William G. Hill

Understanding and using quantitative genetic variation.

Quantitative genetics, or the genetics of complex traits, is the study of those characters which are not affected by the action of just a few major genes. Its basis is in statistical models and methodology, albeit based on many strong assumptions. While these are formally unrealistic, methods work. Analyses using dense molecular markers are greatly increasing information about the architecture of these traits, but while some genes of large effect are found, even many dozens of genes do not explain all the variation. Hence, new methods of prediction of merit in breeding programmes are again based on essentially numerical methods, but incorporating genomic information. Long-term selection responses are revealed in laboratory selection experiments, and prospects for continued genetic improvement are high. There is extensive genetic variation in natural populations, but better estimates of covariances among multiple traits and their relation to fitness are needed. Methods based on summary statistics and predictions rather than at the individual gene level seem likely to prevail for some time yet.

Variation in actual relationship as a consequence of Mendelian sampling and linkage.

Although the expected relationship or proportion of genome shared by pairs of relatives can be obtained from their pedigrees, the actual quantities deviate as a consequence of Mendelian sampling and depend on the number of chromosomes and map length. Formulae have been published previously for the variance of actual relationship for a number of specific types of relatives but no general formula for non-inbred individuals is available. We provide here a unified framework that enables the variances for distant relatives to be easily computed, showing, for example, how the variance of sharing for great grandparent-great grandchild, great uncle-great nephew, half uncle-nephew and first cousins differ, even though they have the same expected relationship. Results are extended in order to include differences in map length between sexes, no recombination in males and sex linkage. We derive the magnitude of skew in the proportion shared, showing the skew becomes increasingly large the more distant the relationship. The results obtained for variation in actual relationship apply directly to the variation in actual inbreeding as both are functions of genomic coancestry, and we show how to partition the variation in actual inbreeding between and within families. Although the variance of actual relationship falls as individuals become more distant, its coefficient of variation rises, and so, exacerbated by the skewness, it becomes increasingly difficult to distinguish different pedigree relationships from the actual fraction of the genome shared.

The population genetics of mutations: good, bad and indifferent.

Population genetics is fundamental to our understanding of evolution, and mutations are essential raw materials for evolution. In this introduction to more detailed papers that follow, we aim to provide an oversight of the field. We review current knowledge on mutation rates and their harmful and beneficial effects on fitness and then consider theories that predict the fate of individual mutations or the consequences of mutation accumulation for quantitative traits. Many advances in the past built on models that treat the evolution of mutations at each DNA site independently, neglecting linkage of sites on chromosomes and interactions of effects between sites (epistasis). We review work that addresses these limitations, to predict how mutations interfere with each other. An understanding of the population genetics of mutations of individual loci and of traits affected by many loci helps in addressing many fundamental and applied questions: for example, how do organisms adapt to changing environments, how did sex evolve, which DNA sequences are medically important, why do we age, which genetic processes can generate new species or drive endangered species to extinction, and how should policy on levels of potentially harmful mutagens introduced into the environment by humans be determined?

Inheritance of hatchability in broiler chickens and its relationship to egg quality traits

The first objective of this study on broiler breeders was to investigate the genetic basis of variability in hatchability over age using a longitudinal model. Weekly percentage hatch of fertile and hatch of set eggs were available for 23,250 dams mated to 3,106 sires of the same age between the 28th and 54th week of life. Hatch of set was very highly correlated with fertility and showed a similar pattern through lay. There was a genetic contribution of the dam but not the sire to hatch of fertile; its heritability was about 6% from peak lay onward but lower earlier. The second objective was to investigate the relationship between hatchability and internal and external egg quality traits measured at 48 wk of age. These traits, specific gravity, weight loss, egg weight, and Haugh units, had moderate to high heritabilities, 0.53, 0.38, 0.65, and 0.38, respectively. Parameters of the genetic trend in weekly hatchability (mean and persistency) were significantly correlated with these egg quality traits, suggesting that in a bulk mating situation in which individual recording of hatchability is not possible, these quality traits could provide some indication on the trend in flock hatchability.

Variation in actual relationship among descendants of inbred individuals

In previous analyses, the variation in actual, or realized, relationship has been derived as a function of map length of chromosomes and type of relationship, the variation being greater the shorter the total chromosome length and the coefficient of variation being greater the more distant the relationship. Here, the results are extended to allow for the relatives ancestor being inbred. Inbreeding of a parent reduces variation in actual relationship among its offspring, by an amount that depends on the inbreeding level and the type of mating that led to that level. For descendants of full-sibs, the variation is reduced in later generations, but for descendants of half-sibs, it is increased.

Change and maintenance of variation in quantitative traits in the context of the Price equation

The Price equation is a general description of evolutionary change in any character from one generation to the next due to natural selection and other forces such as mutation and recombination. Recently it has been widely utilised in many fields including quantitative genetics, but these applications have focused mainly on the response to selection in the mean of characters. Many different and, in some cases, conflicting models have been investigated by quantitative geneticists to examine the change and maintenance of both genetic and environmental variance of quantitative traits under selection and other forces. In this study, we use the Price equation to derive many such well-known results for the dynamics and equilibria of variances in a straightforward way and to develop them further.

Can more be learned from selection experiments of value in animal breeding programmes? Or is it time for an obituary?

Selection experiments in laboratory animals and livestock have provided a wealth of information on genetic parameters of quantitative traits and on the effectiveness of selection in the short and long term on both directly selected and correlated traits. They have stimulated developments in theory and tests of it, and extreme selected lines continue to be source material for biological study. Some of the main questions and findings are briefly reviewed. Yet much of successful animal breeding practice has been based essentially on statistical methods, assuming where necessary the infinitesimal model, and new developments such as genomic selection are similarly not based on selection experiments. Information on the genetic architecture of quantitative traits is provided by selection experiments, but new methods for deeper studies of the biology are available. I discuss the future role for selection experiments in view of changes in funding streams and technology and conclude that there is little case for starting new experiments, but retention of existing long-term lines is desirable and DNA should be collected from all lines on a continuing basis.

Contributions of genetic and environmental components to changes in phenotypic variation between generations.

We evaluate the extent to which changes in phenotypic variation among generations of populations kept in the same environment are due to changes in genetic (V(A)) or in environmental (V(E)) variance. Data were available on body weight of adult poultry on a total of 89186 birds (mainly females) from six generations of each of seven lines of layers. There was substantial heterogeneity of variation between generations, shown to be in both V(A) and V(E) components. Based on the Akaike information criterion (AIC), the best fit was with both components changing, and a better fit was obtained if V(A)/V(E) (i.e. heritability) or V(E), rather than V(A), was assumed constant. In analyses of quantitative genetic data spanning environmental groups, attention should be paid to whether and how the variance components change among groups before undertaking detailed variance partition that may be sensitive to such changes.