Evolution__3rd_Edition

234 PART 2 / Evolutionary Genetics
Relatives, such as siblings or
parents and offspring, are
similar because of shared
environments ...
. . . and shared genes
We construct a quantitative genetic
model to predict parent–offspring
similarity
9.5 Relatives have similar genotypes, producing the
correlation between relatives
Figure 9.1 above was a graph of beak depth in many parent–offspring pairs in Geospiza
fortis. Each point is for one offspring and the average of its parents. Beak depth in
G. fortis, like many characters in most species, shows a correlation between parent and
offspring. This is an example of the correlation between relatives, for just as parents
and offspring are similar to each other, so are siblings and more distant relatives to
some extent.
Similarity among relatives may be either environmental or genetic, and the two
effects may have different relative importance in different kinds of species. In humans,
where parents and offspring live together in social groups, much of the similarity will be
due to the family’s common environment (i.e., there is gene–environment correlation).
At the other extreme, in a species like a bivalve mollusk in which eggs are released into
the sea at an early stage, relatives will not necessarily grow up in similar environments.
The environment may not have such a strong influence on similarity among relatives.
Darwin’s finches are probably somewhere between these two extremes. It is easy to
understand the similarity among relatives that is caused by similar environments: in so
far as relatives grow up in correlated environments, and there is environmental variation
in a character, relatives will be more similar than non-relatives.
The similarity between relatives due to their shared genes is evolutionarily more
important. It is possible to deduce the correlation due to shared genes among any
two classes of relatives from the variance terms we have already defined. We shall
consider only one case, the correlation between parents and offspring, to see how it
is done. We can keep things simple by assuming that the environments of parent
and offspring are uncorrelated so environmental effects can be ignored (because any
environmental effect in the parent will not show up in the offspring: if the parent is
larger than average because it chanced on a good food supply, that does not mean its
offspring will too). Any correlation between parent and offspring will then be due to
their genetic effects.
The genetic value of the character in the parent is, we have seen, made up of several
components of which only the additive component is inherited by the offspring. When
mating is random, half that additive component of the individual parent is diluted. At a
locus, a parent has an additive deviation from the population mean in both its genes.
When an offspring is formed, one of the parental genes goes into the offspring together
with another gene drawn at random from the population (because we are assuming
random mating). The average value of the character in the offspring is, as we saw above,
half the additive value of the parent ( 1 /2A); the average genetic value in the parent is
A + D. The correlation between parent and offspring is the covariance between the two
(see Box 9.1):
cov OP =
1
∑ AA ( + D)
2
where the sum is over all offspring–parent pairs. The covariance can be re-expressed as:
..