The Biology Project > Biomath > Polynomials > Applications> Underdominance

Polynomial Applications

Underdominance

Problem 6- Find the frequency of an allele as time increases.

In the case of underdominance, it turns out that the positive equilibrium frequency of alleles A and a given by,

is unattainable. This means that unless the initial allele frequencies are these exact equilibrium frequencies,the positive equilibrium frequencies will never be reached. For this reason, we call such a equilibrium unstable.

The stable equilibria are the monomorphic states, (peq, qeq) = (1, 0), in other words all individuals have genotype AA, and, (peq, qeq) = (0, 1), i.e. all individuals have genotype aa. These monomorphic equilibria are said to be locally stable because what happens to the allele frequencies as t → ∞ depends on the initial allele frequencies (p0 and q0). In particular, if (p, q) → (peq, qeq) = (0, 1) as t → ∞.

Using this information, what happens to the frequency of allele A as t → ∞ if q0 = 0.9 and the fitness values for genotypes AA: Aa : aa are 1.8: 1 : 1.2, respectively?

 

 

 

A.

 

As t → ∞, p → 0.

B.

 

As t → ∞, p → 1.

C.

 

As t → ∞, p → 0.2.

D.

 

As t → ∞, p → 0.8.
E. As t → ∞, p → 0.4.
F. As t → ∞, p → 0.6.

End of Problems.

The Biology Project > Biomath > Polynomials > Applications > Underdominance


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