Page 254 - 20dynamics of cancer

INHERITANCE 239

1
Force of selection 0.6
0.8

0.4
0.2

0
0 20 40 60 80
Age

Figure 11.8 The force of selection at different ages. Loss in fitness caused by
cancer is the force of selection averaged over the probabilities of death at dif-
T
ferent ages. This loss is pr = 0 ˙ x n (t)f(t)dt, where pr, the fractional loss in
fitness, is the averaged product of the age-specific incidence, ˙ x n (t), and the loss
in reproduction caused by death at age t, f(t). The age-specific incidence pro-
vides a measure of penetrance at different ages. No good data exist to estimate
the force of selection at different ages for humans; however, the curve shown
here gives the approximate shape of the force of selection.

shows the technical details. The following paragraphs describe the main
points.
Suppose the probability of expression in a carrier—the penetrance—
is p, and the reduction in reproductive success is r.If q is the frequency
of the mutant allele in the population, then qp is the frequency of cases,
and the rate at which mutations are removed in each generation is qpr,
the frequency of cases multiplied by the reduction in reproductive suc-
cess in each case. Equilibrium occurs when mutant alleles purged by
selection match the influx of new mutations at rate u, so at equilibrium,
qpr ≈ u.

Familial adenomatous polyposis.—Inherited mutations of the APC gene
act in a dominant manner and cause the colon cancer syndrome familial
adenomatous polyposis (FAP) (Kinzler and Vogelstein 2002). Nearly all
carriers develop cancer, with a median age of onset of about 40 years.
The frequency of cases, qp, is of the order of 10 −4 . We do not have
historical data on the reduction in reproductive success that occurs in
the absence of treatment. A reasonable value is r ≈ 10 −1 , which takes