On epistasis: why it is unimportant in polygenic directional selection.

There is a difference in viewpoint of developmental and evo-devo geneticists versus breeders and students of quantitative evolution. The former are interested in understanding the developmental process; the emphasis is on identifying genes and studying their action and interaction. Typically, the genes have individually large effects and usually show substantial dominance and epistasis. The latter group are interested in quantitative phenotypes rather than individual genes. Quantitative traits are typically determined by many genes, usually with little dominance or epistasis. Furthermore, epistatic variance has minimum effect, since the selected population soon arrives at a state in which the rate of change is given by the additive variance or covariance. Thus, the breeder's custom of ignoring epistasis usually gives a more accurate prediction than if epistatic variance were included in the formulae.

Wright and Fisher on inbreeding and random drift.

Sewall Wright and R. A. Fisher often differed, including on the meaning of inbreeding and random gene frequency drift. Fisher regarded them as quite distinct processes, whereas Wright thought that because his inbreeding coefficient measured both they should be regarded as the same. Since the effective population numbers for inbreeding and random drift are different, this would argue for the Fisher view.

Mayr, mathematics and the study of evolution.

In 1959 Ernst Mayr challenged the relevance of mathematical models to evolutionary studies and was answered by JBS Haldane in a witty and convincing essay. Fifty years on, I conclude that the importance of mathematics has in fact increased and will continue to do so.

Mid-century controversies in population genetics.

Beginning in the 1930s, evolution became an experimental subject. New techniques, especially in Drosophila, made possible quantitative analysis of natural populations. In addition to a large number of studies on many species, there were four major controversies that dominated much of the discussion and experimentation. Some of the arguments were quite heated. These controversies were: Wright vs Fisher on Wright's shifting-balance theory; dominance vs overdominance as an explanation of heterosis; the classical vs balance hypothesis for genetic variability; the neutral theory of molecular evolution. Curiously, most of these issues were not really resolved. Rather they were abandoned in favor of more tractable studies made possible by the new molecular methods.

Maintaining evolvability.

Although molecular methods, such as QTL mapping, have revealed a number of loci with large effects, it is still likely that the bulk of quantitative variability is due to multiple factors, each with small effect. Typically, these have a large additive component. Conventional wisdom argues that selection, natural or artificial, uses up additive variance and thus depletes its supply. Over time, the variance should be reduced, and at equilibrium be near zero. This is especially expected for fitness and traits highly correlated with it. Yet, populations typically have a great deal of additive variance, and do not seem to run out of genetic variability even after many generations of directional selection. Long-term selection experiments show that populations continue to retain seemingly undiminished additive variance despite large changes in the mean value. I propose that there are several reasons for this. (i) The environment is continually changing so that what was formerly most fit no longer is. (ii) There is an input of genetic variance from mutation, and sometimes from migration. (iii) As intermediate-frequency alleles increase in frequency towards one, producing less variance (as p --> 1, p(1 - p) --> 0), others that were originally near zero become more common and increase the variance. Thus, a roughly constant variance is maintained. (iv) There is always selection for fitness and for characters closely related to it. To the extent that the trait is heritable, later generations inherit a disproportionate number of genes acting additively on the trait, thus increasing genetic variance. For these reasons a selected population retains its ability to evolve. Of course, genes with large effect are also important. Conspicuous examples are the small number of loci that changed teosinte to maize, and major phylogenetic changes in the animal kingdom. The relative importance of these along with duplications, chromosome rearrangements, horizontal transmission and polyploidy is yet to be determined. It is likely that only a case-by-case analysis will provide the answers. Despite the difficulties that complex interactions cause for evolution in Mendelian populations, such populations nevertheless evolve very well. Longlasting species must have evolved mechanisms for coping with such problems. Since such difficulties do not arise in asexual populations, a comparison of epistatic patterns in closely related sexual and asexual species might provide some important insights.

Inferring purging from pedigree data.

The harmful effects of inbreeding can be reduced if deleterious recessive alleles were removed (purged) by selection against homozygotes in earlier generations. If only a few generations are involved, purging is due almost entirely to recessive alleles that reduce fitness to near zero. In this case the amount of purging and allele frequency change can be inferred approximately from pedigree data alone and are independent of the allele frequency. We examined pedigrees of 59,778 U.S. Jersey cows. Most of the pedigrees were for six generations, but a few went back slightly farther. Assuming recessive homozygotes have fitness 0, the reduction of total genetic load due to purging is estimated at 17%, but most of this is not expressed, being concealed by dominant alleles. Considering those alleles that are currently expressed due to inbreeding, the estimated amount of purging is such as to reduce the expressed load (inbreeding depression) in the current generation by 12.6%. That the reduction is not greater is due mainly to (1) generally low inbreeding levels because breeders in the past have tended to avoid consanguineous matings, and (2) there is essentially no information more than six generations back. The methods used here should be applicable to other populations for which there is pedigree information.

Age and sex effects on human mutation rates: an old problem with new complexities.

Base substitution mutations are far more common in human males than in females, and the frequency increases with paternal age. Both can be accounted for by the greater number of pre-meiotic cell divisions in males, especially old ones. In contrast, small deletions do not show any important age effect and occur with approximately equal frequency in the two sexes. Mutations in most genes include both types, and the sex and paternal age effect depends on the proportion of the two types. A few traits, of which Apert Syndrome is best understood, are mutation hot spots with all the mutations occurring in one or two codons, usually at one nucleotide. They occur with very high frequency almost exclusively in males and the frequency increases rapidly with paternal age. It has been suggested that the mutant cells have a selective advantage in the male germ-line prior to meiosis. Evidence for this surprising, but important, hypothesis is discussed. A possible mechanism is the conversion of asymmetrical stem-cell divisions into symmetric ones. Some traits with complex etiology show a slight paternal age effect. There is also a short discussion of the high deleterious mutation rate and the role of sexual reproduction in reducing the consequent mutation load.

Timeline: Hermann Joseph Muller, evolutionist.

This essay is dedicated to the proposition that Hermann Joseph Muller, widely regarded as the greatest geneticist of the first half-century of the subject, was also one of the greatest evolutionists of this period. His Nobel Prize-winning work, which showed that radiation increases the mutation rate, is in every genetics textbook, and his prescient ideas have influenced almost every aspect of the discipline. Here I emphasize his less well-known contribution to the neo-Darwinian theory of evolution.

Essay: early American genetics journals.

Before the Second World War, there were only two North-American journals exclusively devoted to genetics - the Journal of Heredity and Genetics. In the late 1940s, Genetics spawned two progeny - the American Journal of Human Genetics and Evolution. This article recounts the early days of these journals, their influential and often colourful founding editors, and their contents. It emphasizes the contrast between those years, when a reader had a realistic chance of keeping up with the whole field, and the current plethora of journals that makes it impossible to keep up with even the tables of contents.