V SEMESTER ZOOLOGY HARDY-WEINBERG S LAW

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1 V SEMESTER ZOOLOGY HARDY-WEINBERG S LAW The most fundamental idea in a population genetics was proposed by English-man G.H. Hardy and German W. Weinberg simultaneously in the year At that time it was thought that alleles of a gene would distribute in 3:1 ratio in F1 generation. But it is now known that heterozygotes appear in much higher frequencies in populations. Further study and treatment of gene frequencies was developed by R.A. Fischer (British), J.B.S. Haldane (British) and Sewall Wright (USA) in This law can be defined as The Relative frequencies of various kinds of genes in a large and randomly mating population tend to remain constant from generation to generation in the absence of mutation and natural selection. Hardy-weinberg s law describes a theoretical situation in which a population is undergoing no evolutionary change. It explains that if the evolutionary forces are absent, the population is large and its individuals have random mating. Thus each parent produces equal number of gametes. Such gametes combine at random and the gene frequency remains constant. Finally the genetic equilibrium of the genes is maintained and the variability present in the population is preserved. Hardy-Weinberg s law describes a tendency of evolution to conserve gains of genetic changes and avoid too frequent changes in genotype. Therefore, the basic factors that cause evolution are: mutation, natural selection, non-random mating, small population and genetic drift. Conditions needed for genetic equilibrium Hardy Weinberg Principle The original proportion of genotypes in a population remains constant 1. Population size is large 2. Random mating is occurring 3. No mutations 4. No genes are introduced or not 5. No selection occurs 1

2 Gene frequency is the proportion of an allele in the gene pool as compared with other alleles at the same locus. It can be calculated by dividing the number of a particular gene by the total number of genes present in the population. For example if there are 100 individuals in a population, 40 of them being dominant MM, 40 heterozygous Mm and 20 recessive mm, the frequency of the dominant gene M, which is depicted by P, would be 40+20/100=0.6 and the frequency of the recessive gene m, denoted by q, would be 20+20/100=0.4. P+q should always be 1.0 and hence when frequency of one gene increases, that of the other must decrease. Genotype frequency is the total number of one kind of individuals in a population exhibiting similar characters (genotype) in respect to the locus. It can be determined by dividing the number of individuals having one kind of genotype by the total number of individuals in a population. Therefore, in the above example, the genotype frequency of the dominant homozygotes MM will be D/N=40/100=0.4, that of Mm will be H/N=40/100=0.4 and that of recessive mm will be r/n=20/100=0.2, where N=total number of individuals and D,H and r denote dominant, heterozygous and recessive respectively. The next generation will have the following composition: 0.25 MM Mm mm, which can also be written as: 1 MM + 2 Mm + 1 mm OR M Mm + m 2. If P is the frequency of gene M and q is the frequency of gene m, then the above equation can be written as P 2 + 2Pq + q 2 = (P+q) 2. This is called Hardy-Weinberg s equation, which can be used to find out genetic composition of a population and also to prove Hardy-Weinberg s Law that gene frequencies remain unchanged from generation to generation, as illustrated in the following example. Example. Let us presume there is population of rats, which has 50% brown (MM) and 50% white (mm) individuals. The gene frequencies will be P=0.5 and q=0.5 (P+q=1.0). 2

3 Both gene frequencies and genotype frequencies are same here. Now let us substitute the figures in the Hardy-Weinberg s equation as follows: P 2 + 2Pq + q 2 = (0.5) (0.5) (0.5) + (0.5) 2 = The genotype frequency in F 1 generation will be 25% MM + 50% Mm + 25% mm but the gene frequencies will still remain as P=0.5 and q=0.5, that is they remain unchanged even in the next generation. In this example dominant gene equals the recessive gene but in nature usually the recessive gene is far less in number. Will the gene frequencies remain unchanged even in such a case is illustrated by the following example. Application of the Hardy-Weinberg s equation: If we know the number of homozygous recessive animals in a population (which is easy because in these recessive gene has expressed), then we can find out the entire gene pool of the population or the entire genotype frequency can be found out using Hardy-Weinberg s equation as in the following examples. Example. If in a population of rats16% individuals are recessive white and rest are brown, what will be the composition of the population (i.e. find out the value of MM and Mm). If white individuals are 16% (mm), then m 2 = 16 OR q 2 = 0.16; q = square root of 0.16; q = 0.4. As we have found out the value of q, the value of P can be known by P=1.0-q; or or P=0.6. Now to calculate the heterozygous Mm rats 2Pq = 2.(0.6)(0.4) = 0.48, which means 48% of rats were heterozygous brown (Mm), and since we know that 16% were white (mm), the rest of the population has to be MM or homozygous brown ( ) = 16%. The final composition of the population will be 36%MM + 48%Mm + 16%mm. Example. In human population one in 20,000 is an albino, let us find out the genotype frequency. q 2 =1/20,000 = ; q=square root of =

4 P=(1.0-q) = ( ) = 0.993; P 2 =(0.993) 2 = Pq=2.(0.993 x 0.007) = Although one in 20,000 is an albino in human population, one in 70 is a carrier of the disease, which is 280 times as many as affected. Hardy-Weinberg s equation is very useful in finding out the genotype frequencies in a population, which have not expressed and are hidden. GENETIC DRIFT (SEWALL WRIGHT EFFECT) The theory of genetic drift was developed by a geneticist SEWALL WRIGHT in It is also known as Sewall Wright effect or scattering of variability. It denotes that the random fluctuations in the gene frequencies in a small population from generation to generation. According to genetic drift, in small, non-randomly mating populations gene frequencies are found to fluctuate purely by chance. Smaller the population, larger will be the fluctuation in gene frequency. Genetic drift works on the principle of tossing of a coin. If a coin is tossed, then chances of getting heads and tail would be equal only if it is tossed for a large number of times, so that the standard error is low. But if the coin is tossed only few times, then standard error will go up and you may get head or tail any number of time. Standard Error = square root of Pxq/n, where P=frequency of dominant gene (or head of a coin), q=frequency of recessive gene (or tail of a coin) and n=number of individuals in a population (or number of times the coin is tossed). For example, let us imagine a small population of black hamsters; say only one pair, one MM and the other mutant Mm. If they can produce only 2 offspring, then the chance that the first offspring will be MM is 0.5 and that the second offspring will also be MM is also 0.5. The chance that both offspring will be MM is reduced to =0.25. In such a case the mutation m will be lost forever. Similarly, by chance both offspring can be Mm, in which case the mutation m will have a chance to express in the next generation. Thus the population may drift towards losing or fixing a 4

5 mutation purely by chance. Gene frequency will continue to fluctuate until one allele is lost and the other fixed. Extinction of certain species, which are left with small populations, is known to be due to genetic drift, when lethal mutations are fixed, e.g. passenger pigeon and cheetah became extinct due to genetic drift that fixed lethal mutations. Carnivores usually have small populations and are affected by genetic drift. Human tribes that marry within their own communities also face genetic drift and accumulate lethal mutations. Effects of Genetic Drift on Gene frequency In small populations or demes, the genetic drifts have the following, effects on the gene-frequency. - I) Homozygocity: In small populations, due to genetic drift gene frequencies continue to fluctuate until one of the allele lost and other fixed. This leads homozygosity in small populations. It means the genetic drift reduces genetic variability by eliminating one of the two alleles either new or old one. ii) Fixation of new mutations: Since genetic drift tend to eliminate one allele and fix the other one, irrespective of its dominance or recessiveness or advantageous or non advantageous nature. So a new mutation has 50% chances of either being lost or be fixed in small population. iii) Genetic divergence: The demes become progressively genetically different. In each sub population, the genes fixed and lost will be different. Thus, In due course of time, (each deme gradually diversifies from the other sister demes) lead to the establishment of new species. 5

6 Founder Effect: Whenever a few organisms from large population encroaches a new or isolated geographical region, these form the founders or founder members. The founders carry only a limited portion of the parental gene pool. The descendants of the founder i.e. the founder population or marginal isolates in a new area will tend to have ratios similar to the founders. The resemblance of the descendants of the founders is called founders effect or founder principle. When a small population migrates to a new area, the frequency of genes is determined by the genetic drift (Mayr, 1963; Sheppard, 1960). For example, American Indians have no B group in their blood. However, in Asia, which is the ancestral home of American Indians, B group is widespread. The ancestral population of mongoloids that migrated across Bering strait to North America might have been very small and must be having all kinds of blood groups, but due to genetic drift, O group has been fixed and B group eliminated purely by chance. Bottleneck effect: It is a phenomenon found in animals that follow seasonal cycle of dormancy and activity, such as insects, amphibians and a large number of invertebrates. During breeding season their populations are very large but as the adverse climate arrives majority of individuals are killed and very few manage to find protective shelters and undergo diapause to tide over adverse period. This small population then produces next generation by way of genetic drift. 6