1. 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.

2. 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

3. 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.

4. 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.

5. 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 alleles
gen 0
gen 1
probability = 1/(2N)

6. Inbreeding in finite populations
Therefore, after 1 generation the level of inbreeding is F1 = 1/2N
After t generations the probability is

7. Why?
gen t-1
gen t
Probability of picking 2nd allele
1/(2N)
1 - 1/(2N)

8. More generally Genetic Drift Hartl and Clark p.286
Ft = Probability that any 2 alleles drawn randomly from the population are identical by descent

9. 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

10. Genetic drift Mathematical Model?
Genetic diversity: HT = (1 – 1/2N) * HT-1
Probability of identity: FT = 1/2N + (1 - 1/2N) * FT-1
Average time to fixation: 4N

11. 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

12. 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

13. 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 1 = n Ni Σ
(Harmonic mean)
Ne =
(Nf + Nm)
4NfNm

14. 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.)

15. Effective population size

16. Effective population size

17. 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.

18. 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 variable
Ne =
(Nf + Nm)
4NfNm

19. Backwards: the coalescent approach
Simplification: 0, 1 or 2 offspring
Coalesce: have the same parent
Probability to coalesce: 1/N
Probability Not to coalesce: 1 – 1/N
t generations: (1-1/N)t
Average time to coalesce for 2 genes: N
For the whole population: 2N

20. 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.

21. A new population emerges from a relatively small group of people.
# 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
120,000,000
Iceland
25,000 40
300,000
Newfoundland 16
500,000
Quebec
2,500
12-16
6,000,000
Sardinia
400
1,660,000

22. 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.

23. 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.

24. 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.

25. 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

26. 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

27. 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.

28. Genetic drift and mutation
no mutation
gen t-1
gen t
1/2N
1 - 1/2N
Probability of neither of 2 alleles being mutated is (1-m)2

29. Equilibrium Between Mutation and Drift
Run the recurrence equation over and over and eventually it will settle down to an equilibrium
gen t-1
gen t
1/2N
1 - 1/2N
Probability of picking 2nd allele and it not being mutated

30. Migration and drift
Migrants will also act to counter genetic drift within a population
Introduce new alleles into population
Immigration rate (probability of allele drawn at random being from a migrant) m
N indvs.

31. 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)
N = 100
m = 0
m = 0.01

32. (Mutation has the same effect)? μ
Probability of identity: FT = [1/2N + (1 - 1/2N) * FT-1] * (1 – μ)2
Assumes that each mutation creates a new allele: Infinite allele model
Mutation also retards the loss of genetic variability due to genetic drift

33. 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 m + 1 1
F 
4N μ + 1 1
Mutation – drift equilibrium
Migration – drift equilibrium

34. Migration Models – Island Model - One Way Migration
m is the probability that a randomly chosen allele is a migrant
Change of allele frequency with one way migration
A is fixed on the island
a arrives from the mainland at rate m =0.01

35. Mutation and Migration
Estimation of m
10 generations
Present allele frequency in “island” = pt = 0.484
Allele frequency in mainland p* = 0.507
Initial allele frequency in island = p0 = 0.474
m = proportion of migrant alleles each generation

36. Estimation of M 10 generations
Present allele frequency in “island” = pt = 0.484
Allele frequency in mainland p* = 0.507
Initial allele frequency in island = p0 = 0.474
m = proportion of migrant alleles each generation

37. Island Model of Migration
Many large subpopulations
Average allele frequency
= frequency in migrants
The change frequency in the subpopulations:
p = 0.2
p = 0.8
m = 0.10

38. Change in allele frequency over time
Five subpopulations
1, 0.75, 0.5, 0.25, 0

39. Change in Allele Frequency Over Time The Effect on the Fixation Index
total number of alleles = 2N
m = proportion of alleles replaced by alleles from migrants
2Nm = number of migrant alleles in any generation
Assumptions:
N is large
m is small

40. Effect of Migration on Genetic Divergence
Extreme case Nm =0 F hat =1
Nm = one migrant every fourth generation: F hat = 0.50
Nm = one migrant every second generation: F hat = 0.33
Nm = 1 one migrant every generation: F hat = 0.20
Nm = 2 two migrants every generation: F hat = 0.11
The equilibrium frequency for the fixation index decreases as the number of migrants increases

41. Quantitative Genetic Variation
The loci involved in quantitative traits are often unknown, and their slight effect on the phenotype does not allow to count alleles in order to determine variation
Quantitative genetic variation is measured statistically: one estimates the variance of the trait in a population
VP = VG + VE (+VGxE + cov(G,E))
The variance has the advantage to be addititve: the variance attributable to several factors can be added to obtain the total variance.

42. Heritability h2 = VG /(VG + VE )
Proportion of genetic variance in the phenotypic variance
h2 = VG /(VG + VE )
Heritability can be measured from correlations between parents and offspring or studies of relatives
Very different degree of heritability in different traits
Artificial selection can be carried out to see if there is a genetic basis for the observed variation
Heritability can also be estimated from the rapidity of change in a trait under artificial selection

43. Genetic distance
Genetic variation among populations can be measured as genetic distance
Example: Nei’s genetic distance D
Probability of identity of two genes: J=pi2 J1, J2, J12
Index of genetic identity:
Genetic distance: D = -ln(I)
There are many other estimators for genetic diversity, some defined particularly for certain types of genetic markers

44. Collared lemmings on small islands (1)
Microsatellite data (4 loci):
Average He = 0.83
Kent region FST = 0.047
(Ehrich et al. 2001)

45. Collared lemmings on small islands (2)
In isolated small populations, variation is lost by genetic drift
E(H) 
4Nμ + 1
4Nμ
at equilibrium
Observed H = Nμ  4.9
Average μ for microsatellites:
5*10-4 N = (10 x) 5* N = 245
The island populations are probably not isolated. Population size (or μ) would have to be much larger than observed in order to maintain the observed level of genetic diversity.

46. Collared lemmings on small islands (3)
Isolated small populations diverge under the effet of genetic drift
FT = [1/2N + (1 - 1/2N) * FT-1] * (1 – m)2
FST = Nm  4.4 immigrants (at equilibrium)
In order to maintain high genetic diversity in small island populations, some migrants have to cross the ice every year.
Alternatively the islands have to be recolonized relatively often after local extinctions

47. Several demes: differentiation
A large population is divided into local demes
Genetic drift will occur in each deme and make allele frequencies diverge
The probability of IBD in each deme will increase
After t generations on average F = 1 – (1 – 1/2N)t
When in all demes all individuals are descendent from one ancestor F = 1
FST is used as measure for population differentiation
Two etimates:

48. Zygosity in the infinite alleles model
Any number of distributions of allele frequency can result in the same homozygosity
Effective number of alleles
The number of equally frequent alleles that would be required to produce the same homozygosity as that actually observed
Population 1: p = 0.7, q = 0.1, r = 0.1, s = 0.1 ke = 1.92
Population 2: p = 0.5, q = 0.3, r = 0.2 ke = 2.63
Population 3: p = 0.6, q = ke = 1.92
Population 4: p = 0.5, q = ke = 2.00

49. Selective neutrality and the infinite alleles model
Amino acid polymorphisms
Are amino acid polymorphisms are selectively neutral?
1. Examine allozyme polymorphisms
Plug in observed homozygosities
Estimate Nm
approximately 10-6
N =
Reasonable?
2. Compare observed distribution of heterozygosity with an observed distribution
Observed heterozygosity of 74 genes (shaded bars)
Expected heterozygosity (open bars)
Are these different?

50. 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