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The Biology Project > Biomath > Polynomials > Applications > Underdominance

Polynomial Applications


Genetics use the terms underdominance or heterozygote disadvantage to describe the condition where organisms that are heterozygotes for a given trait are less fit than organisms that are homozygotes. In other words, given a single locus with two alleles, A , and a, underdominance occurs when the heterozygote, Aa, is less fit than either homozygote, AA or aa.

We can use polynomial functions to calculate the equilibrium allele frequency for a trait that exhibits underdominance.

Consider a single locus with two alleles A and a, with frequencies p and q, respectively. Suppose we assign fitness values 1 + s1 : 1 : 1 + s2 to AA: Aa: aa where s1 and s2 are positive. Using these fitness values, we can find the equilibrium allele frequencies by solving the equation,

Equilibrium allele frequencies are special values of p and q that satisfy the above equation and, once attained, result in no change in allele frequency in future generations. These equilibrium allele frequencies may or may not be attainable.


Some herbicide resistance genes in plants exhibit underdominance in the absence of herbicides. This can be studied in the laboratory using Arabidopsis thaliana, pictured above. Photo credit: Keith Weller, courtesy of United States Department of Agriculture, Agricultural Research Service.


Use the equation above to answer the following questions:

Rewrite the equation for finding equilibrium allele frequencies.

Find the equilibrium frequency for a given allele.

Determine how many equilibrium frequencies exist for a given allele.

Describe the characteristics for the polynomial function that describes equilibrium allele frequencies.

Find the positive equilibrium frequency of a given allele.

Find the frequency of an allele as time increases.


The Biology Project > Biomath > Polynomials > Applications> Underdominance

The Biology Project
Department of Biochemistry and Molecular Biophysics

The University of Arizona

February 2007
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