Editing Heritability (section)

=====The ANOVA=====
In an experiment with <math>n</math> sires and <math>r</math> progeny per sire, we can calculate the following ANOVA, using <math>V_g</math> as the genetic variance and <math>V_e</math> as the environmental variance:

{| class="wikitable"
|+ Table 1: ANOVA for Sire experiment
! Source
! d.f.
! Mean Square
! Expected Mean Square
|-
|Between sire groups
|<math>n-1</math>
|<math>S</math>
|<math>\frac{3}{4}V_g + V_e + r({\frac{1}{4}V_g})</math>
|-
|Within sire groups
|<math>n(r-1)</math>
|<math>W</math>
|<math>\frac{3}{4}V_g + V_e</math>
|}

The <math>\frac{1}{4}V_g</math> term is the [[intraclass correlation]] between half sibs. We can easily calculate <math>H^2 = \frac{V_g}{V_g+V_e} = \frac{4(S-W)}{S+(r-1)W}</math>. 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.

The use of ANOVA to calculate heritability often fails to account for the presence of [[Gene–environment interaction|gene–-environment interactions]], because ANOVA has a much lower [[statistical power]] for testing for interaction effects than for direct effects.<ref>{{Cite journal |last=Wahlsten |first=Douglas |date=March 1990 |title=Insensitivity of the analysis of variance to heredity-environment interaction |journal=Behavioral and Brain Sciences |language=en |volume=13 |issue=1 |pages=109–120 |doi=10.1017/S0140525X00077797 |s2cid=143217984 |issn=1469-1825 |url=http://libres.uncg.edu/ir/uncg/f/D_Wahlsten_Insensitivity_1990.pdf |access-date=2020-09-06 |archive-date=2020-10-05 |archive-url=https://web.archive.org/web/20201005031444/http://libres.uncg.edu/ir/uncg/f/D_Wahlsten_Insensitivity_1990.pdf |url-status=live }}</ref>