xia@cc.helsinki.fi (10/21/90)
A Quick and Dirty Method for Measuring Gene Flow
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Let P(A) represent frequency of allele A of a neutral
polymorphic locus. For n populations, let P1t(A) be the
frequency of A in population 1 at generation t, P2t(A) be the
frequency of A in population 2 at generation t,......, and
Pnt(A) be the frequency of A in population n at generation t.
Let P1_t+1(A), P2_t+1(A),......, Pn_t+1(A) be the corresponding
allelic frequency at generation t+1.
Now we have the following table.
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PopulationPt(A) Pt+1(A)
1 P1t(A) P1_t+1(A)
2 P2t(A) P2_t+1(A)
3 P3t(A) P3_t+1(A)
. .
. .
. .
n Pnt(A) Pn_t+1(A)
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The relationship between Pt+1(A) and Pt(A) is
Pt+1(A) = a + b*Pt(A) + E.
When there is neither gene flow nor random factors such as
drift, we have a linear relationship with intercept=0, slope=1
and E=0.
When there is only random drift, we have a linear relationship
with a < 0, b > 1 and E<>0 (not equal to 0). This is because the
probability of an allelic frequency, say 0.8, drifting to 1 is
always greater than the probability of an allelic frequency of
1 drifting to 0.8 (The latter probability is 0). Similarly, the
probability of an allelic frequency of 0.2 drifting to 0 is always
greater than the probability of an extinct allele drifting back to
0.2, the latter probability again being 0. In this special
case, b-1 (a positive value) is a measure of random drift.
When there is only gene flow, we have a linear relationship with
a > 0, b < 1 and E<>0 (not equal to 0). This is because the
probability of an allelic frequency of 1 becoming smaller than 1
is always greater than that of becoming larger than 1, if only
gene flow is involved. Similarly, the probability of an allelic
frequency of 0 becoming larger than 0 is always greater that that
of becoming smaller than 0. In this special case, b-1 (a negative
value) is a measure of gene flow.
When there are both gene flow and random drift, then we need to
calculate b not only for allele A of one particular locus, but
also for many other loci. Although allelic frequency of most
loci may be under control of both random drift and gene flow,
some loci may be affected only by random drift and some only by
gene flow. Thus, if we obtain b for each of many loci, then the
largest b value minus 1 is a measure of random drift and the
smallest b value minus 1 is a measure of gene flow.
This method apparently is not affect by historical factors.
Please note that the validity and utility of the method has not
been checked. I propose it just to be criticized.
Xuhua