Page 250 - 20dynamics of cancer

INHERITANCE 235

size 2Nλ. As long as αλ is not too small, we can use the normal approx-
imation for the Poisson distribution, which tells us that the number of
variant gene copies in the next generation approximately follows a nor-
√
mal distribution with mean αλ and standard deviation αλ. In terms
of variant gene frequency p in the next generation, the 95% confidence
√
interval is p(1 ± 2/ αλ).
How much does drift change gene frequency in one generation in a
stable population, λ = 1? Suppose the gene frequency starts at p = 10 −5
7
in a gene pool of size 2N = 10 , so there are originally α = p2N = 100
variant gene copies. In the next generation, the frequency of the variant
gene has a 95% confidence interval of p(1 ± 0.2), which shows that 5%
of the time the gene frequency will change by more than 20% in one
generation. Over relatively short time periods, significant changes in
the frequency of rare variants may occur.

LINKAGE AND HITCHHIKING
Consider a new variant that exists as a single copy in the population
at frequency p = 1/2N. Suppose that focal variant resides on a chromo-
some near another site that has a rare, favorable variant. Let the only
force acting on the focal variant be the benefit derived from residing
near a favorable variant at a nearby site.
Suppose the neighboring site causes an average increase in reproduc-
tion of 1 + s compared with the normal value of one. Further, suppose
the focal site and beneficial neighbor recombine at a rate of r per gen-
eration. Then the frequency of the focal site tends to increase if s> r,
that is, if the selective benefit, s, of being linked to an advantageous al-
lele is greater than the rate, r, at which that linkage is broken down by
recombination. If the selective benefit happens to be fairly strong, then
the beneficial site will significantly increase the frequency of all of the
closely linked variants.

PLEIOTROPY
Many variants affect more than one phenotype or more than one com-
ponent of survival and reproduction. Suppose, for example, that a vari-
ant enhanced the rate of wound healing. On the one hand, rapid healing
would probably provide some benefit, perhaps against infection. On
the other hand, wound healing can be carcinogenic probably because of