Genetic Drift

In small, reproductively isolated populations, special circumstances exist that can produce rapid changes in gene frequencies totally independent of mutation, recombination, and natural selection.   These changes are due solely to chance factors.  The smaller the population, the more susceptible it is to such random changes.  This phenomenon is known as genetic drift.

Neutral alleles

Controversial when first proposed (Kimura 1968) Incontrovertible in 2001:

DNA sequence polymorphisms are abundant In Eukarya, most of the genome is noncoding most sequence polymorphism lies in noncoding regions Most sequence polymorphisms appear selectively neutral

• Not useful for studies of genetic adaptation

• Ideal for detection of population substructure and phylogenetic relationships

Genetic Drift

For example, when women and their mates are both heterozygous (Aa) for a trait, we would expect that 1/4 of their children will be homozygous recessive (aa).  By chance, however, a particular couple might not have any children with this genotype (as shown below in the Punnett square on the right).

Unless other families have an unpredictably large number of homozygous (aa) children for this trait, the population's gene pool frequencies will change in the direction of having fewer recessive alleles.

Genetic Drift

The net effect of genetic drift on a small population's gene pool can be rapid evolution, as illustrated in the hypothetical inheritance patterns shown below.  Note that the red trait dramatically increases from generation to generation.  It is important to remember that this can occur independent of natural selection or any other evolutionary mechanism.

Inbreeding in finite populations

Assume a population size of N, therefore 2N alleles in population. Imagine eggs and sperm released randomly into environment (e.g. sea)

What is the probability of 2 gametes drawn randomly having the same allele?

2N allelesgen 0

gen 1

probability = 1/(2N)

Inbreeding in finite populations

Therefore, after 1 generation the level of inbreeding is F1 = 1/2N

After t generations the probability is

Ft 1

2N 1

1

2N

Ft 1

Why?

gen t-1

gen t

1/(2N) 1 - 1/(2N) Probability ofpicking 2nd allele

Ft 1

2N 1

1

2N

Ft 1

Genetic drift and heterozygosity

Genetic drift will to a gradual loss of genetic diversity

Follow an individual locus and gene frequency will drift until one allele becomes fixed

Ft 1 11

2N

t

Genetic diversity: HT = (1 – 1/2N) * HT-1

Probability of identity: FT = 1/2N + (1 - 1/2N) * FT-1

Average time to fixation: 4N

Several populations

Genetic drift will make initially identical population different

Eventually, each population will be fixed for a different allele

If there are very many populations, the proportion of populations fixed for each allele will correspond to the initial frequency of the allele

Small populations will get different more rapidly

Importance of genetic drift

Two causes for allele substitutions: Selection -> adaptive evolution Genetic drift ->non-adaptive evolution

Most populations are geographically structured All populations are finite in size All genetic variation is subject to genetic drift but

not necessarely to selection Genetic drift as a null hypothesis against which

evidence for selection has to be tested

Effective population size

Effective population size < Census size (in most cases)

The effective population size is the size of an ”ideal” population having the genetic properties of the studied population

The effective population size is determined by

Large variation in the number of offspring

Overlapping generation

Fluctuations in population size

Unequal numbers of males and females contributing to reproduction Ne =(Nf + Nm)

4NfNm

Ne 1

= n 1

Ni 1Σ

(Harmonic mean)

Effective population size

What is an ideal population like? (Remember - each parent a has an equal and independent chance of

being the parent of each descendent allele.) This is approximated by a Poisson distribution of reproductive success. (Reproductive success = # of offspring per parent, or per parental

allele.)

Effective population size

e

et

et

tt

N

NF

NF

FF

2

1

2

11 1

1

Effective population size

2

1

2

1

2

11

1

1

e

et

et

t

N

NF

NF

F

Effective population size

For diploids: where V is the variance in

reproductive success among diploid individuals. (Note that the variance among individuals in reproductive success with a Poisson distribution is 2 in a steady-state population, so that Ne = N-1/2.)Note also that Ne can also be as great as 2N-1, if there is no variance in reproductive success. This fact is often used in animal and plant breeding to slow the loss of genetic material.

2

24

V

NNe

Effective population size

 Population size in natural populations does not remain constant

Ne with population size fluctuations is approximately the harmonic mean of N over time:

The harmonic mean is very sensitive to small values.

(Ne << ) if N is variableNe =(Nf + Nm)

4NfNm

0321

11....

2

11

2

11

2

111

FNNNF

tttt

Ne 1

= n 1

Ni 1Σ

(Harmonic mean)

Simplification: 0, 1 or 2 offspringCoalesce: have the same parentProbability to coalesce: 1/NProbability Not to coalesce: 1 – 1/Nt generations: (1-1/N)t

Average time to coalesce for 2 genes: NFor the whole population: 2N

Backwards: the coalescent approach

Founder effects

Another important small population effect is the founder effect or founder principle.  This occurs when a small amount of people have many descendants surviving after a number of generations.  The result for a population is often high frequencies of specific genetic traits inherited from the few common ancestors who first had them.

Population# of

founders# of

generations Current size

Costa Rica 4,000 12 2,500,000

Finland 500 80-100 5,000,000

Hutterites 80 14 36,000

Japan 1,000 80-100 120,000,000

Iceland 25,000 40 300,000

Newfoundland 25,000 16 500,000

Quebec 2,500 12-16 6,000,000

Sardinia 500 400 1,660,000

A new population emerges from a relatively small group of people.

Founder effect example

In the Lake Maracaibo region of northwest Venezuela, for instance, there is an extremely high frequency of a severe genetically inherited degenerative nerve disorder known as Huntington's disease.  Approximately 150 people in the area during the 1990's had this fatal condition and more than 1,000 others were at high risk for developing it.

All of the Lake Maracaibo region Huntington's victims trace their ancestry to one woman who moved into the area a little over a century ago.  She had an unusually large number of descendents and was therefore the "founder" of this population with its unpleasant genetically inherited trait.

Founder effect example

It is also possible to find the results of the founder effect even though the original ancestors are unknown.  For example, South and Central American Indians were nearly 100% type O for the ABO blood system.  Since nothing in nature seems to strongly select for or against this trait, it is likely that most of these people are descended of a small band of closely related "founders" who also shared this blood type.  They migrated into the region from the north, mostly by the end of the last Ice Age.

Bottleneck

In some species, there have been periods of dramatic ecological crisis caused by changes in natural selection, during which most individuals died without passing on their genes.  The few survivors of these evolutionary "bottlenecks" then were reproductively very successful, resulting in large populations in subsequent generations.  The consequence of this bottleneck effect is the dramatic reduction in genetic diversity of a species since most variability is lost at the time of the bottleneck.

Migration

A cline is a gradual change in allele frequency along a geographic gradient

Ecotypes are genetically distinct forms that are consistently found in certain habitats.

Changes in allele frequency can be mapped across geographical or linguistic regions.

Allele frequency differences between current populations can be correlated to certain historical events.

Contrary to selection and genetic drift gene flow homogenizes allele frequencies

Genetic diversity is restored if immigrants carry new alleles or alleles which are rare in the population

Patterns of geographic variation

Sympatric, parapatric and allopatric variants

Subspecies are recognizable geographic variants within a species (usually subject to discussions)

A hybrid zone is a region where genetically different parapatric species or population interbreed.

Character displacement: sympatric populations of two species differ more than allopatric populations

Allele distributions can reflect historical events

Creutzfeldt-Jakob disease (CJD) is caused by a mutation in the prion protein

70% of families with CJD share the same allele Families from Libya, Tunisia, Italy,Chile and Spain

share a common haplotype. These populations were expelled from Spain in the

Middle Ages.

Genetic drift and mutation

Probability ofneither of 2 alleles beingmutated is (1-)2

Ft 1

2N1 2 1

1

2N

1 2

Ft 1

gen t-1

gen t

1/2N 1 - 1/2N

Ft 1

2N 1

1

2N

Ft 1no mutation

Equilibrium Between Mutation and Drift

Run the recurrence equation over and over and eventually it will settle down to an equilibrium

Ft 1

2N1 2 1

1

2N

1 2

Ft 1

ˆ F Ft Ft 1 1

1 4N

gen t-1gen t

1/2N 1 - 1/2N

Probability ofpicking 2nd alleleand it not beingmutated

Gene flow

2N

?

m

Probability of identity: FT = [1/2N + (1 - 1/2N) * FT-1] * (1 – m)2

(assumes that the immigrants are different from each other)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 50 100 150 200

N = 100

m = 0

N = 100

m = 0.010

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 50 100 150 200

(Mutation has the same effect)

Probability of identity: FT = [1/2N + (1 - 1/2N) * FT-1] * (1 – μ)2

2N

?

μ

Assumes that each mutation creates a new allele: Infinite allele model

Mutation also retards the loss of genetic variability due to genetic drift

Equilibrium

After a long time (the longer the larger the population) there will be an equilibrium between genetic drift, gene flow and mutation

F and H will not change any more (if everything remains constant !!)

FT = [1/2N + (1 - 1/2N) * FT-1] * (1 – m- μ)2

F 4N μ + 1

1 F 4N m + 1

1

Mutation – drift equilibrium Migration – drift equilibrium

0

P A in generation 1 on the island

P A in generation 2 on the island

1 *

* 1 *

* 1 *t

t

p

p

p m p mp

p p m p p

p p m p p

Change of allele frequency with one way migration •A is fixed on the island•a arrives from the mainland at rate m =0.01

m is the probability that a randomly chosen allele is a migrant

Migration Models – Island Model - One Way Migration

Main LandP*

Islandp

= 10-4

0 1t

tp p

m = 10-2

10

10

10

10

0.484 0.507 1 0.474 0.507

0.484 0.507 1 0.474 0.507

0.484 0.5071

0.474 0.507

0.484 0.5071 0.964

0.474 0.5070.035

m

m

m

m

m

Estimation of m10 generationsPresent allele frequency in “island” = pt = 0.484Allele frequency in mainland p* = 0.507Initial allele frequency in island = p0 = 0.474m = proportion of migrant alleles each generation

0* 1 *t

tp p m p p

Mutation and Migration

10

10

10

10

0.484 0.507 1 0.474 0.507

0.484 0.507 1 0.474 0.507

0.484 0.5071

0.474 0.507

0.484 0.5071 0.964

0.474 0.5070.035

m

m

m

m

m

Estimation of M

10 generationsPresent allele frequency in “island” = pt = 0.484Allele frequency in mainland p* = 0.507Initial allele frequency in island = p0 = 0.474m = proportion of migrant alleles each generation

Many large subpopulationsAverage allele frequency = frequency in migrantsThe change frequency in the subpopulations:

01t

tp p m p p p

0.2 0.8

2p

p

p = 0.2 p = 0.8

m = 0.10

10

10

10

10

0.5 1 0.1 0.2 0.5 0.395

0.5 1 0.1 0.8 0.5 0.605

p

p

Island Model of Migration

Five subpopulations1, 0.75, 0.5, 0.25, 0

Change in allele frequency over time

Summary

Genetic drift: In a finite population allele frequencies fluctuate at random and eventually one allele will be fixed

After 4N generations all individuals descend from one ancestor Genetic diversity is lost more rapidly in small populations Inbreeding reduces the number of heterozygotes Inbred individuals can have lower fitness: inbreeding depression The genetic composition of isolated populations diverges under the

effect of genetic drift Gene flow homogenizes allele frequencies among populations After a long time, the genetic variability in a population reaches an

equilibrium level: mutation – immigration – drift equilibrium