So far in this course we have dealt entirely with the evolution of characters that are controlled by simple Mendelian inheritance at a single locus. There are notes on the course website about gametic disequilibrium and how allele frequencies change at two loci simultaneously, but we didn’t discuss them. In every example we’ve considered we’ve imagined that we could understand something about evolution by examining the evolution of a single gene. That’s the domain of classical population genetics. For the next few weeks we’re going to be exploring a field that’s actually older than classical population genetics, although the approach we’ll be taking to it involves the use of population genetic machinery. If you know a little about the history of evolutionary biology, you may know that after the rediscovery of Mendel’s work in 1900 there was a heated debate between the “biometricians” (e.g., Galton and Pearson) and the “Mendelians” (e.g., de Vries, Correns, Bateson, and Morgan). Biometricians asserted that the really important variation in evolution didn’t follow Mendelian rules. Height, weight, skin color, and similar traits seemed to

Human biochemical genetics

Statistics for Spatial Data.

The standard bootstrap (SBS), despite being computationally intensive, is widely used in maximum likelihood phylogenetic analyses. We recently proposed the ultrafast bootstrap approximation (UFBoot) to reduce computing time while achieving more unbiased branch supports than SBS under mild model violations. UFBoot has been steadily adopted as an efficient alternative to SBS and other bootstrap approaches. Here, we present UFBoot2, which substantially accelerates UFBoot and reduces the risk of overestimating branch supports due to polytomies or severe model violations. Additionally, UFBoot2 provides suitable bootstrap resampling strategies for phylogenomic data. UFBoot2 is 778 times (median) faster than SBS and 8.4 times (median) faster than RAxML rapid bootstrap on tested data sets. UFBoot2 is implemented in the IQ-TREE software package version 1.6 and freely available at http://www.iqtree.org.

UFBoot2: Improving the Ultrafast Bootstrap Approximation.

Genetics and analysis of quantitative traits

The harmful effects of close inbreeding have been noticed for many centuries (34, 35, 165). With the rise of Mendelian genetics, it was realized that the main genetic consequence of inbreeding is homozygosis (165, Ch. 2). Two main theories were early proposed to account for inbreeding depression and its converse, heterosis (the increase in vigor observed in an F1 between two inbred lines). These are the overdominance and partial dominance hypotheses, discussed in more detail below. Research into this question has continued up to the present, and this is one of the topics that we discuss. Darwin (35, 36) was the first to point out that the evident adaptations of many plants for ensuring outcrossing could be understood in terms of the selective advantage of avoiding inbreeding depression. We review the evidence that the evolution of breeding systems of animals and plants has been significantly influenced by the occurrence of inbreeding depression. In order to do this, we consider the contemporary genetic theory of inbreeding depression and heterosis, and the experimental data concerning the strength of inbreeding depression. We emphasize data and theory relevant to natural, rather than domesticated, populations as we are chiefly concerned to evaluate the evolutionary significance of inbreeding depression. We do not attempt to give a complete bibliography of this very extensive field but try to concentrate on what seem to be the most significant findings in relation to this aim.

https://www.jstor.org/stable/pdf/2097132.pdf

Inbreeding depression and its evolutionary consequences

There are two distinct reasons for making comparisons of genetic variation for quantitative characters. The first is to compare evolvabilities, or ability to respond to selection, and the second is to make inferences about the forces that maintain genetic variability. Measures of variation that are standardized by the trait mean, such as the additive genetic coefficient of variation, are appropriate for both purposes. Variation has usually been compared as narrow sense heritabilities, but this is almost always an inappropriate comparative measure of evolvability and variability. Coefficients of variation were calculated from 842 estimates of trait means, variances and heritabilities in the literature. Traits closely related to fitness have higher additive genetic and nongenetic variability by the coefficient of variation criterion than characters under weak selection. This is the reverse of the accepted conclusion based on comparisons of heritability. The low heritability of fitness components is best explained by their high residual variation. The high additive genetic and residual variability of fitness traits might be explained by the great number of genetic and environmental events they are affected by, or by a lack of stabilizing selection to reduce their phenotypic variance. Over one-third of the quantitative genetics papers reviewed did not report trait means or variances. Researchers should always report these statistics, so that measures of variation appropriate to a variety of situations may be calculated.

/pdf/comparing-evolvability-and-variability-of-quantitative-4inmsaci3d.pdf

Comparing evolvability and variability of quantitative 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.

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

A key goal of biology is to understand phenotypic characteristics, such as health, disease and evolutionary fitness. Phenotypic variation is produced through a complex web of interactions between genotype and environment, and such a 'genotype-phenotype' map is inaccessible without the detailed phenotypic data that allow these interactions to be studied. Despite this need, our ability to characterize phenomes - the full set of phenotypes of an individual - lags behind our ability to characterize genomes. Phenomics should be recognized and pursued as an independent discipline to enable the development and adoption of high-throughput and high-dimensional phenotyping.

Phenomics: the next challenge.

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

/pdf/measuring-and-comparing-evolvability-and-constraint-in-19g693mqqq.pdf

Measuring and comparing evolvability and constraint in multivariate characters

The genetic variance-covariance matrix, G, is determined in part by functional architecture, the pathways by which variation in genotype influences phenotype. I develop a simple architectural model for G for two traits under directional selection constrained by their dependence on a common limiting resource. I assume that genetic variance is maintained by mutation-selection balance. The relative numbers of loci that play a role in acquiring versus allocating a limiting resource play a crucial role in determining genetic covariance. If many loci are involved in acquiring a resource, genetic covariance may be either negative or positive at equilibrium, depending on the fitness function and the input of mutational variance. The form of G does not necessarily reveal the constraint on resource acquisition inherent in the system, and therefore studies estimating G do not test for the existence of life-history tradeoffs. Characters may evolve in patterns that are unpredictable from G. Experiments are suggested that would indicate if this model could explain observations of positive genetic covariance.

https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.1558-5646.1991.tb04334.x

David Houle

Papers

Comparing evolvability and variability of quantitative traits.

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

Phenomics: the next challenge.

Measuring and comparing evolvability and constraint in multivariate characters

Genetic covariance of fitness correlates: what genetic correlations are made of and why it matters.