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Dominance
• Refers to an allele’s phenotypic effect in
the heterozygous condition
• NOT its numerical prevalence
• For example, a Dominant allele may be
LESS common than a recessive allele!
Dominance
• If the dominant and recessive alleles A
and a (with freq. of p and q) are in H-W
Equilibrium
• The frequency of the dominant phenotype is
p2 and 2pq
• The frequency of the recessive phenotype is
q2
Dominance – Moth Example
• Black Phenotype (Dominant) = 10%
• Grey Phenotype (Recessive) = 90%
p=Black allele
q=Grey allele
• Assume this population H-W Equil. (Rounding)
• q2 = 0.9  q = 0.95 (0.94868)
• therefore  p = 0.05 (0.051316)
• This implies that p2 = (0.05)2 = 0.0025 (0.0026334)
•
.25% are dominant homozygote
• Heterozygotes = 2pq = 2(0.05)(0.95) = 0.095
0.095 (or 9.5%) are heterozygotes
Dominance
• A dominant allele may well be less
common than a recessive allele.
Estimating the Proportion of
Polymorphic Loci
• Why?
 To know how much genetic
variation exists within a population
-Also, allows us to understand patterns of
variation (as we will see in a few minutes...)
• HOW?
Methods Used to Estimate
Genetic Polymorphism
• Protein electrophoresis
• RFLP’s
restriction fragment length polymorphisms
• DNA Sequences
• Microsatellites
Polymorphism of Adh
Polymorphism of Ldh
Variation at the DNA Level
Allelic diversity across loci
• Heterozygosity or mean heterozygosity
• As the avg. frequency of heterozygotes
across loci
• As the fraction of loci that are heterozygous
in the genotype of the avg. individual.
• % of polymorphic loci
• Fraction of loci in a population that have
multiple alleles.
Heterozygosity
Genetic variation at allozyme loci
How is polymorphism maintained?
• Do forces of natural selection maintain
these polymorphisms, or are they neutral,
subject only to the operation of random
genetic drift?
Multiple Loci
•Genes do not exist in isolation
•Multiple genes probably effect a
single character
•Physically associated on
chromosome
•Linkage disequilibrium
Evolution at Multiple Loci
• We have considered the Hardy-Weinberg
•
•
Equilibrium Principle for one locus at a
time
Can this model be extended to a two or
higher locus case?
Must make a more realistic model
Evolution at Two Loci
• Consider two loci on the same
chromosome: A and B
• Alleles A and a; B and b
• Track both allele frequencies and
•
chromosome frequencies
Four possible chromosome genotypes:
AB, Ab, aB, and ab
• Haplotypes: multilocus genotype of a
chromosome
Evolution at Two Loci
• Loci are in linkage equilibrium if the
•
frequency of one allele does not affect
the frequency of the other
Linkage disequilibrium = locus
frequencies affect each other
• May affect evolution of each other by genetic
linkage
• Genes may be inherited as a group
• May be based on physical distance between
the loci
Evolution at Two Loci
• Numerical example
• Two hypothetical populations with 25
•
chromosomes each
We can calculate allele frequencies and
chromosome frequencies
Evolution at Two Loci
• Numerical example
• Allele frequencies same for both populations
• Chromosome frequencies differ slightly
• To see difference, can calculate frequency of
allele B on chromosomes carrying A versus
frequency of chromosomes carrying a
• Can depict this graphically
Evolution at Two Loci
• Numerical example
• Top population is in linkage equilibrium
• Chromosome genotype of one locus is
independent of other locus
• Bottom population is in linkage
disequilibrium
• Nonrandom association between a genotype at
one locus and another
• If we know one genotype we have a clue about the
other
Evolution at Two Loci
• Conditions for Linkage Equilibrium
• The frequency of B on chromosomes
•
•
carrying A is equal to the frequency of B
on chromosomes carrying a
The frequency of any chromosome
haplotype can be calculated by
multiplying frequencies of constituent
alleles
The quantity D, the coefficient of linkage
disequilibrium, is equal to zero
• D = gABgab - gAbgaB
• gs are frequencies of chromosomes
Evolution at Two Loci
•
Assess conditions for hypothetical
example
• Frequencies of chromosomes are equal
• True for top, not for bottom
• Frequencies of haplotypes can be
calculated by multiplying allele frequencies
• A X B = (0.6)(0.8) = 0.48
• A X B = (0.6)(0.8) = 0.48
• D=0
YES
NO AB = 0.44
• gABgab - gAbgaB = (0.48)(0.08) = (0.12)(0.32)
• gABgab - gAbgaB = (0.44)(0.04) = (0.16)(0.36)
YES
NO
Evolution at Two Loci
• If the population is in linkage
equilibrium, Hardy-Weinberg
equations can be used for each locus
independently
• Assume no selection, no mutation, no
migration, infinite population, panmixia
• What creates linkage disequilibrium?
• Selection on multilocus genotypes
• Genetic drift
• Population admixture
Evolution at Two Loci
• How to eliminate linkage disequilibrium
• Sexual reproduction reduces linkage
•
•
•
disequilibrium
Meiosis, crossing over, outbreeding
Meiosis breaks up old genotype
combinations and creates new ones
Genetic Recombination
• Randomizes genotypes of loci with respect to
each other
Evolution at Two Loci
• Why does linkage disequilibrium matter?
• If two loci are in linkage disequilibrium,
•
•
selection at one locus changes allele
frequencies at the other
Cannot use Hardy-Weinberg to calculate
allele or genotype frequencies
In practice the change in one locus due to
linkage disequilibrium could erroneously be
interpreted as selection on that locus
Evolution at Two Loci
• Why does linkage disequilibrium matter?
• If in linkage equilibrium Hardy-Weinberg can
•
still be used
Random sexual reproduction is very efficient
at eliminating linkage disequilibrium
• Most loci are in linkage equilibrium
• Empirical study of 5000 human loci found that
only 4% were in linkage disequilibrium
Evolution at Two Loci
•
CCR5-D32 allele
•
•
•
•
•
•
Where did the allele come from?
Why is it mainly in Europe?
Stephens measured linkage disequilibrium in CCR5D32 with two loci nearby on same chromosome
• GAAT and AFMB
• Neutral alleles
192 Europeans
GAAT and AFMB are nearly in linkage equilibrium
CCR5-D32 in strong linkage disequilibrium with both
Evolution at Two Loci
•
CCR5-D32 allele
• Linked alleles
• + - 197 - 215
• How did linkage disequilibrium arise?
• Selection, genetic drift, or population admixture
• Not selection because GAAT and AFMB are
•
•
selectively neutral
Not population admixture or the allele would be
elsewhere in the world
Must be genetic drift
Evolution at Two Loci
• CCR5-D32 allele
• At some time in past only the wild type allele
•
•
(+) existed
Then on the chromosome CCR5-GAAT-AFMB
with alleles + - 197 - 215 a mutation occurred
to D32
Linkage is now breaking down
• Some individuals with + - 197 - 217 are now found
Evolution at Two Loci
• CCR5-D32 allele
• Stephens used rates of crossing over and
•
•
mutation to calculate how fast the linkage
disequilibrium would be expected to break
down
Used this calculation to estimate how long
ago D32 appeared
This allele first appeared between 275 and
1875 years ago
• Probably about 700 years ago
Evolution at Two Loci
• CCR5-D32 allele
• Unique mutation must have happened in
•
•
•
Europe
Probably occurred elsewhere but was not
favored by selection
Why was D32 favored in Europe?
Must have been strong selection to raise
from nearly 0% to 20% in 700 years
Evolution at Two Loci
• CCR5-D32 allele
• Perhaps D32 provides protection from other
•
•
diseases
It has been hypothesized that it protects
against the bacterium Yersinia pestis, the
pathogen that caused the Black Death
Investigations are being performed now to
test this theory
Geographic Variation
• Differences in phenotype (or genotype)
among different geographic populations
of the same species
Patterns of Geographic Variation
• Sympatric Populations
• (syn = “together”; patra = “fatherland”)
• Overlapping ranges
• Parapatric Populations
• (para = “besides”)
• adjacent but not overlapping ranges
• e.g. High elevation and low elevation separate
populations
• Allopatric Populations
• (allos = “other”)
• non-overlapping
Rat Snakes (Elaphe obsoleta)
Allopatric
geographic variation
Molecular Phylogeny of Rat
Snakes (Elaphe obsoleta)
Historical dispersal patterns in
Rat Snakes (Elaphe obsoleta)
Genetic Distance
• Quantify the degree of genetic
differentiation among two or more
populations of the same species, or
among different species.
• Nei’s D
Geographically Variable
Characters
• Morphological
• Life history
• Behavior
• Ecology
Character Displacement
• Sympatric populations of two species
differ more than allopatric populations in
their food use etc. these differences are
generally reflected in morphology.
Conclusions about variation
• A species is not genetically uniform over
its geographic range
• Some differences appear to be adaptive
consequences
• Genetic differences between populations
are the same in kind as genetic
differences among individuals within a
pop.
Origin of Genetic Variation
• Gene mutation – an alteration of the
genetic (DNA) sequence
• Mutations have evolutionary
consequences only if they are transmitted
to the next generation
• Somatic cell
• Germ line cell
Various types of mutations
• Point mutations
• Transition – substitution of a purine for a
purine or a pyrimidine for pyrimidine
(A G)
or (C T)
• Transversion – substitution of a purine for a
pyrimidine or vice-versa
(A T)
or (A C) ... and so-on
Categories of Point Mutations
• Synonymous
• Change in DNA sequence  No Change in
Amino Acid sequence
• Non-Synonymous
• Change in DNA sequence  Change in
Amino Acid sequence
Synonymous VS. Nonsynonymous
DNA1
DNA2
= AAA GCT CAT
= AAT GCT GAT
Protein1 = Lys
Protein2 = Lys
Ala
Ala
Synonymous
mutation
His
Asp
GTA GAA
GTA GAA
Val
Val
Glu
Glu
Nonsynonymous
mutation
Various types of mutations
• Frameshift Mutations
• Where nucleotides in the DNA sequence are
added or deleted, creating a change in the
reading frame for the protein encoded by the
gene
Frameshift Mutations
Transposable elements
• Sequences that can move to any of the
many places in the genome
• Barbara McClintock
Maize
Transposable elements
• Carry genes that code for transposases.
• Carryout transposition
• Conservative transposition
• Replicative transposition
• Process of insertion generates 4-12bp
repeats of the host DNA at the end of the
element.
Transposable elements
• Insertion sequences: 700-2600bp only
code for transposases
• Transposons: 500-7000bp encode
transposases + other functional genes.
• Retroelements: use reverse transcriptase
to transcribe. HIV like. Except they do
not cross cell boundaries and spread
only by cell division
Effects on host genome
• Increase total genome size
• Alteration of host gene expression
• Increase in mutation rate of host genes
• Chromosome rearrangements (host)
• Retrogenes. Reverse transcription
• Most non functional
• psuedogenes
Mutation Rates
• Estimates of u (mutation) depend on how you
calculate them
• Phenotypic studies
• White vs red eye in Drosophila
• DNA sequence studies
• Count number between 2 closely related organisms
Mutation estimates
• Usually count the number of mutations, scored
my their phenotypic effects among the offspring
of an initially homozygous stock.
• In Drosophila and other multi-cell organisms
usually measure # of chromosomes bearing a
particular mutation from a homozygous
population for an allele. Use special crosses to
visualize phenotypic effect.
Mutation estimates
• The autosomal chromosomes of N flies
represents 2N gametes that form them, so
mutation rate is calculated a number of
new mutations per gamete per generation
• Avg. locus mutation rate based on
phenotypic effects 10-6 - 10-5 mutations
per gamete per generation
Mutation Rates
• Back mutations-mutation of an allele from
the mutant type back to “wild type”
• Multiple hits; multiple substitutions at
same sit.
Estimating Substitution rate from
DNA sequence
Outgroup)
Taxon 1)
Taxon 2)
Taxon 3)
Taxon 4)
ATGTCAGGGACTCAGATCGAATGGGATCTAG
.....C......T..................
.....G......T........C.........
.....C...........A.............
.....G...........A........G....
Average mutation rate per base pair has
been estimated at 10-9

A
G




C

Purines
T
Pyrimidines
Substitutions Time 0
Outgroup)
Taxon 1)
Taxon 2)
Taxon 3)
Taxon 4)
ATGTCAGGGACTCAGATCGAATGGGATCTAG
.....C......T..................
.....G......T........C.........
.....C...........A.............
.....G...........A........G....
Substitutions Time 1
Outgroup)
Taxon 1)
Taxon 2)
Taxon 3)
Taxon 4)
ATGTCAGGGACTCAGATCGAATGGGATCTAG
.....A......T..................
.....G......G........C.........
.....G...........A.............
.....G...........A........G....
Substitutions Time 2
Outgroup)
Taxon 1)
Taxon 2)
Taxon 3)
Taxon 4)
ATGTCAGGGACTCAGATCGAATGGGATCTAG
.....G......T..................
.....G......T........C.........
.....G...........A.............
.....G...........A........G....
Multiple Substitutions at the same site
Evolutionary implications of
Mutation rates
• Avg. per-locus mutation rate of 10-5 (1 in
100,000 generations) is so low that the
rate of change in the frequency of an
allele, due to mutation alone, is very low.
• Phenotypically distinguishable alleles A1
and A2
Evolutionary implications of
Mutation rates
• These have allele freq. p(=1-q) and q.
• A1 mutates to A2 at rate u= 10-5
• Therefore in each generation, the frequency of
A2 is increased by u x p (that is, a fraction u of
A1 alleles mutate.
• Thus change in freq of A2
∆q = up=u(1-q)
Mutation rates
• q = 0.5
• In the following generation
• q’ = q + ∆q =
• ∆q = up = 10-5 (0.5) = 0.000005
• 0.5 + 0.000005 = 0.5000005
Mutation rates
• How does mutation affect the freq. of
alleles on a pop.
•
assume no back mutation
e-ut
pt = po
qt = 1-poe-ut
u = forward mutation
t = # of generations
q = .5 change q = .75 = 70,000 generations
q = .75 change q = .875 = 70,000 generations
Mutation rates
• Very low mutation rate
• Therefore mutation alone will probably
not account for the actual speed of
evolutionary change observed in nature.
Mutation rates
• But 150,000 genes in humans
• 10-5 mutations per gene x 105 genes = 1
mutation per haploid genome in humans.
• Probably an underestimate
• If even a tiny fraction of there were
advantageous, the amount of new “raw
material” is substantial.
Mutation rates
• Neutral Theory of molecular evolution
• Mutations that neither enhance nor lower fitness
• Fixed (go to 1) or lost (go to 0) entirely by chance
• The probability that this will occur is u
• That is, a mutation that occurred in the past will
become fixed
• After the passage of t generations the mutations
that have become fixed would equal x = ut
Mutation rates
• If 2 species diverged from a common
ancestor t generations ago, the expected
fraction of fixed mutations is D = 2ut
• If we are talking bps then a fraction of D =
2ut of the bps of a gene should differ
between species, assuming equal prob. of
mutation.
Mutation rates
• Avg. mutation rate per bp per generation
is u = D/2t
• Where D is the number of bp differences
between 2 sequences
• Human chimp split 1.3 x 10-9 per site per
year (7mill) assuming 15-20 years generat.
Mutations
• Then the mutation rate is 2 x10 -8 per
generation.
• Human diploid genome has 6 x 109
nucleotide pairs, so this implies 120 new
mutations per genome per generation.
• Page 273 Futuyma