Definition of Evolution The Operational Definition of Evolution at the Level of a Deme is a Change...
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Definition of Evolution
The Operational Definition of Evolution at the Level of a Deme is a Change in Allele or Gamete
Frequency In the Gene Pool.
Evolutionary Force
A Factor or Process That Can Change The Frequency of an
Allele In the Gene Pool.
A
p = 1
Gene Pool BeforeMutation
A
p = 1-1/(2N)
a
Deme of N Individuals
q = 1/(2N)
Mutation
Gene Pool AfterMutation
Mutation Is an Evolutionary Force
Genetic Drift
Genetic Drift Occurs When Sampling Error Alters Allele
Frequencies.
Sampling Error Occurs When Populations Are Finite in Size.
Therefore, Finite Population Size is An Evolutionary Force
Mendel’s Ratios Were Not “Perfect” Because They Are Based On A Finite Number of
Observations.A Frequency In A Sample Only Converges To
the Probability As The Sample Size Gets Larger and Larger.
e.g., the two largest samples have ratios closest to 3:1, but still not “perfect”
A Deme Is A Collection of Such Crosses, Each Subject to Random Sampling Error in Its Mendelian
Ratios
Probabilities Vs. Frequencies in Demes and Gene Pools:
MM
0.59
MN
0.33
NN
.08
M
1(0.59) + 1/2(0.33) = 0.76N
1(.08) + 1/2(.33) = .24
MendelianProbabilities
In Meiosis
diploid
haploid
Meiosis1 11/2
1/2
This is a Mendelian Probability. In a finite sample of gametes from MN individuals you will often get deviations from Mendel’s 1:1 ratio.
Probabilities Vs. Frequencies in Demes and Gene Pools:
MM
0.59
MN
0.33
NN
.08
M
1(0.59) + 1/2(0.33) = 0.76N
1(.08) + 1/2(.33) = .24
MendelianProbabilities
In Meiosis
diploid
haploid
Meiosis1 11/2
1/2
These are the probabilities that MM and MN individuals live and have offspring. In a finite sample, can get deviations by chance alone.
Probabilities Vs. Frequencies in Demes and Gene Pools:
MM
0.59
MN
0.33
NN
.08
M
1(0.59) + 1/2(0.33) = 0.76N
1(.08) + 1/2(.33) = .24
MendelianProbabilities
In Meiosis
diploid
haploid
Meiosis1 11/2
1/2
In a finite population, this is the probability of an M allele in the gene pool, and not necessarily the frequency in the offspring produced.
A1/2
a1/2
Gene Pool
Sample 10 Gametes to Create 5 Individuals
Computer Simulation of Genetic Drift
Number (Frequency) of A Alleles
Do This 20 Times To Show Sampling Variation
A1/2
a1/2
Number (Frequency) of A Alleles
Property 1 of Genetic Drift: No Direction
p = 0.5
A1/2
a1/2
10 Gametes
Property 2 of Genetic Drift: It Is Cumulative
Let This Be The Sample That Actually Occurs
A1/2
a1/2
10 Gametes
Property 2 of Genetic Drift: It Is Cumulative
10 Gametes
Generation
p
Property 2 of Genetic Drift: It Is Cumulative
Bigger Deviations From Initial Gene PoolBecome More Likely With Passing Time
2N = 10
Property 2 of Genetic Drift: It Is Cumulative
Simulations of N = 50, p = 0.5
BottleneckSim[50,50,20,40,.5]MultiSim[50, 50, 20, 40, .5]
A1/2
a1/2
Gene Pool
10Gametes
20Gametes
Property 3 of Genetic Drift: Strength 1/2N
Number (Frequency) of A Alleles
Property 3 of Genetic Drift: Strength 1/2N
Simulations of p=0.5 with N=25, 100 and 1000
MultiSim[N, N, 20, 40, .5]
A1/2
a1/2
10 Gametes
Property 4 of Genetic Drift: Loss of Alleles
10 Gametes
Properties 3 & 4 of Genetic Drift: Rate of Loss of Alleles
Rate of Loss = 1/2N
Properties 3 & 4 of Genetic Drift: Loss of Alleles = Coalescence
Under Genetic Drift:
Rate of Loss = 1/2N
Average Time for 2Genes to Coalesce= 2N Generations
Average Time for allGenes To Coalesce= 4N Generations
Properties 3 & 4 of Genetic Drift: Loss of Alleles = Coalescence
DriftSim[N, .5]
Property 5 of Genetic Drift: Isolated Demes
Become Genetically Differentiated (From Property 1)
Generation
p
2N = 20
4 Isolated Demes Started From One Ancestral Deme With p = 0.5
Property 6 of Genetic Drift: Random Changes In Multi-locus Gamete Frequencies Create Linkage
Disequilibrium
Properties of Genetic Drift
1. Has No Direction2. Is Cumulative
3. Strength is Proportional to 1/2N
4. Leads to Loss (and Fixation and Coalescence) of Alleles Within Demes
5. Leads to Genetic Differentiation Between Isolated Demes
6. Creates |D| > 0
Although Strength of Genetic Drift is Proportional to 1/2N, Drift Can be Important in Large Populations
1. Founder Effects -- A Large Population Today Was Founded By A Small Number of Founders in the Past.
2. Bottleneck Effects -- A Large Population Today Underwent One or More Generations of Small Size in the Past.
3. Neutral Alleles -- Alleles With No Impact on Any Phenotype Related to Reproductive Success. Their Fate is Determined by Drift and Mutation.
Although Strength of Genetic Drift is Proportional to 1/2N, Drift Can be Important in Large Populations
1. Founder Effects -- A Large Population Today Was Founded By A Small Number of Founders in the Past.
2. Bottleneck Effects -- A Large Population Today Underwent One or More Generations of Small Size in the Past.
MultiSim[500, 2, 20, 40, .5]
A Human Founder Event• The Population of the Mountain Village of Salinas in the
Dominican Republic Was 4,300 in 1974.• The Village Was Founded By A Handful of People 7
Generations Before• One Founder, Altagracia Carrasco, Had Many Children by
Four Women• The Alleles Carried by Him Were Therefore in High
Frequency in the Founder Population Gene Pool• Subsequent Population Growth Reduced the Force of Drift
But “Freezes In” The Allele Frequencies Created by the Initial Founder Event So His Alleles Remain In High Frequency Even Today
Altagracia Carrasco, Like Most People, Was A Heterozygous
Carrier For an Autosomal Recessive Genetic Disease:
5- Steroid Reductase Deficiency
testosterone dihydrotestosterone5- Steroid Reductase
Under The Control of Testosterone
Default Pathway in
All Mammals
Under The Control of Dihydro-
testosterone
Linkage Disequilibrium In a Founder Population From Costa Rica
Linkage Disequibrium Is Created By Population Subdivision In A Manner Not Related To Recombination (Creates Serious Problems For Disequilibrium Mapping)
gAB=1
Gene Pool for Population 1
gab=1
Gene Pool for Population 2
gAB=1/2
Gene Pool for Pooled Populations
gab=1/2
D=gABgab=1/4, D’=1
D=0 D=0
Problem!Population Structure or Historical Isolates Can Create
Spurious Phenotypic Associations. E.g., in Quebec there are French and English Speaking Canadians. French Canadians Have Been Strongly Influenced by a Past Founder Event and Show Allele Frequency Differences At Many Loci From the
English Population. Therefore, A Mapping Study of the “Quebec” Population Would Reveal A Strong Association
Between Many Loci and the Language One Spoke. Similarly, A Candidate Locus Study Would Find An
Association With Language If The Candidate Locus Showed Haplotype Frequency Differences Between English and
French Canadians.
Avoiding Problem of Hidden Population Structure
1. Use founder or bottleneck populations (but must make sure they truly are and have been highly isolated since the drift event)
2. Use several loci to reconstruct recent evolutionary history and population structure prior to initiating association study, and then choose populations accordingly or use as a control set of loci in the association study.
Founder & Bottleneck Events• Can Drastically Alter Allele Frequencies, Including
Making Certain Genetic Disease Allele or Disease Risk Alleles Common (makes obtaining pedigrees for linkage mapping much easier)
• Leads to pedigree inbreeding (Speke’s gazelles; humans on Tristan da Cunha)
• Creates Linkage Disequilibrium, Which Rarely Extends Over 1 cM in Large Demes (makes disequilibrium mapping much easier)
• Reduce Overall Genetic Variation, Creating A Simpler Genetic Background
• For The Above Reasons, Such Populations Are Important In Biomedical Research & Conservation
E.g., Positional Cloning & QTL’s
• The First Case of Positional Cloning Was the Gene for Huntington’s Chorea
• Nancy Wexler Realized That The Key Was to Find a Founder Population With A High Frequency of HD.
• She Found Such A Population On Lake Maracaibo
• Now, Founder Populations Such As This Are Regarded As Commercially Valuable Assets.
E.g., Positional Cloning & QTL’s
About 200 years ago, a single woman who happened to carry the Huntington's allele bore 10 children — and today, many residents of Lake Maracaibo trace their ancestry (and their disease-causing gene) back to this lineage.
Effective Population Size
• Founder And Bottleneck Events Show That The Current Size Of A Population May Not Be A Good Indicator Of The Impact Of Genetic Drift Upon That Population
• The Concept of EFFECTIVE POPULATION SIZE Solves This Problem.
Effective Population Size
measures the strength of genetic drift in influencing some population
genetic feature of interest relative to how that same feature evolves
through genetic drift in an idealized population over the same number of
generations
The Idealized Reference Population• a diploid population of hermaphroditic, self-compatible organisms
• constant size of N breeding Adults
• random mating
• complete genetic isolation (no contact with any other population)
• discrete generations with no age structure
• all individuals contribute the same number of gametes on the average to the next generation (no natural selection)
• the sampling variation in the number of gametes contributed to the next generation by an individual is given by a Poisson probability distribution.
The Most Common Parameters Used To Monitor Genetic Drift are:
• The Average Level of Identity by Descent (inbreeding effective size)
• The Variance In Allele Frequency Induced By Genetic Drift (variance effective size)
Generation
p
Animal ID
Males Females
0.35
0.30
0.25
0.20
0.15
0.10
0.05
0.00
0.00
0.01
0.02
0.03
0.04
0.05
1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950
Decade of Birth
Tristan da Cunha
Impact of Drift On Average F In An Idealized Population
F(t) = + (1 - )F(t-1)1
2N1
2N
AverageProbabilityOf IdentityBy Descent
At generation t
ProbabilityRandomly
Draw 2GametesFrom The
SameIndividual
ProbabilityThe 2
GametesFrom The
SameIndividual
AreIdentical
Impact of Drift On Average F In An Idealized Population
F(t) = + (1 - )F(t-1)1
2N1
2N
Probability OfIdentity By DescentDue To Drawing 2
Copies of TheSame Gamete
From The PreviousGeneration
Probability OfNot Drawing 2Copies of TheSame Gamete
From The PreviousGeneration
Probability That2 Randomly DrawnGametes That AreNot Copies of The
Same GameteFrom The Previous
Generation AreIdentical By Descent
Due to Earlier Inbreeding
Impact of Drift On Average F In An Idealized Population
F(t) = + (1 - )F(t-1)1
2N1
2N
Can Use The Above Equation Recursively To Obtain:
F(t) = 1- (1 - )t12N
[F(0) = 0]
Impact of Drift On Average F In An Idealized Population
F(t) = 1- (1 - )t12N
If A Real Population Has An ObservedAverage F of F(t) After t GenerationsFrom the Reference Generation WithF = 0; Then The Inbreeding EffectiveSize Is Given By: 0.00
0.01
0.02
0.03
0.04
0.05
1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950
Decade of Birth
Tristan da Cunha
F(t) = 1- (1 - )t12Nef
or Nef = 2{1-[1-F(t)]1/t}
1
Impact of Drift On Allele Freq. Variance In An Idealized Population
2(t) = pq{1- (1 - )t}
12N
If A Real Population Has An ObservedVariance of v(t) After t GenerationsFrom the Reference Generation; ThenThe Variance Effective Size Is Given By:
12Nev
or Nev = 2{1-[1-v(t)/(pq)]1/t}
1v(t) = pq{1- (1 - )t
}
There Is No Such Thing As The Effective Size of a Population
• The effective size depends upon which genetic parameter you are using
• The effective size depends upon which reference generation you are using
• Therefore, a single population can have many different effective sizes associated with it, all biologically meaningful but distinct
Example: Speke’s Gazelle• Herd Started in 1969 With 4 Animals• By 1979 There Were 19 Animals With An Average F of
0.1283 After 1.7 Generations• Therefore, Nef Relative to the Founders is 6.4 < 19 (Founder
Effect)• In 1979, Management Was Changed, and 15 New Animals
Bred with F = 0.149 and t = 2.7, yielding Nef = 8.6 < 15 (Founder Effect & f < 0)
• Using the parents of the 19 Animals in 1979 as Reference Generation, then F = 0.0207 and t = 2, yielding Nef = 96.1 > 15 (Effect of Avoidance of Inbreeding in System of Mating Sense)
• Herd Started in 1969 With 4 Animals• In 1979, Management Was Changed, and 15 New Animals
Bred with v/(pq) = 0.135 and t = 2.7 (computer simulation of exact pedigree), yielding Nev = 9.6 < 15 (Founder Effect)
• The same 15 animals have– Nev = 9.6 < 15 (relative to founder generation)– Nef = 8.6 < 15 (relative to founder generation)– Nef = 96.1 > 15 (relative to the management change
generation)
• WHAT IS THE EFFECTIVE SIZE OF THIS POPULATION?
Example: Speke’s Gazelle
In Most Cases, Do Not Have Complete Pedigree Information, Precluding the
Calculation of Various Effective Sizes.Many Formulae Have Been Derived as
Estimators or Approximations to Effective Size.
The Literature Is A Mess, Because Many Do Not Distinguish Among The Various Effective Sizes, and Often Mix
Inappropriate Formulae
Interactions of System of Mating with Genetic Drift via Effective Size• The ideal reference population assumes random mating.
• Suppose mating is non-random, either due to inbreeding or assortative mating such that f > 0.
• Then:
€
F ( t) = f +(1− f )1
2N+ 1−
1
2N
⎛
⎝ ⎜
⎞
⎠ ⎟F (t −1)
⎡
⎣ ⎢
⎤
⎦ ⎥
I by D created by system of mating beyond random mating expectations.
I by D created by genetic drift at random mating expectations.
Interactions of System of Mating with Genetic Drift via Effective Size
€
F ( t) = 1− (1− f ) 1−1
2N
⎛
⎝ ⎜
⎞
⎠ ⎟
⎡
⎣ ⎢
⎤
⎦ ⎥
t
€
N ef =N
1+ f (2N −1)
Interactions of System of Mating with Genetic Drift via Effective Size• The ideal reference population assumes random mating.
• Suppose mating is non-random, either due to inbreeding or assortative mating such that f > 0.
• Then:
variance created by system of mating beyond random mating expectations.
variance created by genetic drift at random mating expectations.€
Variance in Allele Frequency = (1 - f )pq
2N+ f
pq
N=
pq(1+ f )
2N
Interactions of System of Mating with Genetic Drift via Effective Size
€
N ev =N
1+ f
Interactions of System of Mating with Genetic Drift via Effective Size
Population Size N
Nev
Nef
f=0.1
Interactions of Population Growth with Genetic Drift via Effective Size
€
Nef =2N −1
k −1+ 1− k2N( )
Nev = N
Where N is an idealized population in every way except that each individual has an average of k offspring (k=2 corresponds to a constant sized population)
Interactions of Population Growth with Genetic Drift via Effective Size
Neutral Alleles
Have no effect on any phenotype that influences reproductive success and
therefore their evolutionary dynamics are determined by mutation and
genetic drift
Effects of 50 Spontaneous Mutation Lines Derived from a Strain of Yeast Growing in a Laboratory Environment.
Neutral
FavorableUnfavorable
Neutral Alleles(Kimura 1968)
• Genetic Drift Determines the Rate of Loss = 1/2N
• Mutation Determines the Rate of Input = (2N)• Rate of Evolution = Rate of Input X Rate of Loss =
(2N)1/2N = Note: The Rate of Neutral Evolution Does Not Depend
upon Population Size. All populations, regardless of size, have an innate tendency to evolve as driven by mutation and drift. Moreover, if the neutral mutations rates are comparable, this tendency is just as strong in a large population as in a small population. GENETIC DRIFT IS IMPORTANT FOR ALL POPULATIONS!
Amino Acid Sequence Data
• The Substitutions Seemed To Define A “Molecular Clock” (King & Jukes, Sci. 154:788-798,1969).
• This Also Seemed To Support Kimura’s Theory Because It Predicted The Rate of Substitution=, which was usually treated as a constant.
Mouse Chicken Newt Carp Shark
Human 16 35 62 68 79
Mouse 39 63 68 79
Chicken 63 72 83
Newt 74 84
Carp 85
Human Mouse Chicken Newt Carp Shark
-Hb Data
Protein Electrophoresis Data
• Lewontin & Hubby (Genetics 54: 595-609, 1966), Johnson et al. (Studies in Genetics. III: 517-532, 1966), and Harris (Proceedings of the Royal Society of London B 164:298-310. 1966) showed that about 1/3 of all protein coding loci were polymorphic for electrophoretically detectable alleles in Drosophila and in humans
•Kimura and Ohta (Nat. 229: 467-489, 1971) could explain this high level of variation with the Neutral Theory
Kimura & Ohta
Most Neutral Mutations Are Lost and Contribute Little to Polymorphism Levels
1/(2N) of Neutral Mutations Go To Fixation and Transiently
Contribute To Polymorphism Levels
Time Period of Transient Polymorphism
Kimura & Ohta
€
F ( t) =1
2N+ 1−
1
2N
⎛
⎝ ⎜
⎞
⎠ ⎟F (t −1)
⎧ ⎨ ⎩
⎫ ⎬ ⎭
(1− μ )2
Average Probability
of Identity by Descent
at Generation t
⎧
⎨ ⎪
⎩ ⎪
⎫
⎬ ⎪
⎭ ⎪=
Probability of Identity
by Descent Due to
Genetic Drift
⎧
⎨ ⎪
⎩ ⎪
⎫
⎬ ⎪
⎭ ⎪
Probability of No
Mutation in Both
Gametes
⎛
⎝
⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟
€
F eq =1
2N 1(1−μ )2 −1[ ] +1
≈1
4Nμ +1 for μ small
Let θ = 4Nef
€
1− F eq = H eq = 1−1
θ +1=
θ
θ +1
Kimura & Ohta
This Implies A Small Range of Population Sizes, and That Almost All Species Have N < 5,000 (Including Insects & Bacteria).
Most Observations Below This Threshold
Effects of 50 Spontaneous Mutation Lines Derived from a Strain of Yeast Growing in a Laboratory Environment.
Neutral & NearlyNeutral
Ohta (1973-1976) Created The Nearly Neutral Theory To Explain The
Heterozygosity Observations
•Showed That Genetic Drift Determines Evolutionary Dynamics For Any Mutation With |s|<1/(2Nev)
•Let (s) describe the probability of a mutation having selection coefficient s, then
•The neutral mutation rate=neutral=
•As Nev , neutral
•This explains why Heterozygosity levels off and has a narrow range (recall θ=4Nneutral)
•Unfortunately, this also means you lose the molecular clock because the rate of substitution is now a function of Nev
€
(s)ds0
12Nev
∫
Evidence for Neutral Alleles
Evidence for Neutral Alleles
Evidence for Neutral Alleles
The pseudogene evolves more rapidly than the functional gene
Neutral Alleles
A substantial portion, perhaps the majority, of the genetic variation
observed at the DNA sequence level is neutral, making genetic drift a
major evolutionary force
This Also Means That It Is Difficult To Find The Minority Of The Variation At the DNA Sequence Level That Has
Functional Significance.