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# Download Quantitative Genetics of Natural Variation: some questions

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```Genetic Linkage
Two pops may have the same
allele frequencies but different
chromosome frequencies.
Conditions for Linkage Equilibrium
(Two locus case)
1) Frequency of B is the same on chromosome A and a
2) Frequency of haplotypes AB, ab, Ab, aB can be calculated
from allele frequencies A=p, a=q, B=t, and b=s.
f(AB) = pt
f(ab) = qs
f(Ab) = ps
f(aB) = pt
3) Coefficient of linkage disequilibrium (D) = 0
f(AB) x f(ab) - f(Ab) x f(aB) = D
ps x qt - pt x qs = 0
(ranges from -0.25 to +0.25)
Hardy Weinberg Principle for Two Loci
Chromosome frequencies remain unchanged across generations
if loci are in linkage equilibria.
If loci are in linkage disequilibria, the chromosome frequencies
will move closer to linkage equilibrium each generation.
What Creates Linkage Disequilibrium in a Population?
selection, drift, and population admixture
Effects of Selection on Chromosome Frequencies
ab/ab = body size of value 10
each additional A or B adds 1 value
predators eat all individuals of size 12 or less
65.28%
survive
Freq a = (0.1536 + 0.1536) / .6528)/2
= 0.24
Freq b = (0.0576 + 0.0576) / .6528)/2
= 0.09
65.28%
survive
Freq ab = .24 x .09 = .02
however!
Locus A and B are in disequilibrium
among the survivors
Genetic Drift, followed by selection
can cause linkage disequilibrium
Combination of Two Different Gene Pools
Admixture
Recombination Breaks Down Linkage Disequilibria
The rate of decline in LD increases with r
LD declines over time
(rate depending on r)
r=
D
sqrt(pqst)
Concept of Linkage
Law of Independent Assortment
= 0.25
A
Meiosis
a
B
b
= 0.25 All allele combinations
in gametes
equally probable
= 0.25
= 0.25
Probability of recombination = 0.5
A
B
a
b
= 0.25
Meiosis
= 0.25
= 0.25
= 0.25
All allele combinations
in gametes
equally probable
Linked Loci
Probability of recombination = 0.3
A
a
B
b
= 0.35
Meiosis
= 0.15
= 0.15
All allele combinations
in gametes NOT
equally probable
= 0.35
Probability of recombination = 0.1
A
B
a
b
= 0.45
Meiosis
= 0.05
= 0.05
= 0.45
All allele combinations
in gametes NOT
equally probable
Concept: The closer two loci are on a chromosome,
the lower the probability of recombination.
Why important?
(1) Affects rate that LD is broken down.
(2) Allows one to determine the linear order of genes
on a chromosome (make a genome map).
(3) Maps allow for the localization of genes, mutant
phenotypes, and QTL in the genome.
Selection at a single locus affects other loci under LD
Selection has
an effect on
frequency of B
alleles
LD among 1504 marker
Loci on Human
Chromosome 22.
(Dawson et al. 2002)
Linkage Disequilibria
Decay of LD
Present level
Time (generations)
How does LD help identify genes that may be under
positive natural selection?
For neutral alleles: Genetic drift is the primary evolutionary
mechanism. So:
If LD is detectable, indicates that an allele is young.
Expect magnitude of LD is proportional to the age of an allele.
If LD is not detectable, indicates that an allele is old.
Expect old and frequent alleles, or old and rare alleles,
But do not expect young, high frequency alleles.
Indicates alleles at the locus may be under selection.
G6PD polymorphism
and deficiency
Countries with malaria
have highest frequency
of a reduced-activity
allele.
Characterized SNPs for G6PD locus of 230 men
Nine different G6PD alleles diagnosed by 11 SNPs
Typed each allele for 14 SNPs outside the G6PD locus
Sabeti et al., 2002
LD is higher for the G6PD-202A allele;
suggests positive selection
Probability
that 2 randomly
chosen “a” chromosomes
have the same snps
across a physical
distance
The Evolutionary Biology of Sex
There is Amazing Diversity in Reproductive Mode
Kiwi
Milk weed aphid
Blueheaded
Wrasse
Sexual Reproduction Probably Evolved Early In Life
Examples of parthenogenesis
Dandelion
Taraxacum officinale
Bdelloid rotifer
What Mode of Reproduction is Better?
An asexual female will have 2x as many grandchildren!
Why Aren’t All Species Asexual?
Because asexual populations
accumulate deleterious mutations
Termed: Muller’s Rachet
Possibly leads to extinction
Evidence for Muller’s Ratchet: Andersson and Hughes (1996)
None of the 444 cultures had
higher fitness than the wild type
Eichhornia paniculata
Barrett and Charlesworth, (1991)
Flower number declined in
a natural out crossing
population, and heterosis
was observed.
Flower number stayed
relatively constant in
a naturally self-fertilizing
population
Recombination Breaks the Ratchet
Sex maybe advantageous
because it can recreate
favorable multilocus genotypes
However, adaptation by this
process is only faster in large
populations
However, Suppression of Recombination
is Important in the Evolution
of Sex Chromosomes
Hypotheses for Short-Term Advantages of Sex
• Recombination allows repair of damaged DNA
• Genetically diverse progeny may outcompete asexual progeny
• Muller’s ratchet
• Deleterious mutations are more easily purged in sexual pops
• Rate of evolution is higher in large sexual populations
```
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