Biology Reference
In-Depth Information
The impaired CFTR function results in decreased secretion of fluids from
gastrointestinal and respiratory epithelia. Without normal fluid
secretion, the delivery of digestive enzymes from the pancreas is
diminished, and the protective mucus in the lungs is rendered viscous
and extremely difficult to clear from the airways. As a result, people
with CF have frequent respiratory infections and impaired digestion,
accompanied by chronic lung infection, infertility, and an early death.
Obviously, this represents a significant selective disadvantage.
We now examine a model describing such situations and study the long-
term behavior of allele proportions that, under these circumstances, are
not in equilibrium and change over time. We care about such changes
for several reasons, including their contribution to our understanding of
the public health implications of genetic diseases. Information on gene
frequencies can help guide our genetic testing and prenatal diagnosis
efforts.
Suppose we have a gene with two alleles, A and a, and the aa
combination is disadvantaged in that a certain predictable proportion of
the aa individuals will die before they reproduce. We would like to
know the effect of such a selective disadvantage for the aa genotype and
examine the change in the proportion of the harmful a allele between
generations. We would also like to know if there is an equilibrium state
for the species' gene pool. The mathematical model we describe makes
the following assumptions:
1. The population size is large.
2. Mating is random.
3. The recessive homozygous genotype is less fit to survive, and only
a fraction, say
< 1), of the individuals with this
genotype survives to reproduce.
, (where 0
a
a
4. There is no net mutation.
5. There is no immigration or emigration.
Notice the only difference between this set of assumptions and that for
the Hardy-Weinberg Equilibrium is in assumption 3, reflecting
differences in natural selection.
We begin with an example that illustrates the change in gene frequencies
over time caused by selective disadvantage.
2
2. To simplify the calculations, in this example we assume that the initial
population size is 100. Because this is not exactly a large number, as we explicitly
require in assumption 1 for the model, the gene proportions and frequencies
calculated in the example should be considered in terms of averages.
