Quantitative genetics

Quantitative genetics is a branch of population genetics that deals with phenotypes that vary continuously (in characters such as height or mass)—as opposed to discretely identifiable phenotypes and gene-products (such as eye-colour, or the presence of a particular biochemical). σ 2 2 = ( 1 )   Δ σ 2 + ( 1 − Δ f ) σ 1 2 {displaystyle sigma _{2}^{2}=left(1 ight) Delta sigma ^{2}+left(1-Delta f ight)sigma _{1}^{2}}     ( 1) σ t 2 = p g q g [ 1 − ( 1 − Δ f ) t ] {displaystyle sigma _{t}^{2}=p_{g}q_{g}left}     ( 2) Quantitative genetics is a branch of population genetics that deals with phenotypes that vary continuously (in characters such as height or mass)—as opposed to discretely identifiable phenotypes and gene-products (such as eye-colour, or the presence of a particular biochemical). Both branches use the frequencies of different alleles of a gene in breeding populations (gamodemes), and combine them with concepts from simple Mendelian inheritance to analyze inheritance patterns across generations and descendant lines. While population genetics can focus on particular genes and their subsequent metabolic products, quantitative genetics focuses more on the outward phenotypes, and makes summaries only of the underlying genetics. Due to the continuous distribution of phenotypic values, quantitative genetics must employ many other statistical methods (such as the effect size, the mean and the variance) to link phenotypes (attributes) to genotypes. Some phenotypes may be analyzed either as discrete categories or as continuous phenotypes, depending on the definition of cut-off points, or on the metric used to quantify them.:27–69 Mendel himself had to discuss this matter in his famous paper, especially with respect to his peas attribute tall/dwarf, which actually was 'length of stem'. Analysis of quantitative trait loci, or QTL, is a more recent addition to quantitative genetics, linking it more directly to molecular genetics. In diploid organisms, the average genotypic 'value' (locus value) may be defined by the allele 'effect' together with a dominance effect, and also by how genes interact with genes at other loci (epistasis). The founder of quantitative genetics - Sir Ronald Fisher - perceived much of this when he proposed the first mathematics of this branch of genetics. Being a statistician, he defined the gene effects as deviations from a central value—enabling the use of statistical concepts such as mean and variance, which use this idea. The central value he chose for the gene was the midpoint between the two opposing homozygotes at the one locus. The deviation from there to the 'greater' homozygous genotype can be named '+a' ; and therefore it is '-a' from that same midpoint to the 'lesser' homozygote genotype. This is the 'allele' effect mentioned above. The heterozygote deviation from the same midpoint can be named 'd', this being the 'dominance' effect referred to above. The diagram depicts the idea. However, in reality we measure phenotypes, and the figure also shows how observed phenotypes relate to the gene effects. Formal definitions of these effects recognize this phenotypic focus. Epistasis has been approached statistically as interaction (i.e., inconsistencies), but epigenetics suggests a new approach may be needed. If 0<d<a, the dominance is regarded as partial or incomplete—while d=a indicates full or classical dominance. Previously, d>a was known as 'over-dominance'. Mendel's pea attribute 'length of stem' provides us with a good example. Mendel stated that the tall true-breeding parents ranged from 6–7 feet in stem length (183 – 213 cm), giving a median of 198 cm (= P1). The short parents ranged from 0.75–1.25 feet in stem length (23 – 46 cm), with a rounded median of 34 cm (= P2). Their hybrid ranged from 6–7.5 feet in length (183–229 cm), with a median of 206 cm (= F1). The mean of P1 and P2 is 116 cm, this being the phenotypic value of the homozygotes midpoint (mp). The allele affect (a) is = 82 cm = -. The dominance effect (d) is = 90 cm. This historical example illustrates clearly how phenotype values and gene effects are linked. To obtain means, variances and other statistics, both quantities and their occurrences are required. The gene effects (above) provide the framework for quantities: and the frequencies of the contrasting alleles in the fertilization gamete-pool provide the information on occurrences. Commonly, the frequency of the allele causing 'more' in the phenotype (including dominance) is given the symbol p, while the frequency of the contrasting allele is q. An initial assumption made when establishing the algebra was that the parental population was infinite and random mating, which was made simply to facilitate the derivation. The subsequent mathematical development also implied that the frequency distribution within the effective gamete-pool was uniform: there were no local perturbations where p and q varied. Looking at the diagrammatic analysis of sexual reproduction, this is the same as declaring that pP = pg = p; and similarly for q. This mating system, dependent upon these assumptions, became known as 'panmixia'.