Evolution__3rd_Edition

232 PART 2 / Evolutionary Genetics
The variation in a population is
measured quantitatively as a
“variance”
Each factor that influences a
character has a variance
The variation seen for the character in any one population could exist because
of variation in any one of, or any combination of, these effects. Thus the individual
differences could be all due to different environmental effects, with every individual
having the same value for G. Or it could be 25% due to the environment, 20% to additive
effects, 30% to dominance effects, and 25% to interaction effects. The proportion of
variation due to the different effects matters when we wish to understand how a population
will respond to selection. If all the variation exists because different individuals
have different values of E, there will be no response to selection; but if the variation
is mainly additive genetic variation, the response will be large. The proportion of the
variation that is due to different values of A in different individuals tells us whether
the population can respond to selection.
The variability in the population due to any particular factor, such as the environment,
is measured by the statistic called the variance. (Box 9.1 explains some statistical
terms used in quantitative genetics.) Variance is the sum of squared deviations from
the mean divided by the sample size minus one. So for all the values x of a character like
beak size in a population, the variance of x is (see Box 9.1 for the notation):
V
n
=
1
− 1
∑
X i
We have seen how the total phenotype, genetic effect, environmental effect, and so on,
can be measured for an individual; the measurements (P for phenotypic effect, etc.) are
expressed as deviations from the mean. We can therefore easily calculate, for a population,
what their variances are:
Phenotypic variance
Environmental variance = =
− ∑
1
VE
E
n 1
Genetic variance
Dominance variance
Additive variance
( x − c)
2
= =
− ∑
1
VP
P
n 1
= =
− ∑
1
VG
G
n 1
= =
− ∑
1
VD
D
n 1
= =
− ∑
1
VA
A
n 1
2
2
2
The phenotypic variance for a population, for example, expresses how spread out
the frequency distribution for the character is. If the frequency distribution is wide,
with different individuals having very different values of the character, the phenotypic
variance will be high. If it is a narrow spike, with most individuals having a similar value
for the character, phenotypic variance will be low.
2
2
..