Gene pool and h w law

Gene Pool

• The sum total of genes of all individuals of a Genetic population constitute the gene pool.

• Therefore, a genetic population is an array of genes, temporarily embodied in individuals but endlessly combining and recombining by the process of sexual reproduction.

• If the gene pool of a population is described completely, it tells us not only the kinds of genes present in the population, but also the way in which these genes are distributed among the individuals of the population in question.

Gene Pool contd…..For example, if we want to know the genetic

information about the smoothness and wrinkling of the pea seeds in the gene pool of pea population, it is possible to know exactly the proportions of the smooth alleles and the wrinkle alleles and how these alleles are distributed among the individuals –

i.e. the proportion of homozygous smooth, the proportion of heterozygous smooth

and the proportion of homozygous wrinkled pea plants.

Gene Pool contd….

• Suppose, if these are present in equal proportions, i.e. half the genes are for smoothness and half the genes are for wrinkleness and these genes are represented by W and w,

• the gene pool in the state of equilibrium will contain ¼ WW, ½ Ww and ¼ ww,

• and this will be maintained as long as random mating occurs.

Gene frequency

• The gene frequency refers to the proportion of an allele in the gene pool as compared with other alleles at the same locus, with no regards to their distribution in the population.

• For example, if we consider a hypothetical population in which there are just two alleles Aa on a particular locus out of which A is dominant and a is recessive.

• Hence, according to genotype three types of individuals may exist in the population.

AA, Aa and aa

Gene frequency• Suppose there are 100 individuals in a population

out of which there are 40 homozygous dominant (AA), 40 heterozygous (Aa) and 20 homozygous recessive (aa), then -

The frequency of gene ‘A’ will be (80+40)/200 =0.6The frequency of gene ‘a’ will be (40+40)/200 =0.4

• Therefore, the gene frequency can be calculated by dividing the number of a particular gene under consideration with the total number of genes present on that locus in the population.

Gene frequency

• Now, if the frequency of gene ‘A’ is represented by ‘p’ and the frequency of gene ‘a’ is represented by ‘q’, then at equilibrium condition there total frequency is represented by ‘1’.

• Or, in other words, at equilibrium

p+ q = 1

Genotype frequency

• Genotype frequency is the total number of a kind of individuals in a population all of which exhibit similar character with respect to the locus under consideration.

• Suppose in a population there are 2 alleles at one gene locus (A and a) and they are related as dominant and recessive. Naturally, 3 kinds of individuals will occur in the population, i.e.

‘AA’, ‘Aa’ and ‘aa’

Genotype frequency

• Therefore: If -

N = Total no. of individuals in the populationD = No. of dominant homozygous individualsH = No. of heterozygous individualsR = No. of homozygous recessive individualsThen,AA genotype frequency = D/NAa genotype frequency = H/Naa genotype frequency = R/N

Genotype frequency

It means that the genotype frequency for a particular gene combination on the same locus can be determined by dividing the number of individuals

with that genotype by the total number of individuals in the

population.

Hardy-Weinberg law of Equilibrium

• The Hardy-Weinberg Law states that –

‘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, selection and gene flow’.

This 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, the individuals have random mating, each parent produces roughly equal number of gametes & the gametes produced by the mates combine at random, and the gene frequency remains constant,

then-

Then -

The genetic equilibrium of the genes in question is maintained and the variability

present in the population is preserved.

For example,

• If a gene with two alleles A and a with known frequencies (e.g. A = 0.6, a = 0.4.) and their respective frequencies are represented by p and q.

Then the combined frequencies of both the alleles will be equal to unit. In other words,

p + q = 1

Further,

• Using allele frequencies we can predict the expected frequencies of genotypes in the next generation.

• With two alleles only three genotypes are possible: AA, Aa and aa

Hardy-Weinberg Equilibrium

• Assume alleles A and a are present in eggs and sperm in proportion to their frequency in population (i.e. 0.6 and 0.4)

• Also assume that sperm and eggs meet at random (one big gene pool).


• Then we can calculate expected genotype frequencies.

• AA: To produce an AA individual, egg and sperm must each contain an A allele.

• This probability is 0.6 x 0.6 = 0.36 (probability sperm contains A times probability egg contains A).


• Similarly, we can calculate frequency of aa.

• 0.4 x 04 = 0.16.


• Probability of Aa is given by probability sperm contains A (0.6) times probability egg contains a (0.4).

0.6 x 0.4 = 0.24• probability egg contains A (0.6) times

probability sperm contains a (0.4). 0.6 x 0.4 = 0.24.


• But, there’s a second way to produce an Aa individual (egg contains A and sperm contains a). Same probability as before: 0.6 x 0.4= 0.24.

• Hence the overall probability of Aa = 0.24 + 0.24 = 0.48.


• Genotypes in next generation:• AA = 0.36• Aa = 0.48 • Aa= 0.16• These frequencies add up to one.


• General formula for Hardy-Weinberg.• Since p= frequency of allele A and q =

frequency of allele a.AA = 0.36 (0.6) 2

Aa = 0.48 (2 x 0.6 x 0.4)Aa= 0.16 (0.4) 2

• Can be expressed asp2 + 2pq + q2 = 1.

summary• Allele frequencies in a population will not change

from one generation to the next just as a result of assortment of alleles and zygote formation.

• Assortment of alleles simply means what occurs during meiosis when only one copy of each pair of alleles enters any given gamete (remember each gamete only contains half the DNA of a body cell).

Conclusions from Hardy-Weinberg Equilibrium

• If the allele frequencies in a gene pool with two alleles are given by p and q, the genotype frequencies will be given by p2, 2pq, and q2.

Question

• If 9 of 100 individuals in a population suffer from a homozygous recessive disorder can you calculate the frequency of the disease-causing allele?

• Can you calculate how many heterozygotes are in the population?

Solution• p2 + 2pq + q2 = 1. The terms in the equation represent the

frequencies of individual genotypes. [A genotype is possessed by an individual organism so there are two alleles present in each case.]

• p and q are allele frequencies. Allele frequencies are estimates of how common alleles are in the whole population.

• It is vital that you understand the difference between allele and genotye frequencies.

Solution

• 9 of 100 (frequency = 0.09) of individuals are homozygous for the recessive allele. What term in the H-W equation is that equal to?

Working with the H-W equation• It’s q2.

• If q2 = 0.09, what’s q? Get square root of q2, which is 0.3, which is the frequency of the allele a.

• If q=0.3 then p=0.7. Now plug p and q into equation to calculate frequencies of other genotypes.

Working with the H-W equation

• p2 = (0.7)(0.7) = 0.49 -- frequency of AA

• 2pq = 2 (0.3)(0.7) = 0.42 – frequency of Aa.

• To calculate the actual number of heterozygotes simply multiply 0.42 by the population size = (0.42)(100) = 42.

Assumptions of Hardy-Weinberg

• 1. No selection.– When individuals with certain genotypes survive

better than others, allele frequencies may change from one generation to the next.


• 2. No mutation– If new alleles are produced by mutation or alleles

mutate at different rates, allele frequencies may change from one generation to the next.


• 3. No migration– Movement of individuals in or out of a population

will alter allele and genotype frequencies.


• 4. No chance events.– Luck plays no role. Eggs and sperm collide at same

frequencies as the actual frequencies of p and q. – When assumption is violated, and by chance some

individuals contribute more alleles than others to next generation, allele frequencies may change. This mechanism of allele frequency change is called Genetic Drift.


• 5. Individuals select mates at random.– If this assumption is violated allele frequencies will

not change, but genotype frequencies may.

Education

Gene pool and h w law