Download Definition Hardy-Weinberg Equilibrium p2+2pq + q2= 1 1 + 2q + q2 = 1

Medical Genetics
Population Genetics
Definition
Population genetics is the study of genetic variation in populations.
Basic concepts of population genetics allow us to understand how and why the prevalence of
various genetic diseases differs among populations.
Hardy-Weinberg Equilibrium
If a population is large and if individuals mate at random with respect to their genotypes at a
locus, the population should be in Hardy-Weinberg equilibrium. This means that there is a
constant and predictable relationship between genotype frequencies and allele frequencies.
The Hardy Weinberg equation, allows one to estimate genotype frequencies if one knows
allele frequencies, and vice versa.
The Hardy-Weinberg Equation
p2+2pq + q2= 1
In this equation:
p = frequency of allele 1 (conventionally the most common, normal allele)
q = frequency of allele 2 (conventionally a minor, disease-producing allele)
p2 = frequency of genotype 1-1 (conventionally homozygous normal)
2pq = frequency of genotype 1-2 (conventionally heterozygous)
q2= frequency of genotype 2-2 (conventionally homozygous affected)
In most cases where this equation is used, a simplification is possible. Generally p, the
normal allele frequency in the population, is very close to 1 (e.g., most of the alleles of this
gene are normal). In this case, we may assume that p ~ 1, and the equation simplifies to:
1 + 2q + q2 = 1
Although the Hardy-Weinberg equation applies equally well to autosomal dominant and
recessive alleles, genotypes, and diseases, the equation are most frequently used with
autosomal recessive conditions.
 A Practical Application of the Hardy-Weinberg Principle
A 20-year-old female has an AR genetic disease called Phenylketonuria (PKU). She asks you 2
questions:
1. What is the chance that she had to marry a man with the disease-producing allele.
2. What is the probability that she will have a child with PKU?
Note: the prevalence of PKU in the population is 1/10,000.
Answer:
Disease prevalence = q2 = 1/10,000, so q = square root of 1/10,000, which is 1/100
Carrier frequency = 2q = 2 x 1/100 = 1/50
Dr. Mohammed Hussein Assi MBChB – MSc – DCH (UK) – MRCPCH
Medical Genetics
Population Genetics
The answer to the second question is based on the joint occurrence of three nonindependent
events:
1. The probability that she will marry a heterozygous carrier (1/50),
2. The probability that she will pass her PKU allele to the child (which is 1 as she is
affected)
3. If her husband is a carrier, the probability that he will pass his PKU allele versus the
normal allele to the child (1/2) as the disease is autosomal recessive.
These probabilities would be multiplied to give:
 1/50 * 1/2 * 1 = 1/100, the probability that she will have a child with PKU.
In summary, there are three major terms one usually works with in the Hardy Weinberg
equation applied to AR conditions:
1. q2, the disease prevalence
2. 2q, the carrier frequency
3. q, the frequency of the disease-causing allele
 Hardy-Weinberg Equilibrium for Dominant Diseases
The calculations for dominant diseases must acknowledge that most of the affected
individuals will be heterozygous.
In this case, the prevalence is 2q.
The term q2 represents the prevalence of homozygous affected individuals who, although
much less commonly seen, may have more severe symptoms.
For example,
 1/500 people in the USA have a form of LDL-receptor deficiency.
 Taking 2q = 1/500, one can calculate that q2 = 1/106, or one in a million live births
are homozygous for the condition.
 Sex Chromosomes and Allele Frequencies
When considering X-linked recessive conditions, one must acknowledge that most cases
occur in hemizygous males (xY).
Therefore, q = disease-producing allele frequency but, paradoxically, it also equals the
prevalence of affected males.
Thus, the statement “1/10,000 males has hemophilia A” also gives the allele frequency for
the disease-producing allele: 1/10,000.
 q2= prevalence of disease in females (1/108, or 1/100,000,000)
 2q = prevalence of female carriers (1/5,000)
This exercise demonstrates that:
 The majority of X-linked recessive genes are hidden in female heterozygous carriers.
 X-linked recessive traits are seen much more commonly in males than in females.
Dr. Mohammed Hussein Assi MBChB – MSc – DCH (UK) – MRCPCH
Medical Genetics
Population Genetics
Factors responsible for genetic variation in/among populations
I.
II.
III.
IV.
V.
Although human populations are typically in H-W equilibrium for most loci, deviations from
equilibrium can be produced by new mutations, nonrandom mating (for example,
consanguinity), the action of natural selection, genetic drift, and gene flow. Although these
factors are discussed independently, often more than one effect contributes to allele
frequencies in a population.
Mutation
Mutation is ultimately the source of all new genetic variation in populations.
Founder effect: In some cases, a new mutation can be introduced into a population when
someone carrying the mutation is one of the early founders of the community. This is
referred to as a founder effect. As the community rapidly expands through generations, the
frequency of the mutation can be affected by natural selection, by genetic drift, and by
consanguinity. (See below)
Natural Selection
Natural selection acts upon genetic variation, increasing the frequencies of alleles that
promote survival or fertility (referred to as fitness) and decreasing the frequencies of alleles
that reduce fitness.
There is now evidence for heterozygote advantages for several other recessive diseases that
are relatively common in some populations. Examples include:
 Cystic fibrosis (heterozygote resistance to typhoid fever)
 Hemochromatosis (heterozygote advantage in iron-poor environments)
 Glucose-6-phosphate dehydrogenase deficiency (heterozygote resistance to malaria)
Genetic Drift
Mutation rates do not vary significantly from population to population, although they can
result in significant differences in allele frequencies when they occur in small populations or
are introduced by a founder effect. Mutation rates and founder effects act along with genetic
drift to make certain genetic diseases more common (or rarer) in small, isolated populations
than in the world at large.
Gene Flow
Gene flow refers to the exchange of genes among populations. Because of gene flow,
populations located close to one another often tend to have similar gene frequencies.
Consanguinity and its Health Consequences
Consanguinity refers to the mating of individuals who are related to one another (typically, a
union is considered to be consanguineous if it occurs between individuals related at the
second-cousin level or closer). Consequently, there is an increased risk of genetic disease in
the offspring of consanguineous matings. Dozens of empirical studies have examined the
health consequences of consanguinity, particularly first-cousin matings. These studies show
that the offspring of first-cousin matings are approximately twice as likely to present with a
genetic disease as are the offspring of unrelated matings. The frequency of genetic disease
increases further in the offspring of closer unions.
Dr. Mohammed Hussein Assi MBChB – MSc – DCH (UK) – MRCPCH