways between the trait and an inclusive proxy of individual fitness. Although variation in weaning mass do not translate to permanent survival differences among individuals in adulthood, it explains heterogeneity and positive covariation between survival and breeding in early life, which contribute to between‐individual variation in fitness.     

Influence of previous agonistic interactions with conspecifics on contest decisions

Recent wins and losses can inform individuals about their relative fighting abilities and modify their subsequent contest decisions. Using a mangrove rivulus, Kryptolebias marmoratus, we tested the hypothesis that visual and limited physical interactions can also convey information and modify subsequent contest decisions. Individuals were exposed to a stronger or weaker conspecific through a glass or a mesh partition before a contest with a size‐matched naïve opponent. Individuals were expected to (a) assess themselves to have worse/better fighting ability and behave less/more aggressively after having interacted with a stronger/weaker conspecific and (b) display different degrees of behavioural modifications for the two partition treatments (mesh‐partition > glass‐partition). The results showed that interactions with a stronger/weaker conspecific through a glass partition did not have a strong effect on the fish's subsequent contest behaviour. Restricted physical interaction with a stronger/weaker conspecific through a mesh partition, however, had an unexpected effect, causing individuals to behave more/less aggressively (matching the behaviour of the conspecifics) and/or win more/fewer subsequent contests. These results indicate that contest resolution is important for the fish to exhibit the loser–winner effects (i.e. behaving less/more aggressively after having lost/won against a stronger/weaker conspecific) detected in previous studies of the fish. We propose and discuss the possibility that the “behavioural matching” of the mesh‐partition treatment results from unresolved physical interactions with a stronger/weaker conspecific causing the individuals to either anticipate stronger/weaker opponents in subsequent competitions or assess themselves to be an equally good/bad fighter as the conspecific. The results of previous studies and the present study of the fish show that pre‐exposing an individual to the same type of conspecifics could elicit diverse, sometimes opposite, behavioural responses depending on how the individual is permitted to interact with the conspecific.