Applications of distribution theory in quantitative genetics

Abstract

The present study was designed to develop procedures for estimating genetic parameters in a quantitative trait and detecting association between a quantitative trait and a genetic marker using a random sample of individuals from the population. An exact distribution of phenotypic values of a quantitative trait was used by which parameters such as number of loci involved, gene frequency at each locus, additive and dominant genotypic value, and the variance of environmental effects were estimated. When association between the quantitative trait and a genetic marker occurred, an additional parameter for the degree of linkage disequilibrium was introduced in the exact distribution. For testing the validity and usefulness of the procedures, individual phenotypic values were simulated by the computer with given parameters. The number of loci involved in the quantitative trait was 2, 5, and la, and gene frequency at each locus was chosen at random. Three heritability values were investigated; namely, 0.2, 0.5, and 0.8. The genotypic values were then calculated by setting degree of the dominance either to zero (no dominance) or one (complete dominance). The environmental effects were assumed to be normally distributed; however, the phenotypic distribution of the quantitative trait under investigation was not specified. Five replicate runs were made for most tests to allow variations in gene frequencies, each sample size being set to 5000. Smaller samples of 100 and 500 individuals were also tested. Based on the log likelihood function values, good estimations by the maximum likelihood method were obtained when heritability of the quantitative trait was moderately high (h^2 ≥.5). When the heritability value was low, the phenotypic distribution of the quantitative trait was mainly determined by environmental effects and, therefore, was expected to be normal by assumption. In this case, the method might not give consistent estimates of genetic parameters. As the number of loci increased, the phenotypic distribution would approach normal by the Central Limit Theorem; however, the procedure was still effective for traits with high heritability. Several cases for the association between one of the loci involved in the quantitative trait and a genetic marker were considered, including (1) complete independence (no linkage), (2) partial linkage, and (3) complete linkage or identical locus. The approach employed was mainly based on the distributions of phenotypic values. Data were subgrouped by the genotypes of the marker locus resulting in several phenotypic distributions, one for each genotype of the genetic marker. When association occurred between a quantitative trait locus and a genetic marker locus, the subclass distributions would be expected to be different from one another. The subsequent estimates of parameters including the degree of linkage disequilibrium were then derived from the exact distributions by the maximum likelihood method. The results were generally good. The present study using simulated data has clearly demonstrated that by employing the distribution of phenotypic values of the quantitative trait, it is possible to establish a genetic basis for the character from a random sample of individual data. When information on other genetic markers is available, the association between the quantitative trait and a genetic marker as measured by linkage disequilibrium may be estimated. However, further research would be needed to apply the procedures to real (non-simulated) data and to consider other parameters such as genotype-environmental interactions and epistatic effects in the phenotypic distribution.