Hardy Weinberg Equililbrium

What is Hardy-Weinberg equilibrium?

A model predicting allele and genotype frequencies across generations when no evolutionary forces operate.

What is the purpose of Hardy-Weinberg equilibrium?

To provide a null model for evaluating whether evolutionary forces may be operating.

Who developed the Hardy-Weinberg principle?

G. H. Hardy, a British mathematician, and Wilhelm Weinberg, a German physician, independently in 1908.

What is evolutionary genetics?

The study of how allele frequencies change across generations.

What are the five forces of evolution?

Finite population size (genetic drift), non-random mating, mutation, migration, and selection.

What is genetic drift?

Random changes in allele frequencies, particularly important in small populations.

What is non-random mating?

Mating in which individuals or gametes do not combine randomly.

What is mutation?

A source of genetic variation that can change allele frequencies.

What is migration?

Movement between populations that can alter allele frequencies.

What is natural selection?

Differences in survival or reproduction that can change allele frequencies and produce adaptive evolution.

What is a population?

A group of interbreeding individuals characterized by their genotypes.

What is a gene pool?

The collection of alleles carried by breeding individuals in a population.

What is genotype frequency?

The proportion of individuals in a population with a particular genotype.

How do you calculate genotype frequency?

Number of individuals with the genotype divided by total population size N.

What is allele frequency?

The proportion of all allele copies at a locus that are of a particular type.

How many allele copies are in N diploid individuals at an autosomal locus?

2N.

What does p represent?

The frequency of one allele, such as A.

What does q represent?

The frequency of the other allele, such as a.

What is the allele frequency equation for two alleles?

p + q = 1.

How do you calculate p from genotype counts?

p = (2N_AA + N_Aa)/(2N).

How do you calculate q from genotype counts?

q = (2N_aa + N_Aa)/(2N).

How do you calculate p from genotype frequencies?

p = G_AA + (1/2)G_Aa.

How do you calculate q from genotype frequencies?

q = G_aa + (1/2)G_Aa.

Why are homozygotes counted twice in allele frequency calculations?

Each homozygote carries two copies of the same allele.

Why do heterozygotes contribute one copy of each allele?

Each heterozygote carries one copy of each allele.

What is the relationship between adult genotype frequencies and gamete allele frequencies?

Normal meiosis produces gametes with allele frequencies p and q matching the adult gene pool.

What is the population genetics life cycle?

Diploid adults undergo meiosis to produce haploid gametes, which combine during fertilization to produce the next diploid generation.

Can allele frequencies always be calculated from complete genotype frequencies?

Yes.

Can genotype frequencies always be uniquely determined from allele frequencies alone?

No; additional information about how gametes combine is required.

What mating assumption does Hardy-Weinberg use?

Random mating and random combination of gametes.

What is the Hardy-Weinberg genotype frequency equation?

p² + 2pq + q² = 1.

What is the expected AA genotype frequency under HWE?

p².

What is the expected Aa genotype frequency under HWE?

2pq.

What is the expected aa genotype frequency under HWE?

q².

Why is the heterozygote frequency 2pq?

There are two ways to form a heterozygote: A from one gamete and a from the other, or the reverse.

What happens to allele frequencies under Hardy-Weinberg assumptions?

They remain constant at p and q across generations.

What happens to genotype frequencies after one generation of random mating?

They reach p², 2pq, and q² and then remain constant under the model.

Can genotype frequencies change without allele frequencies changing?

Yes; genotype frequencies can change during the first generation while allele frequencies remain constant.

If p = 0.5 and q = 0.5, what are the expected genotype frequencies?

AA = 0.25, Aa = 0.50, aa = 0.25.

If p = 0.7 and q = 0.3, what is the expected AA frequency?

p² = 0.49.

If p = 0.7 and q = 0.3, what is the expected Aa frequency?

2pq = 0.42.

If p = 0.7 and q = 0.3, what is the expected aa frequency?

q² = 0.09.

At what allele frequencies is heterozygote frequency highest?

p = q = 0.5, giving 2pq = 0.5.

What happens to the homozygous genotype of a rare allele?

It becomes especially rare because its expected frequency is the square of the allele frequency.

If q = 0.1, what is the expected aa frequency?

q² = 0.01.

If q = 0.1, what is the expected Aa frequency?

2(0.9)(0.1) = 0.18.

What are the observed genotype counts in the Pueblo MN example?

MM = 83, MN = 46, NN = 11, total N = 140.

What are the observed genotype frequencies in the Pueblo example?

MM ≈ 0.59, MN ≈ 0.33, NN ≈ 0.08.

How many allele copies are in the Pueblo sample?

2(140) = 280.

What is the M allele frequency in the Pueblo example?

p = [2(83) + 46]/280 ≈ 0.76.

What is the N allele frequency in the Pueblo example?

q = [2(11) + 46]/280 ≈ 0.24.

What are the expected HWE genotype frequencies in the Pueblo example?

MM ≈ 0.58, MN ≈ 0.36, NN ≈ 0.06.

How do you calculate an expected genotype count?

Multiply the expected HWE genotype frequency by population size N.

What are the expected genotype counts used in the professor's Pueblo example?

MM = 81.2, MN = 50.4, NN = 8.4, using rounded expected frequencies.

What is the chi-square formula?

χ² = Σ[(Observed − Expected)² / Expected].

What is the purpose of the chi-square test in Hardy-Weinberg analysis?

To test whether observed genotype counts differ significantly from HWE expectations.

What is the degrees of freedom formula for the professor's HWE test?

df = number of genotype combinations − number of alleles.

What is df for two alleles and three genotype combinations?

df = 3 − 2 = 1.

What is df for three alleles and six genotype combinations?

df = 6 − 3 = 3.

What is df for four alleles and ten genotype combinations?

df = 10 − 4 = 6.

What chi-square result did the professor obtain for the Pueblo example?

χ² ≈ 1.23 with df = 1, using the rounded values on the slide.

What was the conclusion of the Pueblo chi-square test?

The result was not statistically significant, so there was insufficient evidence of departure from HWE at the MN locus.

What does a significant HWE chi-square result suggest?

Observed genotype counts depart from HWE expectations; evolutionary forces or other violations may be involved.

Does a nonsignificant chi-square result prove HWE?

No; it means the test did not detect a statistically significant departure.

What did the human population graphs show?

Many loci in Yoruba and Utah European-ancestry samples had observed genotype frequencies close to HWE expectations.

Why can real populations be approximately at HWE?

Evolutionary forces may be weak enough at many loci that observed frequencies remain close to HWE expectations.