Adaptive topography of fluctuating selection in a Mendelian population

An adaptive topography is derived for a large randomly mating diploid population under weak density-independent selection in a fluctuating environment. Assuming a stationary distribution of environmental states with no temporal autocorrelation, a diffusion approximation for population size and allele frequency, p, reveals that the expected change in p involves the gradient with respect to p of the stochastic intrinsic rate of increase (the density-independent long-run growth rate), r = r - sigma 2 e/2, where r is the mean Malthusian fitness in the average environment and is the environmental variance in population growth rate. The expected relative fitness of a genotype is its Malthusian fitness in the average environment minus the covariance of its fitness with population growth rate. The influence of fitness correlation between genotypes is illustrated by an analysis of the Haldane-Jayakar model of fluctuating selection on a single diallelic locus, and on two loci with additive effects on a quantitative character.     

Darwinian fitness and the intensity of natural selection: studies in sensitivity analysis

Darwinian fitness, the capacity of a variant type to establish itself in competition with the resident population, is determined by evolutionary entropy, a measure of the uncertainty in age of the mother of a randomly chosen newborn. This article shows that the intensity of natural selection, as measured by the sensitivity of entropy with respect to changes in the age-specific fecundity and mortality variables, is a convex function of age, decreasing at early and increasing at later ages. We exploit this result to provide quantitative evolutionary explanations of the large variation in survivorship curves observed in natural populations. Previous studies to explain variation in survivorship curves have been based on the proposition that Darwinian fitness is determined by the Malthusian parameter. Hence the intensity of natural selection will be determined by the sensitivity of the Malthusian parameter with respect to changes in the age-specific fecundity and mortality variables. This measure of the selection gradient is known to be a decreasing function of age, with implications which are inconsistent with empirical observations of survivorship curves in human and animal populations. The analysis described in this paper point to the mitigated import of sensitivity studies based on the Malthusian parameter. Our analysis provides theoretical and empirical support for the ecological and evolutionary significance of sensitivity analysis based on entropy, which is the appropriate measure of Darwinian fitness.     

Comparing environmental and genetic variance as adaptive response to fluctuating selection

Phenotypic variation within populations has two sources: genetic variation and environmental variation. Here, we investigate the coevolution of these two components under fluctuating selection. Our analysis is based on the lottery model in which genetic polymorphism can be maintained by negative frequency-dependent selection, whereas environmental variation can be favored due to bet-hedging. In our model, phenotypes are characterized by a quantitative trait under stabilizing selection with the optimal phenotype fluctuating in time. Genotypes are characterized by their phenotypic offspring distribution, which is assumed to be Gaussian with heritable variation for its mean and variance. Polymorphism in the mean corresponds to genetic variance while the width of the offspring distribution corresponds to environmental variance. We show that increased environmental variance is favored whenever fluctuations in the selective optima are sufficiently strong. Given the environmental variance has evolved to its optimum, genetic polymorphism can still emerge if the distribution of selective optima is sufficiently asymmetric or leptokurtic. Polymorphism evolves in a diagonal direction in trait space: one type becomes a canalized specialist for the more common ecological conditions and the other type a de-canalized bet-hedger thriving on the less-common conditions. All results are based on analytical approximations, complemented by individual-based simulations.     

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.     

Probing the adaptive landscape using experimental islands: density-dependent natural selection on lizard body size

Anolis lizards in the Greater Antilles are thought to have diversified through natural selection on body size and shape, presumably due to interspecific competition and variation in locomotor performance. Here we measure natural selection on body size over three years and across seven replicate populations of the brown anole, A. sagrei. We experimentally manipulated an important component of the environment (population density) on several small islands to test the role of density in driving natural selection. Results indicate that the strength of natural selection was proportional to population density (r2 = 0.81), and favored larger body sizes at higher density, presumably owing to the enhanced competitive ability afforded by large size. Changes in the distribution of body size by selective releases of lizards to islands show that this effect did not arise by pure density dependence, since smaller individuals were disproportionately selected against at higher densities. We measured significant broad sense heritability for body size in the laboratory (h2 = 0.55) indicating that selection in the wild could have an evolutionary response. Our results suggest an important effect of population density on natural selection in Anolis lizards.     

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.     

Evolutionarily unstable fitness maxima and stable fitness minima of continuous traits

Summary We present models of adaptive change in continuous traits for the following situations: (1) adaptation of a single trait within a single population in which the fitness of a given individual depends on the population's mean trait value as well as its own trait value; (2) adaptation of two (or more) traits within a single population; (3) adaptation in two or more interacting species. We analyse a dynamic model of these adaptive scenarios in which the rate of change of the mean trait value is an increasing function of the fitness gradient (i.e. the rate of increase of individual fitness with the individual's trait value). Such models have been employed in evolutionary game theory and are often appropriate both for the evolution of quantitative genetic traits and for the behavioural adjustment of phenotypically plastic traits. The dynamics of the adaptation of several different ecologically important traits can result in characters that minimize individual fitness and can preclude evolution towards characters that maximize individual fitness. We discuss biological circumstances that are likely to produce such adaptive failures for situations involving foraging, predator avoidance, competition and coevolution. The results argue for greater attention to dynamical stability in models of the evolution of continuous traits.     

昆虫抗药性种群相对适合度指标的改进

相对适合度(Relative fitness)是衡量害虫抗药性种群生物学变化的重要指标,用于测度昆虫对杀虫剂的适应性,由抗药性种群和敏感种群净增殖率(R0)相除获得。本文在对多种昆虫抗药性种群相对适合度研究实例分析中发现抗药性昆虫除了后代数量发生变化外,发育时间(如世代历期)也可能会发生变化。因此,提出了基于净增殖率-世代历期(T)、内禀增长率(rm)的2个相对适合度指标模型Rf=R0R/TR/ROS/TS、Rf=rmR/rm S。应用该方法对多个研究实例进行计算,基于净增殖率-世代历期的模型获得的相对适合度值与原模型值相比无显著差异,基于内禀增长率的模型计算出的相对适合度值一般高于原模型值;三个指标之间均极显著相关。改进后的适合度指标包含了抗药性种群发育时间、后代数量或者增殖潜力参数,因此,其结果更具科学性。     

Context dependence in complex adaptive landscapes: frequency and trait‐dependent selection surfaces within an adaptive radiation of Caribbean pupfishes

The adaptive landscape provides the foundational bridge between micro‐ and macroevolution. One well‐known caveat to this perspective is that fitness surfaces depend on ecological context, including competitor frequency, traits measured, and resource abundance. However, this view is based largely on intraspecific studies. It is still unknown how context‐dependence affects the larger features of peaks and valleys on the landscape which ultimately drive speciation and adaptive radiation. Here, I explore this question using one of the most complex fitness landscapes measured in the wild in a sympatric pupfish radiation endemic to San Salvador Island, Bahamas by tracking survival and growth of laboratory‐reared F2 hybrids. I present new analyses of the effects of competitor frequency, dietary isotopes, and trait subsets on this fitness landscape. Contrary to expectations, decreasing competitor frequency increased survival only among very common phenotypes, whereas less common phenotypes rarely survived despite few competitors, suggesting that performance, not competitor frequency, shapes large‐scale features of the fitness landscape. Dietary isotopes were weakly correlated with phenotype and growth, but did not explain additional survival variation. Nonlinear fitness surfaces varied substantially among trait subsets, revealing one‐, two‐, and three‐peak landscapes, demonstrating the complexity of selection in the wild, even among similar functional traits.     

r‐ and K‐selection in fluctuating populations is determined by the evolutionary trade‐off between two fitness measures: Growth rate and lifetime reproductive success

In a stable environment, evolution maximizes growth rates in populations that are not density regulated and the carrying capacity in the case of density regulation. In a fluctuating environment, evolution maximizes a function of growth rate, carrying capacity and environmental variance, tending to r‐selection and K‐selection under large and small environmental noise, respectively. Here we analyze a model in which birth and death rates depend on density through the same function but with independent strength of density dependence. As a special case, both functions may be linear, corresponding to logistic dynamics. It is shown that evolution maximizes a function of the deterministic growth rate r₀ and the lifetime reproductive success (LRS) R₀, both defined at small densities, as well as the environmental variance. Under large noise this function is dominated by r₀ and average lifetimes are small, whereas R₀ dominates and lifetimes are larger under small noise. Thus, K‐selection is closely linked to selection for large R₀ so that evolution tends to maximize LRS in a stable environment. Consequently, different quantities (r₀ and R₀) tend to be maximized at low and high densities, respectively, favoring density‐dependent changes in the optimal life history.     

On the standardization of fitness and traits in comparative studies of phenotypic selection

Comparisons of the strength and form of phenotypic selection among groups provide a powerful approach for testing adaptive hypotheses. A central and largely unaddressed issue is how fitness and phenotypes are standardized in such studies; standardization across or within groups can qualitatively change conclusions whenever mean fitness differs between groups. We briefly reviewed recent relevant literature, and found that selection studies vary widely in their scale of standardization, but few investigators motivated their rationale for chosen standardization approaches. Here, we propose that the scale at which fitness should be relativized should reflect whether selection is likely to be hard or soft; that is, the scale at which populations (or hypothetical populations in the case of a contrived experiment) are regulated. We argue that many comparative studies of selection are implicitly or explicitly focused on soft selection (i.e., frequency and density‐dependent selection). In such studies, relative fitness should preferably be calculated using within‐group means, although this approach is taken only occasionally. Related difficulties arise for the standardization of phenotypes. The appropriate scale at which standardization should take place depends on whether groups are considered to be fixed or random. We emphasize that the scale of standardization is a critical decision in empirical studies of selection that should always warrant explicit justification.     

Heritability and evolvability of fitness and nonfitness traits: Lessons from livestock

Data from natural populations have suggested a disconnection between trait heritability (variance standardized additive genetic variance, V_A) and evolvability (mean standardized V_A) and emphasized the importance of environmental variation as a determinant of trait heritability but not evolvability. However, these inferences are based on heterogeneous and often small datasets across species from different environments. We surveyed the relationship between evolvability and heritability in >100 traits in farmed cattle, taking advantage of large sample sizes and consistent genetic approaches. Heritability and evolvability estimates were positively correlated (r = 0.37/0.54 on untransformed/log scales) reflecting a substantial impact of V_A on both measures. Furthermore, heritabilities and residual variances were uncorrelated. The differences between this and previously described patterns may reflect lower environmental variation experienced in farmed systems, but also low and heterogeneous quality of data from natural populations. Similar to studies on wild populations, heritabilities for life‐history and behavioral traits were lower than for other traits. Traits having extremely low heritabilities and evolvabilities (17% of the studied traits) were almost exclusively life‐history or behavioral traits, suggesting that evolutionary constraints stemming from lack of genetic variability are likely to be most common for classical “fitness” (cf. life‐history) rather than for “nonfitness” (cf. morphological) traits.     

Natural selection and the maximization of fitness

The notion that natural selection is a process of fitness maximization gets a bad press in population genetics, yet in other areas of biology the view that organisms behave as if attempting to maximize their fitness remains widespread. Here I critically appraise the prospects for reconciliation. I first distinguish four varieties of fitness maximization. I then examine two recent developments that may appear to vindicate at least one of these varieties. The first is the ‘new’ interpretation of Fisher's fundamental theorem of natural selection, on which the theorem is exactly true for any evolving population that satisfies some minimal assumptions. The second is the Formal Darwinism project, which forges links between gene frequency change and optimal strategy choice. In both cases, I argue that the results fail to establish a biologically significant maximization principle. I conclude that it may be a mistake to look for universal maximization principles justified by theory alone. A more promising approach may be to find maximization principles that apply conditionally and to show that the conditions were satisfied in the evolution of particular traits.     

Life‐history evolution under fluctuating density‐dependent selection and the adaptive alignment of pace‐of‐life syndromes

We present a novel perspective on life‐history evolution that combines recent theoretical advances in fluctuating density‐dependent selection with the notion of pace‐of‐life syndromes (POLSs) in behavioural ecology. These ideas posit phenotypic co‐variation in life‐history, physiological, morphological and behavioural traits as a continuum from the highly fecund, short‐lived, bold, aggressive and highly dispersive ‘fast’ types at one end of the POLS to the less fecund, long‐lived, cautious, shy, plastic and socially responsive ‘slow’ types at the other. We propose that such variation in life histories and the associated individual differences in behaviour can be explained through their eco‐evolutionary dynamics with population density – a single and ubiquitous selective factor that is present in all biological systems. Contrasting regimes of environmental stochasticity are expected to affect population density in time and space and create differing patterns of fluctuating density‐dependent selection, which generates variation in fast versus slow life histories within and among populations. We therefore predict that a major axis of phenotypic co‐variation in life‐history, physiological, morphological and behavioural traits (i.e. the POLS) should align with these stochastic fluctuations in the multivariate fitness landscape created by variation in density‐dependent selection. Phenotypic plasticity and/or genetic (co‐)variation oriented along this major POLS axis are thus expected to facilitate rapid and adaptively integrated changes in various aspects of life histories within and among populations and/or species. The fluctuating density‐dependent selection POLS framework presented here therefore provides a series of clear testable predictions, the investigation of which should further our fundamental understanding of life‐history evolution and thus our ability to predict natural population dynamics.     

Determinants of male fitness: disentangling intra- and inter-sexual selection

Both intra- and inter-sexual selection may crucially determine a male's fitness. Their interplay, which has rarely been experimentally investigated, determines a male's optimal reproductive strategy and thus is of fundamental importance to the understanding of a male's behaviour. Here we investigated the relative importance of intra- and inter-sexual selection for male fitness in the common lizard. We investigated which male traits predict a male's access to reproduction allowing for both selective pressures and comparing it with a staged mating experiment excluding all types of intra-sexual selection. We found that qualitatively better males were more likely to reproduce and that sexual selection was two times stronger when allowing for both selective pressures, suggesting that inter- and intra-sexual selection determines male fitness and confirming the existence of multi-factorial sexual selection. Consequently, to optimize fitness, males should trade their investment between the traits, which are important for inter- and intra-sexual selection.     

The consequences of sexual selection in well‐adapted and maladapted populations of bean beetles†

Whether sexual selection generally promotes or impedes population persistence remains an open question. Intralocus sexual conflict (IaSC) can render sexual selection in males detrimental to the population by increasing the frequency of alleles with positive effects on male reproductive success but negative effects on female fecundity. Recent modeling based on fitness landscape theory, however, indicates that the relative impact of IaSC may be reduced in maladapted populations and that sexual selection therefore might promote adaptation when it is most needed. Here, we test this prediction using bean beetles that had undergone 80 generations of experimental evolution on two alternative host plants. We isolated and assessed the effect of maladaptation on sex‐specific strengths of selection and IaSC by cross‐rearing the two experimental evolution regimes on the alternative hosts and estimating within‐population genetic (co)variance for fitness in males and females. Two key predictions were upheld: males generally experienced stronger selection compared to females and maladaptation increased selection in females. However, maladaptation consistently decreased male‐bias in the strength of selection and IaSC was not reduced in maladapted populations. These findings imply that sexual selection can be disrupted in stressful environmental conditions, thus reducing one of the potential benefits of sexual reproduction in maladapted populations.     

Polyandry and fitness in the western harvester ant, Pogonomyrmex occidentalis

Using four highly polymorphic microsatellite markers (12-28 alleles), we gentoyped workers from 63 colonies of Pogonomyrmex occidentalis. Colonies have a single, multiply mated queen, and an average number of 6.3 patrilines per colony. Colony growth was measured over an 8-year period in the study population. Intracolonial relatedness and colony growth are correlated negatively, indicating a substantial fitness benefit to multiple mating.     

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.     

Spatial and temporal patterns of nest distribution influence sexual selection in a marine fish

In many species, the natural distribution of material resources important for reproduction can profoundly impact reproductive success among individuals and, hence, the opportunity and intensity of sexual selection. Here, we report on a field‐based experiment investigating the effects of nest aggregation on sexual selection in a fish, the sand goby Pomatoschistus minutus. We found that the distribution of potential nests (sparse versus aggregated nest treatments) affected patterns of nest colonization and reproductive success. Specifically, in the treatment with aggregated nesting resources, a greater proportion of nests remained unoccupied by sand goby males. Although the size of nesting males did not differ between treatments, eggs accumulated more rapidly when nests were sparsely distributed. We found that the opportunity for selection decreased over time with the accumulation of eggs in the nests in both the aggregated and sparse treatments. Moreover, the effect of male size on reproductive success was influenced by an interaction between nest distribution and time, with the selection gradient being highest right after nest colonization when nests were aggregated, while the opposite pattern was observed in the sparse nest treatment. Such findings highlight the vital role that environmental and social factors can play in determining the importance of male phenotypic traits (in this case, male size). More broadly, our results also underscore how the natural distribution of resources, both in space and time, can impact the strength of sexual selection acting on wild animal populations.     

Intralocus sexual conflict,adaptive sex allocation,and the heritability of fitness

Intralocus sexual conflict arises when selection favours alternative fitness optima in males and females. Unresolved conflict can create negative between‐sex genetic correlations for fitness, such that high‐fitness parents produce high‐fitness progeny of their same sex, but low‐fitness progeny of the opposite sex. This cost of sexual conflict could be mitigated if high‐fitness parents bias sex allocation to produce more offspring of their same sex. Previous studies of the brown anole lizard (Anolis sagrei) show that viability selection on body size is sexually antagonistic, favouring large males and smaller females. However, sexual conflict over body size may be partially mitigated by adaptive sex allocation: large males sire more sons than daughters, whereas small males sire more daughters than sons. We explored the evolutionary implications of these phenomena by assessing the additive genetic (co)variance of fitness within and between sexes in a wild population. We measured two components of fitness: viability of adults over the breeding season, and the number of their progeny that survived to sexual maturity, which includes components of parental reproductive success and offspring viability (RS^V). Viability of parents was not correlated with adult viability of their sons or daughters. RS^V was positively correlated between sires and their offspring, but not between dams and their offspring. Neither component of fitness was significantly heritable, and neither exhibited negative between‐sex genetic correlations that would indicate unresolved sexual conflict. Rather, our results are more consistent with predictions regarding adaptive sex allocation in that, as the number of sons produced by a sire increased, the adult viability of his male progeny increased.