Suppose 100,000 newborn
mice are produced by a group of parents among which the
frequency of allele A is 0.3. The newborns are
distributed according to Hardy-Weinberg expectations, such
that there are 9,000 AA, 42,000 AB, and 49,000
BB mice. The fitness of the three types measured as viability (the
probability of survival to reproductive age) of each
of the three phenotypes corresponding to genotypes AA,
AB, and BB is 0.5, 0.4, and 0.3,
respectively. Note that this is an additive model, in
which each B allele decreases viability by 0.1.
Therefore, the expected numbers of survivors to reproductive
age are:
AA: 0.5 x 9,000
newborns = 4,500 AA adults
AB: 0.4 x 42,000 newborns = 16,800
AB adults
BB: 0.3 x 49,000 newborns = 14,700
BB adults
The total number of
surviving adults is (4,500 + 16,800 + 14700) = 36,000.
Following established principles, f(A) = [(2)(4,500) +
16,800] / (2)(36,000) = 0.3583, and f(B) =
[(2)(14,700) + 16,800] / (2)(36,000) = 0.6417 = 1 - f(A).
Viability selection has therefore decreased the relative
frequency f(B)' by 0.7000 - 0.6417 = 0.0583,
about 6%.
Allele frequency change in the model just
given is determined from relative rather than absolute
viability. For example, if relative viabilities were 0.05,
0.04, and 0.03, the total number of mice
surviving to adulthood would be only 3,600, but the
calculated allele frequency change would be the same as before
[PROVE this to yourself].
This also shows that evolution, defined as changes in
allele frequencies, can occur in a population that is
declining in numbers.
Alternatively, viability selection
may allow population size to remain constant is, if the
expected number of newborn mice of each genotype surviving to
adulthood is weighted by the ratio of newborns
to adults, in this case 100,000/36,000 = 2.778. Then
AA: 0.5 x 9,000
newborns x 2.778 = 12,500 AA adults
AB: 0.4 x 42,000 newborns x
2.778 = 46,670 AB adults
BB: 0.3 x 49,000 newborns x 2.778
= 40,830 BB adults
The expected total
number of adults is now 100,000.
Calculated allele frequency change would be the same as in
the original model [PROVE
this to yourself].
[The original FORTRAN form of the Matlab NatSel program
achieved the same result by repeatedly sampling from the
post-selection adult population pool until the
pre-selection population size is recovered. This is
essentially K-selection, which maintains N near a constant
carrying capacity].
Finally,
note that weighting by a larger factor of (say
3.0) would result in an increase in the population size,
but once again calculated allele frequency changes would
be the same. Population increase would not be due
to an increase in the frequency of the allele at a fitness
advantage. This again shows that relative Darwinian
fitness and absolute survival are unrelated.