Analysis of variance methods of estimation of heritability - Basic model

$y\_i\; =\; \backslash mu\; +\; g\_i\; +\; e$

where

$g\_i$ is the effect of [genotype]Create? G_i

and $e$ is the environmental effect.

Consider an experiment with a group of sires and their progeny from random dams. Since the progeny get half of their genes from the father and half from their (random) mother, the progeny equation is

$z\_i\; =\; \backslash mu\; +\; \backslash frac\{1\}\{2\}g\_i\; +\; e$

Intraclass correlations

The second group of progeny are comparisons of means of half sibs with each other (called among sire group). In addition to the error term as in the within sire groups, we have an addition term due to the differences among different means of half sibs. The intraclass correlation is :$corr(z,z\text{'})\; =\; corr(\backslash mu\; +\; \backslash frac\{1\}\{2\}g\; +\; e,\; \backslash mu\; +\; \backslash frac\{1\}\{2\}g\; +\; e\text{'})\; =\; \backslash frac\{1\}\{4\}V\_g$ , since environmental effects are independent of each other.

The ANOVA

{| class="wikitable"

The $\backslash frac\{1\}\{4\}V\_g$ term is the intraclass correlation among half sibs. We can easily calculate $H^2\; =\; \backslash frac\{V\_g\}\{V\_g+V\_e\}\; =\; \backslash frac\{4(S-W)\}\{S+(r-1)W\}$. The Expected Mean Square is calculated from the relationship of the individuals (progeny within a sire are all half-sibs, for example), and an understanding of intraclass correlations.

See also:

• Analysis of variance methods of estimation of heritability
• heritability