Change in frequency
of a rare allele under Positive
Directional Selection
Dominant, Semi-Dominant, & Recessive cases
In a single-locus model with two alleles A1
and A2, initial p =
f(A1)
= 0.001. The three curves
trace f(A1)
over time for three
modes of dominance.
The Blue curve
shows the case of dominance of
W11 to W12 (W11
= W12 = 1.0). The Red curve shows an additive (semi-dominance) model, in
which each W2 allele
decreases dW = 0.4, such that W12
= 1.0 - 0.4 = 0.6., and W22
= 1.0 - (0.4+0.4) = 0.2. The Green curve shows
the case where
W22
is recessive to
W12
(W12
= 0.2). The difference between
the shapes of the curves reflects how mean population fitness
(
)
varies as f(A1) 
1.0
(SR2019 4.2).
NB: The dominance relationships of
any two alleles at a locus are fixed genetically.
The graph also shows the fate of a common allele under negative
directional selection, if the Y-axis values are
inverted top to bottom (1 0)
and labelled f(A2) = q.
That is, the behaviors of advantageous and disadvantageous
alleles are complementary for any particular
dominance model.
The principles presented in this graph will be
explored in greater depth in the laboratory exercises for
Natural Selection.
HOMEWORK:
Demonstrate that these curves can be obtained from
appropriate values entered in the Hardy- Weinberg program
GSM in Excel.