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.     

THE DISTRIBUTION OF PHENOTYPIC VARIANCE WITH INBREEDING

Fifty-two inbred populations of Drosophila melanogaster, each founded from a single pair, and a large number of control, outbred flies were measured for fitness and a set of six traits. A survey of the literature on the effects of inbreeding and population bottlenecks demonstrates that the commonly observed pattern of an apparent variance among characters and among species in changes of phenotypic variance may in fact be largely the result of sampling error, given the pattern of change that we demonstrate within a species for the same character. In our study, population bottlenecks on average decrease the amount of phenotypic variance for a suite of wing characteristics and size, but there is large and significant variation among lines in the amount of phenotypic variance. As a result, several lines increased in variance in spite of the average decrease. Interestingly, the changes in phenotypic variance for fitness are in sharp contrast to those seen for phenotypic variance for morphological traits. The amount of phenotypic variance for fitness varies highly significantly among lines but, on average, is increased by bottlenecks. The changes in phenotypic variance as a result of population bottlenecks are large enough to significantly affect the probability of peak shifts by the variance-induced peak shift model.     

FOUNDER EFFECTS AND PEAK SHIFTS WITHOUT GENETIC DRIFT: ADAPTIVE PEAK SHIFTS OCCUR EASILY WHEN ENVIRONMENTS FLUCTUATE SLIGHTLY

Two similar evolutionary theories, the shifting balance theory and founder-flush models, invoke random genetic drift to allow evolution on complex adaptive landscapes. These models, in their usual incarnations, deal with fitness as a static entity, and the probability of transition from one form to another is predicted to be quite small by analysis of these models. Fitness itself can change, however, and the amount of change in the parameters of the fitness functions required to allow deterministic evolution to new adaptive peaks is very small. The probability of environmental changes sufficient to allow substantial morphological evolution or reproductive isolation is large relative to the probability that similar changes could occur by processes requiring genetic drift, even with very small population sizes. The rapid evolution or speciation following a population founding event is more closely linked with environmental changes than genetic drift.     

Niche construction and the environmental term of the price equation: How natural selection changes when organisms alter their environments

Organisms construct their own environments and phenotypes through the adaptive processes of habitat choice, habitat construction, and phenotypic plasticity. We examine how these processes affect the dynamics of mean fitness change through the environmental change term of the Price Equation. This tends to be ignored in evolutionary theory, owing to the emphasis on the first term describing the effect of natural selection on mean fitness (the additive genetic variance for fitness of Fisher's Fundamental Theorem). Using population genetic models and the Price Equation, we show how adaptive niche constructing traits favorably alter the distribution of environments that organisms encounter and thereby increase population mean fitness. Because niche-constructing traits increase the frequency of higher-fitness environments, selection favors their evolution. Furthermore, their alteration of the actual or experienced environmental distribution creates selective feedback between niche constructing traits and other traits, especially those with genotype-by-environment interaction for fitness. By altering the distribution of experienced environments, niche constructing traits can increase the additive genetic variance for such traits. This effect accelerates the process of overall adaption to the niche-constructed environmental distribution and can contribute to the rapid refinement of alternative phenotypic adaptations to different environments. Our findings suggest that evolutionary biologists revisit and reevaluate the environmental term of the Price Equation: owing to adaptive niche construction, it contributes directly to positive change in mean fitness; its magnitude can be comparable to that of natural selection; and, when there is fitness G × E, it increases the additive genetic variance for fitness, the much-celebrated first term.     

Environmental stress, inbreeding, and the nature of phenotypic and genetic variance in Drosophila melanogaster

Fifty-two lines of Drosophila melanogaster founded by single-pair population bottlenecks were used to study the effects of inbreeding and environmental stress on phenotypic variance, genetic variance and survivorship. Cold temperature and high density cause reduced survivorship, but these stresses do not cause repeatable changes in the phenotypic variance of most wing morphological traits. Wing area, however, does show increased phenotypic variance under both types of environmental stress. This increase is no greater in inbred than in outbred lines, showing that inbreeding does not increase the developmental effects of stress. Conversely, environmental stress does not increase the extent of inbreeding depression. Genetic variance is not correlated with environmental stress, although the amount of genetic variation varies significantly among environments and lines vary significantly in their response to environmental change. Drastic changes in the environment can cause changes in phenotypic and genetic variance, but not in a way reliably predicted by the notion of 'stress'.     

The pace of evolution across fitness valleys

How fast does a population evolve from one fitness peak to another? We study the dynamics of evolving, asexually reproducing populations in which a certain number of mutations jointly confer a fitness advantage. We consider the time until a population has evolved from one fitness peak to another one with a higher fitness. The order of mutations can either be fixed or random. If the order of mutations is fixed, then the population follows a metaphorical ridge, a single path. If the order of mutations is arbitrary, then there are many ways to evolve to the higher fitness state. We address the time required for fixation in such scenarios and study how it is affected by the order of mutations, the population size, the fitness values and the mutation rate.     

Environmental change exposes beneficial epistatic interactions in a catalytic RNA

Natural selection drives populations of individuals towards local peaks in a fitness landscape. These peaks are created by the interactions between individual mutations. Fitness landscapes may change as an environment changes. In a previous contribution, we discovered a variant of the Azoarcus group I ribozyme that represents a local peak in the RNA fitness landscape. The genotype at this peak is distinguished from the wild-type by four point mutations. We here report ribozyme fitness data derived from constructing all possible combinations of these point mutations. We find that these mutations interact epistatically. Importantly, we show that these epistatic interactions change qualitatively in the three different environments that we studied. We find examples where the relative fitness of a ribozyme can change from neutral or negative in one environment, to positive in another. We also show that the fitness effect of a specific GC-AU base pair switch is dependent on both the environment and the genetic context. Moreover, the mutations that we study improve activity at the cost of decreased structural stability. Environmental change is ubiquitous in nature. Our results suggest that such change can facilitate adaptive evolution by exposing new peaks of a fitness landscape. They highlight a prominent role for genotype-environment interactions in doing so.     

Estimating selection on neonatal traits in red deer using elasticity path analysis

Van Tienderen recently published a method that links selection gradients between a phenotypic trait and multiple fitness components with the effects of these fitness components on the population growth rate (mean absolute fitness). The method allows selection to be simultaneously estimated across multiple fitness components in a population dynamic framework. In this paper we apply the method to a population of red deer living in the North Block of the Isle of Rum, Scotland. We show that (1) selection on birth date and birth weight can operate through multiple fitness components simultaneously; (2) our estimates of the response to selection are consistent with the observed change in trait values that we cannot explain with environmental and phenotypic covariates; (3) selection on both traits has fluctuated over the course of the study; (4) selection operates through different fitness components in different years; and (5) no environmental covariates correlate with selection because different fitness components respond to density and climatic variation in contrasting ways.     

Fundamental theorem of natural selection and frequency-dependent selection: analysis of the matrix game diploid model

Following Ewens' interpretation about Fisher's fundamental theorem of natural selection, the matrix game model for diploid populations undergoing non-overlapping, discrete generations is investigated. The total genetic variance is decomposed and it is shown that the partial change in the mean fitness, which is equal to the additive genetic variance over the mean fitness, can be thought of as a change due only to the partial changes in the phenotypic frequencies.     

Change of Genetic Architecture in Response to Sex

A traditional view is that sexual reproduction increases the potential for phenotypic evolution by expanding the range of genetic variation upon which natural selection can act. However, when nonadditive genetic effects and genetic disequilibria underlie a genetic system, genetic slippage (a change in the mean genotypic value contrary to that promoted by selection) in response to sex may occur. Additionally, depending on whether natural selection is predominantly stabilizing or disruptive, recombination may either enhance or reduce the level of expressed genetic variance. Thus, the role of sexual reproduction in the dynamics of phenotypic evolution depends heavily upon the nature of natural selection and the genetic system of the study population. In the present study, on a permanent lake Daphnia pulicaria population, sexual reproduction resulted in significant genetic slippage and a significant increase in expressed genetic variance for several traits. These observations provide evidence for substantial genetic disequilibria and nonadditive genetic effects underlying the genetic system of the study population. From these results, the fitness function of the previous clonal selection phase is inferred to be directional and/or stabilizing. The data are also used to infer the effects of natural selection on the mean and the genetic variance of the population.     

Evolutionary walks through a land plant morphospace

A model for mimicking land plant evolution is here expanded and re-evaluated. The model consists of (1) a morphospace containing on the order of 10⁹ phenotypic variants, (2) 15 different fitness landscapes, each defined on the basis of performing one or more of four tasks (i.e. maximizing light interception, mechanical stability and reproduction, and minimizing total surface area), and (3) an algorithm driving a search through fitness landscapes for more fit variants. The model is used to predict the effects of the number of simultaneously performed tasks ('complexity'), abrupt changes in environmental conditions (mimicked by random replacement of one fitness landscape with another), and developmental barriers (mimicked by barring searches from entering specific subdomains in the morphospace) on number and accessibility of variants occupying fitness maxima. The model predicts that (1) the number and accessibility of fitness peaks will increase (while the difference between the relative fitness of peaks and valleys will decrease) in proportion to functional complexity, (2) abrupt shifts in landscapes will increase rather than decrease phenotypic diversity, and (3) obstructed searches have an equal or higher probability of reaching fitness peaks than unfettered searches. These results follow axiomatically from the way hypothetical variants are spatially ordered in the morphospace, the manner in which relative fitness is defined, and the protocol used to locate fitness peaks. A critique of the model's predictions and desiderata for future research are provided.     

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.     

EVOLUTION OF GENERALISTS AND SPECIALISTS IN SPATIALLY HETEROGENEOUS ENVIRONMENTS

Quantitative genetic models are used to investigate the evolution of generalists and specialists in a coarse-grained environment with two habitat types when there are costs attached to being a generalist. The outcomes for soft and hard selection models are qualitatively different. Under soft selection (e.g., for juvenile or male-reproductive traits) the population evolves towards the single peak in the adaptive landscape. At equilibrium, the population mean phenotype is a compromise between the reaction that would be optimal in both habitats and the reaction with the lowest cost. Furthermore, the equilibrium is closer to the optimal phenotype in the most frequent habitat, or the habitat in which selection on the focal trait is stronger. A specialist genotype always has a lower fitness than a generalist, even when the costs are high. In contrast, under hard selection (e.g., for adult or female-reproductive traits) the adaptive landscape can have one, two, or three peaks; a peak represents a population specialized to one habitat, equally adapted to both habitats, or an intermediate. One peak is always found when the reaction with the lowest cost is not much different from the optimal reaction, and this situation is similar to the soft selection case. However, multiple peaks are present when the costs become higher, and the course of evolution is then determined by initial conditions, and the region of attraction of each peak. This implies that the evolution of specialization and phenotypic plasticity may not only depend on selection regimes within habitats, but also on contingent, historical events (migration, mutation). Furthermore, the evolutionary dynamics in changing environments can be widely different for populations under hard and soft selection. Approaches to measure costs in natural and experimental populations are discussed.     

The fitness threshold model: Random environmental change alters adaptive landscapes

We used a probabilistic optimization model to explore the joint evolutionary effects of random phenotypic and environmental variation. Two forms of environmental noise were defined in which the optimal phenotype remained constant but all organisms experienced either the same proportionate or the same absolute fitness gains and losses. There was no evolutionary effect of proportionate fitness fluctuations. In contrast, the optimal genotype varied with absolute fitness fluctuations, despite the environmental effect being phenotype-independent. We refer to such phenotype-independent fluctuation in absolute fitness as the fitness threshold model, because shared fitness effects determine the zero-fitness points (i.e. the baseline) on an intrinsic fitness function. Thus, environmental effects that are unrelated to a focal trait can cause peak shifts in the genetic optimum for the trait. Changes in the fitness threshold not only changed peak locations, but also altered the slopes defining the peaks, and so should alter the rate of evolution towards optima. This model pertains to evolution in any system, unless there is no phenotypic or environmental variance, or the selection function and distribution of phenotypic error assume similar shapes. Our results have many basic and applied implications for topics such as the maintenance of genetic variation, the canalization of development and the management of natural populations.     

Social effects of territorial neighbours on the timing of spring breeding in North American red squirrels

Organisms can affect one another's phenotypes when they socially interact. Indirect genetic effects occur when an individual's phenotype is affected by genes expressed in another individual. These heritable effects can enhance or reduce adaptive potential, thereby accelerating or reversing evolutionary change. Quantifying these social effects is therefore crucial for our understanding of evolution, yet estimates of indirect genetic effects in wild animals are limited to dyadic interactions. We estimated indirect phenotypic and genetic effects, and their covariance with direct effects, for the date of spring breeding in North American red squirrels (Tamiasciurus hudsonicus) living in an array of territories of varying spatial proximity. Additionally, we estimated indirect effects and the strength of selection at low and high population densities. Social effects of neighbours on the date of spring breeding were different from zero at high population densities but not at low population densities. Indirect phenotypic effects accounted for a larger amount of variation in the date of breeding than differences attributable to the among‐individual variance, suggesting social interactions are important for determining breeding dates. The genetic component to these indirect effects was however not statistically significant. We therefore showcase a powerful and flexible method that will allow researchers working in organisms with a range of social systems to estimate indirect phenotypic and genetic effects, and demonstrate the degree to which social interactions can influence phenotypes, even in a solitary species.     

Evolutionary advantage of small populations on complex fitness landscapes

Recent experimental and theoretical studies have shown that small asexual populations evolving on complex fitness landscapes may achieve a higher fitness than large ones due to the increased heterogeneity of adaptive trajectories. Here, we introduce a class of haploid three-locus fitness landscapes that allow the investigation of this scenario in a precise and quantitative way. Our main result derived analytically shows how the probability of choosing the path of the largest initial fitness increase grows with the population size. This makes large populations more likely to get trapped at local fitness peaks and implies an advantage of small populations at intermediate time scales. The range of population sizes where this effect is operative coincides with the onset of clonal interference. Additional studies using ensembles of random fitness landscapes show that the results achieved for a particular choice of three-locus landscape parameters are robust and also persist as the number of loci increases. Our study indicates that an advantage for small populations is likely whenever the fitness landscape contains local maxima. The advantage appears at intermediate time scales, which are long enough for trapping at local fitness maxima to have occurred but too short for peak escape by the creation of multiple mutants.     

Was Wright Right? The Canonical Genetic Code is an Empirical Example of an Adaptive Peak in Nature; Deviant Genetic Codes Evolved Using Adaptive Bridges

The canonical genetic code is on a sub-optimal adaptive peak with respect to its ability to minimize errors, and is close to, but not quite, optimal. This is demonstrated by the near-total adjacency of synonymous codons, the similarity of adjacent codons, and comparisons of frequency of amino acid usage with number of codons in the code for each amino acid. As a rare empirical example of an adaptive peak in nature, it shows adaptive peaks are real, not merely theoretical. The evolution of deviant genetic codes illustrates how populations move from a lower to a higher adaptive peak. This is done by the use of “adaptive bridges,” neutral pathways that cross over maladaptive valleys by virtue of masking of the phenotypic expression of some maladaptive aspects in the genotype. This appears to be the general mechanism by which populations travel from one adaptive peak to another. There are multiple routes a population can follow to cross from one adaptive peak to another. These routes vary in the probability that they will be used, and this probability is determined by the number and nature of the mutations that happen along each of the routes. A modification of the depiction of adaptive landscapes showing genetic distances and probabilities of travel along their multiple possible routes would throw light on this important concept.     

Dominance Genetic Variance for Traits Under Directional Selection in Drosophila serrata

In contrast to our growing understanding of patterns of additive genetic variance in single- and multi-trait combinations, the relative contribution of nonadditive genetic variance, particularly dominance variance, to multivariate phenotypes is largely unknown. While mechanisms for the evolution of dominance genetic variance have been, and to some degree remain, subject to debate, the pervasiveness of dominance is widely recognized and may play a key role in several evolutionary processes. Theoretical and empirical evidence suggests that the contribution of dominance variance to phenotypic variance may increase with the correlation between a trait and fitness; however, direct tests of this hypothesis are few. Using a multigenerational breeding design in an unmanipulated population of Drosophila serrata, we estimated additive and dominance genetic covariance matrices for multivariate wing-shape phenotypes, together with a comprehensive measure of fitness, to determine whether there is an association between directional selection and dominance variance. Fitness, a trait unequivocally under directional selection, had no detectable additive genetic variance, but significant dominance genetic variance contributing 32% of the phenotypic variance. For single and multivariate morphological traits, however, no relationship was observed between trait–fitness correlations and dominance variance. A similar proportion of additive and dominance variance was found to contribute to phenotypic variance for single traits, and double the amount of additive compared to dominance variance was found for the multivariate trait combination under directional selection. These data suggest that for many fitness components a positive association between directional selection and dominance genetic variance may not be expected.     

Differences in the Phenotypic Mean and Variance Between Two Geographically Separated Populations of Wood Frog (Lithobates sylvaticus)

Intraspecific phenotypic variation between populations separated by large geographic distances is common. Differences in the mean and variance of traits among populations can be used to infer the relative strength, direction, and type of selection on traits. Patterns in the mean provide information on the type of selection, and patterns in variance provide information on the strength of selection. However, interpretation of mean/variance patterns is difficult when two traits are linked and strongly correlated to fitness because it is unlikely that each trait will reach phenotypic optima. In amphibians time to metamorphosis and size at metamorphosis are positively related both phenotypically and genetically. Using a common-garden experiment we investigated whether selection favours shorter time to metamorphosis or increased mass at metamorphosis between two populations which differ in the length of the post-metamorphic growing season by 2–4 weeks. Animals from the population a shorter growing season took longer to reach and metamorphosed at a greater mass, while animals from the population with a longer period for post metamorphic growth reached metamorphosis faster, but at a smaller mass. Greater phenotypic variance was observed in both traits in the population with the shorter growing season. These data suggest that animals from the population with a restricted growth period maximise mass at metamorphosis at the expense of longer larval periods while animals from population with the longer post-metamorphic growth period sacrifice mass at metamorphosis to shorten the larval period and maximise larval survival. Differences in phenotypic variance among populations suggest either directional or diversifying selection has acted on both traits.     

Evolutionary aspects and sensitivity studies of some major gene models

Extensive biometrical and statistically oriented studies in segregation and pedigree analyses reflect current efforts to demonstrate major gene factors playing a significant role for a whole hierarchy of multifactorial diseases and related risk factors exhibiting continuous variation. The evolutionary aspects of the changes in gene frequencies of some major gene one locus models admitting a broad range of genotype-phenotype associations and different forms of selection functions are investigated. The flexibility of differences among the genotypic-phenotypic distribution can take account of variable penetrance expressivity, complex multifarious heterogeneous background effects, or partial dominance concepts. The phenotype distribution and selection function are assumed to be time invariant such that the environments with which the population interacts do not depend on either the phenotypes or the genotypes present in the population of any particular generation. Viability selection optimizing or directional acts on the phenotypic level. We consider random mating, and concentrate mostly on evaluating the nature of the equilibrium structure for the cases of “strong” and “weak” selection. For weak stabilizing selection the determinants of superior genotypic fitness in the class of phenotypic symmetric distributions reside in minimizing a combination of the phenotypic variance and the deviation of the phenotypic mean from the optimal phenotype. With equal means of central phenotype values, a canalizing selection effect signifying fitness superiority for the genotype with minimal variance is in force. For strong stabilizing selection the genotype-phenotype density at the optimal value determines the relative genotype fitness value. For directional selection the determinants of the selection realizations depend on a “standardized” deviation of the mean phenotype distributional value relative to its total variance. The effects of symmetry as against asymmetry in the genotype distributions with prescribed means and variances were investigated by numerical computations.