Biology Reference
In-Depth Information
Similarly, the proportion of the allele in the F
1
will be:
2N
1
q
2
2N
1
pq
2N
1
þ
2N
1
q
ð
q
þ
p
Þ
¼
¼
q
ð
q
þ
p
Þ¼
q
:
2N
1
Thus, the allele proportions remain unchanged from the parental
generation, and the proof of claim 2 is complete.
To prove claim 3, notice we obtained the genotypic distribution in the
F
1
presented in Eq. (3-4) by using a Punnett square based on the
proportions p and q of the A and a alleles in the previous generation.
We now know, from claim 2, these proportions remain unchanged in the
F
1
generation. The argument can now be repeated to show that the
genotypic proportions in the F
2
will be P
2
(aa)
q
2
,P
2
(Aa)
¼
¼
2pq, and
p
2
, implying, again, that the allelic proportions in the F
2
remain unchanged, and so on. Thus, beginning with the F
1
, the system
remains in genotypic equilibrium.
P
2
(AA)
¼
The Hardy-Weinberg Law of Genetic Equilibrium gives a mathematical
explanation for a well-known biological fact—equally fit genotypes
are generally preserved in nature and coexist in equilibrium.
Although the equilibrium genotypic frequencies need not be exactly
those of the original population, under the assumptions of the
model, the equilibrium is reached in the first generation and
is preserved for all later generations. In contrast, under the same
assumptions, the allelic frequencies remain constant from the very
beginning.
It is clear that changes in the genetic constitution of a population must
occur under some conditions, or evolution would not occur. This
gradual change is caused by the presence in the population of alleles
with varying degrees of fitness. In this case, the genotype proportions
change from generation to generation, and the dynamic behavior of the
system is more complex. We next investigate the effect of natural
selection in populations containing maladaptive alleles.
IV. THE EFFECT OF A MALADAPTIVE OR LETHAL GENE
The Hardy-Weinberg Law of Genetic Equilibrium assumes that each of
the genotypes in the population is equally successful or equally fit, and
therefore natural selection is not acting on any of the genotypes.
However, there are many genetic diseases, such as Tay-Sachs,
phenylketonuria, severe combined immune deficiency, and hemophilia,
for which this is not the case. Cystic fibrosis (CF), for instance, is a
genetic disease caused by a mutation in the gene for a chloride ion-
transporting protein, the cystic fibrosis transmembrane regulator
(CFTR). People who are homozygous for the recessive mutant CFTR
allele will have CF, while those who carry only one CFTR allele will not.
