II. Hardy-Weinberg law.

III. Allele frequencies.

IV. Deviations from Hardy-Weinberg.

V. Applications.

Terms

Note Page 411, paragraph 2: "...Since the phenotypic ratio of dominant traits is 3:1, ..."  This is the ratio among the offspring of a mating of two heterozygotes, as in the F2 of a Mendelian intercross. For rare dominant traits, the usual mating is Dd × dd, corresponding to a backcross. In this case the ratio is 1:1.

I. The genetic constitution of a population can be expressed in part in terms of a gene pool.

A. The alleles at any particular locus can be pooled (at least in the imagination). For example, a population could have gene frequencies of 30% G¹, 60% G², and 10% G³ alleles. Each individual, of course, has only two alleles, which can be any homozygous or heterozygous combination.

B. Many loci are monomorphic, i.e. they have only one common allele, i.e. with a frequency >0.01 (or 1%). Other loci are polymorphic, with two or more alleles with frequencies >0.01. Examples of polymorphic loci include the ABO and Rh blood groups.

A. The following conditions must exist:
1. The population is reasonably large.

2. There is random mating (panmixis).

3. All genotypes must be equally viable and fertile.

B. Chance combinations can be expressed by the binomial expansion. In this particular application, it is called the Hardy-Weinberg Law.

C. For a two-allele locus, let p = frequency of allele G¹ and q = frequency of allele G². Since there are no other alleles, p + q = 1.0. The distribution of genotypes would be

(p + q)² = p² + 2pq + q² = 1,

where p² and q² are the frequencies of the two homozygotes and 2pq is the frequency of the heterozygote.

D. For three or more alleles, the appropriate polynomial is used:

(p + q + r + . . .)² = 1,

where p, q, r . . . = frequencies of alleles.

E. In the absence of selection or genetic drift (next lecture), the frequencies of alleles do not change.

A. For autosomal codominant traits, each genotype can be distinguished. Therefore, frequencies can be established by direct gene count. This method simply counts the number of each type of allele and divides by the total number of alleles. Random mating is not assumed.
Example: MN blood groups.

B. For autosomal dominant and recessive traits, homozygous dominant and heterozygous genotypes cannot be distinguished from each other by the phenotypes. If one assumes random mating, one can obtain the frequency of the recessive allele by the square root of the homozygous recessive phenotype. Since p + q = 1, the frequency of the dominant allele = 1 – (frequency of recessive allele), or p = 1 – q.
Example: Let q = frequency of the cystic fibrosis allele. Frequency of cystic fibrosis = 1/2500 = q². Therefore q = 1/50 or 0.02, p = 0.98, 2pq = 0.0392.

C. For X-linked traits, the allele frequency is simply the frequency of males with the corresponding phenotype.
Example: 8% of males are colorblind. Therefore the frequency of the colorblind allele is 0.08.

A. Assortative mating is the opposite of random mating: people select mates (or avoid them) on the basis of genotype. At the level of individual loci, assortative mating leads to excess homozygotes at the expense of heterozygotes.
Examples: stature, intelligence, ethnic group, religious group.

B. Inbreeding can be viewed as an extreme case of assortative mating, with the same results.

C. Even though mating practices can alter the genotype frequencies, the allele frequencies are not changed by them.

D. One cycle of random mating is sufficient to bring genotype frequencies into conformity with the Hardy-Weinberg Law.

A. For recessive traits, the frequency of heterozygotes can be calculated. (See IIIB.) In the example of cystic fibrosis, the frequency of heterozygotes is 2pq = 0.0392, or ca. 4% of the population are carriers (heterozygotes).

B. Allele frequencies are used to characterize populations.

C. One can plot allele frequencies in geographic areas much easier than genotype frequencies.

D. One can compare populations on the basis of allele frequencies. Similarity of frequencies at several loci often reflect closer genetic relationships than would be the case if the frequencies were different.

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