The evolution of resource specialization through frequency-dependent and frequency-independent mechanisms

Levins's fitness set approach has shaped the intuition of many evolutionary ecologists about resource specialization: if the set of possible phenotypes is convex, a generalist is favored, while either of the two specialists is predicted for concave phenotype sets. An important aspect of Levins's approach is that it explicitly excludes frequency-dependent selection. Frequency dependence emerged in a series of models that studied the degree of character displacement of two consumers coexisting on two resources. Surprisingly, the evolutionary dynamics of a single consumer type under frequency dependence has not been studied in detail. We analyze a model of one evolving consumer feeding on two resources and show that, depending on the trait considered to be subject to evolutionary change, selection is either frequency independent or frequency dependent. This difference is explained by the effects different foraging traits have on the consumer-resource interactions. If selection is frequency dependent, then the population can become dimorphic through evolutionary branching at the trait value of the generalist. Those traits with frequency-independent selection, however, do indeed follow the predictions based on Levins's fitness set approach. This dichotomy in the evolutionary dynamics of traits involved in the same foraging process was not previously recognized.     

Maintenance of Genetic Variability under Strong Stabilizing Selection: A Two-Locus Model

We study a two locus model with additive contributions to the phenotype to explore the relationship between stabilizing selection and recombination. We show that if the double heterozygote has the optimum phenotype and the contributions of the loci to the trait are different, then any symmetric stabilizing selection fitness function can maintain genetic variability provided selection is sufficiently strong relative to linkage. We present results of a detailed analysis of the quadratic fitness function which show that selection need not be extremely strong relative to recombination for the polymorphic equilibria to be stable. At these polymorphic equilibria the mean value of the trait, in general, is not equal to the optimum phenotype, there exists a large level of negative linkage disequilibrium which ``hides' additive genetic variance, and different equilibria can be stable simultaneously. We analyze dependence of different characteristics of these equilibria on the location of optimum phenotype, on the difference in allelic effect, and on the strength of selection relative to recombination. Our overall result that stabilizing selection does not necessarily eliminate genetic variability is compatible with some experimental results where the lines subject to strong stabilizing selection did not have significant reductions in genetic variability.     

Probabilistic optimization of phenotype distributions: a general solution for the effects of uncertainty on natural selection?

Summary Explorations of optimizing selection often find discrepancies between the theoretically expected and observed phenotypes. Such discrepancies are usually attributed to a variety of potential constraints. We suggest that one common constraint, environmental uncertainty, may reduce the applicability of traditional deterministic or stochastic optimization methods and that many apparent discrepancies might be artifacts of these methods. Since natural selection is essentially a statistical process, we propose that a probabilistic optimization procedure, that includes all of the variability in phenotype distributions and associated fitness potential functions might offer better results. The traditional methods define an optimal gene or genotype as that which produces a phenotype distribution with a mean or other measure of central tendency that equals the value yielding the maximum fitness potential. Our method defines the optimal gene or genotype as that which produces the phenotype distribution that maximizes fitness summed or integrated over its associated fitness potential function. Often the central tendency of the phenotype distribution yielding the probabilistic optimum will differ from the deterministic expectation. This method is an extension of utility theory to any phenotypic character. We illustrate our method using an example based on Price and Waser's (1979) notion of optimal inbreeding via optimal pollen dispersal.     

UNIFICATION OF REGRESSION‐BASED METHODS FOR THE ANALYSIS OF NATURAL SELECTION

Regression analyses are central to characterization of the form and strength of natural selection in nature. Two common analyses that are currently used to characterize selection are (1) least squares–based approximation of the individual relative fitness surface for the purpose of obtaining quantitatively useful selection gradients, and (2) spline‐based estimation of (absolute) fitness functions to obtain flexible inference of the shape of functions by which fitness and phenotype are related. These two sets of methodologies are often implemented in parallel to provide complementary inferences of the form of natural selection. We unify these two analyses, providing a method whereby selection gradients can be obtained for a given observed distribution of phenotype and characterization of a function relating phenotype to fitness. The method allows quantitatively useful selection gradients to be obtained from analyses of selection that adequately model nonnormal distributions of fitness, and provides unification of the two previously separate regression‐based fitness analyses. We demonstrate the method by calculating directional and quadratic selection gradients associated with a smooth regression‐based generalized additive model of the relationship between neonatal survival and the phenotypic traits of gestation length and birth mass in humans.     

Expected relative fitness and the adaptive topography of fluctuating selection

Wright's adaptive topography describes gene frequency evolution as a maximization of mean fitness in a constant environment. I extended this to a fluctuating environment by unifying theories of stochastic demography and fluctuating selection, assuming small or moderate fluctuations in demographic rates with a stationary distribution, and weak selection among the types. The demography of a large population, composed of haploid genotypes at a single locus or normally distributed phenotypes, can then be approximated as a diffusion process and transformed to produce the dynamics of population size, N, and gene frequency, p, or mean phenotype, . The expected evolution of p or is a product of genetic variability and the gradient of the long-run growth rate of the population, , with respect to p or . This shows that the expected evolution maximizes , the mean Malthusian fitness in the average environment minus half the environmental variance in population growth rate. Thus, as a function of p or represents an adaptive topography that, despite environmental fluctuations, does not change with time. The haploid model is dominated by environmental stochasticity, so the expected maximization is not realized. Different constraints on quantitative genetic variability, and stabilizing selection in the average environment, allow evolution of the mean phenotype to undergo a stochastic maximization of . Although the expected evolution maximizes the long-run growth rate of the population, for a genotype or phenotype the long-run growth rate is not a valid measure of fitness in a fluctuating environment. The haploid and quantitative character models both reveal that the expected relative fitness of a type is its Malthusian fitness in the average environment minus the environmental covariance between its growth rate and that of the population.     

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.     

An exact form of the breeder's equation for the evolution of a quantitative trait under natural selection

Starting with the Price equation, I show that the total evolutionary change in mean phenotype that occurs in the presence of fitness variation can be partitioned exactly into five components representing logically distinct processes. One component is the linear response to selection, as represented by the breeder's equation of quantitative genetics, but with heritability defined as the linear regression coefficient of mean offspring phenotype on parent phenotype. The other components are identified as constitutive transmission bias, two types of induced transmission bias, and a spurious response to selection caused by a covariance between parental fitness and offspring phenotype that cannot be predicted from parental phenotypes. The partitioning can be accomplished in two ways, one with heritability measured before (in the absence of) selection, and the other with heritability measured after (in the presence of) selection. Measuring heritability after selection, though unconventional, yields a representation for the linear response to selection that is most consistent with Darwinian evolution by natural selection because the response to selection is determined by the reproductive features of the selected group, not of the parent population as a whole. The analysis of an explicitly Mendelian model shows that the relative contributions of the five terms to the total evolutionary change depends on the level of organization (gene, individual, or mated pair) at which the parent population is divided into phenotypes, with each frame of reference providing unique insight. It is shown that all five components of phenotypic evolution will generally have nonzero values as a result of various combinations of the normal features of Mendelian populations, including biparental sex, allelic dominance, inbreeding, epistasis, linkage disequilibrium, and environmental covariances between traits. Additive genetic variance can be a poor predictor of the adaptive response to selection in these models. The narrow-sense heritability sigma2A/sigma2P should be viewed as an approximation to the offspring-parent linear regression rather than the other way around.     

THE COADAPTATION OF PARENTAL AND OFFSPRING CHARACTERS

Parents often have important influences on their offspring's traits and/or fitness (i.e., maternal or paternal effects). When offspring fitness is determined by the joint influences of offspring and parental traits, selection may favor particular combinations that generate high offspring fitness. We show that this epistasis for fitness between the parental and offspring genotypes can result in the evolution of their joint distribution, generating genetic correlations between the parental and offspring characters. This phenomenon can be viewed as a coadaptive process in which offspring genotypes evolve to function with the parentally provided environment and, in turn, the genes for this environment become associated with specific offspring genes adapted to it. To illustrate this point, we present two scenarios in which selection on offspring alone alters the correlation between a maternal and an offspring character. We use a quantitative genetic maternal effect model combined with a simple quadratic model of fitness to examine changes in the linkage disequilibrium between the maternal and offspring genotypes. In the first scenario, stabilizing selection on a maternally affected offspring character results in a genetic correlation that is opposite in sign to the maternal effect. In the second scenario, directional selection on an offspring trait that shows a nonadditive maternal effect can result in selection for positive covariances between the traits. This form of selection also results in increased genetic variation in maternal and offspring characters, and may, in the extreme case, promote host-race formation or speciation. This model provides a possible evolutionary explanation for the ubiquity of large genetic correlations between maternal and offspring traits, and suggests that this pattern of coinheritance may reflect functional relationships between these characters (i.e., functional integration).     

The Properties of Adaptive Walks in Evolving Populations of Fungus

The rarity of beneficial mutations has frustrated efforts to develop a quantitative theory of adaptation. Recent models of adaptive walks, the sequential substitution of beneficial mutations by selection, make two compelling predictions: adaptive walks should be short, and fitness increases should become exponentially smaller as successive mutations fix. We estimated the number and fitness effects of beneficial mutations in each of 118 replicate lineages of Aspergillus nidulans evolving for approximately 800 generations at two population sizes using a novel maximum likelihood framework, the results of which were confirmed experimentally using sexual crosses. We find that adaptive walks do indeed tend to be short, and fitness increases become smaller as successive mutations fix. Moreover, we show that these patterns are associated with a decreasing supply of beneficial mutations as the population adapts. We also provide empirical distributions of fitness effects among mutations fixed at each step. Our results provide a first glimpse into the properties of multiple steps in an adaptive walk in asexual populations and lend empirical support to models of adaptation involving selection towards a single optimum phenotype. In practical terms, our results suggest that the bulk of adaptation is likely to be accomplished within the first few steps.     

THE EVOLUTION OF CANALIZATION AND THE BREAKING OF VON BAER'S LAWS: MODELING THE EVOLUTION OF DEVELOPMENT WITH EPISTASIS

Evolution can change the developmental processes underlying a character without changing the average expression of the character itself. This sort of change must occur in both the evolution of canalization, in which a character becomes increasingly buffered against genetic or developmental variation, and in the phenomenon of closely related species that show similar adult phenotypes but different underlying developmental patterns. To study such phenomena, I develop a model that follows evolution on a surface representing adult phenotype as a function of underlying developmental characters. A contour on such a “phenotype landscape” is a set of states of developmental characters that produce the same adult phenotype. Epistasis induces curvature of this surface, and degree of canalization is represented by the slope along a contour. I first discuss the geometric properties of phenotype landscapes, relating epistasis to canalization. I then impose a fitness function on the phenotype and model evolution of developmental characters as a function of the fitness function and the local geometry of the surface. This model shows how canalization evolves as a population approaches an optimum phenotype. It further shows that under some circumstances, “decanalization” can occur, in which the expression of adult phenotype becomes increasingly sensitive to developmental variation. This process can cause very similar populations to diverge from one another developmentally even when their adult phenotypes experience identical selection regimes.     

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.     

On adaptive accuracy and precision in natural populations

Adaptation is usually conceived as the fit of a population mean to a fitness optimum. Natural selection, however, does not act only to optimize the population mean. Rather, selection normally acts on the fitness of individual organisms in the population. Furthermore, individual genotypes do not produce invariant phenotypes, and their fitness depends on how precisely they are able to realize their target phenotypes. For these reasons we suggest that it is better to conceptualize adaptation as accuracy rather than as optimality. The adaptive inaccuracy of a genotype can be measured as a function of the expected distance of its associated phenotype from a fitness optimum. The less the distance, the more accurate is the adaptation. Adaptive accuracy has two components: the deviance of the genotypically set target phenotype from the optimum and the precision with which this target phenotype can be realized. The second component, the adaptive precision, has rarely been quantified as such. We survey the literature to quantify how much of the phenotypic variation in wild populations is due to imprecise development. We find that this component is often substantial and highly variable across traits. We suggest that selection for improved precision may be important for many traits.     

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.     

The length of adaptive walks is insensitive to starting fitness in Aspergillus nidulans

Adaptation involves the successive substitution of beneficial mutations by selection, a process known as an adaptive walk. Gradualist models of adaptation, which assume that all mutations are small relative to the distance to a fitness optimum, predict that adaptive walks should be longer when the founding genotype is less well adapted. More recent work modeling adaptation as a sequence of moves in phenotype or genotype space predicts, by contrast, much shorter adaptive walks irrespective of the fitness of the founding genotype. Here, we provide what is, to the best of our knowledge, the first direct test of these alternative models, measuring the length of adaptive walks in evolving lineages of fungus that differ initially in fitness. Contrary to the gradualist view, we show that the length of adaptive walks in the fungus Aspergillus nidulans is insensitive to starting fitness and involves just two mutations on average. This arises because poorly adapted populations tend to fix mutations of larger average effect than those of better-adapted populations. Our results suggest that the length of adaptive walks may be independent of the fitness of the founding genotype and, moreover, that poorly adapted populations can quickly adapt to novel environments.     

Evolution of unconditional dispersal in periodic environments

Organisms modulate their fitness in heterogeneous environments by dispersing. Prior work shows that there is selection against 'unconditional' dispersal in spatially heterogeneous environments. 'Unconditional' means individuals disperse at a rate independent of their location. We prove that if within-patch fitness varies spatially and between two values temporally, then there is selection for unconditional dispersal: any evolutionarily stable strategy (ESS) or evolutionarily stable coalition (ESC) includes a dispersive phenotype. Moreover, at this ESS or ESC, there is at least one sink patch (i.e. geometric mean of fitness less than one) and no sources patches (i.e. geometric mean of fitness greater than one). These results coupled with simulations suggest that spatial-temporal heterogeneity is due to abiotic forcing result in either an ESS with a dispersive phenotype or an ESC with sedentary and dispersive phenotypes. In contrast, the spatial-temporal heterogeneity due to biotic interactions can select for higher dispersal rates that ultimately spatially synchronize population dynamics.     

Natural selection, fitness entropy, and the dynamics of coevolution

The coevolutionary dynamics of interacting populations were studied by combining continuous time Lotka-Volterra models of population growth with single-locus genetic models of weak selection. The effects of natural selection on population growth were evaluated using Ginzburg's fitness entropy function as a measure of the deviation of a population's initial allele frequencies from their polymorphic equilibrium values. This entropy measure was used to relate the dynamics of a community composed of evolving populations to the dynamics of a "reference community" whose populations are initially in genetic equilibrium. Specifically, a quantity called the "selective difference area" was defined as the total difference between the population size trajectories of a reference and evolving population. The selective difference area represents the amount of extra life a species would realize if the entire community were at genetic equilibrium. It was shown that this selective difference area is a simple linear function of the initial fitness entropies of each species. This prediction is independent of the strength of selection and holds for any arbitrary set of initial population densities. Numerical examples were presented to illustrate the results. Under the assumption of weak selection, a generalization for arbitrary population growth models was outlined.     

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.     

Live fast, die young: trade-offs between fitness components and sexually antagonistic selection on weaponry in Soay sheep

Males are predicted to compete for reproductive opportunities, with sexual selection driving the evolution of large body size and weaponry through the advantage they confer for access to females. Few studies have explored potential trade-offs of investment in secondary sexual traits between different components of fitness or tested for sexually antagonistic selection pressures. These factors may provide explanations for observed polymorphisms in both form and quality of secondary sexual traits. We report here an analysis of selection on horn phenotype in a feral population of Soay sheep (Ovis aries) on the island of Hirta, St. Kilda, Scotland. Soay sheep display a phenotypic polymorphism for horn type with males growing either normal or reduced (scurred) horns, and females growing either normal, scurred, or no (polled) horns; further variation in size exists within horn morphs. We show that horn phenotype and the size of the trait displayed is subject to different selection pressures in males and females, generating sexually antagonistic selection. Furthermore, there was evidence of a trade-off between breeding success and longevity in normal-horned males, with both the normal horn type and larger horn size being associated with greater annual breeding success but reduced longevity. Therefore, selection through lifetime breeding success was not found to act upon horn phenotype in males. In females, a negative association of annual breeding success within the normal-horned phenotype did not result in a significant difference in lifetime fitness when compared to scurred individuals, as no significant difference in longevity was found. However, increased horn size within this group was negatively associated with breeding success and longevity. Females without horns (polled) suffered reduced longevity and thus reduced lifetime breeding success relative the other horn morphs. Our results therefore suggest that trade-offs between different components of fitness and antagonistic selection between the sexes may maintain genetic variation for secondary sexual traits within a population.     

Character displacement as the "best of a bad situation": fitness trade-offs resulting from selection to minimize resource and mate competition

Abstract Character displacement has long been considered a major cause of adaptive diversification. When species compete for resources or mates, character displacement minimizes competition by promoting divergence in phenotypes associated with resource use (ecological character displacement) or mate attraction (reproductive character displacement). In this study, we investigated whether character displacement can also have pleiotropic effects that lead to fitness trade-offs between the benefits of avoiding competition and costs accrued in other fitness components. We show that both reproductive and ecological character displacement have caused spadefoot toads to evolve smaller body size in the presence of a heterospecific competitor. Although this shift in size likely arose as a by-product of character displacement acting to promote divergence between species in mating behavior and larval development, it concomitantly reduces offspring survival, female fecundity, and sexual selection on males. Thus, character displacement may represent the "best of a bad situation" in that it lessens competition, but at a cost. Individuals in sympatry with the displaced phenotype will have higher fitness than those without the displaced trait because they experience reduced competition, but they may have reduced fitness relative to individuals in allopatry. Such a fitness trade-off can limit the conditions under which character displacement evolves and may even increase the risk of "Darwinian extinction" in sympatric populations. Consequently, character displacement may not always promote diversification in the manner that is often expected.     

THE EVOLUTION OF MATERNAL CHARACTERS

We develop quantitative-genetic models for the evolution of multiple traits under maternal inheritance, in which traits are transmitted through non-Mendelian as well as Mendelian mechanisms, and maternal selection, in which the fitness of offspring depends on their mother's phenotype as well as their own. Maternal inheritance results in time lags in the evolutionary response to selection. These cause a population to evolve for an indefinite number of generations after selection ceases and make the rate and direction of evolution change even when the strength of selection and parameters of inheritance remain constant. The rate and direction of evolution depend on the inheritance of traits that are not under selection, unlike under classical Mendelian inheritance. The models confirm earlier findings that the response to selection can be larger or smaller than what is possible with simple Mendelian inheritance, and even in a direction opposite to what selection favors. Maternal selection, in which a mother's phenotype influences her offspring's fitness, is frequency-dependent and can cause a population to evolve maladaptively away from a fitness peak, regardless of whether traits are transmitted by Mendelian or maternal inheritance. Maternal selection differs from other forms of selection in that its force depends not only on the fitness function but also on the phenotypic resemblance of parents and offspring.