Suppose
100,000 newborn mice are born in a population for which f(A)
= 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. Suppose that fitness,
measured as viability (the
expectation of survival to reproductive age), of the
corresponding three phenotypes are 0.5, 0.4,
and 0.3, respectively. 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
newborns surviving as reproductive 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)'
in the adults by 0.7000 - 0.6417 = 0.0583, about 6%,
with respect to newborns.
In this case, change in allele
frequencies occurs in a population that declines in
numbers between the parents and offspring. Allele
frequency change is determined from relative rather
than absolute viability. With more intense selection,
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 [HOMEWORK:
Prove this].
Viability selection may occur while
population size remains constant,
iff the expected number of newborn
mice of each genotype surviving to adulthood is proportional
to
a constant carrying capacity K of the environment, in
this case 100,000. Expected numbers can be predicted by weighting
by the ratio of newborns to that of the 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 newborns that survive to adulthood is now 100,000.
Calculated allele frequency change would be the same as in
the original model [HOMEWORK:
Prove this]. This is a K-selection
model that acts to maintain N near a constant
carrying capacity K. Computer models (such as NatSel)
simulate this by generating genotypes at random, applying
the viability of each type, and continuing to add to the
population in the same manner, until the total number of
individuals again reaches the carrying capacity of
100,000.
Finally,
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 [HOMEWORK: Prove
this]. This is still a K-selection
model, where K varies according to
environmental quality. Although population size increases,
this would not be due to an increase in the
frequency of the allele that offers the greater fitness
advantage. This again shows that relative
Darwinian fitness and absolute
survival are unrelated.