Biology Reference
In-Depth Information
Only 80% of the 22 aa individuals will reproduce. Therefore,
0.8
22
¼
17.6, or 18 people, will pass along their a alleles, contributing
2
18 or 36 a alleles.
þ
þ
¼
A total of 28
50
18
96 individuals will reproduce, so the total gene
pool will consist of 96
2 or 192 alleles.
p
2
(new frequency of the A allele)
¼
(56
þ
50)/192
¼
106/192
¼
0.5521.
q
2
(new frequency of the a allele)
¼
(50
þ
36)/192
¼
86/192
¼
0.4479.
After two generations, we see the a allele frequency has already fallen
substantially because of the selective disadvantage of the aa genotype,
showing the population is not in Hardy-Weinberg equilibrium. It also
raises the following questions: Because the pool of the a allele will be
reduced when the aa individuals die, it is intuitive that the a allele will
diminish, but will it eventually die out? Does the answer depend on
what fraction of those with paired aa alleles die?
To answer these questions, we derive a general formula describing the
dependence of allele frequencies in any given generation upon those of
the previous generation and enabling us to determine the long-term
behavior of the population. To reinforce the informal notation used
above, suppose the initial proportions of the alleles are:
p
0
¼
proportion of A allele;
q
0
¼
p
0
¼
1
proportion of a allele.
Then
p
0
;
P
ð
AA
Þ¼
P
ð
Aa
Þ¼
2p
0
q
0
;
and
q
0
:
P
ð
aa
Þ¼
Now suppose the aa combination is harmful so that only a fraction, say
a
(where 0
< 1), of the homozygous recessive genotype survives to
reproduce. Thus, before reproduction, the genotype distribution in the
population will change to:
a
p
0
;
P
ð
AA
Þ¼
P
ð
Aa
Þ¼
2p
0
q
0
;
and
q
0
:
P
ð
aa
Þ¼
a
The decreased amount of aa genotype at the time of reproduction causes
a decrease in the a allele frequencies in the next generation, calculated as
follows: assume the total number of individuals in the original
population was N (we assumed N to be very large), which implies there
were Nq
0
homozygous recessive individuals to start with. Because only a
fraction
a
of them survives, the number of those individuals has changed
