THE PROBABILITY OF PEAK SHIFTS IN A FOUNDER POPULATION. II. AN ADDITIVE POLYGENIC TRAIT

Stochastic shifts between two alternative stable equilibria in an additive polygenic system are modelled. The effect of selection on the character is represented by a double-peaked function relating individual fitness to phenotypic value. The mean of a large population will equilibrate near one of the two peaks, although with weak selection there may be a substantial displacement from the closest peak, due to the attraction exerted by the other peak. It is assumed that a small population is founded as a random sample from a large population at equilibrium under selection, and that genetic drift and selection interact to determine the evolution of the mean and variance of the polygenic character during the phase of exponential population growth that follows the foundation of the population. The effects on the frequencies of peak shifts of selectively induced linkage disequilibrium, randomly induced linkage disequilibrium, and random deviations from Hardy-Weinberg equilibrium are investigated by computer simulation. The results are compared with the probabilities of shifts calculated by an approximate analytic method. It is found that the approximations are reasonably accurate when the heights of the peaks in fitness are similar, but the approximations fail when one of the peaks is much higher than the other. The probability of a peak shift is shown to be a decreasing function of the strength of selection on the character. Although substantial changes in phenotypic mean can be induced by a founder event, the probability of a peak shift that induces a significant degree of reproductive isolation is low. The significance of these findings in relation to theories of speciation is discussed.     

Experimental evidence for multivariate stabilizing sexual selection

Stabilizing selection is a fundamental concept in evolutionary biology. In the presence of a single intermediate optimum phenotype (fitness peak) on the fitness surface, stabilizing selection should cause the population to evolve toward such a peak. This prediction has seldom been tested, particularly for suites of correlated traits. The lack of tests for an evolutionary match between population means and adaptive peaks may be due, at least in part, to problems associated with empirically detecting multivariate stabilizing selection and with testing whether population means are at the peak of multivariate fitness surfaces. Here we show how canonical analysis of the fitness surface, combined with the estimation of confidence regions for stationary points on quadratic response surfaces, may be used to define multivariate stabilizing selection on a suite of traits and to establish whether natural populations reside on the multivariate peak. We manufactured artificial advertisement calls of the male cricket Teleogryllus commodus and played them back to females in laboratory phonotaxis trials to estimate the linear and nonlinear sexual selection that female phonotactic choice imposes on male call structure. Significant nonlinear selection on the major axes of the fitness surface was convex in nature and displayed an intermediate optimum, indicating multivariate stabilizing selection. The mean phenotypes of four independent samples of males, from the same population as the females used in phonotaxis trials, were within the 95% confidence region for the fitness peak. These experiments indicate that stabilizing sexual selection may play an important role in the evolution of male call properties in natural populations of T. commodus.     

The conflict between natural and artificial selection in finite populations

Summary A single locus model of the interaction between natural selection and artificial selection for a quantitative character in a finite population, assuming heterozygote superiority in natural fitness but additive action on the character, has been studied using transition probability matrices.If natural selection is strong enough to create a selection plateau in which genetic variance declines relatively slowly, then the total response to artificial selection prior to the plateau will be much less than that expected in the absence of natural selection, and the half-life of response will be shorter. Such a plateau is likely to have a large proportion, if not all, of the original genetic variance still present. In selection programmes using laboratory animals, it seems likely that the homozygote favoured by artificial selection must be very unfit before such a plateau will occur. A significant decrease in population fitness as a result of artificial selection does not necessarily imply that the metric character is an important adaptive character.These implications of this model of natural selection are very similar to those derived by James (1962) for the optimum model of natural selection. In fact, there seems to be no aspect of the observable response to artificial selection that would enable anyone to distinguish between these two models of natural selection.     

Epistasis Can Facilitate the Evolution of Reproductive Isolation by Peak Shifts: A Two-Locus Two-Allele Model

The influence of epistasis on the evolution of reproductive isolation by peak shifts is studied in a two-locus two-allele model of a quantitative genetic character under stabilizing selection. Epistasis is introduced by a simple multiplicative term in the function that maps gene effects onto genotypic values. In the model with only additive effects on the trait, the probability of a peak shift and the amount of reproductive isolation are always inversely related, i.e., the higher the peak shift rate, the lower the amount of reproductive isolation caused by the peak shift. With epistatic characters there is no consistent relationship between these two values. Interestingly, there are causes where both transition rates as well as the amount of reproductive isolation are increased relative to the additive model. This effect has two main causes: a shift in the location of the transition point, and the hybrids between the two alternative optimal genotypes have lower average fitness in the epistatic case. A review of the empirical literature shows that the fitness relations resulting in higher peak shift rates and more reproductive isolation are qualitatively the same as those observed for genes causing hybrid inferiority.     

Peak shifts and extinction under sex-specific selection

A well-known property of sexual selection combined with a cross-sex genetic correlation (r_mf) is that it can facilitate a peak shift on the adaptive landscape. How do these diversifying effects of sexual selection + r_mf balance with the constraints imposed by such sexual antagonism, to affect the macroevolution of sexual dimorphism? Here, I extend existing quantitative genetic models of evolution on complex adaptive landscapes. Beyond recovering classical predictions for the conditions promoting a peak shift, I show that when r_mf is moderate to strong, relatively weak sexual selection is required to induce a peak shift in males only. Increasing the strength of sexual selection leads to a sexually concordant peak shift, suggesting that macroevolutionary rates of sexual dimorphism may be largely decoupled from the strength of within-population sexual selection. Accounting explicitly for demography further reveals that sex-specific peak shifts may be more likely to be successful than concordant shifts in the face of extinction, especially when natural selection is strong. An overarching conclusion is that macroevolutionary patterns of sexual dimorphism are unlikely to be readily explained by within-population estimates of selection or constraint alone.     

ASSORTATIVE MATING AND THE ADAPTIVE LANDSCAPE

The ability of a population to shift from one adaptive peak to another was examined for a two-locus model with different degrees of assortative mating, selection, and linkage. As expected, if the proportion of the population that mates assortatively increases, so does its ability to shift to a new peak. Assortative mating affects this process by allowing the mean fitness of a population to increase monotonically as it passes through intermediate gene frequencies on the way to a new, higher, homozygotic peak. Similarly, if the height of the new peak increases or selection against intermediates becomes less severe, the population becomes more likely to shift to a new peak. Close linkage also helps the shift to a new adaptive peak and acts similarly to assortative mating, but it is not necessary for such a shift as was previously thought. When a population shifts to a new peak, the number of generations required is significantly less than that needed to return to the original peak when that happens. The short period of time required may be an explanation for rapid changes in the geological record. Under extremely high degrees of assortative mating, the shift takes longer, presumably because of the difficulty of breaking up less favored allelic combinations.     

A SIMULATION OF WRIGHT'S SHIFTING-BALANCE PROCESS: MIGRATION AND THE THREE PHASES

Wright partitioned the shifting-balance process into three phases. Phase one is the shift of a deme within a population to the domain of a higher adaptive peak from that of the historical peak. Phase two is mass selection within a deme towards that higher peak. Phase three is the conversion of additional demes to the higher peak. The migration rate between demes is critical for the existence of phases one and three. Phase one requires small effective population sizes, hence low migration rates. Phase three is optimal under high migration rates that spread the most-fit genotype from deme to deme. Thus, a population-wide peak shift requires intermediate levels of migration. By altering the rates of phases one and three, migration affects the predominant direction of mass selection within a population. This study examines the degree to which migration, through its effects on phases one and three, determines the probability of a simulated population arriving at its genotypic optimum after 12,000 generations. These simulations reveal that there is a range of migration rates for which an entire population might be expected to shift to a higher peak. Below m = 0.001 peak shifts occur frequently (phases I and II) but are not successfully exported out of subpopulations (phase III), and above 0.01 peak shifts within demes (phase I and II), required to initiate phase III, become increasingly uncommon. Because it is unlikely that real populations will have uniform migration rates from generation to generation, the probable effects of varying migration rates on broadening the range of conditions producing peak shifts are discussed.     

WHY WE ARE NOT DEAD ONE HUNDRED TIMES OVER

The possibility of pervasive weak selection at tens or hundreds of millions of sites across the genome, suggested by recent studies of silent site DNA sequence variation and divergence, raises the problem of the survival of the population in the face of the large genetic load that may result. Two alternative resolutions of this problem are presented for populations where recombination is sufficiently frequent that different sites under selection evolve independently. One invokes weak stabilizing selection, of the magnitude compatible with abundant silent site variability. This can be shown to produce only a modest genetic load, due to the effectiveness of even weak stabilizing selection in keeping the trait mean close to the optimum. The other invokes soft selection, whereby individuals compete for a limiting resource whose abundance determines the absolute fitness of the population. Weak purifying selection at a large number of sites produces only a small variance in fitness among individuals within the population, due to the fact that most sites are fixed rather than polymorphic. Even when it produces a large genetic load, it is compatible with the observations on fitness variance when selection is soft. It may be very difficult to distinguish between these two possibilities.     

An analysis of continent-wide patterns of sexual selection in a passerine bird

Patterns of selection are widely believed to differ geographically, causing adaptation to local environmental conditions. However, few studies have investigated patterns of phenotypic selection across large spatial scales. We quantified the intensity of selection on morphology in a monogamous passerine bird, the barn swallow Hirundo rustica, using 6495 adults from 22 populations distributed across Europe and North Africa. According to the classical Darwin-Fisher mechanism of sexual selection in monogamous species, two important components of fitness due to sexual selection are the advantages that the most attractive males acquire by starting to breed early and their high annual fecundity. We estimated directional selection differentials on tail length (a secondary sexual character) and directional selection gradients after controlling for correlated selection on wing length and tarsus length with respect to these two fitness components. Phenotype and fitness components differed significantly among populations for which estimates were available for more than a single year. Likewise, selection differentials and selection gradients differed significantly among populations for tail length, but not for the other two characters. Sexual selection differentials differed significantly from zero across populations for tail length, particularly in males. Controlling statistically for the effects of age reduced the intensity of selection by 60 to 81%, although corrected and uncorrected estimates were strongly positively correlated. Selection differentials and gradients for tail length were positively correlated between the sexes among populations for selection acting on breeding date, but not for fecundity selection. The intensity of selection with respect to breeding date and fecundity were significantly correlated for tail length across populations. Sexual size dimorphism in tail length was significantly correlated with selection differentials with respect to breeding date for tail length in male barn swallows across populations. These findings suggest that patterns of sexual selection are consistent across large geographical scales, but also that they vary among populations. In addition, geographical patterns of phenotypic selection predict current patterns of phenotypic variation among populations, suggesting that consistent patterns of selection have been present for considerable amounts of time.     

Reproductive character displacement and the genetics of gamete recognition in tropical sea urchins

Reproductive character displacement occurs when sympatric and allopatric populations of a species differ in traits crucial to reproduction, and it is commonly thought of as a signal of selection acting to limit hybridization. Most documented cases of reproductive character displacement involve characters that are poorly understood at the genetic level, and rejecting alternative hypotheses for biogeographic shifts in reproductive traits is often very difficult. In sea urchins, the gamete recognition protein bindin evolves under positive selection when species are broadly sympatric, suggesting character displacement may be operating in this system. We sampled sympatric and allopatric populations of two species in the sea urchin genus Echinometra for variation in bindin and for the mitochondrial cytochrome oxidase I to examine patterns of population differentiation and molecular evolution at a reproductive gene. We found a major shift in bindin alleles between central Pacific (allopatric) and western Pacific (sympatric) populations of E. oblonga. Allopatric populations of E. oblonga are polyphyletic with E. sp. C at bindin, whereas sympatric populations of the two species are reciprocally monophyletic. There is a strong signal of positive selection (P(N)/P(S) = 4.5) in the variable region of the first exon of bindin, which is associated with alleles found in sympatric populations of E. oblonga. These results indicate that there is a strong pattern of reproductive character displacement between E. oblonga and E. sp. C and that the divergence is driven by selection. There is much higher population structure in sympatric populations at the bindin locus than at the neutral mitochondrial locus, but this difference is not seen in allopatric populations. These data suggest a pattern of speciation driven by selection for local gamete coevolution as a result of interactions between sympatric species. Although this pattern is highly suggestive of speciation by reinforcement, further research into hybrid fitness and egg-sperm interactions is required to address this potential mechanism for character displacement.     

TESTS OF INBREEDING EFFECTS ON HOST-SHIFT POTENTIAL IN THE PHYTOPHAGOUS BEETLE OPHRAELLA COMMUNA

Although inbreeding, on average, decreases additive genetic variance, some inbred populations may show an increase in phenotypic variance for some characters. In those populations with increased phenotypic variance, character changes by peak shifts may occur because of the effects of the higher variance on the adaptive landscape. A population's increased phenotypic variance may place it in the domain of attraction of a new adaptive peak or increase the likelihood of a selection-driven peak shift as the landscape of mean fitness flattens. The focus of this study was to test for increased variance, in inbred populations, in a behavioral character involved in adaptive diversification and probably speciation. We examined the effect of inbreeding on feeding responses of the leaf beetle Ophraella communa in a series of inbred lineages across a range of levels of inbreeding (f = 0.25, 0.375, 0.5). We measured the feeding response of inbred lineages of O. communa on its normal host, Ambrosia artemisiifolia, and on two novel plants, Chrysopsis villosa and Iva frutescens, that are the hosts of other Ophraella species. The results show that feeding responses on the different plants are not correlated, indicating that the feeding responses to the different plants are to some degree genetically independent. Despite apparent genetic variation in lineage feeding responses, we could not statistically demonstrate increases in phenotypic variance within the lineages. Thus, the experimental results do not support the idea that host shifts in this beetle evolved by peak shifts in bottlenecked populations.     

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.     

GENE FLOW FROM DOMESTICATED SPECIES TO WILD RELATIVES: MIGRATION LOAD IN A MODEL OF MULTIVARIATE SELECTION

Domesticated species frequently spread their genes into populations of wild relatives through interbreeding. The domestication process often involves artificial selection for economically desirable traits. This can lead to an indirect response in unknown correlated traits and a reduction in fitness of domesticated individuals in the wild. Previous models for the effect of gene flow from domesticated species to wild relatives have assumed that evolution occurs in one dimension. Here, I develop a quantitative genetic model for the balance between migration and multivariate stabilizing selection. Different forms of correlational selection consistent with a given observed ratio between average fitness of domesticated and wild individuals offsets the phenotypic means at migration–selection balance away from predictions based on simpler one-dimensional models. For almost all parameter values, correlational selection leads to a reduction in the migration load. For ridge selection, this reduction arises because the distance the immigrants deviates from the local optimum in effect is reduced. For realistic parameter values, however, the effect of correlational selection on the load is small, suggesting that simpler one-dimensional models may still be adequate in terms of predicting mean population fitness and viability.     

The evolution of genetic canalization under fluctuating selection

Abstract.— If the direction of selection changes from generation to generation, the ability to respond to selection is maladaptive: the response to selection in one generation leads to reduced fitness in the next. Because the response is determined by the amount of genetic variance expressed at the phenotypic level, rapidly fluctuating selection should favor modifier genes that reduce the phenotypic effect of alleles segregating at structural loci underlying the trait. Such reduction in phenotypic expression of genetic variation has been named "genetic canalization." I support this argument with a series of two- and multilocus models with alternating linear selection and Gaussian selection with fluctuating optimum. A canalizing modifier gene affects the fitness of its carriers in three ways: (1) it reduces the phenotypic consequences of genetic response to previous selection; (2) it reduces the genetic response to selection, which is manifested as linkage disequilibrium between the modifier and structural loci; and (3) it reduces the phenotypic variance. The first two effects reduce fitness under directional selection sustained for several generations, but improve fitness when the direction of selection has just been reversed. The net effect tends to favor a canalizing modifier under rapidly fluctuating selection regimes (period of eight generations or less). The third effect improves fitness of the modifier allele if the fitness function is convex and reduces it if the function is concave. Under fluctuating Gaussian selection, the population is more likely to experience the concave portion of the fitness function when selection is stronger. Therefore, only weak to moderately strong fluctuating Gaussian selection favors genetic canalization. This paper considerably broadens the conditions that favor genetic canalization, which so far has only been postulated to evolve under long-term stabilizing selection.     

Does runaway sexual selection work in finite populations?

Fisher's runaway process is an explanation for the origin of conspicuous features which make one sex more attractive to the other. It has been suggested that it could lead to the evolution of sexual characters that significantly impair viability. Runaway selection requires a genetic correlation between alleles affecting the sexual character and alleles affecting the preference. Correlations may be expected because of assortative mating when there is variation in both the sexual character and sexual preferences. We contend that such genetic correlations are unlikely to persist in finite populations. We present simulations which confirm our expectations. They suggest that assortative mating is inefficient at generating correlations, especially if sexual selection maintains characters away from their viability optimum. In finite populations, such weak correlations will be overwhelmed by drift.     

Inter‐ and intrasexual genetic correlations of exaggerated traits and locomotor activity

Exaggerated traits in males can be costly and therefore can negatively affect fitness. Although these costs are thought to be male specific, traits that have a negative effect due to exaggeration are often shared between the sexes as life‐history traits. When there are genetic intersexual correlations for these shared characters, the evolution of the exaggerated traits can impose these costs on nonadorned females through the intersexual correlation. Thus, the exaggerated traits can constrain optimum development of female characters, even if the females lack these exaggerations completely. However, investigation of this pattern has been largely ignored, and thus, it is necessary to investigate genetic architectures of these traits within and across the sexes. Male flour beetles, Gnatocerus cornutus, have enlarged mandibles that are used in male–male competition, but females lack this character completely. Using a traditional full‐sib/half‐sib breeding design, we detected a negative intrasexual genetic correlation between male weapon size and locomotor activity, but not an intersexual genetic correlation for locomotor activity. After subjecting this weapon to 17 generations of bidirectional selection, we found a correlated response to locomotor activity in the male, whereas there was no correlated response in the female. Our results suggest that the costs of exaggerated traits to locomotion are not imposed on females and would be male specific. This is partly explained by genetic decoupling of locomotor activities across the sexes.     

Phenotypic selection in a natural population of Impatiens pallida Nutt. (Balsaminaceae)

In the annual plant Impatiens pallida, individuals exhibit a floral heteromorphism consisting of autogamously selfing, cleistogamous (CL) flowers and partially outcrossing, chasmogamous (CH) flowers. As part of an investigation into natural selection and mating system evolution in I. pallida, we measured the magnitude and direction of phenotypic selection on nine life history characters (two traits measured on three dates, one measured on two dates and one measured once). Three of these characters were positively correlated with the ratio of CH/CL flowers produced per plant, which is an important determinant of the mating system. Values for the nine characters and three different measures of fitness (viability, fecundity, lifetime) were estimated for 500 plants in five locations over a single growing season. Based on lifetime fitness, linear selection differentials were significant for all nine characters, indicating a selective advantage to tall, leafy, highly branched plants that flowered early. However, only two of these characters had a direct effect on fitness. Selection was significant on all nine characters when based on fecundity as well as lifetime fitness; however, only three of five characters examined had significant selection based on viability fitness. For all fitness components, the frequency of significant linear and nonlinear selection coefficients was comparable (23% vs 17% of all cases, respectively), but nonlinear coefficients were generally larger. Finally, the magnitude and direction of direct linear selection was heterogeneous among locations, for all characters and all fitness components. Collectively these results suggest that selection is strong, favouring large size, high allocation to reproduction and high CH/CL flower ratios. However, any directional evolutionary changes in vegetative or reproductive characters may be constrained by strong non-linear and correlational selection.     

Subtle but ubiquitous selection on body size in a natural population of collared flycatchers over 33 years

Understanding the magnitude and long‐term patterns of selection in natural populations is of importance, for example, when analysing the evolutionary impact of climate change. We estimated univariate and multivariate directional, quadratic and correlational selection on four morphological traits (adult wing, tarsus and tail length, body mass) over a time period of 33 years (≈ 19 000 observations) in a nest‐box breeding population of collared flycatchers (Ficedula albicollis). In general, selection was weak in both males and females over the years regardless of fitness measure (fledged young, recruits and survival) with only few cases with statistically significant selection. When data were analysed in a multivariate context and as time series, a number of patterns emerged; there was a consistent, but weak, selection for longer wings in both sexes, selection was stronger on females when the number of fledged young was used as a fitness measure, there were no indications of sexually antagonistic selection, and we found a negative correlation between selection on tarsus and wing length in both sexes but using different fitness measures. Uni‐ and multivariate selection gradients were correlated only for wing length and mass. Multivariate selection gradient vectors were longer than corresponding vector of univariate gradients and had more constrained direction. Correlational selection had little importance. Overall, the fitness surface was more or less flat with few cases of significant curvature, indicating that the adaptive peak with regard to body size in this species is broader than the phenotypic distribution, which has resulted in weak estimates of selection.     

GENOTYPE-ENVIRONMENT INTERACTION AND THE EVOLUTION OF PHENOTYPIC PLASTICITY

Studies of spatial variation in the environment have primarily focused on how genetic variation can be maintained. Many one-locus genetic models have addressed this issue, but, for several reasons, these models are not directly applicable to quantitative (polygenic) traits. One reason is that for continuously varying characters, the evolution of the mean phenotype expressed in different environments (the norm of reaction) is also of interest. Our quantitative genetic models describe the evolution of phenotypic response to the environment, also known as phenotypic plasticity (Gause, 1947), and illustrate how the norm of reaction (Schmalhausen, 1949) can be shaped by selection. These models utilize the statistical relationship which exists between genotype-environment interaction and genetic correlation to describe evolution of the mean phenotype under soft and hard selection in coarse-grained environments. Just as genetic correlations among characters within a single environment can constrain the response to simultaneous selection, so can a genetic correlation between states of a character which are expressed in two environments. Unless the genetic correlation across environments is ± 1, polygenic variation is exhausted, or there is a cost to plasticity, panmictic populations under a bivariate fitness function will eventually attain the optimum mean phenotype for a given character in each environment. However, very high positive or negative correlations can substantially slow the rate of evolution and may produce temporary maladaptation in one environment before the optimum joint phenotype is finally attained. Evolutionary trajectories under hard and soft selection can differ: in hard selection, the environments with the highest initial mean fitness contribute most individuals to the mating pool. In both hard and soft selection, evolution toward the optimum in a rare environment is much slower than it is in a common one. A subdivided population model reveals that migration restriction can facilitate local adaptation. However, unless there is no migration or one of the special cases discussed for panmictic populations holds, no geographical variation in the norm of reaction will be maintained at equilibrium. Implications of these results for the interpretation of spatial patterns of phenotypic variation in natural populations are discussed.     

Statistical Genetics of an Annual Plant, Impatiens Capensis. II. Natural Selection

Measurement of natural selection on correlated characters provides valuable information on fitness surfaces, patterns of directional, stabilizing, or disruptive selection, mechanisms of fitness variation operating in nature, and possible spatial variation in selective pressures. We examined effects of seed weight, germination date, plant size, early growth, and late growth on individual fitness. Path analysis showed that most characters had direct or indirect effects on individual fitness, indicating directional selection. For most early life-cycle characters, indirect effects via later characters exceed the direct causal effect on fitness. Selection gradients were uniform across the experimental site. There was no evidence for stabilizing or disruptive selection. We discuss several definitions of stabilizing and disruptive selection. Although early events in the life of an individual have important causal effects on subsequent characters and fitness, there is no detectable genetic variance for most of these characters, so little or no genetic response to natural selection is expected.