Evolution__3rd_Edition

236 PART 2 / Evolutionary Genetics
Heritability is a measure of the
genetic influence on a character
Heritability can be measured by
several methods
offspring. For instance, many of the properties of an individual phenotype are accidentally
acquired characters, such as cuts, scrapes, and wounds; if we measure these in
parent and offspring they will show no correlation: V A = 0. Moreover, some characters,
such as the number of legs per individual in a natural population of, say, zebra, show
practically no variation of any sort and for them V A trivially is zero. Additive variance
is therefore often discussed as a fraction of total phenotypic variance, and it is this
fraction that is called the heritability (h 2 ) of a character:
h
2
V
=
V
A
P
Heritability is a number between zero and one. If heritability is one, all the variance
of the character is genetic and additive. Given that V P = V E + V A + V D , all the terms on
the right other than V A must then be zero. In so far as the factors other than additive
variance account for the variance of a character, heritability is less than one.
Heritability has an easy intuitive meaning. Consider two parents that differ from the
population by a certain amount. If their offspring also deviate by the same amount,
heritability is one; if the offspring have the same mean as the population, heritability
is zero; if the offspring deviate from the mean in the same direction as their parents
but to a lesser extent, heritability is between zero and one. Heritability, therefore, is
the quantitative extent to which offspring resemble their parents, relative to the population
mean.
How can we estimate the heritability of a real character? One method is to cross two
pure lines. This is mainly of interest in applied genetics, where the problem might be to
breed a new variety of crops; it has little interest in evolutionary biology. The two other
main methods are to measure the correlation between relatives and the response to
artificial selection. Figure 9.1 is an example which uses the correlation between relatives.
The slope of the graph, which shows the beak size in offspring finches in relation to
the average beak size of the two parents, is equal to the heritability of beak size in that
population. The reason is as follows. The slope of the line is the regression of offspring
beak size on mid-parental beak size. The regression of any variable y on another variable
x equals cov xy /var x (Box 9.1). The covariance of offspring and mid-parental value
equals 1 /2V A (Table 9.1) and the variance of the mid-parental beak size is equal to 1 /2V P .
(It is half the total population variance because two parents have been drawn from the
population and their values averaged: if Figure 9.1 had the value for one parent on the
x-axis, its variance would be V P .) The regression slope simply equals V A /V P , which is the
character’s heritability. For beak depth in Geospiza fortis on Daphne Major, the regression
and therefore heritability is 0.79.
9.7 A character’s heritability determines its response to
artificial selection
How can quantitative genetics be applied to understand evolution? There are many
ways, and we shall consider two of them here: directional selection and stabilizing
selection. As we have seen (Section 4.4, p. 76), three main kinds of selection are usually
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