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In genetics, Heritability is the proportion of phenotypic variation in a population that's attributable to genetic variation among individuals. Variation among individuals may be due to genetic and/or environmental factors. Heritability analyses estimate the relative contributions of differences in genetic and non-genetic factors to the total phenotypic variance in a population.==Definition== Consider a statistical model for describing some particular phenotype: » Phenotype (P) = Genotype (G) + Environment (E).

Considering variances (Var), this becomes: » Var(P) = Var(G) + Var(E) + 2 Cov(G,E).

In planned experiments, we can often take Cov(G,E) = 0. Heritability is defined as: » H^2 = frac

Larger models

When a large, complex pedigree is available for estimating heritability, the most efficient use of the data is in a restricted maximum likelihood (REML) model. The raw data will usually have three or more datapoints for each individual: a code for the sire, a code for the dam and one or several trait values. Different trait values may be for different traits or for different timepoints of measurement. The currently popular methodology relies on high degrees of certainty over the identities of the sire and dam; it isn't common to treat the sire identity probabilistically. This isn't usually a problem, since the methodology is rarely applied to wild populations (although it has been used for several wild ungulate and bird populations), and sires are invariably known with a very high degree of certainty in breeding programmes. There are also algorithms that account for uncertain paternity.
   The pedigrees can be viewed using programs such as Pedigree Viewer (External Link), and analysed with programs such as ASReml, VCE (External Link) or WOMBAT (External Link).

Response to Selection

In selective breeding of plants and animals, the expected response to selection can be estimated by the following equation:
R = h2S
   In this equation, the Response to Selection (R) is defined as the realized average difference between the parent generation and the next generation. The Selection Differential (S) is defined as the average difference between the parent generation and the selected parents.
   For example, imagine that a plant breeder is involved in a selective breeding project with the aim of increasing the number of kernels per ear of corn. For the sake of argument, let us assume that the average ear of corn in the parent generation has 100 kernels. Let us also assume that the selected parents produce corn with an average of 120 kernels per ear. If h2 equals 0.5, then the next generation will produce corn with an average of 0.5(120-100) = 10 additional kernels per ear. Therefore, the total number of kernels per ear of corn will equal, on average, 110.

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