HARDY-WEINBERG EQUILIBRIUM

Transcription

1 HARDY-WEINBERG EQUILIBRIUM At the time that Mendel's work was rediscovered, people began to question if "dominant genes" (alleles) shouldn't "take over" and spread through the population. Hardy and Weinberg both published rational explanations of why gene frequencies will not change "unless" forced to do so. Basically, if there is "random mating" with regard to a trait (that is, matings are made without consideration of the trait), the frequencies of the dominant and recessive alleles in the population will also be the frequencies found in the gametes. p (A) eggs q(a) sperm p (A) q(a) p2 (AA) pq(aa) pq(aa) q2 (aa) or p2 AA + 2pq Aa + q2 aa Thus when there is random mating, the genotypic frequencies in the next generation will be p 2 (AA) : 2pq (Aa) : q 2 (aa), and the allele frequencies will still be p and q. This situation is referred to as Hardy- Weinberg Equilibrium The "forces" that can change gene frequencies are; "Drift" or chance fluctuations Mutation Migration Selection

2 Drift will be the primary factor affecting gene frequency when populations are small. If the reproductive population only contains a few individuals it is not surprising that chance is a major factor. For example if we closed our eyes and counted out 10 jelly beans from a bowl that contained an even mix of white and black beans, we would not be surprised if we ended up with more of one color than the other, or if by chance we got 7 white and 3 black beans. In genetics, to get to the next generation, we would next draw from a bowl that had 70% white and 30 % black beans, rather than the 50:50 split we started with. Then it would not be surprising if we happened to get 6:4 or 8:2 in the next draw. If we follow the same procedure over several generations, we will end up at "fixation" ie, where all the (alleles) in a sample are either white or black. From then on, we will be drawing from populations where only one type of allele is present. How quickly fixation occurs is primarily a function of sample size; the smaller the number of interbreeding individuals that contribute to the next generation, the more rapidly fixation is likely to occur. There are two special situations where chance can have an effect on subsequent gene frequencies. Founder effect: when a few individuals leave one population to start a new population any allele present in one or more of the individuals that was rare in the old population is automatically increased in frequency. By the same token, any allele that is not present will be lost. For example, none of the 28 original "Dunkers" passed on a B blood type allele, so there are no persons with blood types B or AB in todays population. Pingelap Island; 2o survivors of 1900 hurricane - now 6% of population have achromatophobia, a recessive condition. Pitcairn's Island, founded by 6 mutineer's from the HMS Bounty along with 2 Tahitian men and 8 Tahitian women shows unusual frequencies for several loci that have been examined in recent years. Bottlenecks occur when a "dissaster" reduces a population to a few individuals. Often after a forest fire, only a few trees may survive to repopulate the area, so any rare allele in a survivor will not be so

3 rare in the future. We may create bottlenecks in animal breeding by selecting one bull for wide use in artificial insemination and later find he carried a recessive lethal. In plants, it is not uncommon for one "outstanding" individual to be selected and propagated asexually, by selfing, or as a common parent in making hybrids.. The same genotype may then be grown over a wide area. Later, as in the case of T cytoplasm that was used in maize to simplify creation of hybrid seed for sale to farmers, we may find that the common genotype has an unexpected drawback. In the 1969 case of maize, the use of "monoculture" in female parents led to disease susceptibility from Florida all the way through the corn-belt as the crop matured. Mutation: Even at high mutation rates, changes in gene frequency are very slow. To go from p = 1 to p =.99 will take 1,000 generations with a mutation rate (µ) of 1 in 100,000 gametes. At the same mutation rate, it would take 10,000 generations to go from p = 0.1 to As "A" mutates to "a", reverse mutations (ϖ) will also become important. If mutation is the only factor in establishing Hardy-Weinberg equilibrium, p eq will in theory eventually be ϖ/µ+ϖ. If the forward and reverse rates are identical, each allele would settle at 0.5. Migration: If migrants from another population with different gene frequencies move in and contribute to the gene pool, a new gene frequency will be established for the affected population. Of course if individuals of a specific genotype leave a population "differentially", there will also be a change in gene frequencies in the remaining population. In general, migration is sporadic; if you know the fraction and gene frequencies of the original populations, it is relatively simple to calculate new frequencies. Only a few migrants between populations will prevent fixation and lead to a "blended" gene frequency in both populations. Selection: Selection can be very effective at changing gene frequencies, even in large populations.

4 Examples: Sickle cell anemia and thalassemia heterozygotes are more reproductive than homozygotes where malaria is a problem. Where malaria is most severe, the frequency of the Hb-S allele can be nearly 0.2, even though Hb-S/Hb-S is lethal. "Industrial melanism" In the industrial cities of England where smoke and coal dust darkened the environment, peppery moths with a gene for dark pigment had a reproductive advantage while in rural areas, those with a light color had an advantage. In either area, those that do not blend well with the background are easy prey for birds. Special case: Equilibrium may be established where selection against a recessive lethal is balanced by mutation. If there was no selective advantage for a recessive lethal in heterozygotes, equilibrium would be established when the loss of q alleles (q 2 ) each generation is equal to the introduction of new recessive lethals by mutation (µ p) That means that when mutation is balanced by selection against a recessive lethal, q eq will be equal to the square root of the mutation rate. Thus: a) it will not be possible to eliminate recessive lethal alleles by selection; b) most of the recessive lethal alleles will be present in heterozygotges. Examples include diseases such as PKU Important point: What will happen to the gene frequency for the pku allele now that a special diet allows pku/pku individuals to reproduce. REMEMBER: Gene frequencies will not change unless "forced to do so". Removing selection in the balance between selection and mutation will not add significantly to the human "Genetic Load" as some people fear. If about 1 in 16,000 births in the past was a PKU infant it seems unlikely that mutation alone (this would be a mutation rate of 1 in 16,000 gametes) accounts for the presence of the pku allele. Even at such a high mutation rate, it would take many generations to see a

5 significant change in the gene frequency. In the meantime, the cure should remain just as effective for future generations as it is today. The relatively high incidence of Tay Sachs disease in Ashkenazi Jews and of cystic fibrosis in Caucasions would not be characteristic of selection balanced by mutation; the mutation rate would have to be very high and differ from one population to another. Alternatively, the differential high frequencies may be a consequence of heterozygous advantage for resistance to TB (Tay-Sachs) or cholera and/or typhoid fever (CF) now or in past generations.