Chapter 14: Constant Allele Frequency

Online Tutorial for Hardy Weinberg with Sample Problems

Vocabulary Review

• Allele- a variation in a trait (F- furred & f- furless)• Genotype- gene combination- one gene from

mom, one from dad (FF, Ff, ff)• Phenotype- physical appearance- furred or

furless• Allele frequency- how common an allele is in a

population. (% F alleles, % f alleles)• Gene frequency- how common a genotype is in

a population. (% FF, %Ff, %ff)

What is population genetics?

• Branch of genetics that considers all the alleles in a population.

• All alleles in a population are called a gene pool.

• Allele frequencies can be tracked within populations to show how that population is changing/ evolving or if it is static.

How is allele frequency calculated?

• In humans, rolling your tongue (R) is dominant to not being able to roll tongue (r)

• In an imaginary population of 500 people, 20 cannot roll their tongue (rr). Of the 450 who can, 160 are heterozygotes (Rr) and 320 are homozygotes (RR). What are the allele frequencies of R and r in this population?

What is the Hardy Weinberg Equilibrium Theorem?

• Describes a non-evolving population

• States that the frequencies of alleles and genotypes in a population’s gene pool remain the same unless it is altered by some external factor.

• This principle helps determine whether or not gene frequencies have changed in a population and whether evolution has occurred.

Hardy-Weinberg Equilibrium Equation

• Used to determine probable genotype frequencies in a population.

• p = dominant traits (A)• q = recessive traits (a)• p + q = 1• p2 + 2pq + q2 = 1

(AA)+ (Aa)+ (aa) = 1

Example

• Albinism occurs in 1/20,000 in North America.

• AA & Aa = normal aa = albinism• Problem… we don’t know who/what the

gene frequency is for homo. dominant and who is heterozygous for normal skin pigment.

• We don’t know “p” but we do know “q”…

• q2 = aa (albinism) = 1/20,000 = 0.00005• Take square root of q…

– q2 = 0.00005 – q = .007– The frequency of the recessive allele for albinism

is .007• To find p…

– p = 1 – q– p = 1 - .007– p = .993– The frequency of the dominant allele for normal

is .993• Now that you know “p” and “q” you can solve

equation…

• p2 + 2pq + q2 = 1• (.993)2 + 2(.993)(.007) + (.007)2 = 1• .986 + .014 + .00005 = 1• p2 = predicted frequency of homo

dominant individuals = .986 x 100 = 98.6%• 2pq = predicted frequency of

heterozygous = .014 x100 = 1.4%• q2 = predicted frequency of homo

recessive individuals (albinos) = .00005 x100 = .005%

Can you do these?

• 1 in 1700 Caucasians in the U.S. have cystic fibrosis. Calculate the gene frequency for all individuals.

• If 9% of an African population is born with a severe form of sickle-cell anemia (ss), what percent of the population will be more resistant to malaria because they are heterozygous (Ss) for sickle-cell gene.

Assumptions of the Hardy-Weinberg Equilibrium Theorem

• These conditions must be met for an allele frequency to be at equilibrium:– Population must be very large– no migration- organisms are not moving between

populations– no mutations – random mating- organisms have no sexual selection– Natural selection is not occurring– All organisms breed & produce same # offspring

• If a population deviates form the Hardy-Weinberg theorem, it is usually because that population is evolving.