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Module 8

1. Module 8

1.13. Page 2

Lesson 3

Module 8—Populations, Individuals, and Gene Pools

 

Explore

 

The Hardy-Weinberg Equation

 

In addition to describing the conditions for equilibrium and microevolution, Hardy and Weinberg developed an equation that determines the frequency of alleles in a population and the frequencies of each genotype. For the following explanation, assume that one gene has two alleles: the dominant allele is A, the recessive is a.

 

Symbols Used in the Hardy-Weinberg Equation

 

The symbol f will be used as a short form of the word frequency.

 

 

Because A and a together make up all the alleles in the gene pool, p + q = 1, or 100%.

 

If you know the allele frequencies of a gene pool, you can predict the frequency of each genotype in the population by using the following Hardy-Weinberg equation. Or, if you know even some of the genotype frequencies, you can use some simple algebra to find both the allele frequencies and the remaining genotype frequencies.

 

p2 + 2pq + q2 = 1, where

 

p2 = the frequency of the homozygous genotype in the population = f(AA)

 

2pq = the frequency of the heterozygous genotype in the population = f(Aa)

 

q2 = the frequency of the homozygous recessive genotype in the population = f(aa)

 

Because the three genotypes together make up the whole population, p2 + 2pq + q2 = 1.

 

Some tips for doing Hardy-Weinberg calculations are provided below.

  • Don’t get psyched out because this is math—the hardest thing you have to do is use the calculator to find the square of a number or a square root.

  • Remember that an “individual” is diploid, so it has two symbols: AA or Aa or aa. An allele is only one symbol: A or a. If you’re asked to find a genotype frequency, it’s either p2, 2pq, or q2. If you’re asked to find an allele frequency, it’s either p or q. For example, “68% of bears in this population have the recessive phenotype of black fur” is q2, not q.

  • Remember that those individuals who have the dominant phenotype include both homozygous dominants (AA) and heterozygotes (Aa). So, if 40% of the population has the dominant phenotype, then p2 + 2pq = 0.4, not p2 = 0.4.

  • Remember that p + q = 1 or p2 + 2pq + q2 = 1. So, if you don’t know q, just subtract: 1 – p to get q. If you only know p2 + 2pq, but you don’t know q2, just subtract: 1 – (p2 + 2pq) = q2.
Read 

 

Read carefully through “Sample Problems” 1 and 2 on pages 682 and 683 of the textbook, and work out the problems yourself using a calculator, pen, and paper.