definition of evolution the operational definition of evolution at the level of a deme is a change...

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.


MM

0.59

MN

0.33

NN

.08

M

1(0.59) + 1/2(0.33) = 0.76N

1(.08) + 1/2(.33) = .24


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.


MM

0.59

MN

0.33

NN

.08

M

1(0.59) + 1/2(0.33) = 0.76N

1(.08) + 1/2(.33) = .24


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


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


10 Gametes

Generation

p


Bigger Deviations From Initial Gene PoolBecome More Likely With Passing Time

2N = 10


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


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


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


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]


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


€

N ev =N

1+ f


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

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.

definition of evolution the operational definition of evolution at the level of a deme is a change...

Documents

coalescenceunder genetic

nagenetic driftgenetic

gene poolsample

loss of alleles

gamete frequency

allele frequencies

initial gene poolbecome

nnumber frequency