FACTORS THAT DISTURB HARDY-WEINBERG EQUILIBRIUM. A number of assumptions underlie the Hardy-Weinberg law:Population is large and mating is random.Allele frequencies are not changing over time. - no migration in or out of the population by groups whose allele frequencies at a locus of interest are radically different3. Selection for or against particular alleles and new mutations adding alleles are not significant.
Genetic Variation in Individuals and Populations: Mutation and Polymorphism
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Genetic Variation in Individuals and Populations: Mutation and Polymorphism
FACTORS THAT DISTURB HARDY-WEINBERG EQUILIBRIUM
A number of assumptions underlie the Hardy-Weinberg law:
Population is large and mating is random.
Allele frequencies are not changing over time. - no migration in or out of the population by groups whose allele frequencies at a locus of interest are radically different
3. Selection for or against particular alleles and new mutations adding alleles are not significant
Exception to Large Population with Random Mating
In human populations, nonrandom mating may occur because of three distinct but related phenomena: stratification, assortative mating, and consanguinity.
Stratification describes a population in which there are a number of subgroups that have remained relatively genetically separate during modern times.
For example, the U.S. population is stratified into many subgroups including whites, African Americans, and numerous Native American, Asian, and Hispanic groups.
When mate selection in a population is restricted to members of one particular subgroup within that population, the result for any locus with more than one allele is an excess of homozygotes in the population as a whole and a corresponding deficiency of heterozygotes compared with what one would predict under random mating from allele frequencies in the population as a whole.
By way of comparison, stratification has no effect on the frequency of autosomal dominant disease and would have only a minor effect on the frequency of X-linked disease by increasing the small number of females homozygous for the mutant allele.
Assortative mating is the choice of a mate because the mate possesses some particular trait.
Assortative mating is usually positive; that is, people tend to choose mates who resemble themselves (e.g., in native language, intelligence, stature, skin color, etc.)
To the extent that the characteristic shared by the partners is genetically determined, the overall genetic effect of positive assortative mating is an increase in the proportion of the homozygous genotypes at the expense of the heterozygous genotype.
A clinically important aspect of assortative mating is the tendency to choose partners with similar medical problems, such as congenital deafness or blindness or exceptionally short stature (dwarfism).
In such a case, the expectations of Hardy-Weinberg equilibrium do not apply because the genotype of the mate at the disease locus is not determined by the allele frequencies found in the general population.
For example, in the case of two parents with achondroplasia, offspring homozygous for the achondroplasia gene have a severe, lethal form of dwarfism that is almost never seen unless both parents are achondroplasia heterozygotes.
Consanguinity and Inbreeding
Consanguinity, like stratification and positive assortative mating, brings about an increase in the frequency of autosomal recessive disease by increasing the frequency with which carriers of an autosomal recessive disorder mate.
Unlike the disorders in stratified populations, in which each subgroup is likely to have a high frequency of a few alleles, the kinds of recessive disorders seen in the offspring of related parents may be very rare and unusual because consanguineous mating allows uncommon alleles to become homozygous.
Exceptions to Constant Allele Frequencies
Genetic Drift in Small Populations
Chance events can have a much greater effect on allele frequencies in a small population than in a large one.
If the population is small, random effects, such as increased fertility or survival of the carriers of a mutation, occurring for reasons unrelated to carrying the mutant allele (which would be selection, not a random event), may cause the allele frequency to change from one generation to the next.
In a large population, such random effects would average out, but in a small population, allele frequencies can fluctuate from generation to generation by chance.
This phenomenon, known as genetic drift, can explain how allele frequencies can change as a result of chance operating on the small gene pool contained within a small population.
Mutation and Selection
Changes in allele frequency due to selection or mutation usually occur slowly, in small increments, and cause much less deviation from Hardy-Weinberg equilibrium, at least for recessive diseases.
Mutation rates are generally well below the frequency of heterozygotes for autosomal recessive diseases, and so new mutation would have little effect in the short term on allele frequencies for such diseases.
In addition, most deleterious recessive alleles are hidden in heterozygotes and not subject to selection. As a consequence, selection is not likely to have major short-term effects on the allele frequency of these recessive alleles.
Therefore, to a first approximation, Hardy-Weinberg equilibrium may apply even for alleles that cause severe autosomal recessive disease.
For dominant or X-linked disease, however, mutation and selection do perturb allele frequencies from what would be expected under Hardy-Weinberg equilibrium by substantially reducing or increasing certain genotypes.
Fitness is the chief factor that determines whether a mutation is lost immediately, becomes stable in the population, or even becomes, over time, the predominant allele at the locus concerned.
The frequency of an allele in a population represents a balance between the rate at which mutant alleles appear through mutation and the effects of selection.
If either the mutation rate or the effectiveness of selection is altered, the allele frequency is expected to change.
Whether an allele is transmitted to the succeeding generation depends on its fitness (f), which is a measure of the number of offspring of affected persons who survive to reproductive age, compared with an appropriate control group.
If a mutant allele is just as likely as the normal allele to be represented in the next generation, f equals 1. If an allele causes death or sterility, selection acts against it completely, and f equals 0.
A related parameter is the coefficient of selection,s, which is a measure of the loss of fitness and is defined as 1 - f, that is, the proportion of mutant alleles that are not passed on and are therefore lost as a result of selection.
In the genetic sense, a mutation that prevents reproduction by an adult is just as lethal as one that causes a very early miscarriage of an embryo, because in neither case is the mutation transmitted to the next generation.
Fitness is thus the outcome of the joint effects of survival and fertility.
Selection in Recessive Disease
Selection against harmful recessive mutations has far less effect on the population frequency of the mutant allele than does selection against dominant mutations because only a small proportion of the genes are present in homozygotes and are therefore exposed to selective forces.
Even if there were complete selection against homozygotes (f = 0), as in many lethal autosomal recessive conditions, it would take many generations to reduce the gene frequencyappreciably because most of the mutant alleles are carried by heterozygotes with normal fitness.
For example, the frequency of mutant alleles causing phenylketonuriaq, is approximately 1% in many white populations. Two percent of the population (2 × p × q) is heterozygous, with one mutant allele, whereas only 1 individual in 10,000 (q2) is a homozygote with two mutant alleles. The proportion of mutant alleles in homozygotes is given by:
Thus, as long as mating is random, genotypes in autosomal recessive diseases can be considered to be in Hardy-Weinberg equilibrium, despite selection against homozygotes for the recessive allele.
The mathematical relationship between genotype and allele frequencies described in the Hardy-Weinberg law holds for most practical purposes in recessive disease.
Selection in Dominant Disorders
Dominant mutant alleles are directly exposed to selection, in contrast to recessive mutant alleles, most of which are "hidden" in heterozygotes.
Consequently, the effects of selection and mutation are more obvious and can be more readily measured for dominant traits.
A genetic lethal dominant allele, if fully penetrant, is exposed to selection in heterozygotes, removing all alleles responsible for the disorder in a single generation.
Several human diseases are thought or known to be autosomal dominant traits with zero or near-zero fitness and thus always result from new rather than inherited autosomal dominant mutations.
Mutation and Selection Balance in Dominant Disease
If a dominant disease is deleterious but not lethal, affected persons may reproduce but will nevertheless contribute fewer than the average number of offspring to the next generation; that is, their fitness, f, may be reduced.
Such a mutation is lost through selection at a rate proportional to the loss of fitness of heterozygotes.
The frequency of the mutant alleles responsible for the disease in the population therefore represents a balance between loss of mutant alleles through the effects of selection and gain of mutant alleles through recurrent mutation.
A stable allele frequency is reached at whatever level balances the two opposing forces: one (selection) that removes mutant alleles from the gene pool and one (new mutation) that adds new ones back.
The mutation rate per generation, μ, at a disease locus must be sufficient to account for that fraction of all the mutant alleles (allele frequency q) that are lost by selection from each generation. Thus,
μ = sq
When a genetic disorder limits reproduction so severely that the fitness is zero (s = 1), it is referred to as a genetic lethal.
For a dominant genetic lethal disorder, every allele in the population must be a new mutation since none can be inherited (in the absence of gonadal mosaicism).
In achondroplasia, the fitness of affected patients is not zero, but they have only about one fifth as many children as people of normal stature in the population.
In the subsequent generation, only 20% of current achondroplasia alleles are passed on from the current generation to the next. Because the frequency of achondroplasia is not decreasing, new mutations must be responsible for replacing the 80% of mutant genes in the population lost through selection.
If the fitness of affected persons suddenly improved (because of medical advances, for example), the observed incidence of the disease in the population would increase and reach a new equilibrium.
Retinoblastoma and certain other dominant embryonic tumors with childhood onset are examples of conditions that now have a greatly improved prognosis, with a predicted consequence of increased disease frequency in the population.
Allele frequency, mutation rate, and fitness are related; thus, if any two of these three characteristics are known, the third can be estimated.
Mutation and Selection Balance in X-Linked Recessive Mutations
For those X-linked phenotypes of medical interest that are recessive, or nearly so, selection occurs in hemizygous males and not in heterozygous females, except for the small proportion of females who are manifesting heterozygotes with low fitness.
Because males have one X chromosome and females two, the pool of X-linked alleles in the entire population's gene pool will be partitioned, with one third of mutant alleles present in males and two thirds in females.
As we saw in the case of autosomal dominant mutations, mutant alleles lost through selection must be replaced by recurrent new mutations to maintain the observed disease incidence.
If the incidence of a serious X-linked disease is not changing and selection is operating against, and only against, hemizygous males, the mutation rate, μ, must equal the coefficient of selection, s (the proportion of mutant alleles that are not passed on), times q, the allele frequency, times 1/3 since selection is operating on only one third of the mutant alleles in the population, that is, those present in males. Thus,
μ = sq / 3
For an X-linked genetic lethal disease, s = 1 and one third of all copies of the mutant gene responsible is lost from each generation.
Therefore, one third of all persons who have such X-linked lethal disorders are predicted to carry a new mutation, and their genetically normal mothers have a low risk of having subsequent children with the same disorder (assuming no mosaicism).
In less severe disorders such as hemophilia A, the proportion of affected individuals representing new mutations is less than one third (currently about 15%).
Because the treatment of hemophilia is improving rapidly, the total frequency of mutant alleles can be expected to rise relatively rapidly and to reach a new equilibrium, as we saw in the case of autosomal dominant conditions.
Assuming that the mutation rate at this locus stays the same, the proportion of hemophiliacs who result from a new mutation will decrease, even though the incidence of the disease increases.
Migration and Gene Flow
Migration can change allele frequency by the process of gene flow, defined as the slow diffusion of genes across a barrier.
Gene flow usually involves a large population and a gradual change in gene frequencies.
The genes of migrant populations with their own characteristic allele frequencies are gradually merged into the gene pool of the population into which they have migrated. (The term migrant is used here in the broad sense of crossing a reproductive barrier, which may be racial, ethnic, or cultural and not necessarily geographical and requiring physical movement from one region to another.)
The frequencies of the 32-base pair deletion allele of the CCR5 cytokine receptor gene, ΔCCR5, have been studied in many populations all over the world.
The frequency of the ΔCCR5 allele is highest, approximately 10%, in western Europe and Russia and declines to a few percent in the Middle East and the Indian subcontinent.
The ΔCCR5 allele is virtually absent from Africa and the Far East, suggesting that the mutation originated in whites and diffused into the more easterly populations.
Figure 9-10 Frequency of ΔCCR5 alleles in populations from Europe, the Middle East, and the Indian subcontinent.
ETHNIC DIFFERENCES IN THE FREQUENCY OF VARIOUS GENETIC DISEASES
Why are allele frequencies different in different populations? In particular, why are some mutant alleles that are clearly deleterious when present in homozygotes relatively common in certain population groups and not in others?
The human species of more than 6 billion members is separated into many subpopulations, or ethnic groups, distinguishable by appearance, geographical origin, and history.
Although the 25,000 genes and their location and order on the chromosomes are nearly identical in all humans, we saw earlier that extensive polymorphism exists between individuals in a population.
Most variation is found in all human populations, at similar frequencies. Other alleles, however, although present in all groups, may demonstrate dramatic differences in frequency among population groups; and finally, some allelic variants are restricted to certain populations, although they are not necessarily present in all members of that group.
It is likely that because modern humans lived in small isolated settlements until quite recently, as mutations occurred in the various groups, the differences in the frequency of certain alleles persisted and could even become magnified.
A number of factors are thought to allow differences in alleles and allele frequencies among ethnic groups to develop.
Two such factors are genetic drift, including nonrandom distribution of alleles among the individuals who founded particular subpopulations (founder effect), and heterozygote advantage under environmental conditions that favor the reproductive fitness of carriers of deleterious mutations.
Differences in frequencies of alleles that cause genetic disease are significant for the medical geneticist and genetic counselor because they cause different disease risks in specific population groups.
Well-known examples include Tay-Sachs disease in people of Ashkenazi Jewish ancestry, sickle cell disease in African Americans, and cystic fibrosis and PKU in white populations.
The inherited disease of hemoglobin, β-thalassemia, is a clear example of ethnic differences both in disease frequency and in which alleles are responsible in populations with a high incidence of disease.
The disease is common in people of Mediterranean or East Asian descent and very rare in other ethnic groups. Even though dozens of different alleles can cause β-thalassemia, certain alleles tend to be far more common in some populations than in others, so that each population has only a few common alleles.
For example, the most common β-thalassemia alleles responsible for more than 90% of the disease in Mediterranean people are very rare in people from Southeast Asia or the Asian subcontinent; similarly, the most common alleles in Southeast Asians and Asian Indians are quite rare in the other two unrelated ethnic groups.
This information is of value in genetic counseling and prenatal diagnosis. For example, in North America, when persons of Mediterranean descent are at risk of having a child with β-thalassemia, testing of parental DNA for just seven mutant alleles has a more than 90% probability of providing the information needed for prenatal diagnosis
Genetic drift can explain a high frequency of a deleterious disease allele in a population. For example, when a new mutation occurs in a small population, its frequency is represented by only one copy among all the copies of that gene in the population.
Random effects of environment or other chance occurrences that are independent of the genotype and operating in a small population can produce significant changes in the frequency of the disease allele.
During the next few generations, although the population size of the new group remains small, there may be considerable fluctuation in gene frequency. These changes are likely to smooth out as the population increases in size.
In contrast to gene flow, in which allele frequencies change because of admixture, the mechanism of genetic drift is chance.
When a small subpopulation breaks off from a larger population, the gene frequencies in the small population may be different from those of the population from which it originated because the new group contains a small, random sample of the parent group and, by chance, may not have the same gene frequencies as the parent group.
This form of genetic drift is known as the founder effect. If one of the original founders of a new group just happens to carry a relatively rare allele, that allele will have a far higher frequency than it had in the larger group from which the new group was derived.
One example is the high incidence of Huntington disease in the region of Lake Maracaibo, Venezuela, but there are numerous other examples of founder effect involving other disease alleles in genetic isolates throughout the world.
The founder effect is well illustrated by the Old Order Amish, a religious isolate of European descent that settled in Pennsylvania and gave rise to a number of small, genetically isolated subpopulations throughout the United States and Canada.
The Old Order Amish tend to have large families and a high frequency of consanguineous marriage.
The incidence of specific rare autosomal recessive syndromes such as the Ellis-van Creveld syndrome of short-limbed dwarfism, polydactyly, abnormal nails and teeth, and high incidence of congenital heart defects in some Amish communities, but not in others, is an illustration of the founder effect.
Figure 9-11 The hands of a patient with Ellis-van Creveld syndrome, a very rare disorder seen with increased frequency in some Amish groups.
The population of Finland, long isolated genetically by geography, language, and culture, has expanded in the past 300 years from 400,000 to about 5 million.
The isolation and population expansion have allowed the Finnish population to develop a distinctive pattern of single-gene disorders.
There is a high frequency of at least 20 diseases that are rare elsewhere. For example, choroideremia, an X-linked degenerative eye disease, is very rare worldwide; only about 400 cases have been described.
Fully one third of the total number of patients, however, are from a small region in Finland, populated by a large extended family descended from a founding couple born in the 1640s.
Another Finnish genetic disease is hyperornithinemia with gyrate atrophy of the choroid and retina, an autosomal recessive condition caused by deficiency of ornithine aminotransferase and leading to loss of vision in young adulthood.
As one might expect with a founder effect, one mutation was found in homozygous form in the majority of apparently unrelated cases of gyrate atrophy in Finland, but it was not observed at all in non-Finnish cases.
Conversely, disorders that are common in other European populations, such as PKU, are quite rare in Finland.
Thus, one of the outcomes of the founder effect and genetic drift is that each population may be characterized by its own particular mutant alleles as well as by an increase or decrease in specific diseases.
As these examples show, genetic drift and founder effect can favor the establishment at high incidence of alleles that are not favorable or even neutral but are actually harmful.
The relative mobility of most present-day populations, in comparison with their ancestors of only a few generations ago, may reduce the effect of genetic drift in the future while increasing the effect of gene flow.
Positive Selection for Heterozygotes (Heterozygote Advantage)
Although certain mutant alleles may be deleterious in homozygotes, there may be environmental conditions in which heterozygotes for some diseases have increased fitness not only over homozygotes for the mutant allele but also over homozygotes for the normal allele, a situation termed heterozygote advantage.
Even a slight heterozygote advantage can lead to an increase in frequency of an allele that is severely detrimental in homozygotes, because heterozygotes greatly outnumber homozygotes in the population. A situation in which selective forces operate both to maintain a deleterious allele and to remove it from the gene pool is described as a balanced polymorphism.
Malaria and Hemoglobinopathies
A well-known example of heterozygote advantage is resistance to malaria in heterozygotes for the sickle cell disease mutation.
The sickle cell allele has reached its highest frequency in certain regions of West Africa, where heterozygotes are more fit than either type of homozygote because heterozygotes are relatively more resistant to the malarial organism.
In regions where malaria is endemic, normal homozygotes are susceptible to malaria; many become infected and are severely, even fatally, affected, leading to reduced fitness.
Sickle cell homozygotes are even more seriously disadvantaged, with a fitness approaching zero, because of their severe hematological disease.
Heterozygotes for sickle cell disease have red cells that are inhospitable to the malaria organism but do not undergo sickling under normal environmental conditions; the heterozygotes are relatively more fit than either homozygote and reproduce at a higher rate.
Thus, over time, the sickle cell mutant allele has reached a frequency as high as 0.15 in some areas of West Africa that are endemic for malaria, far higher than could be accounted for by recurrent mutation.
The heterozygote advantage in sickle cell disease demonstrates how violating one of the fundamental assumptions of Hardy-Weinberg equilibrium-that allele frequencies are not significantly altered by selection-causes the mathematical relationship between allele and genotype frequencies to diverge from what is expected under the Hardy-Weinberg law.
Consider two alleles, the normal A allele and the mutant S allele, which give rise to three genotypes: A/A (normal), A/S (heterozygous carriers), and S/S (sickle cell disease).
In a sample of 12,387 individuals from an adult West African population, the three genotypes were detected in the following proportions: 9365 A/A : 2993 A/S : 29 S/S.
By counting the A and S alleles in these three genotypes, one can determine the allele frequencies to be p = 0.877 for the A allele and q = 0.123 for the S allele.
Under Hardy-Weinberg equilibrium, the ratio of genotypes should be A/A : A/S : S/S = p2 : 2pq : q2 = 9527 : 2672 : 188. The observed ratios, however, A/A : A/S : S/S = 9365 : 2993 : 29, differ significantly from expectations.
The example of the sickle cell allele illustrates how the forces of selection, operating not only on the relatively rare S/S genotype but also on the other two, much more frequent A/A and A/S genotypes, distort the transmission of the A and S alleles and cause a deviation from Hardy-Weinberg equilibrium in a population.
Change in the selective pressures would be expected to lead to a rapid change in the relative frequency of the sickle cell allele. Today, many sickle cell heterozygotes live in non-malarial regions, and even in malarial areas, major efforts are being made to eradicate the mosquito responsible for transmitting the disease.
There is evidence that in the African American population in the United States, the frequency of the sickle cell gene may already be falling from its high level in the original African population of several generations ago, although other factors, such as the introduction of alleles from non-African populations into the African American gene pool, may also be playing a role.
Some other deleterious alleles, including genes for hemoglobin C, the thalassemias, and glucose-6-phosphate dehydrogenase deficiency, as well as the benign FY allele of the Duffy blood group system, are also thought to be maintained at their present high frequencies in certain populations because of the protection that they provide against malaria.
Heterozygote advantage has also been proposed to explain the high frequencies of cystic fibrosis in white populations and of Tay-Sachs disease and other disorders affecting sphingolipid metabolism in the Ashkenazi Jewish population.
Drift Versus Heterozygote Advantage
Determining whether drift or heterozygote advantage is responsible for the increased frequency of some deleterious alleles in certain populations is not simple to do.
The environmental selective pressure responsible for heterozygote advantage may have been operating in the past and not be identifiable in modern times. The northwest to southeast gradient in the frequency of the ΔCCR5 allele, for example, reflects major differences in the frequency of this allele in different ethnic groups.
For example, the highest frequency of the ΔCCR5 allele is 21%, seen among Ashkenazi Jews, and it is nearly that high in Iceland and the British Isles. The current AIDS pandemic is too recent to have affected gene frequencies through selection; the variation in allele frequencies in Europe itself is most consistent with genetic drift acting on a neutral polymorphism.
It is, however, possible that another selective factor (perhaps another infectious disease such as bubonic plague) may have elevated the frequency of the ΔCCR5 allele in northern European populations during a period of intense selection. Thus, geneticists continue to debate whether genetic drift or heterozygote advantage (or both) adequately accounts for the unusually high frequencies that some deleterious alleles achieve in some populations.
Population genetics uses quantitative methods to explain why and how differences in the frequency of genetic disease and the alleles responsible for them arose among different individuals and ethnic groups.
Population genetics is also important to our attempts to identify susceptibility alleles for common, complex disorders by use of population-based association methods.
Not only can the fascinating history of our species be read in the patterns of genetic variation we now see, but genetic heterogeneity also has important practical implications for professionals seeking to deliver appropriate, personalized health care to the world's populations in ways that are both efficient and sensitive.