Biology Reference
In-Depth Information
BOX 11.2
CALCULATION OF r, THE COEFFICIENT OF RELATEDNESS
r
is the probability that a gene in one individual is an identical copy, by descent,
of a gene in another individual.
General method
Draw a diagram with the individuals concerned and their common ancestors,
indicating the generation links by arrows. At each generation link there is a
meiosis, so a 0.5 probability that a copy of a particular gene will get passed on.
For
L
generation links the probability is (0.5)
L
. To calculate
r,
sum this value for
all possible pathways between the two individuals:
∑
L
r
=
(0.5) .
Specific examples
These diagrams show calculations of
r
between two individuals represented
by solid circles. Other relatives are indicated by open circles. In all cases,
outbreeding is assumed. The solid lines are the generation links used in the
calculations; the dotted lines are the other links in the pedigrees.
(a)
Parent and offspring
(b)
Grandparent and grandchild
r
=
1(0.5)
1
r
=
1(0.5)
2
=
0.5
=
0.25
(c)
Full siblings (brother, sister)
(d)
Half-siblings
r
=
2(0.5)
2
r
=
1(0.5)
2
=
0.5
=
0.25
(Identical genes by descent can be
inherited by two pathways, either
mother or father)
(Identical genes by descent can only be
inherited from one parent)
(e) Cousins
r
=
2(0.5)
4
=
0.125
individual will be present, by virtue of descent from a common ancestor, in a brother,
sister, cousin and so on. For brothers and sisters
r
is 0.5, for grandchildren it is 0.25
and for cousins it is 0.125 (Box 11.2). Bill Hamilton (1963, 1964) realized the
important implication of this for the evolution of altruism, showing that just as gene
proliferation can occur through parental care so it can through care for siblings,
cousins or other relatives. Table 11.1 shows various values of
r
for descendant kin and
non-descendant kin, and Box 11.3 describes how neutral molecular markers can be
used to measure relatedness in natural populations.
