In this section we will explore polynomial functions. We have already looked at three relatively simple types of polynomials: constant functions, linear functions, and quadratic functions. However, some biological applications require that we use higher degree polynomials.

At first glance, population geneticists typically assume that genotypes have constant fitness values, which are a measure of their reproductive success. A great example of this is the Hardy-Weinberg equation, which we considered when we discussed quadratic function. However, in some cases this is not a reasonable assumption. One of the factors that can alter this calculation frequency-dependent selection. Positive frequency-dependent selection occurs when the fitness of a genotype increases as it becomes more common in a population. In contrast, negative frequency-dependent selection favors rare alleles by assigning the highest fitness to the rarest allele. Under these conditions, if you want to find the equilibrium frequency of an allele p, you would use the following polynomial function,

Are you comfortable this function? If not, the following tutorial will refresh your memory about such polynomial functions.

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In the next section, we will explore the basics of polynomials.

The Basics