Download Genetic Drift The Founder Effect The Founder Effect

Genetic Drift
• toss a coin 10 times
• odds of a head (blue eyes) = 0.5 / toss
• odds of 10 heads = 0.5 = 1/1000
• odds of 6 heads ! 1/5
• toss a coin 1000 times, the chance of flipping
10
The Founder Effect
• part one: a new population is established
from a small number of colonizers or
survivors.
• part two: their gene frequencies are
unrepresentative of those in their
predecessor population.
• what is the chance a subsample of the
originating population will lose an allele?
600 heads is a very much smaller number.
The Founder Effect
• high frequencies of otherwise rare
diseases in populations founded by small
number of colonists.
•
achromatopsia (total colour blindness / rod
monochromy)
•
recessive, occurs at frequency <0.0001 (carriers !
1/200) -- a cone defect found on cVIII.
•
5-10% occurence; carriers found > 30% in
Pingelapese.
•
3000 Pingelaps founded from 20 survivors of
Typhoon Lengkieki in 1775.
• chance an individual founder is AA = p
• chance two individuals are AA = (p )
• chance n individuals are AA = (p )
• chance of total homozygosity in founder
2
2 2
2 n
population: (p2)n+(q2)n
e.g., chance of losing an allele that has frequency of 10%:
- in founder population of 2: (0.81)2 = 0.64
- in population of 10: (0.81)10 = 0.122
- in population of 20: (0.81)20 = 0.015
Many alleles
General Consequences
• The odds of fixing any single allele by drift
• chance of losing a common allele very
• The probability of losing any allele will be
• drift is adirectional.
• chance of changing gene frequencies
are simply its (frequency2)N
the sum of the other individual fixation
probabilities.
Alleles
1 @ 0.6
2 @ 0.3
3 @ 0.1
probability of losing allele 1 is (0.42)N
= 1 x 10-8
10 founders
probability of losing allele 3 is (0.92)N
= 0.122
• chance of losing some rare alleles is high.
NI
ML
A
1830 - 1904
PN
CI
Allelic Diversity
T
SI
small, even with a strong bottleneck.
very large.
•
Dutch Afrikaaners arrived in S. Africa in 1652 on
one ship.
•
50% of current 2.5 million population have 20
names traceable to that ship. 1/3 white South
Africans descended from 40 founders.
•
Huntington’s Disease, Porphyria variegata at
extremely high frequencies.
>8000 cases alone traceable to
Gerrit Jansz (settler) or Ariaantje
Jacobs (wife)
Fixation by Drift
• drift is integrally related to population size.
• due to drift alone, the chance of an
individual copy of a gene fixing is 1/2N (if
population is diploid).
• assuming there are multiple copies of the
same gene (allele) then the probability of an
allele fixing is: its copy number / 2N.
• sooner or later one allele will fix due to
selection or drift.
• heterozygosity -- the frequency of
heterozygotes -- will decline with time.
population heterozygosity
Sewall Wright
frequency of allele
It follows that...
N=40
• by drift, the number of heterozygotes in the
N=400
next generation will be H* {1-1/2N}
generations
Buri’s Drift Exp’t
• founded and maintained 107 populations of
D. melanogaster with 8 pairs each (N = 16).
• all founders heterozygous for bw /bw
• no measured fitness effect of bw mutant
+
75
allele in large cage experiments
• ran experiment for 19 generations.
75
generations
Effective Population Size
•
Wrightian prediction,
N=16
populations are genetically never as large as their census
size.
•
•
observed & N=9
differences in survival and repro success lead to unequal
contributions of gametes to next generation.
•
•
•
Ne reflects the
variance in male mating success may be particularly high.
skewed sex ratios have a strong effect on Ne
the effective population size is sensitive to population
fluctuations / bottlenecks over time.
Sexual Selection & Ne
Calculating Ne
an approximation of effective size that accounts for
sex ratio is given by:
Ne ! (4Nm* Nf) / (Nm + Nf)
• a population with 100 breeding males and
900 females has an effective size of 360.
• in lekking species or those with extreme
dominance heirarchies, whole social groups
of females may mate with the same male.
Ne = (4Nm* Nf) / (Nm + Nf) ! 4
[this is approximate because fitness is not taken into consideration: all
organisms have equal survival and reproductive success].
note: this calculation assumes only one round of breeding and
no migration between groups.
Measures of Diversity
Habitat Fragmentation
•
when populations become
fragmented, interrupted gene
flow will often lead to:
Components of Heterozygosity
1
1. Allele Richness: the average number of
alleles per locus in the genome.
• increased homozygosity via
2. Genetic Polymorphism: the fraction of loci
in the genome with 2+ alleles at frequency
of >0.01.
drift and the Wahlund Effect.
• inbreeding depression
• reduced adaptability
•
2
less variation to resist environmental
challenges, disease, parasitism.
Collared Lizards
3
Both strongly related to population size (e.g., see study by Young et al.
1996 in F&H)
Ozark Collared Lizards
• Relict populations in the Ozark Mountains
•
occupy small glades (remnants of SW deserts) that
were once isolated by savannah lands.
•
savannahs burned periodically.
•
clear cutting & fire extinguishing
• human intervention:
•
•
allowed oak-hickory forest to take over.
allowed red cedar to grow into glades.
MDH allele
r DNA
(s/f)
(i-iii)
mt DNA
(a-d)
Habitat Fragmentation in Glade
Populations
Perils of Fragmentation
• Occupants of any given glade genetically
homogeneous
•
•
•
unable to adapt to further changes in the environment
sitting ducks for diseases
ever more sickly due to inbreeding depression.
• Remediate via restoration of empty glade
populations, creation of migration corridors
with controlled burns.
•
When mating is non-random it can lead to reduction
in the effective population size.
•
Inbreeding occurs when genetic relatives breed with
one another.
• Inbreeding results in an increase in homozygosity in
populations.
• Inbreeding does not directly affect allele frequencies.
Frequency of Hetero- or Homozygotes
Inbreeding
Inbreeding via Selfing
1
HETERO
0.9
HOMO
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
1
2
3
4
Generations of Self-Fertilization
Frequency of heterozygotes is halved in each generation
More General Treatment of Inbreeding
• Coefficient of Inbreeding, F, is the probability that
two alleles in an individual are identical by descent.
•
i.e., that coinheritance is non-random due to ancestry
Modifying H-W =bm
• If F represents a probability of non-random inheritance of
two copies of the same allele, then it can be added to the
calculation of expected genotype frequencies as follows:
• The probability that offspring of two half-siblings
will inherit two identical alleles is 1/8.
AR
AR
x
0.5
x
A1
A2
x
AR
AR
A1
AR
0.5
A1
AR
0.5
0.5
A1
A1
The odds progeny of the
union of two half-siblings will
inherit one of the two alleles
as a homozygote
=
1/2 x 1/2 x 1/2 x 1/2
=
1/16
Expected
Frequency
Homozygote
Expected
Frequency
Heterozygote
Expected
Frequency
Homozygote
A1 A1
A1 A2
A2 A2
p2(1-F) + pF
2pq(1-F)
q2(1-F) + qF
Inbreeding depression
Kissing Cousins
-
-
1/32 loci will be homozygous in progeny of first
cousins.
-
e.g., 1/64 recessive lethals would be expressed.
HF (inbred population) = HOutbred(1-F)
70
Number of Lines
• Half-siblings have 1/4 of loci identical by descent.
• First cousins have 1/8 of loci IBD.
80
60
50
40
30
20
10
0
0
5
10
15
20
25
30
Generations of full sib mating
• exposure of recessive deleterious variation
leads to a syndrome of low performance:
– low survival & low fertility
data from Chippindale, unpublished
• Meagher et al. (PNAS 2000) examined the
effects of inbreeding on wild house mice
under two different conditions:
-
laboratory standard conditions
semi-natural conditions in a barn environment
!
•
males establish territories, fight, court &c.
they also tested both males and females.
outbred
inbred
I
semi-natural
laboratory
Mutational Meltdown
Population
Size Reduced
More Mating
Between
Relatives
Fitness
Reduced
Expose
Deleterious
Recessives
genetic load increases
Conservation of the Greater Prairie
Chicken
• allelic richness had declined to about 60%
of neighbouring populations (or since the
1930s).
• strategies based on habitat recovery were
largely unsuccessful.
• importation of neighbouring stock from
other states lead to dramatic reversal
– a little bit of gene flow goes a long way
– conservation also needs to be cognizant of the
breeding system and effective population size
Meltdown or Vortex?
• Inbreeding is a form of genetic drift
• Causes exposure of deleterious recessive
variation hidden in large populations.
• As fitness declines because of increased
Genetic Load, population size shrinks
further.
• This intensifies drift (i.e., further
inbreeding)
• Cycling / synergism of effects leads to
extinction.