David Houle

The lek paradox and the capture of genetic variance by condition dependent traits

Recent evidence suggests that sexually selected traits have unexpectedly high genetic variance. In this paper, we offer a simple and general mechanism to explain this observation. Our explanation offers a resolution to the lek paradox and rests on only two assumptions; condition dependence of sexually selected traits and high genetic variance in condition. The former assumption is well supported by empirical evidence. We discuss the evidence for the latter assumption. These two assumptions lead inevitably to the capture of genetic variance into sexually selected traits concomitantly with the evolution of condition dependence. We present a simple genetic model to illustrate this view. We then explore some implications of genic capture for the coevolution of female preference and male traits. Our exposition of this problem incidentally leads to new insights into the similarities between sexually selected traits and life history traits, and therefore into the maintenance of high genetic variance in the latter. Finally, we discuss some shortcomings of a recently proposed alternative solution to the lek paradox; selection on variance.

Comparative quantitative genetics: evolution of the G matrix

Abstract Quantitative genetics provides one of the most promising frameworks with which to unify the fields of macroevolution and microevolution. The genetic variance–covariance matrix ( G ) is crucial to quantitative genetic predictions about macroevolution. In spite of years of study, we still know little about how G evolves. Recent studies have been applying an increasingly phylogenetic perspective and more sophisticated statistical techniques to address G matrix evolution. We propose that a new field, comparative quantitative genetics, has emerged. Here we summarize what is known about several key questions in the field and compare the strengths and weaknesses of the many statistical and conceptual approaches now being employed. Past studies have made it clear that the key question is no longer whether G evolves but rather how fast and in what manner. We highlight the most promising future directions for this emerging field.

PERSPECTIVE: SPONTANEOUS DELETERIOUS MUTATION

Mildly deleterious mutation has been invoked as a leading explanation for a diverse array of observations in evolutionary genetics and molecular evolution and is thought to be a significant risk of extinction for small populations. However, much of the empirical evidence for the deleterious‐mutation process derives from studies of Drosophila melanogaster, some of which have been called into question. We review a broad array of data that collectively support the hypothesis that deleterious mutations arise in flies at rate of about one per individual per generation, with the average mutation decreasing fitness by about only 2% in the heterozygous state. Empirical evidence from microbes, plants, and several other animal species provide further support for the idea that most mutations have only mildly deleterious effects on fitness, and several other species appear to have genomic mutation rates that are of the order of magnitude observed in Drosophila. However, there is mounting evidence that some organisms have genomic deleterious mutation rates that are substantially lower than one per individual per generation. These lower rates may be at least partially reconciled with the Drosophila data by taking into consideration the number of germline cell divisions per generation. To fully resolve the existing controversy over the properties of spontaneous mutations, a number of issues need to be clarified. These include the form of the distribution of mutational effects and the extent to which this is modified by the environmental and genetic background and the contribution of basic biological features such as generation length and genome size to interspecific differences in the genomic mutation rate. Once such information is available, it should be possible to make a refined statement about the long‐term impact of mutation on the genetic integrity of human populations subject to relaxed selection resulting from modern medical procedures.

Measuring and comparing evolvability and constraint in multivariate characters

The Lande equation forms the basis for our understanding of the short‐term evolution of quantitative traits in a multivariate context. It predicts the response to selection as the product of an additive genetic variance matrix and a selection gradient. The selection gradient approximates the force and direction of selection, and the genetic variance matrix quantifies the role of the genetic system in evolution. Attempts to understand the evolutionary significance of the genetic variance matrix are hampered by the fact that the majority of the methods used to characterize and compare variance matrices have not been derived in an explicit theoretical context. We use the Lande equation to derive new measures of the ability of a variance matrix to allow or constrain evolution in any direction in phenotype space. Evolvability captures the ability of a population to evolve in the direction of selection when stabilizing selection is absent. Conditional evolvability captures the ability of a population to respond to directional selection in the presence of stabilizing selection on other trait combinations. We then derive measures of character autonomy and integration from these evolvabilities. We study the properties of these measures and show how they can be used to interpret and compare variance matrices. As an illustration, we show that divergence of wing shape in the dipteran family Drosophilidae has proceeded in directions that have relatively high evolvabilities.

Direct estimation of per nucleotide and genomic deleterious mutation rates in Drosophila.

Spontaneous mutations are the source of genetic variation required for evolutionary change, and are therefore important for many aspects of evolutionary biology. For example, the divergence between taxa at neutrally evolving sites in the genome is proportional to the per nucleotide mutation rate, u (ref. 1), and this can be used to date speciation events by assuming a molecular clock. The overall rate of occurrence of deleterious mutations in the genome each generation (U) appears in theories of nucleotide divergence and polymorphism, the evolution of sex and recombination, and the evolutionary consequences of inbreeding. However, estimates of U based on changes in allozymes or DNA sequences and fitness traits are discordant. Here we directly estimate u in Drosophila melanogaster by scanning 20 million bases of DNA from three sets of mutation accumulation lines by using denaturing high-performance liquid chromatography. From 37 mutation events that we detected, we obtained a mean estimate for u of 8.4 × 10-9 per generation. Moreover, we detected significant heterogeneity in u among the three mutation-accumulation-line genotypes. By multiplying u by an estimate of the fraction of mutations that are deleterious in natural populations of Drosophila, we estimate that U is 1.2 per diploid genome. This high rate suggests that selection against deleterious mutations may have a key role in explaining patterns of genetic variation in the genome, and help to maintain recombination and sexual reproduction.

Comparing strengths of directional selection: how strong is strong?

Abstract The fundamental equation in evolutionary quantitative genetics, the Lande equation, describes the response to directional selection as a product of the additive genetic variance and the selection gradient of trait value on relative fitness. Comparisons of both genetic variances and selection gradients across traits or populations require standardization, as both are scale dependent. The Lande equation can be standardized in two ways. Standardizing by the variance of the selected trait yields the response in units of standard deviation as the product of the heritability and the variance‐standardized selection gradient. This standardization conflates selection and variation because the phenotypic variance is a function of the genetic variance. Alternatively, one can standardize the Lande equation using the trait mean, yielding the proportional response to selection as the product of the squared coefficient of additive genetic variance and the mean‐standardized selection gradient. Mean‐standardized selection gradients are particularly useful for summarizing the strength of selection because the mean‐standardized gradient for fitness itself is one, a convenient benchmark for strong selection. We review published estimates of directional selection in natural populations using mean‐standardized selection gradients. Only 38 published studies provided all the necessary information for calculation of mean‐standardized gradients. The median absolute value of multivariate mean‐standardized gradients shows that selection is on average 54% as strong as selection on fitness. Correcting for the upward bias introduced by taking absolute values lowers the median to 31%, still very strong selection. Such large estimates clearly cannot be representative of selection on all traits. Some possible sources of overestimation of the strength of selection include confounding environmental and genotypic effects on fitness, the use of fitness components as proxies for fitness, and biases in publication or choice of traits to study.

Fluctuating Asymmetry as a Bioindicator of Stress: Comparing Efficacy of Analyses Involving Multiple Traits

Researchers have suggested fluctuating asymmetry (FA) as an indicator of environmental stress and have usually tested this assertion by examining relations between FA of single traits and stress. Fluctuating asymmetry stress relations are real but are typically weak and difficult to detect. Researchers would like to maximize the probability of detecting FA‐stress relations when they exist. We assert that analyses based on the FA of multiple traits may provide better methods for detecting stress. In this article, we used computer simulations to compare the ability of six analyses to detect differences in FA between stressed and unstressed populations. We show that the optimal analysis depends upon the underlying form of the FA distributions. We also show that two of the analyses had inflated Type I errors in some situations. Finally, we quantify the advantage of our preferred analysis over those of single‐trait FA in detecting stress.

Coevolution of costly mate choice and condition-dependent display of good genes.

Females often choose their mates, instead of mating at random, even when a father contributes nothing but genes to his offspring. Costly female preferences for males with exaggerated traits that reduce viability, such as the peacocks tail, are particularly puzzling. Such preferences can evolve if directly favoured by natural selection or when the exaggerated trait, although maladaptive per se, indicates high overall quality of the males genotype. Two recent analyses suggested that the advantage to mate choice based on genetic quality is too weak to explain extreme cases of exaggeration of display traits and the corresponding preferences. We studied coevolution of a female mate-preference function and a genotype–dependent male display function where mutation supplies variation in genotype quality and mate preference is costly. Preference readily evolves, often causing extreme exaggeration of the display. Mate choice and trait expression can approach an equilibrium, or a limit cycle, or exaggeration can proceed forever, eventually causing extinction.

Genotype-environment interactions and the estimation of the genomic mutation rate in Drosophila melanogaster

We have studied the relative fitnesses of three genotypes of Drosophila melanogaster in 50 environments. Two genotypes, the MA lines, had accumulated mutations in the absence of natural selection over 62 generations. The third was a related strain where selection had continued to act. The environments differed in three factors: parental density, dilution of the medium, and the temperature régime and medium composition. Our measure of fitness assessed fecundity and viability relative to a reference genotype. Both MA lines always had lower fitnesses than the selected line, but the difference increased dramatically with dilution of the medium and, especially, crowding. Under the most severe conditions, the performance of the MA lines approached 0. This increased difference in harsh conditions may be caused both by a uniform increase in the magnitude of deleterious effects of all mutations and by the exposure of mutations which are essentially neutral under benign conditions. If the second cause is important, previous experiments are likely to have underestimated the genomic deleterious mutation rate in Drosophila melanogaster more than previously thought.

How should we explain variation in the genetic variance of traits

Recent work has called attention to large differences among traits in the amount of standardized genetic variance they possess. There are four general factors which could play a role in causing this variation: mutation, elimination of deleterious variation, selection of favorable alleles, and balancing selection. Three factors could directly influence the mutational variability of traits: canalization, the mutational target size, and the timing of trait expression. Here I carry out simple tests of the importance of some of these factors using data from Drosophila melanogaster. I compiled information from the literature on the mutational and standing genetic variances in outbred populations, inferred the relative mutational target size of each trait, its a timing of expression, and used models of life history to calculate fitness sensitivities for each trait. Mutation variation seems to play an important role, as it is highly correlated with standing variance. The target size hypothesis was supported by a significant correlation between mutational variance and inferred target size. There was also a significant relationship between the timing of trait expression and mutational variance. These hypotheses are confounded by a correlation between timing and target size. The elimination and canalization hypotheses were not supported by these data, suggesting that they play a quantitatively less important role in determining overall variances. Additional information concerning the pleiotropic consequences of mutations would help to validate the fitness sensitivities used to test the elimination and canalization hypotheses.