PowerPoint Presentation · 2008. 10. 17. · [Population Genetics] What population genetics...

Population Genetics

[Population Genetics]

Population genetics

• began in 1930s

• recognizes extensive variation within populations

• Mendelism and Darwinism were reconciled:

Darwin felt that natural selection must operate on continuous (polygenic) traits

Mendel showed the inheritance of discrete traits

selection acts on individuals, but populations evolve

Architects of the Neo-Darwinian Synthesis

Theodosius Dobzhansky Ernst Mayr

Sir Ronald Fisher George Gaylord Simpson

J.B.S. “Jack” Haldane

Sewall Wright

Integrates ideas from many different fields:

The Modern Synthesis

• Darwin

• Mendel

• Population genetics

• Comparative morphology & molecular biology

• Taxonomy – relationships of taxa

• Paleontology – study of fossils

• Biogeography – distribution of species

Key points

The Modern Synthesis

• importance of populations as units of evolution

populations evolve, individuals do not

evolution as changes in gene frequencies within populations

• central role of natural selection

most important mechanism of evolution

NOT the only mechanism of evolution

• idea of gradualism

changes occur over long periods of time

accumulation of small changes large changes

What population genetics studies?

Introduction

• genetic variation among individuals within groups

(populations, gene pools)

• genetic basis for evolutionary change and

• how patterns vary geographically and through time

• focus on one or a few loci within a “Mendelian population”

(= group of sexually interbreeding individuals who share a common set of genes)

Types of population genetics:

• Empirical Population Genetics measures and quantifies genetic variation in populations

• Theoretical Population Geneticsexplains variation in terms of mathematical models of the forces that change

allele frequencies

Population Genetics is important

Introduction

• disease susceptibility, genetic testing, and personalized medicine

• statistical interpretation of forensic DNA evidence

• human evolution and cultural history

• crop and animal improvement

• traditional breeding

• genetic engineering

• conservation plans for plant and animal communities

• responses of plant and animal communities to climate change

Types of questions studied by population geneticists:

Introduction

• how much variation occurs in natural populations? and

• what processes control the variation observed?

• what forces are responsible for divergence among populations?

• Mutation ↑ genetic diversity

• Selection (↑)↓ genetic diversity

• Genetic drift ↓ genetic diversity

• Migration ↑(↓) genetic diversity

• Non-random mating ↓ genetic diversity

• how demographic factors such as breeding system, fecundity, changes in population size, and age structure influence the gene pool in the population

How much variation occurs in natural populations?

Genetic Diversity

Diversity Within Species

• local populations consist of individuals that are adapted to their environments

• those individuals inadequately adapted tend to die or migrate to another region

Mountain Bighorn Sheep Desert Bighorn Sheep

Genetic Diversity

Mutations introduction of new genetic information into a population by

modifying alleles already present

Anopheles mosquito with the mutation giving them tolerance to certain insecticides

Genetic Diversity

Migrations Movement of organisms from one genetically distinct population to another

• the new population gains new genes, increasing genetic diversity

• the former population loses genes, decreasing genetic diversity

Genetic Diversity

Population Size the number of organisms in a population will effect genetic diversity

• the larger the population, the more genetic

Genetic Diversity

Geographical barriers create new sub-species

Mountains, canyons, water are geographical barriers

Major topics within population genetics:

Outline

• Genetic structure of populations

• genotypic and allelic frequencies

• Hardy-Weinberg Equilibrium

• assumptions and predictions

• HWE at work

• Genetic variation in space and time

• Variation in natural populations, Wright’s FST

• Forces that change gene frequencies

• Speciation

• Role of genetics in conservation biology

Outline

• HWE at work

• Speciation

Genotypic Frequencies

Ways to describe genetic structure of populations

• way to study the genes in a particular gene pool by quantifying the genotypes (pairs of alleles) at a given locus

to calculate genotypic frequency• count individuals with one genotype, and divide by total individuals

in the population• repeat for each genotype in the population

a frequency is a proportion with a range of 0–1• if 43% of population has a trait, the frequency of that trait is 0.43• for any given trait, the sum of the genotypic frequencies in a

population should be 1

Genotypic Frequencies

gene with 2 alleles, A and a3 genotypes: AA, Aa, aapopulation of 100 monkeyes with the following genotypes

AA = 50 Aa = 30 aa = 20

f(AA) = NAA/N --> 50/100 = 0.5

f(Aa) = NAa/N --> 30/100 = 0.3

f(aa) = Naa/N --> 20/100 = 0.2

Allelic Frequencies

more informative about the structure of the population

n° of copies of a given allele / Sum of counts of all alleles in the population

can be calculated in two different ways:

• Allele (gene) counting method: (from observed number of different genotypes at a particular locus)

p = f(A) = (2 x count of AA) + (1 count of Aa)/ 2 x total No. of individuals

• Genotypic frequency method:(from genotypic proportions)

p = f(A) = (frequency of the AA homozygote) + (1/2 x frequency of the Aa)

p = f(a) = (frequency of the aa homozygote) + (1/2 x frequency of the Aa)

Allelic Frequencies

AA = 50 Aa = 30 aa = 20

f(A) = p = (50 + 50 + 30)/200 = 0.65

f(a) = q = (20 + 20 + 30)/200 = 0.35

p + q = 1

Note, every individual carries 2 copies of the gene thus, the total number of alleles is 2N

Allelic Frequencies at X-linked loci

are more complex because females have 2 X-linked alleles, and males have 1 X-linked allele

p = f(XA) = (2 x XAXA females) + (XAXa females) + (XAY males)/

(2 x # females) + (# males)

q = f(Xa) = (2 x XaXa females) + (XaXa females) + (XaY males)/

(2 x # females) + (# males)

If number of females and males are equal:

p = f(XA) = 2/3[f(XAXA) +1/2f(XAXa)] + 1/3f(XAY)

q = f(Xa) = 2/3[f(XaXa) +1/2f(XAXa)] + 1/3f(XaY)

Outline

• HWE at work

• Speciation

Hardy-Weinberg law

• independently discovered by the British mathematician Godfrey H. Hardy (1877-1947) and the German physician Wilhelm Weinberg (1862-1937)

• explains how Mendelian segregation influences allelic and genotypic frequencies in a population

under certain conditions, allele and genotypic frequencies will remain constant in a population from one generation to the next

Assumptions

Hardy-Weinberg law

1. Population is infinitely large, to avoid effects of genetic drift (= change in genetic frequency due to chance)

2. Mating is random (with regard to traits under study)

3. No natural selection (for traits under study)

4. No mutation

5. No migration

Predictions

Hardy-Weinberg law

If the conditions are met, the population will be in genetic equilibrium, with 2 expected results:

1. allele frequencies do not change over generations, so the gene pool is not evolving at the locus under study

2. after one generation of random mating, genotypic frequencies will remain in the following proportions

p2 (frequency of AA)

2pq (frequency of Aa) p2 + 2pq + q2 = 1 q2 (frequency of aa)

and will stay constant in these proportions as long as the conditions above are met

This is Hardy-Weinberg equilibrium, which allows predictions to be made about genotypic frequencies

Predictions

Hardy-Weinberg law

p2 + 2pq + q2 = (p + q)2 = 1

Outline

• HWE at work

• Speciation

At Work

Hardy-Weinberg law

…if HWE assumptions are satisfied, allele and genotypic frequencies will remain constant in a population from one generation to the next

At Work

Hardy-Weinberg law

p = frequency of A = normal normal skin coloration = 0.70q = frequency of a = albino skin = 0.30

AA Aa aaGenotype

Genotypefrequencies p2=(0.7)2=0.49 2pq = 2(0.7)(0.3)= 0.42 q2=(0.3)2=0.09

Gametefrequencies

A 0.49

a 0.09

A 0.21

a 0.21

A 0.70

a 0.30

Generation 1

At Work

Hardy-Weinberg law

♂ gametes

A=(p=0.7) a=(q=0.3)

gametes

A=(p=0.7)AA

p2= 0.49Aa

pq = 0.21

a=(q=0.3)Aa

pq = 0.21aa

q2= 0.09

Population mates at random

Generation 2

AA Aa aa0.49 0.42 0.09

Genotypefrequencies

Testing for deviations from H.W.E.

Hardy-Weinberg law

H.W.E serves as a null hypothesis tells us what to expect if nothing interesting is happening if we sample a population and find that the predictions of H.W.E

are not met, then we can conclude that one or more of the assumptions is violated some kind (???) of evolutionary force is in action!

Hardy-Weinberg law

ExampleWe are studying a population of African elephants (N = 260) for the ADH locus and find that the population contains 2 alleles Genotypic counts: FF = 65, Ff = 125, ff = 70

Step 1: Determine allele frequenciesp = F = (65 + 65 + 125)/520 = 0.4904q = f = 1 - p = 1 - 0.4904 = 0.5096

Step 2: Calculate Expected genotypic frequenciesP = p2 = (0.4904)2 = 0.2405H = 2pq = 2(0.4904)(0.5096) = 0.4998Q = q2 = (0.5096)2 = 0.2597

Hardy-Weinberg law

Step 3: Calculate chi-square statistic:χ2 = Σ(observed - expected)2/expected

O E (O-E)2/EP 65 0.2405 X 260 = 62.53 0.098H 125 0.4998 X 260 = 129.95 0.189Q 70 0.2597 X 260 = 67.52 0.091 χ2 = 0.378

Hardy-Weinberg law

Step 4: Compare calculated χ2 with tabled χ2:Degrees of freedom = 3(# of genotypes) - 2(# of alleles)= 1

Look up critical values for χ2 statistic: Level of SignificanceD.f. 0.05 0.01 0.0011 3.84 6.64 10.832 5.99 9.21 13.82 3 7.82 11.34 16.27

Calculated χ2 (0.378) is less than tabled value therefore we fail to reject the null hypothesis

Some notes on assumptions of the Hardy-Weinberg law

Hardy-Weinberg law

1. Population is infinitely large

• assumption is unrealistic

• large populations are mathematically similar to infinitely large populations

• finite populations with rare mutations, rare migrants, and weak selection generally fit Hardy-Weinberg proportions

Hardy-Weinberg law

2. Population Mating is random

• few organisms mate randomly for all traits or loci

• Hardy-Weinberg applies to any locus for which mating occurs randomly, even if mating is non-random for other loci

2 two types of non-random mating

a. those where mate choice is based on ancestry

inbreeding (and crossbreeding)

b.those whose choice is based upon genotypes at a particular locus

assortative (and disassortative mating)

Hardy-Weinberg law

3. No natural selection4. No mutation5. No migration

• gene pool must be closed to the addition/subtraction of new alleles

• like random mating, condition applies only to the locus under study

Hardy-Weinberg lawRelationship of the frequencies of the genotypes AA, Aa, and aa to the frequencies of alleles A and a in populations in Hardy-Weinberg equilibrium

Max. heterozygosity@ p = q = 0.5

Extension of the Hardy-Weinberg Law to… …loci with more than 2 alleles

Hardy-Weinberg law

1. often more than 2 alleles are possible at a given locus2. the frequencies of possible genotypes are still given by the

square of the allelic frequencies3. if 3 alleles are present (e.g., alleles A, B and C) with frequencies

p, q, and r, the frequencies of the genotypes at equilibrium will result from the polynomial expansion:

(p + q + r)2 = p2(AA) + 2pq(AB) + q2(BB) + 2pr(AC) + 2qr(BC) + r2(CC)

4. For 4 alleles (A, B, C, and D) with frequencies p, q, r, and s:

(p + q + r + s)2 = p2(AA) + 2pq(AB) + q2(BB) + 2pr(AC) + 2qr(BC) +

r2(CC) + 2ps(AD) + 2qs(BD) + 2rs(CD) + s2(DD)

Extension of the Hardy-Weinberg Law to… …X-linked alleles

Hardy-Weinberg law

• in species where the sex is chromosomally determined (e.g. humans), females have 2 X chromosomes while males have only one• because males receive their X chromosome from their mothers, the

frequency of an X-linked allele will be the same as the frequency of that allele in their mothers

• for females the frequency will be the average of both parents

Females Hardy-Weinberg frequencies are the same for any other

locus: p2 + 2pq + q2 = 1

Males Genotype frequencies are the same as allele frequencies:

p + q = 1

Hardy-Weinberg law

• in species where the sex is chromosomally determined (e.g. humans), females have 2 X chromosomes while males have only one• because males receive their X chromosome from their mothers, the

frequency of an X-linked allele will be the same as the frequency of that allele in their mothers

• for females the frequency will be the average of both parents

Females Hardy-Weinberg frequencies are the same for any other

locus: p2 + 2pq + q2 = 1

Males Genotype frequencies are the same as allele frequencies:

p + q = 1

XA(p) Xa(q) Y

XA(p) XAXA

Xa(q) XAXa

pqXaXa

Hardy-Weinberg law

• if alleles are X-linked and sexes differ in allelic frequency, Hardy-Weinberg equilibrium is approached over several generations

• allelic frequencies oscillate each generation until the allelic frequencies of males and females are equal

Calculating the Carrier Frequency of an Autosomal Recessive

Hardy-Weinberg law

Cystic fibrosis is caused by a loss of function mutation at locus on chromosome 7 that codes for CFTR protein (cell surface protein in lungs and intestines)Major function of protein is to destroy Pseudomonas aeruginosa bacteria

Hardy-Weinberg law

Cystic fibrosis is caused by a loss of function mutation at locus on chromosome 7 that codes for CFTR protein (cell surface protein in lungs and intestines)Major function of protein is to destroy Pseudomonas aeruginosa bacteria

Hardy-Weinberg law

Calculating the Carrier Frequency for X-linked Traits

Hardy-Weinberg law

Calculating the Carrier Frequency for X-linked Traits

Hardy-Weinberg law

Czar Nicholas II of Russia and his family, photographed c. 1916, showing his wife Alexandra (who was a carrier of hemophilia), his four daughters, and (in the foreground) his son Alexis, perhaps the most famous European royal with hemophilia.

Outline

• HWE at work

• Speciation

Genetic Variation in Space and Time

Hardy-Weinberg law

The genetic structure of populations can vary in space and time

an allele frequency cline is a clear pattern of variation across a

geographic transect, usually correlated with a physical feature like

temperature or rainfall

statistical tools are used to quantify spatial patterns of genetic

variation

important in conservation biology

Hardy-Weinberg law

Geographic variation in frequencies of three alleles of the locus coding for the enzyme leucine amino peptidase (LAP) in the blue mussel

Hardy-Weinberg law

Temporal variation in the locus coding for the enzyme esterase 4F in the prairie vole, Microtus ochrogaster

Measuring genetic variation in space and time

Genetic Variation in Natural Populations

Useful to partition genetic variation into components:• within populations• between populations• among populations

Sewall Wright’s Fixation index (FST) is a useful index of genetic differentiation and comparison of overall effect of population substructure

measures reduction in heterozygosity (H) expected with non-random mating at any one level of population hierarchy relative to another more inclusive hierarchical level

FST = (HTotal - Hsubpop)/HTotal

FST ranges between minimum of 0 and maximum of 1:

= 0 ⇒ no genetic differentiation << 0.5 ⇒ little genetic differentiation

>> 0.5 ⇒ moderate to great genetic differentiation = 1.0 ⇒ populations fixed for different allele

Hemoglobin alpha-A - Thr/Ala polymorphism at position 77: FST = 0.75

Not in Hardy-Weinberg equilibrium (χ2 = 14.4, P < 0.001)

Missing genotypesHomozygotes of different classes are not observed in each sub-population

Methods used to measure genetic variation

Genetic variation contains information about an organism’s ancestry and determines an organism’s potential for evolutionary change, adaptation, and survival

1960s-1970s: genetic variation was first measured by protein electrophoresis (e.g., allozymes) protein electrophoresis separates proteins on the basis of

size charge conformationo and so often can separate the gene products of different alleles

proteins with similar sizes and charges will conform in gel electrophoresis, and so allele differences are likely to be underestimated

o even so, much more variation is seen at most loci than would be predicted by the classical model

Protein polymorphism

detected variation in structural genes by gel electrophoresis

Electrophoretic gel showing homozygotes for three different alleles at the esterase-5 locus in Drosophila pseudoobscura

1980s-2000s: genetic variation measured directly at the DNA level:• Restriction Fragement Length Polymorphisms (RFLPs)

• Minisatellites (VNTRs)

• DNA sequence

• DNA length polymorphisms

• #s of copies of a gene

• Single-stranded Conformation Polymorphism (SSCP)

• Microsatellites (STRs)

• Random Amplified Polymorphic DNAs (RAPDs)

• Amplified Fragment Length Polymorphisms (AFLPs)

• Single Nucleotide Polymorphisms (SNPs)

Genetic Variation in Natural PopulationsDNA from individual 1 and individual 2 differ in one nucleotide, found

within the sequence recognized by the restriction enzyme BamHI

Genetic Variation in Natural PopulationsRestriction patterns from five mice

DNA Profiling • repeats are distributed all over the genome

• detects differences in repeat copy number

• calculates probability that certain combinations can occur in

two sources of DNA

• requires molecular techniques and population studies

• developed in 1980s

• identifies individuals

• used in forensics, agriculture, paternity testing, and

historical investigations

• DNA can be obtained from many sources

Genetic Variation in Natural PopulationsRepeated DNA used for DNA Profiling

Genetic Variation in Natural PopulationsMinisatellite DNA Fingerprinting

Genetic Variation in Natural PopulationsMicrosatellite DNA Profiling

Types of measures of genetic variation

Polymorphism = % of loci (or nucleotide) positions showing more than one allele (or base pair)

Heterozygosity (H) = % of individuals that are heterozygotes

Allele/haplotype diversity = measure of # and diversity of different alleles/haplotypes within a population.

Nucleotide diversity = measure of number and diversity of variable nucleotide positions within sequences of a population.

Genetic distance = measure of number of base pair differences between two homologous sequences.

Synonomous/nonsynonomous substitutions = % of nucleotide substitutions that do not/do result in amino acid replacement.

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