Genetic Drift -- the role of finite population size
Evolution can be thought of as a change in allele frequency, and finite
population size alone insures that evolution will occur through sampling error.
For example, suppose a population has a gene pool with two alleles, say H and T,
each with a frequency of 0.5 Suppose N (a finite number) of gametes are drawn
from this gene pool to form the next generation. Will the frequency of H and T be
0.5 in this finite population? If not, evolution will have occurred.
You can simulate this situation. E.g., let N=10, and place 10 coins in a box,
shake the box, and count number of heads (i.e., allele "H"). Do this several times to
show that finite population size causes random changes in allele frequency. These
random changes in allele frequency due to sampling error in finite populations is
known as "genetic drift." Genetic drift is an evolutionary force that can alter
populations through time, and shows that the Hardy-Weinberg "equilibrium" does
hold exactly for any finite population. Now use 20 coins for the simulation, and
repeat several times. Results will show that there are still random deviations from
0.5, but the proportional deviation from 0.5 is smaller when N=20 then when N=10.
This shows that the amount of evolutionary change associated with random
sampling error is inversely related to population size; the larger the population, the
less the allele frequency will change. Hence, genetic drift is most effective as an
evolutionary force when N is small.
The coin box simulation above only simulates one generation of genetic drift
starting with an allele frequency of 0.5. It does not simulate the fact that the
evolutionary changes induced by drift tend to accumulate through time. In the coin
box experiment, it was equally likely to deviate above and below 0.5. Hence, on the
average (i.e., in a large number of identical populations), the average allele
frequency remains 0.5, although in any individual population, it is quite likely that
the allele frequency will change from 0.5. The fact that deviations are equally likely
above and below 0.5 simply means that there is no direction to pure genetic drift.
However, suppose drift causes the allele frequency to change from 0.5 to 0.6 in one
particular population. How about the next generation? Is it equally likely to be above
or below 0.5, as was the first generation? The answer is no, drift at one generation is
always around the allele frequency of the previous generation only; and allele
frequencies in more ancient generations are totally irrelevant. THERE IS NO
TENDENCY TO RETURN TO ANCESTRAL ALLELE FREQUENCIES. Hence, drift
in the second generation will cause deviations around 0.6. This is turn means that
after two generations of drift and given that the first had a deviation above 0.5, it is
no longer true that deviations will be equally likely above and below 0.5; now, the
allele frequencies are more likely to stay above 0.5. With each passing generation, it
becomes more and more likely to deviate from the initial conditions. The action of
drift over several generations can be simulated on a computer in which each
generation drifts around the allele frequency of the previous generation only.
Handouts show the impact of this simulated drift in populations of size 10 and 25.
In both cases, one starts out with the initial allele frequency of 0.5, but with
increasing generation number, more and more of the populations deviate from 0.5,
and by larger amounts. HENCE, CHANGES CAUSED BY GENETIC DRIFT
ACCUMULATE WITH TIME. As can be seen by contrasting N=10 with N=25, the
smaller N, the more radical these changes will be in a given amount of time, but
even with the larger N, substantial changes have occurred by generation 20. Hence,
N determines the rate of change caused by drift, but even very large populations can
be effected by drift if given enough time. Also note in these simulations
(particularly for N=10), that eventually all populations go to allele frequencies of 0
(loss of the allele) or 1 (fixation of the allele). Genetic drift, like any other
evolutionary force, can only operate when there is genetic variability. Hence, as
long as p is not equal to 0 or 1, drift will cause changes in allele frequency. However,
once an allele is lost or fixed, no more genetic drift is possible, and the allele stays
lost or fixed, barring new mutations or reintroduction by gene flow. Hence, drift is
like a genetic fly paper. The walls are loss and fixation, and sooner or latter
(depending upon population size), the fly (allele frequency) will hit a wall and be
"stuck". These properties of genetic drift have been demonstrated empirically by
Buri (handout). He initiated 107 populations of 8 males and 8 females of Drosophila
melanogaster, all with two eye color alleles (bw and bw75) at equal frequency. The
handout shows what happened over 19 generations. Note the following:
1. When allele frequencies are averaged over all 107 populations, there is
almost no change from the initial allele frequencies of 0.5. DRIFT HAS NO
DIRECTION.
2. The chances of any subpopulation deviating from 0.5 and the magnitude of
that deviation increase with each generation. DRIFT ACCUMULATES WITH
TIME.
3. With increasing time, more and more populations become fixed for one
allele. Ultimately, all populations are expected to become fixed. HENCE, DRIFT
CAUSES THE LOSS OF GENETIC VARIABILITY WITHIN A POPULATION.
4. All populations started out with identical gene pools, but with time, the
populations deviate not only from the ancestral condition, but from each other as
well. E.g., at generation 19, 30 populations are fixed for bw, 28 for bw75. These
populations no longer share any alleles at this locus, even though they are
derived from genetically identical ancestral populations. HENCE, DRIFT CAUSES
AN INCREASE OF GENETIC VARIABILITY BETWEEN POPULATIONS.
Generation
Number of
Populations
Fixed for bw
Number of
Populations
Fixed for bw75
1
0
0
2
0
0
3
0
0
4
0
1
5
0
2
6
1
3
7
8
18
23
30
28
7
8
9
10
11
12
13
14
15
16
17
18
19
0
2 4
6 8 10 12 14 16 18 20 22 24 26 28 30 32
Number of bw 75 genes
Allele Frequency distributions in 107
populations of 16 Drosophila melanogaster
each, discrete generations
Founder and Bottleneck Effects
As shown previously, genetic drift can cause its most radical and rapid changes
in small populations. However, because there is no tendency to return to the initial
state, even one generation of very small size can induce radical evolutionary
changes that will tend to persist. Indeed, if the population size grows large after a
generation of small size, the increased population size tends to decrease the impact
of subsequent drift, so that the drift effects that occurred in the generation of small
size tend to be "frozen in" the population for many future generations. Hence,
genetic drift can cause radical changes in a population that is normally large as long
as either 1) the population was derived from a small number of founding
individuals (founder effect), or the population went through one or more
generations of very small size (bottleneck effect).
Examples of founder effects.
1. 5-alpha-steroid reductase deficiency. All cases derived from Alta-Gracia. It is in
high frequency in the village of Salinas, Santa Domingo, because Alta-Gracia was
one of just a few founders 7 generations ago.
2. Amish colonies. Founded in Penn. in 1720-1770, usually by less than 200 people.
Only married within religion, and few converts after 1800 -- hence have socially
defined founder event, but genetic and evolutionary consequences are very real.
E.g., currently about 8,000 Amish in Lanchaster, Co., but derived from only about 100
founders. A genetic disease known as Ellis-van Creveld syndrome (dwarfism, heart
trouble, extra digits) is very rare in general population -- only 50 cases in the world
during this century. However, in the Lancaster Amish, p=.13, and 43 of the 50 cases
were found in the Lancaster Amish. All the Amish cases trace back to Mr. and Mrs.
Samuel King, who joined group in 1744. Hence, a gene very rare in humanity in
general, through the founder effect, became very common in this one
reproductively isolated subpopulation. Amish show other genes in high frequency
that are rare elsewhere. E.g., the genetic disease pyruvate kinase deficiency found
only in the Amish -- all cases trace back to Strong Jacob Yoder, 1742. The Amish in
Ohio have a high incidence of hemophilia -- all cases trace back to 2 sisters who
converted in 1820.
Example of the Bottleneck Effect:
Tristan da Cunha is an example of both founder and bottleneck effects. It was
founded as a religous colony about 1816 with only 20 initial founders by 1822. The
figure below shows the changes in population size on the island from 1816 to 1960.
Because we have complete pedigree information over the entire colony history, we
can reconstruct the gene pool at any time as the percentage of genes in the total
population derived from a particular individual (see histograms). The first
histogram shows the gene pool composition in 1855 & 1857. Note from the size
graph that a radical drop in population size occurred between 1855-1857. This was
caused by a boat capsizing that drowned most of the adult males of the colony. After
their death, many of their wives and children left as well. There was another
260
Population Size
220
180
Population Size of Tristan
da Cunha on Dec. 31 of each
year from 1816 to 1960
140
100
60
20
1820
1840
1860
1880
1900
DATE
1920
1940
1960
bottleneck around
1890
when a popular minister died; many people didn't like his replacement and left.
Note that in going from 1855 to 1857, the gene pool composition changes quite a bit;
relative contributions of some individuals shift radically (eg. 1-4), and many
individuals just drop out entirely (loss due to drift). However, the population grew
steadily between 1857-1884. With the exception of a few new immigrant individuals
(21-26), the basic shape of histogram changed very little in those 27 years (the second
histogram); much less change than in the 2 years between 1855-1857. Hence,
changes induced by the first bottleneck were "frozen in" by subsequent population
growth. Once again, many changes occurred between 1884-1891 (the second
bottleneck) (third histogram), but the shape of the histogram changes very little
from 1891-1961 (fourth histogram, with the exception of additional immigrants)
during the phase of increased population growth.
Tristan da Cunha Before & After the First Bottleneck
20
18
1855
1857
14
12
10
8
6
4
2
Founder
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
0
1
% Contribution to Gene Pool
16
Tristan da Cunha During Growth After First Bottleneck
20
1857
16
1884
14
12
10
8
6
4
2
Founder
25
23
21
19
17
15
13
11
9
7
5
3
0
1
% Contribution to Gene Pool
18
Tristan da Cunha Before & After 2nd Bottleneck
20
1884
16
1891
14
12
10
8
6
4
2
Founder
25
23
21
19
17
15
13
11
9
7
5
3
0
1
% Contribution to Gene Pool
18
Tristan da Cunha During Recovery From 2nd Bottleneck
% Contribution to Gene Pool
20
18
1891
16
1961 (minus immigrants)
14
12
10
8
6
4
2
Founder
Founder effects and pedigree inbreeding
.05
.04
.03
.02
.01
18- 30 40 50
60 70 80 90 1900 10 20 30
40 50
60
Decade of Birth
On Tristan da Cunha figures, note the increase in mean inbreeding coefficient
(pedigree definition -- prob. of uniting gametes bearing alleles identical by descent)
25
24
23
22
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
with time. This occurred despite the fact that the people avoided incest as much as
possible. The reason is straightforward. Because of the founder effect and the closed
population, everybody quickly became related to everyone else. By 1871 all females
on the island were related to all potential male mates; hence, pedigree inbreeding
became unavoidable.
A second example is Speke's gazelle. The entire North American herd was derived
from 1 male and 3 females. Obviously, from very first generation, all individuals
breed in captivity were related (all had to have single male founder as a common
ancestor). Hence, pedigree inbreeding unavoidable. Thus, founder and bottleneck
effects promote rapid increases in pedigree inbreeding.
Founder effects and disequilibrium
Just as drift causes changes in allele frequencies, it also changes multi-locus
gamete frequencies. Tends to destroy linkage equilibrium and creates many
associations. If the loci are closely linked, the particular associations will persist for
many generations, causing extensive disequilibrium. Eg., G-6-PD deficiency and
color blindness in Sardinia. The disequilibrium induced by founder and bottleneck
effects can interact strongly with system of mating. Eg., Drosophila melanogaster
has a pheromone system leading to strong disassortative mating. Genetically
controlled by a handfull of loci scattered over the genome. Dissassortative mating
maintains heterozygosity at these loci. However, D. mel. has only a few
chromosomes (1 X, 2 major autosome, and a very small autosome), and little
recombination among these chromsoomes. Hence, with a severe bottleneck effect,
virtually the entire genome will be in linkage disequilibrium with the pheromone
loci. Hence, disassortative mating at the pheromone loci will also effectively cause
dissassortative mating at all loci for a few generations after the bottleneck effect.
Hence, if the small population size does not persist long enough for the
disequilibrium to break down, disassortative mating and disquilibrium insure that
very little genetic variation will be lost due to drift during a temporary bottleneck or
founder event. Other Drosophila (e.g., D. pseudoobscura) do not have this
pheromone mating system. Hence, different species show different genetic and
evolutionary responses to founder and bottleneck effects as a function of the
recombinational properties of their genomes and their system of mating.