Download lecture 5

7/25/11
Molecular Evolution
Genes in populations
Genes in context
Genes in genome
Dr. Erica Bree Rosenblum
Genes in context
Genes in context
Genes in genome
Genes in genome
Gene in individuals
Gene in individuals
Genes in populations
Genes in genomes
Genes in individuals
Locus: position on a chromosome of gene (or genes)
Homozygous: same allele at a locus for diploid (or
(plural: loci)
polyploid) individuals
Allele: variant of DNA sequence at a particular locus
Heterozygous: different allele at a locus for diploid
(or polyploid) individuals
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Genes in populations
Genes in populations
Gene pool: the set of all alleles at all loci in a population
Gene pool: the set of all alleles at all loci in a population
Population size: generally denoted as N for haploid and 2N for diploid
N=5
2N = 10
Genes in populations
Genes in populations
Polymorphic: >1 genetically distinct type in a population
Polymorphic: >1 genetically distinct type in a population
Monomorphic: a single genetic type in a population
Monomorphic: a single genetic type in a population
Polymorphism can refer to the:
Genetic scale: i.e., Single Nucleotide Polymorphism (SNP)
C
C
C
C
G
G
G
G
A
A
A
A
T
A
T
C
T
T
T
T
C
C
C
C
C
C
G
C
G
G
G
G
A
A
A
A
T
T
T
T
T
G
G
T
C
C
C
C
Population scale: i.e., color morphs of jaguars in South America
Genes in populations
Genes in populations
Allele frequency (gene frequency):
Allele frequencies remain constant over
time in an idealized population.
relative proportion of allele in population
locus 1
A
locus 1:
a
p = 0.5
2
3
This is called Hardy Weinberg Equilibrium
(HWE).
locus 2:
locus 3:
p = 0.2
For a 2 allele locus:
p = frequency of A allele
q = frequency of a allele (1 - p)
p+q=1
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Genes in populations
Genes in populations
What is an idealized population at equilibrium?
What is an idealized population at equilibrium?
infinite population size, random mating, no mutation,
no selection, no gene flow...
infinite population size, random mating, no mutation,
no selection, no gene flow...
Is this realistic???
Generally NO, but HWE
provides an important “null
hypothesis”.
Deviations from HWE tell us
that something interesting is
happening (e.g., selection,
small pop size, assortative
mating, etc).
Genes in populations
Genes in populations
If a population is in HWE, what will genotype
frequencies be?
If a population is in HWE, what will genotype
frequencies be?
For a 2 allele locus:
p = frequency of A allele
q = frequency of a allele (1 - p)
Genotype:
AA
Frequency:
p2 + 2pq + q 2 = 1
A
a
p+q=1
Aa
aa
How do we get these genotype frequencies?
This tells us allele but not genotype frequencies
Population level Punnett square:
Females
With 2 alleles, we have 3 possible genotypes:
AA
Aa
A (p)
aa
Males
Genes in populations
Genes in populations
HW can be generalized for more than 2 alleles.
HW can be used to:
a (q)
A (p)
AA (p²)
Aa (pq)
a (q)
Aa (pq)
aa (q²)
- Calculate genotype frequencies for a population in HWE
- Test for statistical deviations from HWE
You don’t need to know how to derive this!
Example: expected genotype frequencies for tetraploidy
Genotype
AAAA
AAAa
AAaa
Aaaa
aaaa
Frequency
p2
4p 3q
6p 2q 2
4pq 3
4
q
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7/25/11
Genes in populations
Genes in populations
HW can be used to:
HW can be used to:
- Calculate genotype frequencies for a population in HWE
- Test for statistical deviations from HWE
- Calculate genotype frequencies for a population in HWE
- Test for statistical deviations from HWE
Example calculation of HWE freq: Disease
Example calculation of HWE freq: Disease
1 in 1700 newborns have cystic fibrosis
1 in 1700 newborns have cystic fibrosis
What proportion of the population
are asymptomatic carriers?
What proportion of the population
are asymptomatic carriers?
q 2 = 1/1700 = 0.00059 = 0.059%
q = 0.024
2
p = 0.976
p+q =1
2pq = 0.468
p 2 + pq + q2 = 1
4.68% of the population are carriers
Genes in populations
Test for HWE deviation
HW can be used to:
- Calculate genotype frequencies for a population in HWE
- Test for statistical deviations from HWE
Phenotype
Genotype
Number
White-spotted
AA
1469
Intermediate
Aa
138
Little spotting
aa
5
Example test for HWE deviation: Data from E.B. Ford (1971)
Scarlet Tiger Moth
Null hypothesis: population is in HWE.
Test for HWE deviation
Phenotype
White-spotted
Intermediate
Little spotting
Test for HWE deviation
Genotype
AA
Aa
aa
Phenotype
White-spotted
Intermediate
Little spotting
Genotype
AA
Aa
aa
Number
1469
138
5
p = 0.954
q = 0.046
Total pop size = 1612
p
p = 0.954
Number
1469
138
5
q = 0.046
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Test for HWE deviation
Test for HWE deviation
Genotype
AA
Aa
aa
Observed
1469
138
5
Expected
1467.4
141.2
3.4
Genotype
AA
Aa
aa
Pearson’s chi-square test:
X
Observed
1469
138
5
Expected
1467.4
141.2
3.4
Pearson’s chi-square test:
2
X
2
= 0.83
df = # phenotypes - # alleles = 1
X
X
2
= 0.83
2
cutoff to reject null hypothesis = 3.84
So we don’t reject null hypothesis.
Some natural populations
DO conform to HWE!
Effective population size
Effective population size
Census population size: denoted as “N”, total # individuals in population
Census population size: denoted as “N”, total # individuals in population
Effective population size: denoted as “N e”, reproductively active #
Effective population size: denoted as “N e”, reproductively active #
Why are N and Ne different?
Why are N and Ne different?
individuals in population
individuals in population
Ne is generally less than N
Can be due to:
Unequal sex ratio (polygamous species or non reproductive caste)
Spatial population structure
Population size fluctuations
Overlapping generations
Effective population size
Effective population size
Census population size: denoted as “N”, total # individuals in population
Census population size: denoted as “N”, total # individuals in population
Effective population size: denoted as “N e”, reproductively active #
Effective population size: denoted as “N e”, reproductively active #
One traditional approach to calculating effective pop size:
Calculating long term effective pop size:
individuals in population
N = Nm + Nf
Ne = 4Nm Nf
Nm + Nf
Ne = N for equal sex ratios
individuals in population
Harmonic mean of N values
Ne =
# generations
1/N1 + 1/N2 + … +1/Nn
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Effective population size
Effective population size
Census population size: denoted as “N”, total # individuals in population
Census population size: denoted as “N”, total # individuals in population
Effective population size: denoted as “N e”, reproductively active #
Effective population size: denoted as “N e”, reproductively active #
individuals in population
individuals in population
Northern Elephant Seal
Reducted to 20 inds in 1896
Now 30,000 inds
Ne =
# generations
1/N1 + 1/N2 + … +1/Nn
Ne =
# generations
1/N1 + 1/N2 + … +1/Nn
Hypothetical example
1800
1810
1820
1830
1840
1850
1860
1870
1880
1890
1900
1910
1920
1930
1940
1950
1960
1970
1980
1990
2000
30000
30000
30000
30000
30000
30000
30000
30000
30000
20
30000
30000
30000
30000
30000
30000
30000
30000
30000
30000
30000
Ne = 375!
Effective population size
There are lots of ways to calculate Ne
(and it is controversial)
Traditional methods
Ne based on inbreeding coefficients
Ne based on variances
with variable sex ratio (4NmNf way)
with variable pop size through time (harmonic mean way)
with variable offspring number
Coalescent methods
Sjodin paper
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