# Heritability in population genetics

What is the difference between narrow sense heritability and broad sense heritability?
Does heritability in the broad sense refer to the degree of genetic determination? Heritability in the narrow sense refers to additive effect of alleles , what does it actually mean?

• The answer to this question should give you everything you need. Apr 29 '17 at 9:24

Heritability in the narrow sense

Heritability in the narrow sense $h_N$ is the genetic variance $V_G$ over the overall phenotypic variance $V_P$

$$h_N = \frac{V_G}{V_P}$$

More information at Why is a heritability coefficient not an index of how “genetic” something is?.

The heritability in the broad sense $h_B$ is the additive genetic variance $V_A$ over the overall phenotypic variance $V_P$

$$h_B = \frac{V_A}{V_P}$$

Decomposing of the genetic variance

Adding together the additive genetic variance $V_A$, the dominance genetic variance $V_D$ (and the epistatic genetic variance $V_I$) sums up to the overall genetic variance $V_G$. Here I will ignore the epistatic genetic variance

$$V_G = V_A + V_D$$

, where

$$V_D = x^2(1-x)^2(2\cdot M_{12} - M_{11} - M_{22})^2$$

$$V_A = 2x(1-x)(xM_{11}+(1-2x)M_{12} - (1-x)M_{22})^2$$

, where $M_{00}$, $M_{01}$ and $M_{11}$ are the measurements of the phenotypic trait in genotypes 00, 01 and 11 respectively.

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