B. W. Kennedy

Genetic Properties of Animal Models

Abstract For traits controlled by a large number of loci acting additively, use of an animal model with the additive genetic relationship matrix can account for changes in genetic mean and variance due to chance or selection. Changes in genetic variance can result from inbreeding and linkage disequilibrium as a result of selection. Through the relationship matrix, breeding values are expressed as linear functions of breeding values of base population animals and subsequent Mendelian sampling contributions that are unaffected by selection and account for inbreeding. Correct definition of the base population is important. With finite numbers of loci, an animal model does not account for changes in genetic variance due to changes in gene frequency. Genotypic values can be expressed in terms of separate gametic contributions of each parent by gametic models, and a gametic relationship matrix can be constructed. With dominance, use of an animal model with the dominance relationship matrix leads to BLUP of dominance genetic merit if number of loci is sufficiently large and no inbreeding occurs. With inbreeding, inclusion of the dominance relationship matrix (even if modified to account for inbreeding contributions) does not account for inbreeding depression. However, effects of inbreeding depression might be accommodated by including the inbreeding coefficient as a covariate in the model.

The use of the relationship matrix to account for genetic drift variance in the analysis of genetic experiments.

SummarySelection experiments can provide information on genetic parameters such as realized heritability and response to selection. Often, due to lack of adequate replication, empirical sampling variances of estimated response cannot be computed and therefore use must be made of theoretical formulae. Most of the variance between a conceptually large number of selected lines drawn from the same base population is contributed by genetic drift, which depends on the population structure and can therefore be predicted before the experiment is carried out. The theory of variation of response to selection has been developed mainly by Hill, who produced formulae to adjust the variance of estimators to take account of genetic drift. In this paper, we draw attention to properties of the additive genetic relationship matrix that lead to well established results in population genetics theory. We show how inclusion of the additive genetic relationship matrix among the observations leads to sampling variances of estimators of genetic means that account for the variance due to genetic drift.

Use of Mixed Model Methodology in Analysis of Designed Experiments

Applications of mixed model methods in the analysis of designed experiments are illustrated and discussed for purposes of: (1) increasing rate of selection response to create genetically diverse lines rapidly or to demonstrate feasibility of selection, (2) estimation of genetic parameters free of bias from selection and inbreeding, (3) estimation of response to selection with or without controls, and (4) verification of experimental design prior to the experiment. For traits controlled by a large number of additive loci, use of the numerator relationship matrix in the mixed model equations accounts for changes in additive genetic variance due to inbreeding, assortative mating and gametic disequilibrium resulting from selection. If the number of loci is small, non-normality of the genotypic distribution and changes in variance due to gene frequency changes (including fixation) are not accounted for but these seem to be of small consequence, at least for short-term selection. Use of mixed model methods do not require prior knowledge of base population heritability which can be estimated from the data unaltered by selection. If dominance effects are important, properties of the dominance relationship matrix and use of mixed model methods are not yet well understood in inbred and selected populations. Simulation results indicate that use of mixed model methods can be effective in randomly mated populations, even if the number of loci is small. There is evidence of bias in selected populations, however, particularly when gene frequencies are extreme. Properties of mixed model methods under dominance and other non-additive genetic models need more study.

Selection for Weaning Weight in Targhee Sheep in Two Environments. I. Direct Response

In 1961, selection for 120-d weight was initiated in two flocks from a common base population of grade Targhee sheep. At Davis, sheep were maintained on a good plane of nutrition, on irrigated pasture or in drylot. At Hopland, sheep grazed annual grassland range, with supplementary feeding only at mating and lambing. Selected (DW) and control (DC) lines were maintained at Davis from 1961 through 1977. A selected (HW) line, replicate control (HC1 and HC2) lines and a line (DH) mated to the Davis DW rams were maintained at Hopland from 1961 through 1980, with the exception that HC2 was terminated in 1977. Multiplicative factors were used to adjust weights for effects of age of dam, sex and type of birth and rearing. Response to selection was estimated as the difference between selected and control line linear regression coefficients of adjusted line means on year. The Hopland replicate controls did not differ significantly from each other (HC1 - HC2 = .004 +/- .056 kg/yr), and the control line data were pooled (HC). The overall control line mean 120-d weights on a female, single, mature-dam basis were 33.2 and 30.4 kg at Davis and Hopland, respectively. Direct response was greater at Davis than at Hopland: DW - DC = .524 +/- .073 kg/yr (P less than .001); HW - HC = .151 +/- .034 kg/yr (P less than .001). Corresponding realized heritabilities were .17 and .06. Direct response for the DH line was DH - HC = .226 +/- .036 (P less than .001); realized heritability was .08. Response in the DH line was greater (P less than .05) than that in the HW line: HW - DH = -.075 +/- .037 kg/yr. This indicates that: (1) genetic improvement made on a higher plane of nutrition was expressed, but to a lesser degree, under range conditions and (2) selection under better feed conditions resulted in at least as much improvement in growth rate in a range environment as did selection under range conditions.

Selection for weaning weight in Targhee sheep in two environments. II. Correlated effects.

Targhee sheep were selected for 120-d weight under irrigated pasture-drylot conditions at Davis (DW) and under range conditions at Hopland (HW). Unselected control lines were maintained in both environments (DC, HC1 and HC2). At Hopland, a line (DH) was maintained in which ewes were mated to Davis (DW) rams. Selection for 120-d weight was successful in both environments, with more improvement made in the drylot environment. The genetic improvement made in the drylot environment was expressed, although to a lesser degree, under range conditions. Correlated responses were analyzed. Birth weight increased significantly in all three selected lines; the increase was less in line DH than in the other two lines. In all selected lines, weights of ewes of all ages at mating increased significantly compared with their respective controls. Proportion of ewes lambing decreased (P less than .05) in line DH; the trend was negative but nonsignificant in line DW. Differences in litter size between lines within location were not significant. Lamb survival to weaning decreased in lines DW (P less than .05) and DH (P less than .01), compared with their respective controls; and the trend in HW was negative but nonsignificant. Fertility and survival data indicated that, under range conditions, the line selected under drylot conditions (DH) was less fit than the line selected under range conditions (HW). As a result of the decreases in lamb survival and fertility, none of the selected lines produced more total lamb weight weaned per ewe than the controls, in spite of the significant direct response to selection. Mature ewes of lines DH and DW produced less total lamb weight weaned per ewe (P less than .001 and P less than .05) than their respective controls. The results indicate that while single trait selection for growth rate to weaning results in heavier lambs, it does not increase and may decrease total lamb production per ewe.

Reproductive Technology and Genetic Evaluation

The effects of use of embryo transfer and embryo splitting, and potential applications of embryo and semen sexing, chimeric and polyploid animals and gene transfer on genetic evaluation of dairy cattle are considered. Procedures for joint cow and bull evaluation under an animal model to accommodate embryo transfer in the population are reviewed. Genetic evaluation models based on data involving animals of identical genotype, as created through embryo splitting or other forms of cloning, are proposed. Approaches to genetic evaluation for traits influenced by both transgenes and polygenes are also suggested. Evaluation of cytoplasmic effects in embryo transfer programs is considered, and of dominance effects in populations where considerable use is made of embryo transfer and splitting. Problems of preferential treatment of genotypes produced through expensive reproductive technology are addressed.