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Principles of genetics

### Transcript of Hardy-Weinberg equilibrium

FACULTY OF APPLIED SCIENCES AND COMPUTINGBABS2213 PRINCIPLES OF GENETICSPRACTICAL 3TITLE: HARDY WEINBERG EQUILIBRIUMNAME: CHOONG MEL JUNEGROUP: RBS 2 A1STUDENT ID: 14WAR10521DATE: 4 JUNE 20140DEMONSTRATER: DR LOH KHYE ER

Objectives:1. To derive the Hardy-Weinberg Equation.2. To calculate the genotypic and allelic frequencies.3. To discuss the conditions under which a population is in Hardy-Weinberg Equation.4. To determine if a population is in Hardy-Weinberg Equation.5. To design and perform a test of a disruption to Hardy-Weinberg Equation.6. To identify why the Hardy-Weinberg Equation is difficult or impossible to demonstrate with living organisms.

Hypothesis:Hardy and Weinberg Equilibrium showed that if there was no migration, no mutation and no selection in a large population, the frequencies of any pair of gene allele will tend to remain constant from generation to generation.

Introduction:A population is a group of organisms of the same species that live and breed in the same area. Alleles are alternate forms of genes. In standard Mendelian genetics, two alleles - one from each parent - control an inherited trait or characteristic (e.g. seed pod color). A gene pool is the collective term representing all the genes, including all the different alleles, found in a population.

The written expression of the DNA code, called the genotype, is normally represented using two letters, each letter representing one allele (e.g. AA). Dominant alleles are represented by capital (uppercase) letters. Recessive alleles are represented by lowercase letters. Genotypes with two dominant alleles (e.g. AA) are referred to as homozygous dominant. Genotypes with two recessive alleles (e.g. aa) are referred to as homozygous recessive. Genotypes with one dominant and one recessive allele (e.g. Aa) are referred to as heterozygous.

The physical expression of the genotype (e.g. brown hair, blue eyes) is called the phenotype. In standard Mendelian genetics, the heterozygous condition (e.g. Aa) retains the homozygous dominant phenotype because the dominant allele masks the phenotype of the recessive allele. An example of this in humans would be a heterozygote for brown eye color. The person would carry both a dominant brown allele A and a recessive blue allele a yet have brown eyes. The dominant brown allele masks the recessive blue allele.

The population is considered the basic unit of evolution. The small scale changes in the genetic structure of populations from generation to generation are called microevolution. Microevolution is the study of the change in the frequency of an allele in a population from one generation to the next. Mathematicians Hardy and Weinberg explained how an allele could change in a population by first showing how it would not change, the Hardy-Weinberg principle.

Genetic equilibrium is the state in which allele frequencies remain constant. In 1908, English mathematician G. H. Hardy and German physician W. Weinberg independently developed models of population genetics that showed that the process of heredity by itself did not affect the genetic structure of a population. It can be said the Hardy-Weinberg Principle is a model used to help clarify evolutionary change by determining what happens if no change occurs. When no change occurs and an environment is stable, genetic equilibrium is maintained. The Hardy-Weinberg theorem states that the frequency of alleles in the population will remain the same from generation to generation. Furthermore, the equilibrium genotypic frequencies will be established after one generation of random mating. This theorem is valid only if certain conditions are met:

Random mating all individuals in a population have equal opportunity to pass on their alleles to offspring.

Large populations genetic drift, or random changes in allele frequency, has less effect on large populations than small populations.

No mutations - if genes randomly mutate, new alleles may be introduced into the population and allele frequencies will change.

No migration individuals cannot move into or out of the population.

No natural selection - all genotypes must have equal probabilities of reproduction.

Two equations are used to model the Hardy-Weinberg Principle. p + q = 1; where p represents the dominant allele, A, and q represents the recessive allele, a. This equation, used to calculate allele frequency, equals 1 or 100% of the population. p2 + 2pq + q2 = 1; where p2 represents the homozygous dominant genotype, 2pq represents the heterozygous genotype, and q2 represents the homozygous recessive genotype. This equation, used to calculate genotype frequency, equals 1 or 100% of the population.

I. Testing the Hardy-Weinberg Equilibrium

Materials:1. 400 of white colour beads. (Two different colours of beans that are approximately the same size)2. 400 of black colour beads. (Two different colours of beans that are approximately the same size)

Methodology:400 of black colour beads and 400 of white colour beads were mixed together into a beaker.

One pair of bead was picked up without looking.

The colour of the pair of bead was observed and recorded down.

The beads were placed back into the beaker and mixed well.

The steps 2, 3 and 4 were repeated 100 times and all the colour of beads were observed and recorded down.

GenotypeObserved number, OAverage observed number, OGenotype FrequencyExpected number, E

G1G2G3G4

AA1730231822p2= 0.52= 0.2525

Aa57504953522pq= 2(0.5)(0.5)= 0.550

aa2620282926q2= 0.52= 0.2525

Total, n1001001001001001100

Calculation: p = 400/800 = 0.5 q = 400/800 = 0.5 AA + 2 Aa + aa = 1 p2 + 2pq + q2 = 1 Male FemalepAqa

pAppAApqAa

qapqAaqqaa

Applying chi square formula

Interpretation: Failed to reject the null hypothesis, as the P value is more than the critical value of 0.05 at degree of freedom to 2, the hypothesis that there was no migration, no mutation and no selection in a large population, the frequencies of any pair of gene allele will tend to remain constant from generation to generation. There is 70% ~ 80% of the time that the deviation of the observed number from the expected is due to the chances.

Discussion:The Hardy-Weinberg theorem provides a mathematical formula for calculating the frequencies of alleles and genotypes in populations. We begin with a population with two alleles at a single gene locus - a dominant allele, A, and a recessive allele, a - then the frequency of the dominant allele is p, and the frequency of the recessive allele is q. Therefore, p + q = 1. The frequency of one allele, p, is known for a population, the frequency of the other allele, q, can be determined by using the formula q = 1 - p. During sexual reproduction, the f frequency of each type of gamete produced is equal to the frequency of the alleles in the population. If the gametes combine at random, the probability of AA in the next generation is p2, and the probability of aa is q2. The heterozygote can be obtained two ways, with either parent providing a dominant allele, so the probability would be 2pq. These genotypic frequencies can be obtained by multiplying p + q by p + q. The general equation then becomes (p + q)2 = p2 + 2pq + q2 = 1To summarize:p2 = frequency of AA2pq = frequency of Aaq2 = frequency of aa

When a population meets all of the of the Hardy-Weinberg conditions, it is said to be in Hardy-Weinberg equilibrium. How far a population deviates from Hardy-Weinberg equilibrium can be measured using the goodness of fit orchi-squared test(2).

Mathematically the chi-squared test is represented:2= [(observed value expected value)2 / expected value]

Since we have three genotypes, therefore we have 3 minus 1, or 2 degrees of freedom. Degrees of freedom is a complex issue, but we could look at this in simple terms: if we have frequencies for three genotypes that are truly representative of the population then, no matter what we calculate for two of them, the frequency of the third must not be significantly different for what is required to fit the population.

Looking across the distribution table for 2 degrees of freedom, we find our chi-squared value of 0.48 is more than that required to satisfy the hypothesis that the differences in the O and E data did not arise by chance. Since the chi-squared value falls above the 0.05 (5%) significance cut-off, we can conclude that the population does differ significantly from what we would expect for Hardy-Weinberg equilibrium.

Conclusion:The hypothesis is accepted. At df = 2, there is 70% ~ 80% of the time that the deviation of the observed number from the expected is due to the chances. There was no migration, no mutation and no selection in a large population, the frequencies of any pair of gene allele will tend to remain constant from generation to generation.

II. Genetic Drift

Materials:1. 400 of white colour beads. (Two different colours of beans that are approximately the same size)2. 400 of black colour beads. (Two different colours of beans that are approximately the same size)

Methodology:400 of black colour beads and 400 of white colour beads were mixed together into a beaker.

One pair of bead was picked up without looking.

The colour of the pair of bead was observed and recorded down.

One pair of beads with different colours (white and black) or black in colour were placed back into the beaker and mixed well. One pair with white colour beads represented lethal allele were excluded and taken out from the beaker.

Steps 2, 3 and 4 were repeated 100 times and all the colour o