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Hardy-Weinberg Mathematical Model
Description: The frequency of all the dominant R and recessive r alleles equals the total frequency
and adds up to 1.0 or 100% of the alleles present. (In other words, remains constant)
The equation:
(p + q ) 2
=
Frequency of allele types
p = frequency of dominant allele A
frequency of recessive allele a
p2 + 2pq + q2
=1
Frequency of allele combinations
p2 = frequency of AA (homozygous dominant) q =
q2 = frequency of aa (homozygous recessive)
2pq = frequency of Aa (heterozygous)
Helpful tips:
1. In most populations, the frequency of two alleles is calculated from the proportion of homozygous
recessives (q2), since it is the only identifiable genotype directly from its phenotype. If only the
dominant phenotype is known, q2 may be calculated (1-frequency of dominant phenotype) .
2. All calculations must be carried out using proportions, not percentages.
To solve Hardy Weinberg Problems follow these steps:
1. Examine the information to determine what piece of information you have been given about the
population.
2. Find out the value of p or q. If this is achieved, then every other value in the equation can be
determined by simple calculation.
3. Take the square root of q2 to find q.
4. Determine p by subtracting q from 1 (i.e. p= 1-q).
5. Determine p2 by multiplying p by itself (i.e. p2 = p x p)
6. Determine 2 pq by multiplying p times q times 2.
7. Check that your calculations are correct by adding up the values for p2 + q2 + 2pq = 1.
Practice Problem: In the American Caucasian population approximately 70% of people can taste the
chemical phenylthiocarbamide (PTC) (the dominant phenotype), while 30% are non-tasters (the
recessive phenotype). Determine the frequency of :
a. homozygous recessive phenotype (q2) _____________
b. The dominant allele (p)
_____________
2
c. Homozygous tasters (p )
_____________
d. Heterozygous tasters (2pq)
_____________
Answer:
The Recessive phenotype q2 = 30% or 0.30
Therefore: q = 0.5477 (square root of 0.30)
Therefore: p = 0.4522 (1 – q = p so 1- 0.5477 = 0.4523)
Then use p and q in the Hardy-Weinberg equation to solve:
Homozygous dominant: p2 = 0.2046 (p x p = 0.4523 x 0.4523 )
Heterozygous: 2pq = 0.4953
Population Genetics Worksheet
Name __________________________
1. In humans, attached ear lobes are caused by the inheritance of two recessive genes. Free ear lobes
are the result of inheriting at least one dominant gene for free ear lobes. The frequency of the recessive
gene is 70% (0.7). What would the frequencies of the following be? RR _____ rr ___________
Rr ______ R ________ r ___________
Answer for #1:
RR = 9%, rr = 49%, Rr = 42% ,
So therefore: p + q = 1
p = 1-q
1-0.7 = 0.3
p = 0.3
p=R
R = 30%, r = 70% (you are given this)
q2 = rr
(0.7)(0.7) = 0.49
p2 = RR
(0.3)(0.3) = 0.09
2pq = Rr
(2)(0.7)(0.3) = 0.42
2. From question 1, how many people in a population of 7000 would carry the allele for free ear
lobes? _______________. (An answer Key comes later)
3. Suppose the gene proportions for the autosomal gene for eye color in females were:
B = 0.4 and b = 0.6. What would be the gene proportions for:
a. males
___________
b. the total gene pool?
___________
c. the genotypes of the population?
__________________________________
d. the genotypes of the fifth generation?
__________________________________
e. the phenotypes of the population?
__________________________________
4. On an isolated Pacific Ocean Island, there exists a gene for psychic ability which enabled the
lucky native to complete witch doctor school. This recessive allele was found in the population
of 2000 natives at a frequency of 10%.
a. How many witch doctors are there on the island? ___________
b. What proportion of the population would be hybrid? _________
5. If 18 out of 50 lizards sampled has the recessive trait for short tails,
a. what would the proportion of t alleles in the lizard population be? _____________
b. what would be the proportion of dominant genes?
_____________
b. what percent of the population would be heterozygous?
______________
6. Assume that the gene for wool color is dominant for the allele for white. If 25% of the sheep in
a large population have black wool, calculate:
a. the gene frequencies of the two types of wool color? __________________________
b. the percent of pure white sheep?
____________
c. the percent of hybrid sheep?
____________
d. the number of white sheep in a population of 750? ____________
7. If a gene occurs in a frequency of .64, its frequency
a. in a sperm cell is
b. frequency in an egg cell is
c. frequency in a gamete is
d. frequency of two such alleles uniting is
________,
_________,
_________,
_________.
8. If everyone in a certain area had the genotype TT, the probability that the gene T would appear
in a gamete would be _____________.
9. If there are 100 people in a population with genotype tt, there would be ________t genes.