Hardy-Weinberg equilibrium

Hardy-Weinberg principle of equilibrium:

• The Hardy-Weinberg equilibrium states that both the allele frequencies and the genotype frequencies are constant from generation to generation in a large random-mating population when they are not influenced by the evolutionary processes.
• In other words, the Hardy-Weinberg Law states that under a limited set of conditions, it is possible to calculate the predicted frequencies of genotypes in a population if the frequency of the distinct alleles in a population is known.
• It was discovered in 1908 by the English mathematician G.H. Hardy and the German physician Wilhelm Weinberg
• The Hardy-Weinberg equilibrium can be disturbed by a number of processes, including mutations, non-random mating, genetic drift, natural selection, and gene flow.
• For example, mutations disturb the equilibrium of allele frequencies, by the introduction of new alleles into a population.
• Likewise, the Hardy-Weinberg equilibrium is disrupted by natural selection and nonrandom mating as they result in shifts in gene frequencies.
• This happens as certain alleles help or harm the survival chances of the organisms that carry them.
• Genetic drift, which occurs when allele frequencies grow higher or lower by chance and usually takes place in small populations, is another aspect that may disrupt this equilibrium.
• The Hardy-Weinberg equilibrium can also be altered by gene flow, which occurs when mating between two species transfers new alleles into a population.
• The Hardy-Weinberg equilibrium scarcely applies in nature, since all of these destructive forces usually occur in nature.
• Thus, the Hardy-Weinberg equilibrium explains an idealized state, and genetic variations in nature can be evaluated as changes from this equilibrium state.

Hardy-Weinberg equation and analysis:

• The Hardy-Weinberg Theorem concerns with Mendelian genetics in the frame of reference of populations of diploid, individuals reproducing sexually.
• On a set of conditions, this theorem states that:
  • In a group, allele frequencies will not alter from generation to generation.
  • If p and q are the allele frequencies in a population with two alleles B and b, at the locus, then p², 2pq, and q² are the predicted genotype frequencies.
• Once a population is in a Hardy-Weinberg equilibrium, this frequency distribution will not alter from generation to generation.
• For instance, if the frequency of allele B in the population is p and the frequency of allele b in the population is q, then the frequency of genotype BB= p², the frequency of genotype Bb= 2pq, and the frequency of genotype bb= q².
• If there are only two alleles at a locus, then by mathematical necessity, p+q equals one.
• The frequencies of the Hardy-Weinberg genotype, p² + 2pq + q², reflect the binomial expansion of (p + q)², and also amount to one.
• If the frequency of B allele is 0.7, then we know that the frequency of b allele is 0.3.
• If there are three alleles, B₁, B₂, and B₃, with frequencies p, q, and r, the equilibrium frequencies corresponding to the six possible genotypes (shown in parentheses) will be determined as follows:
• (p+q+r)²= p²(B₁B₁) +q² (B₂B₂) +r²(B₃B₃) + 2pq(B₁B₂) + 2pr(B₁B₃)+ 2qr(B₂B₃)
• The Hardy-Weinberg Theorem can be applicable to loci with more than two alleles, in which case the predicted frequencies of the genotype are given by the multinomial expansion for all k alleles segregating in the population: (p1 + p2 + p3 +…+ pk)².
• The results of the Hardy-Weinberg Theorem apply only when the population corresponds to the following assumptions:
• Natural selection does not function on the locus concerned (i.e. there are no consistent differences in likelihoods of survival or reproduction between genotypes).
• New alleles are not introduced into the population by either mutation (the origin of new alleles) or migration (the transport of individuals and their genes into or out of the population).
• Population size is infinite, which suggests that genetic drift does not cause random variations in allele frequencies from one generation to the next due to sampling error. All natural populations are finite and thus subject to drift, of course, but it is expected that the effects of drift to be more pronounced in small populations than in large ones.
• With regard to the locus in concern, individuals in the population mate randomly. Even if non-random mating does not alter allele frequencies from one generation to the next when the other assumptions hold, it can create deviations from predicted genotype frequencies, and it can set the stage for natural selection to trigger evolutionary change.
• If the genotype frequencies in a population deviate from the standards of Hardy-Weinberg, it takes only one generation of random mating to put them into equilibrium proportions, given that the above-mentioned assumptions hold that male and female allele frequencies are identical (or else that individuals are hermaphrodites) and that the locus is autosomal.
• It takes two generations of random mating to achieve the Hardy-Weinberg equilibrium if allele frequencies vary between the sexes.
• Since one sex has two copies of the gene and the other sex has only one, sex-linked loci take many generations to reach equilibrium.
• Given these cases, if we consider random mating in terms of the likelihood of generating each genotype through random union of gametes into zygotes, the predicted Hardy-Weinberg genotype frequencies can be easily derived.
• If each allele occurs in sperm and eggs at the same frequencies, and gametes combine at random to create zygotes, then the likelihood of any two alleles combining to form a specific genotype is equal to the product of the frequencies of the alleles.
• Since the heterozygous genotype (B egg and b sperm, or b egg and B sperm) is produced in two ways, we sum up the probabilities of those two forms of union to meet the predicted Hardy-Weinberg frequency of the heterozygous genotype (2pq).
• It is essential to note that the Hardy-Weinberg equilibrium is a neutral equilibrium, which implies that after a single generation of random mating, a population disrupted by its Hardy-Weinberg genotype frequencies will still achieve equilibrium (if it conforms to the other assumptions of the theorem), but if allele frequencies have changed, it will be a new equilibrium.
• This property differentiates a neutral equilibrium from a stable equilibrium, where a disturbed system returns to the same equilibrium state.
• It makes good sense that the Hardy-Weinberg equilibrium is unstable, since a change from the equilibrium genotype frequencies will usually be linked with a change in allele frequencies (p and q), which will in turn yield new values of p², 2pq and q².
• After that, a population that matches Hardy-Weinberg assumptions will persist at the new equilibrium until disturbed again.

A punnet square showing all the possibilities of genotypes at a diallelic Mendelian locus in a populations that meets the Hardy-Weinberg assumptions:

Egg/Sperm	B (p)	b (q)
B (p)	BB (P2)	Bb (pq)
b (q)	Bb (pq)	bb (q2)

The Hardy-Weinberg Theorem’s Evolutionary Implications:

• The Hardy-Weinberg Theorem shows that in the absence of forces that change allele frequencies, Mendelian loci segregating for multiple alleles in diploid populations can maintain predictable levels of genetic variation.
• Plotting p², 2pq and q² as a function of allele frequencies is a common way of visualising these expectations.
• Two major implications of the Hardy-Weinberg theory are emphasized in this graphical presentation:
• The heterozygosity of the population (frequency of heterozygotes) is greatest when p = q = 0.5.
• Rare alleles are mostly found in heterozygotes, as they must be, provided that when q is near zero, q² is much smaller than 2pq and when p is near zero, p² is much smaller than 2pq.
• If we consider the ability for natural selection to affect the frequencies of new mutations, the second statement takes on specific significance.
• If a population conforms to all other Hardy-Weinberg assumptions, a beneficial allele in the population will inevitably be set by selection so that all individuals are homozygous for that allele.
• A uncommon, advantageous, dominant allele’s initial rise in frequency is higher than that of a rare, advantageous, recessive allele.
• This is because, as we have noticed, rare alleles are often present in heterozygotes, so that natural selection will not see a new recessive mutation until it reaches a sufficiently high frequency (perhaps through drift in a true, finite population) to begin to occur in homozygotes.
• However a new dominant mutation is noticeable to natural selection immediately because its effect on fitness is seen in heterozygotes.
• Even though Hardy(1908) showed that dominance alone does not alter allele frequencies at a locus, there can be a major impact on evolutionary trajectories of the dominance relationships between alleles.
• The processes that cause changes in allele frequencies are selection, mutation, migration, and genetic drift, and when one or more of these factors function, the population violates the assumptions of Hardy-Weinberg, and evolution happens.

Thus the Hardy-Weinberg Theorem is a null model for the discipline of population genetics and is central to evolutionary research