Abstract

Recent developments in the technology for sequencing the genomes of various species has had a profound effect of the working paradigms of various fields of genetics. Included among these fields is the classical field of quantitative genetics, which is a subfield of statistical genetics, that is devoted to traits that can be quantified on some continuous scale and are often influenced by alleles at many loci. In recent years, many investigators have conducted genome wide sweeps and have used a variety of statistical criteria to judge whether identified regions of the human genome have a significant influence on the expression of some quantitative trait such as measurements on patients with Alzheimer's disease. From the point of view of quantitative genetics, the regions of a genome that have some influence on a quantitative trait may be viewed as loci, and variations among these loci at the $DNA$ level, such as nucleotide substitutions or other markers, may be used as working definitions of alleles, and, therefore, can be used to determine whether an individual carries a particular allele at some locus. Given such data, an investigator can identify the genotype of each individual in a study, with respect to the loci under consideration as well as the two alleles present at each locus in a diploid species such as man. This ability to use these working definitions to identify the genotype of each individual in a sample results in a significant change in the working paradigm of sub-field of quantitative genetics, called variance and covariance analysis, because effects and components of variance and covariance may be estimated directly in a sense that will be described in detail in the paper.

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