Population GeneticsPopulation Genetics

Lab No (5)

Population genetics – Population genetics – OutlineOutline

What is population genetics?

Calculate

Why is genetic variation important?

- genotype frequencies- allele frequencies

How does genetic structure change?

PopulationPopulationA “population” is a group of organisms of A “population” is a group of organisms of

the same species that reproduce with the same species that reproduce with each other. each other.

The “gene pool” is the collection of all the The “gene pool” is the collection of all the alleles present within a population.alleles present within a population.

Population geneticists generally examine Population geneticists generally examine many different genes simultaneouslymany different genes simultaneously

Gene: A sequence of nucleotides coding for a protein (or, in some cases, part of a protein); a unit of heredity

Allele: A variant segment of the genetic material

( alternative form of the gene)

Genotype: The set of DNA variants found at one or more loci in an individual. (More generally, the genetic profile of an individual)

Phenotype: The outward expression of a genotype (length, color etc..)

Haplotype: A set of genes at more than one locus inherited by an individual from one of its parents. It is the multi-locus analog of an allele.

PolymorphismPolymorphism• A locus is defined as polymorphic if the A locus is defined as polymorphic if the

frequency of one of its alleles is less than or frequency of one of its alleles is less than or equal to 0.95 or 0.99equal to 0.95 or 0.99

A gene is called “polymorphic” if there is more A gene is called “polymorphic” if there is more than 1 allele present in at least 1% of the than 1 allele present in at least 1% of the population. population.

Genes with only 1 allele in the population are Genes with only 1 allele in the population are

called “monomorphic”. Some genes have 2 called “monomorphic”. Some genes have 2 alleles: they are “dimorphic”.alleles: they are “dimorphic”.

HeterozygosityHeterozygosityHeterozygosity is the percentage of Heterozygosity is the percentage of

heterozygotes in a populationheterozygotes in a population

The average HThe average Hee over all loci is an estimate of the over all loci is an estimate of the extent of genetic variability in the populationextent of genetic variability in the population

What is Population Genetics?What is Population Genetics?

The genetic study of the process of evolutionThe genetic study of the process of evolution Evolution is the changes in the gene pool of the Evolution is the changes in the gene pool of the

population over time.population over time. The forces that cause changes and maintain The forces that cause changes and maintain

diversity are:diversity are: 1-Genomic: mutation and recombination1-Genomic: mutation and recombination 2-Evolutionary: natural selection, genetic drift, 2-Evolutionary: natural selection, genetic drift,

non random mating and migration.non random mating and migration.

Mutation:Mutation: A gene mutation is an alteration in the A gene mutation is an alteration in the

nucleotide sequence of it. nucleotide sequence of it. It can be caused by mutagenes or It can be caused by mutagenes or

spontaneous.spontaneous. It produces new allele.It produces new allele.

Recombination:Recombination: It can directly affect the level of variation by It can directly affect the level of variation by

decreasing variation.decreasing variation. It can increase the genetic variance. If It can increase the genetic variance. If

beneficial fitness alleles are not randomly beneficial fitness alleles are not randomly distributed among population members and are distributed among population members and are found in different individuals more often than found in different individuals more often than expected by chance.expected by chance. contcont

Genetic driftGenetic drift It is the random fluctuation of gene It is the random fluctuation of gene

frequencies from one generation to frequencies from one generation to another as a result of random sampling of another as a result of random sampling of the gametes.the gametes.

Ideally, a population must infinitely large Ideally, a population must infinitely large for genetic drift to be ruled out completely for genetic drift to be ruled out completely as an agent for evolution. as an agent for evolution.

Genetic drift, which changes gene Genetic drift, which changes gene frequencies at random, may cause a frequencies at random, may cause a favored allele to be lost.favored allele to be lost. contcont

Natural Selection:Natural Selection: It can be identified with the popular phrase “survival It can be identified with the popular phrase “survival

of the fittest’’ provided one define the word “fit’’ as of the fittest’’ provided one define the word “fit’’ as the capacity to leave fertile progeny. the capacity to leave fertile progeny.

It acts directly on the phenotypes, but it acts on It acts directly on the phenotypes, but it acts on genotypes in an indirect fashion, depending on the genotypes in an indirect fashion, depending on the extent to which phenotype is determined by extent to which phenotype is determined by genotype.genotype.

It is the only evolutionary factor that has direct It is the only evolutionary factor that has direct adaptive consequences.adaptive consequences. contcont

Other factors That can Affect the Other factors That can Affect the population diversity population diversity

Migration:Migration: When migration takes When migration takes place in one direction (i.e. from one place in one direction (i.e. from one group to another) it is referred to as group to another) it is referred to as gene flow. gene flow.

Non Random MatingNon Random Mating: There are two : There are two types of non-random mating: types of non-random mating: assortative mating and inbreeding.assortative mating and inbreeding. contcont

Allele frequency is the concept used to quantify Allele frequency is the concept used to quantify genetic variation. genetic variation.

It is defined as a measure of the commonness of a It is defined as a measure of the commonness of a given allele in a population, that is, the given allele in a population, that is, the proportion of all alleles of that locus in the proportion of all alleles of that locus in the population that are specifically this type.population that are specifically this type.

Allele and Genotype FrequenciesAllele and Genotype Frequencies

Each diploid individual in the population Each diploid individual in the population has 2 copies of each gene. The allele has 2 copies of each gene. The allele frequency is the proportion of all the genes frequency is the proportion of all the genes in the population that are a particular allele.in the population that are a particular allele.

The genotype frequency of the proportion The genotype frequency of the proportion of a population that is a particular of a population that is a particular genotype.genotype.

Statistical Population Statistical Population GeneticsGenetics

For example: consider the MN blood group. In a For example: consider the MN blood group. In a certain population there are 60 MM individuals, certain population there are 60 MM individuals, 120 MN individuals, and 20 NN individuals, a 120 MN individuals, and 20 NN individuals, a total of 200 people. total of 200 people.

The genotype frequency of MM is 60/200 = 0.3.The genotype frequency of MM is 60/200 = 0.3. The genotype frequency of MN is 120/200 = 0.6The genotype frequency of MN is 120/200 = 0.6 The genotype frequency of NN is 20/200 = 0.1The genotype frequency of NN is 20/200 = 0.1

In an infinitely large, randomly mating population in which selection, migration, and mutation do not occur, the frequencies of alleles and genotypes do not change from generation to generation.

The Hardy-Weinberg equilibrium

Allele Frequency: The proportion of all alleles in all individuals in the group in question which are of a particular type.

Genotype Frequency: The proportion of individuals in a group with a particular genotype.

For a gene with just two alleles A and a, if the frequency of allele: A is p, a is q

The sum of the frequencies of the alleles must equal 1; (p + q = 1)

After one generation of Random mating the genotype frequencies would remain fixed in and would be in the ratio:

Hardy Weinberg frequencies

Genotype frequency

AA p2

Aa 2pq

aa q2

And accordingly: And accordingly: p²+ 2pq + q² = 1p²+ 2pq + q² = 1This is called Hardy-Weinberg equation This is called Hardy-Weinberg equation

which is used for calculating the genotype which is used for calculating the genotype frequencies.frequencies.

X² is used to determine the probability X² is used to determine the probability that the observed number differs from the that the observed number differs from the expected number due to chance alone. expected number due to chance alone. Standardized statistical charts have been Standardized statistical charts have been developed which correlate the developed which correlate the PP value value and degrees of freedom (the number of and degrees of freedom (the number of independent variables) with probability independent variables) with probability values (values (pp). ).

  AA Aa aa Total# of individuals

40 47 13 100

# of A alleles 80 47 0 127# of a alleles 0 47 26 73

Total # of alleles

      200

Review of Hardy-Weinberg

Allele frequency:pA (p) = ((40 x 2) + 47) /200) = 127/200 = 0.635pa (q) = ((13 x 2)+47) /200) = 73/200 = 0.365 ( = 1- Pa)Genotype Frequency: 40 AA- 47 Aa -13 aa Total =100 individualspAA = 40/100 = 0.4pAa = 47/100 = 0.47paa = 13/100 = 0.13

Statistical test for deviations from HWE.It is done by calculating the P-value from Chi-square (X²): X² = (O-E)² / E P is significant when it is < 0.05.

e.g.. Among 1000 people: MM: 298, MN: 489, NN: 213P = fre of MQ = fre of N

Total no of alleles = 1000 x 2 = 2000

No of M = (298 x 2) + 489No of N = (213 x2) + 489

Allele frequencies are estimated to be:Allele frequencies are estimated to be: p=(596+489)/2000=0.5425p=(596+489)/2000=0.5425 q=(426+489)/2000=0.4575q=(426+489)/2000=0.4575 from the equation: from the equation: p² + 2pq + q² = 1p² + 2pq + q² = 1 The expected genotype frequencies under HWE:The expected genotype frequencies under HWE: P=P=p p 2 =0.5425 ×0.5425=0.29432 =0.5425 ×0.5425=0.2943 Q=Q=2p2pq=2 ×0.5425 ×0.4575=0.4964q=2 ×0.5425 ×0.4575=0.4964 R=R=q q 2 =0.4575 ×0.4575=0.20932 =0.4575 ×0.4575=0.2093

Observed Expected (O-E)² (O-E)²/E MM: 298 294.3 13.69 0.234MN: 489 496.4 54.76 0.110NN: 213 209.3 13.96 0.065

X²=∑ (O-E)²/E = 0.409http://faculty.vassar.edu/lowry/tabs.html#csq. P = 0.8151Which means that this population is in HWE.

Example continued from Hardy-Example continued from Hardy-Weinberg discussion aboveWeinberg discussion above

In the above example, the In the above example, the PP value value of of XX²² = =27.77 is < 0.0001 which 27.77 is < 0.0001 which correlates to a greater than 99% chance correlates to a greater than 99% chance that the difference between the that the difference between the observed and the expected is NOT due observed and the expected is NOT due to chance alone. This high probability to chance alone. This high probability indicates that some external factor (i.e., indicates that some external factor (i.e., migration, selection, inbreeding, or drift) migration, selection, inbreeding, or drift) is influencing the frequencies of allelesis influencing the frequencies of alleles

The allele frequencies can be determined The allele frequencies can be determined by adding the frequency of the homozygote by adding the frequency of the homozygote to 1/2 the frequency of the heterozygote.to 1/2 the frequency of the heterozygote.

The allele frequency of M is 0.3 (freq of The allele frequency of M is 0.3 (freq of MM) + 1/2 * 0.6 (freq of MN) = 0.6MM) + 1/2 * 0.6 (freq of MN) = 0.6

The allele frequency of N is 0.1 + 1/2 * 0.6 The allele frequency of N is 0.1 + 1/2 * 0.6 = 0.4= 0.4

Note that since there are only 2 alleles Note that since there are only 2 alleles here, the frequency of N is 1 - freq(M).here, the frequency of N is 1 - freq(M).

Hardy-Weinberg EquilibriumHardy-Weinberg Equilibrium Early in the 20th century G.H. Hardy and Wilhelm Early in the 20th century G.H. Hardy and Wilhelm

Weinberg independently pointed out that under ideal Weinberg independently pointed out that under ideal conditions you could easily predict genotype frequencies conditions you could easily predict genotype frequencies from allele frequencies, at least for a diploid sexually from allele frequencies, at least for a diploid sexually reproducing species.reproducing species.

For a dimorphic gene (two alleles, which we will call A For a dimorphic gene (two alleles, which we will call A and a), the Hardy-Weinberg equation is based on the and a), the Hardy-Weinberg equation is based on the binomial distribution:binomial distribution:

pp22 + 2pq + q + 2pq + q22 = 1 = 1 where p = frequency of A and q = frequency of a, with p + where p = frequency of A and q = frequency of a, with p +

q = 1.q = 1. pp22 is the frequency of AA homozygotes is the frequency of AA homozygotes 2pq is the frequency of Aa heterozygotes2pq is the frequency of Aa heterozygotes qq2 2 is the frequency of aa homozygotes is the frequency of aa homozygotes

Necessary Conditions for Hardy-Necessary Conditions for Hardy-Weinberg EquilibriumWeinberg Equilibrium

The relationship between allele frequencies and The relationship between allele frequencies and genotype frequencies expressed by the H-W equation genotype frequencies expressed by the H-W equation only holds if these 5 conditions are met. only holds if these 5 conditions are met.

If a population is not in equilibrium, it takes only 1 If a population is not in equilibrium, it takes only 1 generation of meeting these conditions to bring it into generation of meeting these conditions to bring it into equilibrium. Once in equilibrium, a population will stay equilibrium. Once in equilibrium, a population will stay there as long as these conditions continue to be met. there as long as these conditions continue to be met.

1. no new mutations1. no new mutations 2. no migration in or out of the population2. no migration in or out of the population 3. no selection (all genotypes have equal fitness)3. no selection (all genotypes have equal fitness) 4. random mating4. random mating 5. very large population5. very large population

Testing for H-W EquilibriumTesting for H-W Equilibrium If we have a population where we can distinguish all If we have a population where we can distinguish all

three genotypes, we can use the chi-square test once three genotypes, we can use the chi-square test once again to see if the population is in H-W equilibrium. The again to see if the population is in H-W equilibrium. The basic steps:basic steps: 1. Count the numbers of each genotype to get the observed 1. Count the numbers of each genotype to get the observed

genotype numbers, then calculate the observed genotype genotype numbers, then calculate the observed genotype frequencies.frequencies.

2. Calculate the allele frequencies from the observed genotype 2. Calculate the allele frequencies from the observed genotype frequencies.frequencies.

3. Calculate the expected genotype frequencies based on the H-3. Calculate the expected genotype frequencies based on the H-W equation, then multiply by the total number of offspring to get W equation, then multiply by the total number of offspring to get expected genotype numbers.expected genotype numbers.

4. Calculate the chi-square value using the observed and 4. Calculate the chi-square value using the observed and expected genotype numbers.expected genotype numbers.

5. Use 1 degree of freedom (because there are only 2 alleles).5. Use 1 degree of freedom (because there are only 2 alleles).

ExampleExample Data: 26 MM, 68 MN, 106 NN, with a total population of 200 individuals.Data: 26 MM, 68 MN, 106 NN, with a total population of 200 individuals. 1. Observed genotype frequencies: 1. Observed genotype frequencies:

MM: 26/200 = 0.13MM: 26/200 = 0.13 MN: 68/200 = 0.34MN: 68/200 = 0.34 NN:106/200 = 0.53NN:106/200 = 0.53

2. Allele frequencies:2. Allele frequencies: M: 0.13 + 1/2 * 0.34 = 0.30M: 0.13 + 1/2 * 0.34 = 0.30 N: 0.53 + 1/2 * 0.34 = 0.70N: 0.53 + 1/2 * 0.34 = 0.70

3. Expected genotype frequencies and numbers:3. Expected genotype frequencies and numbers: MM: pMM: p22 = (0.30) = (0.30)22 = 0.09 (freq) x 200 = 18 = 0.09 (freq) x 200 = 18 MN: 2pq = 2 * 0.3 * 0.7 = 0.42 (freq) * 200 = 84MN: 2pq = 2 * 0.3 * 0.7 = 0.42 (freq) * 200 = 84 NN: qNN: q22 = (0.70) = (0.70)22 = 0.49 (freq) * 200 = 98 = 0.49 (freq) * 200 = 98

4. Chi-square value: 4. Chi-square value: (26 - 18)(26 - 18)22 / 18 + (68 - 84) / 18 + (68 - 84)22 / 84 + (106 - 98) / 84 + (106 - 98)2 2 / 98/ 98 = 3.56 + 3.05 + 0.65= 3.56 + 3.05 + 0.65 = 7.26= 7.26

5. Conclusion: The critical chi-square value for 1 degree of freedom is 5. Conclusion: The critical chi-square value for 1 degree of freedom is 3.841. Since 7.26 is greater than this, we reject the null hypothesis that the 3.841. Since 7.26 is greater than this, we reject the null hypothesis that the population is in Hardy-Weinberg equilibrium.population is in Hardy-Weinberg equilibrium.

Levels of VariationLevels of Variation Expected Heterozygosity (HExpected Heterozygosity (Hexpexp) = 1- ) = 1- ppii

22, where , where ppii = frequency of ith allele = frequency of ith allele Estimated from allele frequenciesEstimated from allele frequencies

Observed Heterozygosity (HObserved Heterozygosity (Hobsobs) = direct count of ) = direct count of proportion of heterozygotes in sampleproportion of heterozygotes in sample Estimated from genotypesEstimated from genotypes

Differences between HDifferences between Hexpexp and H and Hobs obs estimate estimate deviations from H-W due to a variety of factorsdeviations from H-W due to a variety of factors

Population genetic is concerned with:

Gene and genotype frequencies and their fluctuation over time.

The factors that tend to keep them constant

The factors that tend to change them in populations.

It is largely concerned with the study of polymorphisms.

It directly impacts counseling, forensic medicine, and genetic screening.

Nei’s Genetic Distance/ IdentityNei’s Genetic Distance/ Identity