Quantitative genetic variability maintained by mutation-stabilizing selection balance: sampling variation and response to subsequent directional selection

A model of genetic variation of a quantitative character subject to the simultaneous effects of mutation, selection and drift is investigated. Predictions are obtained for the variance of the genetic variance among independent lines at equilibrium with stabilizing selection. These indicate that the coefficient of variation of the genetic variance among lines is relatively insensitive to the strength of stabilizing selection on the character. The effects on the genetic variance of a change of mode of selection from stabilizing to directional selection are investigated. This is intended to model directional selection of a character in a sample of individuals from a natural or long-established cage population. The pattern of change of variance from directional selection is strongly influenced by the strengths of selection at individual loci in relation to effective population size before and after the change of regime. Patterns of change of variance and selection responses from Monte Carlo simulation are compared to selection responses observed in experiments. These indicate that changes in variance with directional selection are not very different from those due to drift alone in the experiments, and do not necessarily give information on the presence of stabilizing selection or its strength.     

It's about time: the temporal dynamics of phenotypic selection in the wild

Selection is a central process in nature. Although our understanding of the strength and form of selection has increased, a general understanding of the temporal dynamics of selection in nature is lacking. Here, we assembled a database of temporal replicates of selection from studies of wild populations to synthesize what we do (and do not) know about the temporal dynamics of selection. Our database contains 5519 estimates of selection from 89 studies, including estimates of both direct and indirect selection as well as linear and nonlinear selection. Morphological traits and studies focused on vertebrates were well-represented, with other traits and taxonomic groups less well-represented. Overall, three major features characterize the temporal dynamics of selection. First, the strength of selection often varies considerably from year to year, although random sampling error of selection coefficients may impose bias in estimates of the magnitude of such variation. Second, changes in the direction of selection are frequent. Third, changes in the form of selection are likely common, but harder to quantify. Although few studies have identified causal mechanisms underlying temporal variation in the strength, direction and form of selection, variation in environmental conditions driven by climatic fluctuations appear to be common and important.     

EXPERIMENTAL EVIDENCE FOR THE EVOLUTION OF THE MAMMALIAN BACULUM BY SEXUAL SELECTION

Male genitalia exhibit a taxonomically widespread pattern of rapid and divergent evolution. Sexual selection is generally believed to be responsible for these patterns of evolutionary divergence, although empirical support for the sexual selection hypothesis comes mainly from studies of insects. Here we show that sexual selection is responsible for an evolutionary divergence in baculum morphology among populations of house mice Mus domesticus. We sourced mice from three isolated populations known to be subject to differing strengths of postcopulatory sexual selection and bred them under common‐garden conditions. Mice from populations with strong postcopulatory sexual selection had bacula that were relatively thicker compared with mice from populations with weak selection. We used experimental evolution to determine whether these patterns of divergence could be ascribed to postcopulatory sexual selection. After 27 generations of experimental evolution, populations of mice subjected to postcopulatory sexual selection evolved bacula that were relatively thicker than populations subjected to enforced monogamy. Our data thereby provide evidence that postcopulatory sexual selection underlies an evolutionary divergence in the mammalian baculum and supports the hypothesis that sexual selection plays a general role in the evolution of male genital morphology across evolutionary diverse taxonomic groups.     

Models of sexual selection on a quantitative genetic trait when preference is acquired by sexual imprinting

The evolution of a quantitative genetic trait under stabilizing viability selection and sexual selection is modeled for a polygynous species in which female mating preferences are acquired by sexual imprinting on the parents and by exposure to the surviving population at large. Stabilizing viability selection acts equally on both sexes in the case of a sexually monomorphic trait and on males only in the case of a dimorphic trait. A genetically fixed sensory or perceptual bias defines the origin of the scale on which the trait is measured, and the possibility is incorporated that female preferences may deviate asymmetrically from the familiar-either toward or away from this origin. When viability selection is strong relative to sexual selection, the models predict that the mean trait value will evolve to the viability optimum. With intermediate ratios of the strength of viability to sexual selection, a stable equilibrium can occur on either side of this viability optimum, depending on the direction of asymmetry in female preferences. When viability selection is relatively weak and certain other conditions are also satisfied, runaway selection is predicted.     

Two locus models of selection and mutation within and among full-sib lines

Summary General models for continued full-sib mating with two diallelic autosomal loci taking account of linkage, mutation and selection within and among lines are considered. The problems are first approached by deriving the full probability transition matrix, taking account of linkage, mutation and within-line selection. Exact solutions to the equilibrium system are possible, but the computational effort is prohibitive, and this is exacerbated by the introduction of between-line selection. A second approach is based on decomposing the transition matrix into blocks whose properties suggest approximations that lead to a rapid iterative solution of the equilibrium system. Extensive numerical analysis of models of within-line selection and of combined within- and between-line selection were made. The results show that equilibrium values are essentially independent of the degree of linkage under models of within-line selection. This is because mutation plays a dominant role in determining equilibrium structure. Results from models of combined within- and between-line selection show that between-line selection has the dominant influence on gene frequency equilibrium. Both within-line and between-line selection produce appreciable linkage disequilibrium only when selection is disruptive. The results also suggest that much of the twolocus equilibrium structure can be predicted from a knowledge of single-locus equilibria.     

Genetic selection in presence of pathogens such as the lymphoid leukosis virus: computer simulation

Summary A computer model was developed to simulate the population dynamics involved when selection is for a trait influenced by the presence of a pathogen in addition to quantitative genetic factors. The lymphoid leukosis virus is such a pathogen, when selection is for egg production in chickens. It is transmitted congenitally from dam to offspring and horizontally from one individual to another. For these simulations, individual selection for high performance in the trait influenced by the pathogen was more effective than family selection for removing infected individuals from populations. The resulting reduction in the incidence of infected individuals in following generations made the overall response to individual selection greater than for family selection. However, the virus would remain in most populations due to horizontal transmission to individuals which later transmit the virus to their offspring. These horizontally infected individuals would not be eliminated in the selection process because their egg production was assumed to be less reduced than that of congenitally infected birds. These simulation results seem to mimic certain experimental results which heretofore have been difficult to explain since they were not consistent with quantitative genetic theoretical expectations from selection.Journal Paper No. 9028 of the Purdue Agricultural Experiment StationAnimal Research Centre Contribution No. 1145     

Concurrent natural and sexual selection in wild male sockeye salmon, Oncorhynchus nerka

Concurrent natural and sexual selection have been inferred from laboratory and comparative studies in a number of taxa, but are rarely measured in natural populations. Because the interaction of these two general categories of selection may be complex when they occur simultaneously, empirical evidence from natural populations would help us to understand this interaction and probably give us greater insight into each separate episode as well. In male sockeye salmon, sexual selection for larger body size has been indicated in both deep and shallow water habitats. However, in shallow habitats male sockeye are generally smaller and less deep-bodied than in deep habitats, a difference that has been ascribed to natural selection. We measured concurrent natural and sexual selection in two years on breeding male sockeye salmon with respect to body size, body shape, and time of arrival to the breeding grounds. Natural selection was variable in effect and sexual selection was variable in intensity in these two years. The patterns of selection also appear to be interdependent; areas where predation on spawning adults is not intense have yielded different patterns of sexual selection than those measured here. It appears that some of the body shape differences in sockeye salmon associated with different spawning habitats, which were previously attributed to selective mortality, may be a result of different patterns of sexual selection in the different habitats. Total selection resulting from the combination of both natural and sexual selection was less intense than either natural or sexual selection in most cases. Measurement of concurrent selection episodes in nature may help us to understand whether the pattern of differential sexual selection is common, and whether observed patterns of habitat-related differentiation may be due to differences in sexual selection.     

Phylogenetic inertia and Darwin's higher law

The concept of 'phylogenetic inertia' is routinely deployed in evolutionary biology as an alternative to natural selection for explaining the persistence of characteristics that appear sub-optimal from an adaptationist perspective. However, in many of these contexts the precise meaning of 'phylogenetic inertia' and its relationship to selection are far from clear. After tracing the history of the concept of 'inertia' in evolutionary biology, I argue that treating phylogenetic inertia and natural selection as alternative explanations is mistaken because phylogenetic inertia is, from a Darwinian point of view, simply an expected effect of selection. Although Darwin did not discuss 'phylogenetic inertia,' he did assert the explanatory priority of selection over descent. An analysis of 'phylogenetic inertia' provides a perspective from which to assess Darwin's view.     

Multistage Selection for Genetic Gain by Orthogonal Transformation

An exact transformed culling method for any number of traits or stages of selection with explicit solution for multistage selection is described in this paper. This procedure does not need numerical integration and is suitable for obtaining either desired genetic gains for a variable proportion selected or optimum aggregate breeding value for a fixed total proportion selected. The procedure has similar properties to multistage selection index and, as such, genetic gains from use of the procedure may exceed ordinary independent culling level selection. The relative efficiencies of transformed to conventional independent culling ranged from 87% to over 300%. These results suggest that for most situations one can chose a multistage selection scheme, either conventional or transformed culling, which will have an efficiency close to that of selection index. After considering cost savings associated with multistage selection, there are many situations in which economic returns from use of independent culling, either conventional or transformed, will exceed that of selection index.     

The effect of gametic-phase disequilibrium on the prediction of response to recurrent selection in plants

Selection reduces additive genetic variation by generating gametic-phase disequilibrium, a phenomenon largely ignored when predicting response in plant breeding programs. The development of gametic-phase disequilibrium is here taken into account when predicting the response to selection for various schemes of recurrent selection applicable to plant populations. A general program permits prediction of response to selection from schemes of recurrent selection in which two or more rounds of selection occur in each cycle. An example from Sugar Beet, with alternate rounds of half-sib and S1 family selection, is illustrated. It is shown that failure to take into account the effects of gametic-phase disequilibrium can result in substantial overestimation of the response to selection as well as to changes in rank of the merits of alternative breeding schemes. For a given scheme, ignoring gametic-phase disequilibrium has only small effects on defining the optimum allocation of plots and the numbers of families tested.     

Evidence for overdominant selection maintaining X-linked fitness variation in Drosophila melanogaster

The role of balancing selection in maintaining genetic variation for fitness is largely unresolved. This reflects the inherent difficulty in distinguishing between models of recurrent mutation versus selection, which produce similar patterns of inbreeding depression, as well as the limitations of testing such hypotheses when fitness variation is averaged across the genome. Signatures of X-linked overdominant selection are less likely to be obscured by mutational variation because X-linked mutations are rapidly eliminated by purifying selection in males. Although models maintaining genetic variation for fitness are not necessarily mutually exclusive, a series of predictions for identifying X-linked overdominant selection can be used to separate its contribution from other underlying processes. We consider the role of overdominant selection in maintaining fitness variation in a sample of 12 X chromosomes from a population of Drosophila melanogaster. Substantial variation was observed for male reproductive success and female fecundity, with heterozygous-X genotypes exhibiting the greatest degree of variance, a finding that agrees well with predictions of the overdominance model. The importance of X-linked overdominant selection is discussed along with models of recurrent mutation and sexually antagonistic selection.     

Insights from modeling protein evolution with context-dependent mutation and asymmetric amino acid selection

We develop an approximate maximum likelihood method to estimate flanking nucleotide context-dependent mutation rates and amino acid exchange-dependent selection in orthologous protein-coding sequences and use it to analyze genome-wide coding sequence alignments from mammals and yeast. Allowing context-dependent mutation provides a better fit to coding sequence data than simpler (context-independent or CpG "hotspot") models and significantly affects selection parameter estimates. Allowing asymmetric (nonreciprocal) selection on amino acid exchanges gives a better fit than simple dN/dS or symmetric selection models. Relative selection strength estimates from our models show good agreement with independent estimates derived from human disease-causing and engineered mutations. Selection strengths depend on local protein structure, showing expected biophysical trends in helical versus nonhelical regions and increased asymmetry on polar-hydrophobic exchanges with increased burial. The more stringent selection that has previously been observed for highly expressed proteins is primarily concentrated in buried regions, supporting the notion that such proteins are under stronger than average selection for stability. Our analyses indicate that a highly parameterized model of mutation and selection is computationally tractable and is a useful tool for exploring a variety of biological questions concerning protein and coding sequence evolution.     

Natural selection then and now

One often reads the following claims: (1) The modern conception of natural selection differs from Darwin's own conception only with respect to incidental features; (2) Natural selection is a very simple idea with enormous explanatory power. Both claims are problematic. R.A. Fisher famously argued that given a particulate view of inheritance, selection could proceed in a powerful manner even with frequent crossing, small fitness advantages and a low mutation rate. This is quite different from Darwin's view, which (roughly translated into a modern idiom) insists on infrequent crossing, large fitness advantages and a high mutation rate. The modern conception of natural selection is not the same as Darwin's, unless we describe natural selection in the most abstract manner. When so described, the ability of natural selection to account for adaptation is questionable.     

THE CAUSES OF NATURAL SELECTION

We discuss the necessary and sufficient conditions for identifying the cause of natural selection on a phenotypic trait. We reexamine the observational methods recently proposed for measuring selection in natural populations and illustrate why the multivariate analysis of selection is insufficient for identifying the causal agents of selection. We discuss how the observational approach of multivariate selection analysis can be complemented by experimental manipulations of the phenotypic distribution and the environment to identify not only how selection is operating on the phenotypic distribution but also why it operates in the observed manner. A significant point of departure of our work from recent discussions is in regard to the role of the environment in the study of natural selection. Instead of viewing the environment as a source of unwanted variation that obscures the relationship between phenotype and fitness, we view fitness as arising from the interaction of the phenotype with the environment. The biotic and abiotic environment is the context that gives rise to the relationship between phenotype and fitness (selection). The analysis of the causes of selection is in essence a problem in ecology. The experimental study of the association between selection gradients and environmental characteristics is necessary to identify the agents of natural selection. We recommend research methods for identifying the agency of selection that depend upon a reciprocity between the observational approach of multivariate selection analysis and the manipulative approach of field experiments in evolutionary ecology.     

Recombination, balancing selection and phylogenies in MHC and self-incompatibility genes.

Using a coalescent model of multiallelic balancing selection with recombination, the genealogical process as a function of recombinational distance from a site under selection is investigated. We find that the shape of the phylogenetic tree is independent of the distance to the site under selection. Only the timescale changes from the value predicted by Takahata's allelic genealogy at the site under selection, converging with increasing recombination to the timescale of the neutral coalescent. However, if nucleotide sequences are simulated over a recombining region containing a site under balancing selection, a phylogenetic tree constructed while ignoring such recombination is strongly affected. This is true even for small rates of recombination. Published studies of multiallelic balancing selection, i.e., the major histocompatibility complex (MHC) of vertebrates, gametophytic and sporophytic self-incompatibility of plants, and incompatibility of fungi, all observe allelic genealogies with unexpected shapes. We conclude that small absolute levels of recombination are compatible with these observed distortions of the shape of the allelic genealogy, suggesting a possible cause of these observations. Furthermore, we illustrate that the variance in the coalescent with recombination process makes it difficult to locate sites under selection and to estimate the selection coefficient from levels of variability.     

Genetic steady-state under BLUP selection for an infinite and homogeneous population with discrete generations

A matrix derivation is proposed to analytically calculate the asymptotic genetic variance-covariance matrix under BLUP selection according to the initial genetic parameters in a large population with discrete generations. The asymptotic genetic evolution of a homogeneous population with discrete generations is calculated for a selection operating on an index including all information (pedigree and records) from a non-inbred and unselected base population (BLUP selection) or on an index restricted to records of a few ancestral generations. Under the first hypothesis, the prediction error variance of the selection index is independent of selection and is calculated from the genetic parameters of the base population. Under the second hypothesis, the prediction error variance depends on selection. Furthermore, records of several generations of ancestors of the candidates for selection must be used to maintain a constant prediction error variance over time. The number of ancestral generations needed depends on the population structure and on the occurrence of fixed effects. Without fixed effects to estimate, accounting for two generations of ancestors is sufficient to estimate the asymptotic prediction error variance. The amassing of information from an unselected base population proves to be important in order not to overestimate the asymptotic genetic gains and not to underestimate the asymptotic genetic variances.     

The Selection Limit Due to the Conflict between Truncation and Stabilizing Selection with Mutation

Long-term selection response could slow down from a decline in genetic variance or in selection differential or both. A model of conflict between truncation and stabilizing selection in infinite population size is analysed in terms of the reduction in selection differential. Under the assumption of a normal phenotypic distribution, the limit to selection is found to be a function of kappa, the intensity of truncation selection, omega 2, a measure of the intensity of stabilizing selection, and sigma 2, the phenotypic variance of the character. The maintenance of genetic variation at this limit is also analyzed in terms of mutation-selection balance by the use of the "House-of-cards" approximation. It is found that truncation selection can substantially reduce the equilibrium genetic variance below that when only stabilizing selection is acting, and the proportional reduction in variance is greatest when the selection is very weak. When truncation selection is strong, any further increase in the strength of selection has little further influence on the variance. It appears that this mutation-selection balance is insufficient to account for the high levels of genetic variation observed in many long-term selection experiments.     

Inevitable evolution: back to the origin and beyond the 20th century paradigm of contingent evolution by historical natural selection

Since neo-Darwinism arose from the work of Darwin and Mendel evolution by natural selection has been seen as contingent and historical being defined by an a posteriori selection process with no a priori laws that explain why evolution on Earth has taken the direction of the major evolutionary trends and transitions instead of any other direction. Recently, however, major life-history trends and transitions have been explained as inevitable because of a deterministic selection that unfolds from the energetic state of the organism and the density-dependent competitive interactions that arise from self-replication in limited environments. I describe differences and similarities between the historical and deterministic selection processes, illustrate concepts using life-history models on large body masses and limited reproductive rates, review life-history evolution with a wider focus on major evolutionary transitions, and propose that biotic evolution is driven by a universal natural selection where the long-term evolution of fitness-related traits is determined mainly by deterministic selection, while contingency is important predominately for neutral traits. Given suitable environmental conditions, it is shown that selection by energetic state and density-dependent competitive interactions unfolds to higher level selection for life-history transitions from simple asexually reproducing self-replicators to large bodied organisms with senescence and sexual reproduction between males and females, and in some cases, to the fully evolved eusocial colony with thousands of offspring workers. This defines an evolutionary arrow of time for open thermodynamic systems with a constant inflow of energy, predicting similar routes for long-term evolution on similar planets.     

Nematode–bacteria mutualism: Selection within the mutualism supersedes selection outside of the mutualism

The coevolution of interacting species can lead to codependent mutualists. Little is known about the effect of selection on partners within verses apart from the association. Here, we determined the effect of selection on bacteria (Xenorhabdus nematophila) both within and apart from its mutualistic partner (a nematode, Steinernema carpocapsae). In nature, the two species cooperatively infect and kill arthropods. We passaged the bacteria either together with (M+), or isolated from (M?), nematodes under two different selection regimes: random selection (S?) and selection for increased virulence against arthropod hosts (S+). We found that the isolated bacteria evolved greater virulence under selection for greater virulence (M?S+) than under random selection (M?S?). In addition, the response to selection in the isolated bacteria (M?S+) caused a breakdown of the mutualism following reintroduction to the nematode. Finally, selection for greater virulence did not alter the evolutionary trajectories of bacteria passaged within the mutualism (M+S+ = M+S?), indicating that selection for the maintenance of the mutualism was stronger than selection for increased virulence. The results show that selection on isolated mutualists can rapidly breakdown beneficial interactions between species, but that selection within a mutualism can supersede external selection, potentially generating codependence over time.     

Estimating Selection Coefficients in Spatially Structured Populations from Time Series Data of Allele Frequencies

Inferring the nature and magnitude of selection is an important problem in many biological contexts. Typically when estimating a selection coefficient for an allele, it is assumed that samples are drawn from a panmictic population and that selection acts uniformly across the population. However, these assumptions are rarely satisfied. Natural populations are almost always structured, and selective pressures are likely to act differentially. Inference about selection ought therefore to take account of structure. We do this by considering evolution in a simple lattice model of spatial population structure. We develop a hidden Markov model based maximum-likelihood approach for estimating the selection coefficient in a single population from time series data of allele frequencies. We then develop an approximate extension of this to the structured case to provide a joint estimate of migration rate and spatially varying selection coefficients. We illustrate our method using classical data sets of moth pigmentation morph frequencies, but it has wide applications in settings ranging from ecology to human evolution.