[For this model, allele A is semi-dominant
to allele B, so we use t for selection coefficient]
AA | AB | BB | ||
|
W0 | W1 | W2 | qinitial |
Island | 1 | 1-t | 1-2t | qi 0 |
Mainland | 0 | 0 | 1 | qm 1 |
What is the equilibrium frequency
f(B)
on the island?
change in f(B)
from
migration: qi
=
m(qm - qi)
change in f(B)
from
selection: qi
= -tqi(1 - qi)) / (1 - 2tqi)
-tqi(1 - qi)
[if
tqi << 1]
Then, combined
change qi
=
m(qm
- qi) - tqi(1 - qi)
= mqm - mqi - tqi + tqi2)
= tqi2 - (m +
t)qi + mqm
For qi
=
0 this can be solved as a quadratic
equation for several special cases:
if
m
t: qi qm
migration
behaves like mutation
if
m
>> t: qi
qm
mainland
alleles 'swamp' island population
if
m
<< t:
qi
(m / t)qm
some equilibrium is
achieved, if
m is constant