Biology Reference
In-Depth Information
BOX 11.5
RELATEDNESS REVISITED
In this and following chapters we discuss relatedness coefficients in terms of
genes shared identically by descent. However, it should be realized that this is
just a very useful approximation, which greatly simplifies discussion. More
formally, the coefficient of relatedness,
r
, is defined statistically, as a measure of
the genetic similarity between social partners, relative to the rest of the
population (Hamilton, 1970; Grafen, 1985).
The statistic
r
can be positive or negative like any statistical correlation, but
will have a mean value within a population of zero. This is shown graphically in
Fig. B11.5.1, where the shaded area represents the proportion of the actors
genes that are shared with three individuals (A, B and C) and the population as
a whole. For clarity, we have made the actor share ½ of its genes with the
population, but this proportion could take any value between zero and one.
Individual A carries the actors genes at a higher frequency than the population,
so they are positively related (
r
0). Individual B carries the actors genes at a
lower frequency than the population, so they are negatively related (
r
>
0).
Finally, individual C carries the actors genes at the same frequency as the
population, and so they are zero related (
r
<
=
0). It follows that the average
relatedness in the population is zero.
A
B
C
Population
Fig. B11.5.1
The geometric view of relatedness. The shaded area shows the
proportion of the actors genes shared with three potential recipients (A, B and C)
and the population as a whole. As described in the text, the actor is positively related
to A, negatively related to B and zero related to C.
large number of genetically identical females and a large number of genetically clonal
males, who are the brothers of the females. While most of these wasp larvae develop
normally, a number develop precociously to form a sterile soldier caste that attacks
other larvae within the host. Gardner
et al
. (2007) suggested that this is spiteful
behaviour aimed at relatively unrelated individuals (brothers;
r
In polyembryonic
wasps, some
larvae develop as
soldiers that
attack other
larvae
=
0.25), to free up
resources for closer relatives (clonal sisters;
r
1; see Chapter 13 for the calculation
of relatedness coefficients in species such as wasps which have haplodiploid
genetics). However, to demonstrate that this really represents spite, the following
conditions are required.
=
