Population Genetics

INTRODUCTION

Population genetics is that branch of medical genetics, which deals with distribution of inheritance of genes and inherited traits in the population. It also studies the factors that maintain or change the frequency of genes. These factors are mutational events, natural selection and genetic drift. The studies are based on mathematical calculations, environmental factors, and population migration. Population genetic studies are important for the calculation of autosomal recessive gene carrier frequencies, for an understanding of linkage disequilibrium, and for its implications for human evolution.

THE HARDY-WEINBERG PRINCIPLE

In the absence of forces that change gene ratios in populations, when random mating is permitted, the frequencies of each allele (as found in the second generation) will tend to remain constant throughout the generations. This led to the concept of Hardy-Weinberg equilibrium, which shows that the frequency of alleles for any character will remain unchanged in a population through any number of generations, unless this frequency is altered by some outside influence, such as non random mating, selection, small populations, migration leading to gene flow or mutations.

Punnett Squares and Probability

A Punnett square is a grid named after its inventor RC Punnett in 1905. This can be used to predict the results of genetic crosses. The alleles that could be present in the female gamete are placed on the left of the grid and the alleles that could be present in the male appear on top of the grid (these could be reversed). The alleles from both are combined in the relevant squares of the grid. This shows all the different possibilities for pairing, hence the different possible genotypes of the offspring. It also gives the probability for each pairing. In the Figure.1, we have a gene locus with two alleles H and h, which have the frequency of p and q. p + q = 100% or 1.

Fig. 1 : Punnett's square showing genotype frequencies for the alleles H and h in the first generation

The Hardy-Weinberg Law and its Extensions

Given the existence of a population, there are implications of Mendelian genetics for the distributions of genotypes in the population. The Hardy-Weinberg law shows that in a population in which individuals mate at random with respect to their genotype, and in the absence of selection, the frequencies of genotypes MM, MN and NN in the population are p2, 2pq and q2 respectively, where p and q are the frequencies of the genes M and N respectively. Counting the genes in the population gives the following result:

p = (frequency of MM) + 1/2 (frequency of MN)

 q = 1-p = (frequency of NN) + 1/2 (frequency of MN)

This distribution is achieved in one generation and remains the same for all future generations. The result of the Hardy Weinberg law is that random mating is equivalent to the random union of gametes, namely those of the M and N genes.

The Hardy Weinberg law has another very important implication, namely, genetic variability once it is established in a population tends to remain, and is not dissipated. This is effectively a result of Mendelian segregation. Maintenance of variability in a population is an essential requirement for Darwin’s theory of evolution by natural selection. Evolution is simply defined as a change in genetic frequencies as a result of selection and genetic variation.

Disturbance of gene frequencies IN A population

These can occur in the following ways:

1-Non-random mating

2-Selection

3-Small population

4-Migration leading to gene flow

Non-random Mating

Random mating is the selection of a mate irrespective of the spousal genotype. In practice, mating is probably never entirely random, as inherited factors such as height, weight, race and intelligence tend to play a role. This is called assortive mating. Consanguinity or mating between genetic relatives is also an example of non-random mating. The offspring of consanguineous mating are at an increased risk of homozygosity for recessive alleles carried by common ancestors.

Selection

Selection can alter gene frequencies and can reduce (negative selection) or increase (positive selection) a particular genotype. Selection acts by modifying an individual’s biological fitness, f. Selection may act on the recessive heterozygote, and this is seen in sickle cell disease. The area where sickle cell disease is most prevalent corresponds geographically with the distribution of plasmodium falciparum malaria. In the sickle cell disease heterozygote, red cells parasitized by plasmodium falciparum undergo sickling and are destroyed. The sickle cell heterozygote thus overcomes malarial infection and is at a reproductive advantage. Heterozygotes for P thalassaemia and G6PD deficiency also have a selective advantage over homozygous normals by virtue of malarial resistance.

Small Communities

With only a small number of individuals in a breeding population, the actual frequencies of alleles varies widely from one generation to the next. This is known as random genetic drift. By chance an allele may fail to be passed on to the next generation and may disappear. This is known as extinction.

Gene Flow (Migration)

Due to migration or intermarriage, a new allele can get introduced into a population and there will be a change in the relevant allele frequencies. This type of slow diffusion is known as gene flow. The blood group B is given as an example, and it is seen throughout the world. It is thought to have its origin in Asia, and has spread slowly towards the west through invasion.

Applications of the hardy-weinberg equilibrium

Application of Hardy-Weinberg principle is important in genetic counseling where estimation of recurrence is to be calculated in various patterns of inheritance. An example of estimation of carrier frequencies is discussed below: For an autosomal recessive trait, if p is the frequency of the normal allele and q is the frequency of the mutant allele, then the frequency of the recessive homozygote is equal to the square of the mutant allele frequency (q2). An example that can be used is that of cystic fibrosis.

Recessive homozygote frequency q² = 1/1600

q = √1/1600 = 1/40

p = 1- q = 39/40

The heterozygote frequency (carrier frequency) is 2pq = ~1 in 20

THE BALANCE BETWEEN MUTATIONS AND SELECTION

The ultimate source of all genetic variation is mutation, namely an alteration in the DNA sequence. The vast majority of deleterious mutations in expressed genes are likely to disrupt the function of a gene, and therefore lead to a selective disadvantage. The disadvantage will lead to the disappearance of the mutant gene from the population. However, new mutations arise continuously each generation. Therefore a balance is achieved between mutations giving rise to new deleterious variants of a gene, and selection removing them from the population.

Estimation of mutation rates

The mutation rate (m) is the frequency of a change in the genetic material. It is expressed as the number of mutations at a locus per million gametes produced.

For rare autosomal dominant traits, the mutation rate may be calculated as:

m = n/2N, where n = number of affected children with normal parents, and N = total number of births.

If an autosomal dominant condition does not prevent reproduction, then some new cases will inherit the trait from an affected parent. Here the birth frequency is given by: 2m/(1-f), where f is the biological fitness.

If affected individuals cannot reproduce, f = 0, and the birth frequency is twice the mutation rate.

For an autosomal recessive trait, the birth frequency is m/(1-f). If the affected homozygote never reproduces (f = 0), the birth frequency equals the mutation rate.

For an X-linked recessive trait, the birth frequency in the population is 3m/(1-f). Thus for individuals with a biological fitness of zero, the birth frequency equals 3 times the mutation rate.

Genetic polymorphisms

The extent of genetic variability in human populations is very high and it is reflected in the unique characteristics of all individuals. This variability includes differential disease susceptibility for both common and rare diseases. It was recognized by Fisher and Haldane in the 1930s that linkage analysis using common polymorphisms is a very powerful tool for the analysis of genetic diseases.

A genetic polymorphism in a population is when two or more discontinuous traits appear at a frequency where the rarest cannot be explained by the mutations. A locus is considered as polymorphic when at least two alleles at the same locus with a frequency greater than 1%. If the frequency is less than 1% it is considered as rare variant. In the normal population about 30 gene loci are considered to be polymorphic. Each individual is 10 to 20% heterozygous for structural gens loci.

Polymorphisms at the DNA level can be used to trace diseases within families. This establishes the position of a mutated gene along a chromosome and is the basis for positional cloning. Polymorphisms that can be detected using PCR include polymorphisms at positions of CA repeats. More variation is identified at the level of single nucleotides called SNP or single nucleotide polymorphisms. The study of polymorphisms provides a basis for understanding genetic variability in the human population as it relates to disease.

References

Purandarey , H. (2009) . Essentials of Human Genetics. Second Edition. Jaypee Brothers Medical Publishers (P) Ltd.

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