Genic Selection
| AA |
AB |
BB |
| W0 |
W1 |
W2 |
| 1 |
1 - s |
(1-s)(1-s) = (1 - s)2 |
In contrast to additive selection where
each copy of the B allele modifies fitness by a
constant amount s, in genic selection each copy
of B modifies fitness by a constant factor
(1- s). That is, fitness is multiplicative.
Also in contrast to additive selection on diploid
individuals, genic selection models selection in populations
of haploids, such as bacteria
or viruses, because each deleterious allele in
the population reduces population fitness
by the same factor.
Thus, rewriting the final expression in Box 7.5 above with p = fA and q = fa, we get
which re-written in terms of q is
Thus, rewriting the final expression in Box 7.5 above with p = fA and q = fa, we get
p' = (p)/(p + (1 - s)(q))
which re-written in terms of q is
(1 - q') = ((1 - q) / (1 - q) + (1 -
s)(q)) = (1 - q) / (1 - q + q - sq) = (1 - q) / (1 - sq)
-q' = (1 - q)/(1 - sq) - 1
q' = 1 - (1 - q)/(1 - sq) = - q / (1-sq)
q' = 1 - (1 - q)/(1 - sq) = - q / (1-sq)
Note
that Genic selection converges on
Additive selection when s <
0.01, because (1 - s)2
= 1 - 2s + s2 ~
(1 - 2s) when the s2
term is negligible
HOMEWORK: Examine the shape of the curves for Additive, Genic, & Dominant selection against a deleterious recessive for the same values of s.
HOMEWORK: Examine the shape of the curves for Additive, Genic, & Dominant selection against a deleterious recessive for the same values of s.
Figure © 2013 by Sinauer; Text material © 2022 by Steven M. Carr