Evolution__3rd_Edition

..
Parent–offspring similarity depends
on the additive genetic variance
Table 9.1
The covariances between several different classes of relatives.
Relatives Covariance
1
One parent and offspring VA 2
1
Mid-parent and offspring VA 2
1
Half sibs VA 4
1 1
Full sibs VA + VD 2 4
1
covOP =
2
1 /2 ∑ AD = 0 because A and D have been so defined as to be uncorrelated. If an individual
has a big value of A, we know nothing about whether its value of D will be big
or small. That leaves:
cov OP =
1
A2+ AD
2
∑ ∑
1 2 1
∑ A = VA 2 2
CHAPTER 9 / Quantitative Genetics 235
In words, the covariance of an offspring and one of its parents is equal to half the
additive genetic variance of the character in the population.
The expression for the covariance between one parent and its offspring is true for
each parent. It is a small step (though we shall not go into it here) to show that the same
expression also gives the covariance between offspring and the midparental value: it is
also 1 /2V A . Other expressions can be deduced, by similar arguments, for the covariance
between other classes of relatives (Table 9.1). The formulae are useful for estimating the
additive variances of real characters. However, the estimates become most interesting,
for the evolutionary biologist, when expressed in terms of the statistic called heritability.
9.6 Heritability is the proportion of phenotypic variance
that is additive
The similarity between relatives in general, and between parents and offspring in
particular, is governed by the additive genetic variance of the character. If a character
has no additive genetic variance in a population, it will not be inherited from parent to