SCN3230-ABED_1: Module 8 Lesson 2 - 2

Lesson 2 — Hardy-Weinberg Calculations

Hardy-Weinberg Formulas

Read pages 680 - 682

In addition to giving us the conditions for genetic equilibrium and micro-evolution, Hardy and Weinberg gave us a mathematical formula that allows us to alternate between determining allele frequencies and genotype frequencies.

Two formulas are used determine the frequencies:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»p«/mi»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mi»q«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mn»1«/mn»«mspace linebreak=¨newline¨/»«msup»«mi»p«/mi»«mn»2«/mn»«/msup»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mn»2«/mn»«mi»p«/mi»«mi»q«/mi»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«msup»«mi»q«/mi»«mn»2«/mn»«/msup»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mn»1«/mn»«/math»

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»p«/mi»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mi»q«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mn»1«/mn»«/math» is used to determine the allele frequencies and «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi»p«/mi»«mn»2«/mn»«/msup»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mn»2«/mn»«mi»p«/mi»«mi»q«/mi»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«msup»«mi»q«/mi»«mn»2«/mn»«/msup»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mn»1«/mn»«/math» is used to determine the genotype frequencies in a population.

Determining Allele Frequencies

Remember from the last lesson that a whole population is made up of its gene pool and these genes come in two allelic forms (dominant and recessive).

The formula uses the symbols p and q.

The symbol p is a symbol for the frequency of the dominant alleles or any capital letter version of an allele.
The symbol q is a symbol for the frequency of the recessive alleles or any lower case version of an allele.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold-italic¨»p«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mi»f«/mi»«mi»r«/mi»«mi»e«/mi»«mi»q«/mi»«mi»u«/mi»«mi»e«/mi»«mi»n«/mi»«mi»c«/mi»«mi»y«/mi»«mo»§#160;«/mo»«mi»o«/mi»«mi»f«/mi»«mo»§#160;«/mo»«mi»t«/mi»«mi»h«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mi»d«/mi»«mi»o«/mi»«mi»m«/mi»«mi»i«/mi»«mi»n«/mi»«mi»a«/mi»«mi»n«/mi»«mi»t«/mi»«mo»§#160;«/mo»«mi»a«/mi»«mi»l«/mi»«mi»l«/mi»«mi»e«/mi»«mi»l«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mfrac»«mrow»«mi»n«/mi»«mi»u«/mi»«mi»m«/mi»«mi»b«/mi»«mi»e«/mi»«mi»r«/mi»«mo»§#160;«/mo»«mi»o«/mi»«mi»f«/mi»«mo»§#160;«/mo»«mi»d«/mi»«mi»o«/mi»«mi»m«/mi»«mi»i«/mi»«mi»n«/mi»«mi»a«/mi»«mi»n«/mi»«mi»t«/mi»«mo»§#160;«/mo»«mi»a«/mi»«mi»l«/mi»«mi»l«/mi»«mi»e«/mi»«mi»l«/mi»«mi»e«/mi»«mi»s«/mi»«/mrow»«mrow»«mi»t«/mi»«mi»o«/mi»«mi»t«/mi»«mi»a«/mi»«mi»l«/mi»«mo»§#160;«/mo»«mi»n«/mi»«mi»u«/mi»«mi»m«/mi»«mi»b«/mi»«mi»e«/mi»«mi»r«/mi»«mo»§#160;«/mo»«mi»o«/mi»«mi»f«/mi»«mo»§#160;«/mo»«mi»a«/mi»«mi»l«/mi»«mi»l«/mi»«mi»e«/mi»«mi»l«/mi»«mi»e«/mi»«mi»s«/mi»«mo»§#160;«/mo»«mi»i«/mi»«mi»n«/mi»«mo»§#160;«/mo»«mi»p«/mi»«mi»o«/mi»«mi»p«/mi»«mi»u«/mi»«mi»l«/mi»«mi»a«/mi»«mi»t«/mi»«mi»i«/mi»«mi»o«/mi»«mi»n«/mi»«/mrow»«/mfrac»«/math»

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold-italic¨»q«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mi»f«/mi»«mi»r«/mi»«mi»e«/mi»«mi»q«/mi»«mi»u«/mi»«mi»e«/mi»«mi»n«/mi»«mi»c«/mi»«mi»y«/mi»«mo»§#160;«/mo»«mi»o«/mi»«mi»f«/mi»«mo»§#160;«/mo»«mi»t«/mi»«mi»h«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mi»r«/mi»«mi»e«/mi»«mi»c«/mi»«mi»e«/mi»«mi»s«/mi»«mi»s«/mi»«mi»i«/mi»«mi»v«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mi»a«/mi»«mi»l«/mi»«mi»l«/mi»«mi»e«/mi»«mi»l«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mfrac»«mrow»«mi»n«/mi»«mi»u«/mi»«mi»m«/mi»«mi»b«/mi»«mi»e«/mi»«mi»r«/mi»«mo»§#160;«/mo»«mi»o«/mi»«mi»f«/mi»«mo»§#160;«/mo»«mi»r«/mi»«mi»e«/mi»«mi»c«/mi»«mi»e«/mi»«mi»s«/mi»«mi»s«/mi»«mi»i«/mi»«mi»v«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mi»a«/mi»«mi»l«/mi»«mi»l«/mi»«mi»e«/mi»«mi»l«/mi»«mi»e«/mi»«/mrow»«mrow»«mi»t«/mi»«mi»o«/mi»«mi»t«/mi»«mi»a«/mi»«mi»l«/mi»«mo»§#160;«/mo»«mi»n«/mi»«mi»u«/mi»«mi»m«/mi»«mi»b«/mi»«mi»e«/mi»«mi»r«/mi»«mo»§#160;«/mo»«mi»o«/mi»«mi»f«/mi»«mo»§#160;«/mo»«mi»a«/mi»«mi»l«/mi»«mi»l«/mi»«mi»e«/mi»«mi»l«/mi»«mi»e«/mi»«mi»s«/mi»«mo»§#160;«/mo»«mi»i«/mi»«mi»n«/mi»«mo»§#160;«/mo»«mi»p«/mi»«mi»o«/mi»«mi»p«/mi»«mi»u«/mi»«mi»l«/mi»«mi»a«/mi»«mi»t«/mi»«mi»i«/mi»«mi»o«/mi»«mi»n«/mi»«/mrow»«/mfrac»«/math»

Follow the logic on the Punnett square on page 682 and you will see how Hardy and Weinberg derived the following equation for determining the frequency of each genotype in the population. For this example in the Punnett square, their assumption is that 0.70 or 70% of the alleles in the gene pool are dominant: f(B) = 0.70. Therefore, 0.30 or 30% of the alleles in the gene pool are recessive: f(b) = 0.30 or 30%.

0.7 + 0.3 = 1, which is equal to the whole populations genes for that trait.

Determining Genotype Frequencies

The Hardy-Weinberg equation used to predict the frequency of genotypes in a population is

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi»p«/mi»«mn»2«/mn»«/msup»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mn»2«/mn»«mi»p«/mi»«mi»q«/mi»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«msup»«mi»q«/mi»«mn»2«/mn»«/msup»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mn»1«/mn»«/math»

where

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

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

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

In other words,

f(BB) + f(Bb) + f(bb) = the whole population

We can alternate between these two formulas to determine allele frequencies and genotype frequencies.

Read carefully through the sample problems on pages 682 to 683 and work them out yourself. You will need a calculator.