Download 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
[Population Genetics]
Architects of the Neo-Darwinian Synthesis
Theodosius Dobzhansky
Sir Ronald Fisher
J.B.S. “Jack” Haldane
George Gaylord Simpson
Ernst Mayr
Sewall Wright
[Population Genetics]
The Modern Synthesis
Integrates ideas from many different fields:
•
Darwin
•
Mendel
•
Population genetics
•
Comparative morphology & molecular biology
•
Taxonomy – relationships of taxa
•
Paleontology – study of fossils
•
Biogeography – distribution of species
[Population Genetics]
The Modern Synthesis
Key points
•
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
[Population Genetics]
Introduction
What population genetics studies?
• 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
•
Theoretical Population Genetics
measures and quantifies genetic variation in populations
explains variation in terms of mathematical models of the forces that change
allele frequencies
[Population Genetics]
Introduction
Population Genetics is important
• 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
[Population Genetics]
Introduction
Types of questions studied by population geneticists:
• 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
[Population Genetics]
How much variation occurs in natural populations?
[Population Genetics]
How much variation occurs in natural populations?
[Population Genetics]
Diversity Within Species
Genetic Diversity
•
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
[Population Genetics]
Diversity Within Species
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
[Population Genetics]
Diversity Within Species
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
[Population Genetics]
Diversity Within Species
Genetic Diversity
Population Size  the number of organisms in a population will effect
genetic diversity
• the larger the population, the more genetic
[Population Genetics]
Diversity Within Species
Genetic Diversity
Geographical barriers  create new sub-species
Mountains, canyons, water are geographical barriers
[Population Genetics]
Outline
Major topics within population genetics:
• 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
[Population Genetics]
Outline
Major topics within population genetics:
• 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
[Population Genetics]
Ways to describe genetic structure of populations
Genotypic Frequencies
• 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
[Population Genetics]
Ways to describe genetic structure of populations
Genotypic Frequencies
gene with 2 alleles, A and a
3 genotypes: AA, Aa, aa
population 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
[Population Genetics]
Ways to describe genetic structure of populations
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)
[Population Genetics]
Ways to describe genetic structure of populations
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
[Population Genetics]
Ways to describe genetic structure of populations
Allelic Frequencies at X-linked loci
 are more complex because females have 2 X-linked alleles, and males have 1 Xlinked 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)
[Population Genetics]
Outline
Major topics within population genetics:
• 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
[Population Genetics]
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
[Population Genetics]
Hardy-Weinberg law
Assumptions
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
[Population Genetics]
Hardy-Weinberg law
Predictions
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)
q2
p2 + 2pq + q2 = 1
(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
[Population Genetics]
Hardy-Weinberg law
Predictions
p2 + 2pq + q2 = (p + q)2 = 1
[Population Genetics]
Outline
Major topics within population genetics:
• 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
[Population Genetics]
Hardy-Weinberg law
At Work
…if HWE assumptions are satisfied, allele and genotypic
frequencies will remain constant in a population from one
generation to the next
[Population Genetics]
Hardy-Weinberg law
At Work
Generation 1
p = frequency of A = normal normal skin coloration = 0.70
q = frequency of a = albino skin = 0.30
AA
Aa
aa
Genotype
frequencies
p2=(0.7)2=0.49
2pq = 2(0.7)(0.3)= 0.42
q2=(0.3)2=0.09
Gamete
frequencies
A
0.49
Genotype
A
0.21
A
0.70
a
0.21
a
0.09
a
0.30
[Population Genetics]
Hardy-Weinberg law
At Work
Population mates at random
♂ gametes
♀
gametes
A=(p=0.7)
a=(q=0.3)
A=(p=0.7)
a=(q=0.3)
AA
Aa
pq = 0.21
p2= 0.49
Aa
pq = 0.21
aa
q2= 0.09
Generation 2
Genotype
frequencies
AA
Aa
aa
0.49
0.42
0.09
[Population Genetics]
Hardy-Weinberg law
Testing for deviations from H.W.E.
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!
[Population Genetics]
Hardy-Weinberg law
Testing for deviations from H.W.E.
Example
We 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 frequencies
p = F = (65 + 65 + 125)/520 = 0.4904
q = f = 1 - p = 1 - 0.4904 = 0.5096
Step 2: Calculate Expected genotypic frequencies
P = p2 = (0.4904)2 = 0.2405
H = 2pq = 2(0.4904)(0.5096) = 0.4998
Q = q2 = (0.5096)2 = 0.2597
[Population Genetics]
Hardy-Weinberg law
Testing for deviations from H.W.E.
Step 3: Calculate chi-square statistic:
2 = Σ(observed - expected)2/expected
χ
P
H
Q
O
65
125
70
E
0.2405 X 260 = 62.53
0.4998 X 260 = 129.95
0.2597 X 260 = 67.52
χ2 =
(O-E)2/E
0.098
0.189
0.091
0.378
[Population Genetics]
Hardy-Weinberg law
Testing for deviations from H.W.E.
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 Significance
D.f.
0.05
0.01
0.001
1
3.84
6.64
10.83
2
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
[Population Genetics]
Hardy-Weinberg law
Some notes on assumptions of the 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
[Population Genetics]
Hardy-Weinberg law
Some notes on assumptions of the 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)
[Population Genetics]
Hardy-Weinberg law
Some notes on assumptions of the Hardy-Weinberg law
3. No natural selection
4. No mutation
5. 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
[Population Genetics]
Hardy-Weinberg law
Relationship 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
[Population Genetics]
Hardy-Weinberg law
Extension of the Hardy-Weinberg Law to…
…loci with more than 2 alleles
1. often more than 2 alleles are possible at a given locus
2. the frequencies of possible genotypes are still given by the
square of the allelic frequencies
3. 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)
[Population Genetics]
Hardy-Weinberg law
Extension of the Hardy-Weinberg Law to…
…X-linked alleles
• 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

locus:
Hardy-Weinberg frequencies are the same for any other
p2 + 2pq + q2 = 1
Males

Genotype frequencies are the same as allele frequencies:
p+q=1
[Population Genetics]
Hardy-Weinberg law
Extension of the Hardy-Weinberg Law to…
…X-linked alleles
• in species where the sex X
isA(p)
chromosomally
determined (e.g.
humans),
Xa(q)
Y
females have 2 X chromosomes while males have only one
XA(p)
XAXA
XAXa
XAY
• because males receive their X chromosome from their mothers, the
p2allele will bepq
p frequency of
frequency of an X-linked
the same as the
that allele
in their mothers
Xa(q)
XAXa
XaXa
XaY
• for females the frequency will be the average
of both parents
2
pq
q
q
Females

locus:
Hardy-Weinberg frequencies are the same for any other
p2 + 2pq + q2 = 1
Males

Genotype frequencies are the same as allele frequencies:
p+q=1
[Population Genetics]
Hardy-Weinberg law
Extension of the Hardy-Weinberg Law to…
…X-linked alleles
• 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
[Population Genetics]
Hardy-Weinberg law
Calculating the Carrier Frequency of an Autosomal Recessive
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
[Population Genetics]
Hardy-Weinberg law
Calculating the Carrier Frequency of an Autosomal Recessive
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
[Population Genetics]
Hardy-Weinberg law
Calculating the Carrier Frequency of an Autosomal Recessive
[Population Genetics]
Hardy-Weinberg law
Calculating the Carrier Frequency for X-linked Traits
[Population Genetics]
Hardy-Weinberg law
Calculating the Carrier Frequency for X-linked Traits
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.
[Population Genetics]
Outline
Major topics within population genetics:
• 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
[Population Genetics]
Hardy-Weinberg law
Genetic Variation in Space and Time
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
[Population Genetics]
Hardy-Weinberg law
Genetic Variation in Space and Time
Geographic variation in frequencies of three alleles of the locus coding for
the enzyme leucine amino peptidase (LAP) in the blue mussel
[Population Genetics]
Hardy-Weinberg law
Genetic Variation in Space and Time
Temporal variation in the locus coding for the enzyme esterase 4F in the
prairie vole, Microtus ochrogaster
[Population Genetics]
Genetic Variation in Natural Populations
Measuring genetic variation in space and time
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
[Population Genetics]
Genetic Variation in Natural Populations
Measuring genetic variation in space and time
[Population Genetics]
Genetic Variation in Natural Populations
Measuring genetic variation in space and time
Hemoglobin alpha-A - Thr/Ala polymorphism at position 77:
FST = 0.75
Not in Hardy-Weinberg equilibrium (χ2 = 14.4, P < 0.001)
Missing genotypes
Homozygotes of different classes are not observed in each sub-population
[Population Genetics]
Genetic Variation in Natural Populations
Measuring genetic variation in space and time
[Population Genetics]
Genetic Variation in Natural Populations
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



o
size
charge
conformation
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
[Population Genetics]
Genetic Variation in Natural Populations
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
[Population Genetics]
Genetic Variation in Natural Populations
[Population Genetics]
Genetic Variation in Natural Populations
Methods used to measure genetic variation
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)
[Population Genetics]
Genetic Variation in Natural Populations
DNA from individual 1 and individual 2 differ in one nucleotide, found
Methods
to measure
genetic
variation
withinused
the sequence
recognized
by the restriction
enzyme BamHI
[Population Genetics]
Genetic Variation in Natural Populations
Restriction patterns from five mice
Methods used to measure genetic variation
[Population Genetics]
Genetic Variation in Natural Populations
Methods used to measure genetic variation
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
[Population Genetics]
Genetic Variation in Natural Populations
Repeated DNA used for DNA Profiling
Methods used to measure genetic variation
[Population Genetics]
Genetic Variation in Natural Populations
Minisatellite DNA Fingerprinting
Methods used to measure genetic variation
[Population Genetics]
Genetic Variation in Natural Populations
Microsatellite DNA Profiling
Methods used to measure genetic variation
[Population Genetics]
Genetic Variation in Natural Populations
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.