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Mendelian Genetics in Populations – 1

Hardy-Weinberg Equilibrium, Selection and Mutation

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Hardy-Weinberg genotype frequencies (Fig. 5.5)

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Hardy-Weinberg genotype frequencies – 2

• Given a locus with 2 alleles, A and a

• If the frequency of A is p, and the frequency of a is q

• And if there is random union of gametes (= random mating of diploid genotypes)

• Then the genotype frequencies of zygotes will be p2 AA; 2pq Aa; q2 aa

• These genotype frequencies are known as the Hardy-Weinberg genotype frequencies or proportions

• In the example on the previous slide: p = 0.6 and q = 0.4, so that p2 = 0.36, 2pq = 0.48, and q2 = 0.16

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Hardy-Weinberg equilibrium: 1

Provided that there are no evolutionary “forces” acting on a population, allele and genotype frequencies will remain constant from one generation to the next, and the genotype frequencies will be the Hardy-Weinberg proportions: p2, 2pq, q2 (for a locus with two alleles).

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Hardy-Weinberg equilibrium – 2

Equal survivorship of genotypes = no natural selection

Equal survivorship of genotypes = no natural selection

Equal fertility of adult genotypes = no natural selection

Random union of gametesStart here

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Allele frequencies in gametes are the same as in adults that make gametes (Fig. 5.6b)

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Requirements for Hardy-Weinberg equilibrium

• Random mating• No natural selection (i.e, equal survivorship

and reproduction of genotypes)• Infinite population size (i.e., no random

genetic drift)• No mutation• No migration

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Why is Hardy-Weinberg important?

• It is a formal statement of the conditions under which evolution will not occur

• Genotype frequencies at many loci in many populations often agree quite closely with H-W expectations (i.e., H-W is a useful tool)

• For example, H-W tells us that “rare” alleles will almost always be found in heterozygotes: suppose p(A) = 0.99 and q(a) = 0.01, then the frequency of heterozygotes Aa is 2pq ≈ 0.02 and the frequency of aa is q2 = 0.0001. In other words, for every a allele that is in a homozygote, 100 more are in heterozygotes

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Natural selection by differential survivorship

Equal survivorship of genotypes = no natural selection

Equal fertility of adult genotypes = no natural selection

Random union of gametes

Start here

Differential survivorship = natural selectionNew frequency of B1

= [(36 x 2) + 36] / [(36 + 36 + 8) x 2]= 108 / 160 = 0.675

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Allele and genotype frequency changes as a result of natural selection

• In the previous slide, the frequency of allele B1 increased from 0.6 to 0.675 as a result of one generation of selection, and the frequency of B2 declined from 0.4 to 0.325

• If there is random mating, the frequency of B1B1 zygotes in the next generation will be (0.675)2 = 0.456; the frequency of B1B2 will be 2(0.675)(0.325) = 0.439; and the frequency of B2B2 will be (0.325)2 = 0.106

• If similar directional selection continues for a large number of generations, virtually all alleles in the population will be B1 and virtually all individuals will be B1B1 homozygotes (= “fixation” of B1)

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Allele frequency change under persistent directional selection (B1B1 most fit, heterozygote intermediate)Think of B1 as a new favorable mutation

Note: Rate of increase in frequency of B1 is slow when B1 is rare because most copies of B1 are in heterozygotes, which have lower fitness than B1B1 homozygotes

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Laboratory natural selection on the alcohol dehydrogenase (Adh) locus of D. melanogaster

Enzyme from AdhF homozygotes breaks down alcohol twice as fast as enzyme from AdhS homozygotes.

Higher fitness of AdhF allele in presence of ethanol could be due to higher survival or more reproduction

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The CCR5-32 allele revisited

• Individuals who are homozygous for the 32 allele are resistant to infection by HIV (CCR5 is a protein on the surface of host cells that is used as a co-receptor by the virus)

• This suggests that HIV may be a selective force to increase the frequency of the 32 allele in human populations: is this likely to happen?

• The frequency of the 32 allele varies among human populations from > 0.20 to < 0.01

• The rate of increase in the frequency of the 32 allele depends on (1) its current frequency in a population, and (2) the prevalence of HIV infection (which determines the strength of selection)

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Predicted changes in allele frequencies at the CCR5 locus due to the AIDS epidemic (Fig. 5.15)(a) high initial 32 allele frequency and high incidence of HIV (= strong selection & rapid increase in allele frequency)

(b) high initial 32 allele frequency and low incidence of HIV (= weak selection and little change in allele frequency)

(c) low initial 32 allele frequency and high incidence of HIV (= strong selection but little change in allele frequency)

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Selection on recessive and

dominant alleles – a

recessive lethal in the flour beetle (Fig.

5.6)

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Selection favoring dominant or recessive alleles (Box 5.7)

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Selection favoring dominant or recessive alleles - 2

• When a low-fitness recessive allele (e.g., a lethal recessive) is rare, it is difficult for natural selection to remove it from the population

• Similarly, when a high-fitness recessive allele is rare, it is hard for natural selection to increase its frequency

• In both cases, this is because most copies of the recessive allele will be “hidden” in heterozygotes, where they are shielded from natural selection

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Selection for heterozygotes = overdominance (Fig. 5.18)

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Selection for heterozygotes – 2

• Overdominant selection results in a stable equilibrium in which both alleles at a 2-allele locus remain in the population

• Compare this to the previous models of directional selection that push the most fit allele toward fixation

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Sickle-cell disease and malaria: overdominance and genetic load – 1

• Sickle-cell disease is inherited as an autosomal recessive disorder (a mutation of the -globin gene) – people with sickle-cell disease have greatly reduced life span

• In regions of the world where malaria is common, heterozygotes have highest fitness because they are more resistant to malaria than are normal homozygotes

• Estimated relative survivorships in regions with high incidence of malaria are:

AA(normal homozygote)

AS(heterozygote)

SS(sickle-cell disease)

0.89 1.0 0.20

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Sickle-cell disease and malaria: overdominance and genetic load – 2

• The cost of overdominance is the continual production of less fit homozygotes (AA and SS) via sexual reproduction (Mendelian segregation and recombination)

• Population geneticists refer to this cost as genetic load, or, in this case, segregational load

• At equilibrium, the frequency (p) of A is about 0.88 and the frequency (q) of S is about 0.12

• This means that about q2 = 0.0144: i.e., about 1.5% of births in these populations have sickle-cell disease

• Although natural selection acts to maximize the mean fitness of the population given the available genetic variation, it clearly is not optimal.

• Wouldn’t it be “best” to have an allele that conferred resistance to malaria but that didn’t cause a debilitating genetic disease when homozygous?

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Sickle-cell disease and malaria: limits to selection

• It turns out, there is such an allele, C, which gives the following relative fitnesses:

AA AS CC AC SC SS

0.89 1.0 1.31 0.89 0.70 0.20

• A population would be most fit if all individuals were CC homozygotes

• The problem, however, is that it is very difficult (maybe impossible) for natural selection to increase the frequency of the C allele when it is rare because virtually all copies of the C allele will be in AC and SC heterozygotes, which don’t have high enough fitness (relative to AS and AA)

• There is no guarantee that just because a “better” allele is available, natural selection will cause it to increase in frequency