Biology Reference
In-Depth Information
2. For generation F
1
, the proportion of the genotypes will be
q
2
p
2
P
1
ð
aa
Þ¼
;
P
1
ð
Aa
Þ¼
2pq
;
and P
1
ð
AA
Þ¼
:
(3-2)
The proportion of the A and a alleles in the F
1
, however, does not
change and remains as it was in the parental generation.
3. The proportion of the genotypes in the F
1
from Eq. (3-2) will be
maintained in all subsequent generations—that is, the system will
be in genotypic equilibrium from generation F
1
on. The same is
true for the proportions of the A and a alleles, which remain the
same as in the parental generation.
Before giving a formal proof, we present a computation that incorporates
all of the ideas of the abstract argument, but may be easier to follow.
Example 3-1
.......................
Imagine a ''colony'' of 50 people selected to begin a settlement. Suppose
the distribution of genotypes is AA
¼
5. Thus, in
this parental generation the proportions of the genotypes will be P(AA)
15, Aa
¼
30, and aa
¼
¼
15/50
¼
0.3, P(Aa)
¼
30/50
¼
0.6, P(aa)
¼
5/50
¼
0.1.
To determine the proportion of A and a alleles in the colony, notice that
the total number of A and a alleles is 100. As each AA individual
contributes two A alleles and each Aa individual contributes one A
allele, there is a total of 15
2
þ
30
1
¼
60 A alleles in the population.
In the same way, there are 40 a alleles (5
2
þ
30
1
¼
40). Thus,
the proportion of A alleles is calculated as p
¼
60/100
¼
0.6, and the
proportion of a alleles is q
¼
40/100
¼
0.4.
We are now ready to proceed with establishing results 1 and 2 in the
general case. Notice that even though we use symbols to denote the
genotypic distribution, the ideas of the computations in the general case
are identical. Again, imagine that we select a colony of N individuals
that have genomes in the following proportions:
P
ð
aa
Þ¼
x
;
P
ð
Aa
Þ¼
y
;
P
ð
AA
Þ¼
1
x
y
:
Therefore, the number of individuals with genotype Aa is Ny, the
number with genotype aa is Nx, and the number with genotype AA is
N(1
y). We can now compute the proportions of alleles in this
group to obtain the proportions of the A and a alleles in the parental
generation:
x
2N
ð
1
x
y
Þþ
Ny
2
ð
1
x
y
Þþ
y
p
¼
¼
2N
2
(3-3)
Ny
þ
2Nx
2N
y
þ
2x
¼
¼
:
q
2
This establishes claim 1 of the theorem.
