Transcript Document

2: Population genetics
Problem of small population size
Small populations
are less fit (more
vulnerable) than
large populations
In small populations drift is dominant.
1
G
1  4 Nu
Small N -> Large G
-> low genetic diversity.
In small populations each individual has higher
chances to be homozygous for deleterious genes.
This is the same problem as in inbreeding.
Notably, small populations do not harbor more
deleterious genes, they just have more homozygotes
for these genes
Population size and drift-selection balance
Selection helps fixing “good” alleles (alleles
that are positively selected). In small
populations drift can be a stronger evolutionary
force than selection and good alleles may
disappear.
Conclusion
Population size and the level of genetic diversity
of a population are good indicators of the health
of a population.
Example
Panthera pardus nimr
2: Population genetics
Effective population size
It was noted that lab populations of drosophila
tend to loose their genetic diversity faster than
expected by genetic drift models.
The reason is that in a population not all individual
reproduce. In other words, the number of
individuals do not always reflects the number of
individuals that contribute their alleles to the next
generation.
Effective population size
The effective size of a population (Ne) is the size
of an ideal population that has the same
properties with respect to genetic drift as our
actual population.
Examples when Ne and N differ
When the number of individual vary through the
time
generation 1 = 10,000 individuals
generation 2 = 10,000 individuals
generation 3 = 100 individuals (bottleneck)
generation 4 = 10,000 individuals
generation 5 = 10,000 individuals
Bottleneck
b
B
b
B
B
B b
b
b
B
b
b
b
b
B
b b
b
b
b
b
b
b
Bottleneck
Population bottlenecks occur when a population
size is reduced for at least one generation. Because
genetic drift acts more quickly in small
populations, undergoing a bottleneck can
substantially reduce the genetic variation of a
population and change the frequencies of alleles,
even if the bottleneck does not last for very many
generations.
Bottleneck
When the number of individual vary through the
time
generation 1 = 10,000 individuals
generation 2 = 10,000 individuals
generation 3 = 100 individuals (bottleneck)
generation 4 = 10,000 individuals
generation 5 = 10,000 individuals
The effective size of the population is closer to
100 individuals than to 1,000.
Founder effect
The loss of genetic variation when a new colony
is established by a very small number of
individuals from a larger population
Derivation of Ne when population size varies
1
1
G '(t  1) 
 (1 
)G '(t ) 
2N
2N
1
H '(t  1)  (1 
) H '(t ) 
2N
1 t
H '(t )  H '(0)(1 
)
2N
When size varies
1
1
1
H '(t )  (1 
) H '(t  1)  (1 
)(1 
) H '(t  2) 
2 Nt 1
2 Nt 1
2 Nt  2
1
1
H '(t )  (1 
)(1 
)
2 Nt 1
2 Nt  2
1
(1 
) H '(0)
2 N0
Derivation of Ne when population size varies
1
1
H '(t )  (1 
)(1 
)
2 Nt 1
2 Nt  2
H '(t )  H '(0)(1 
1
(1 
) H '(0)
2 N0
1 t
)
2N
1 t
1
1
(1 
)  (1 
)(1 
)
2N
2 Nt 1
2 Nt  2
1
(1 
)
2 N0
Approximations
(1 
1 t
t
1
)  1
 O( 2 )
2N
2N
N
(1 
1
1
)(1 
)
2 Nt 1
2 Nt  2
(1 
1
1
)  1 (

2 N0
2 N0

1
1
)  O( 2 )
2 Nt 1
N
Derivation of Ne when population size varies
1 t
1
1
(1 
)  (1 
)(1 
)
2N
2 Nt 1
2 Nt  2
1
(1 
)
2 N0
1 t
t
1
(1 
)  1
 O( 2 )
2N
2N
N
(1 
1
1
)(1 
)
2 Nt 1
2 Nt  2
(1 
1
1
)  1 (

2 N0
2 N0
N is big, 1/N2 is small…

1
1
)  O( 2 )
2 Nt 1
N
t
1
1
 1 (

2N
2 N0
t
1


N 2 N0
1 1 1
 (

N t 2 N0
1

)
2 Nt 1
1

2 Nt 1
1

)
2 Nt 1
Derivation of Ne when population size varies
1 1 1
 (

Ne t 2 N0
1

)
2 Nt 1
An ideal population with size Ne will behave
similar to a population that varies in size
according to the above equation in terms of H’.
Examples when Ne and N differ
When the number of breeding male Nm and
breeding female Nf differ.
In lions Nm< Nf
Lion group structure
Lions are the only 'social' cats, whereby related
female lions live together and form groups
called 'prides'. Lion prides are family groups
with all of the females related, mothers and
daughters, sisters and cousins, etc, While
female lions will live with the pride for life,
male lions will only last two to four years
before they are evicted or killed by a new
coalition of male lions that take over the pride.
Drift and sex ratio: the formula
Ne 
4Nm  N f
Nm  N f
Ne is the effective population size
Nf is the number of females
Nm is the number of males
(without proof)
Example
A population of 100 individuals, consisting of
10 breeding males and 90 breeding females ,
would lose genetic variability as rapidly as a
population consisting of only 18 males and 18
females or 36 individuals
Number
of Males
Number sex ratio
of
m/f
Females
4NmNf
Nm+Nf
Ne
100
100
1
40000
200
200
90
110
0.818182
39600
200
198
80
120
0.666667
38400
200
192
70
130
0.538462
36400
200
182
60
140
0.428571
33600
200
168
50
150
0.333333
30000
200
150
40
160
0.25
25600
200
128
30
170
0.176471
20400
200
102
20
180
0.111111
14400
200
72
10
190
0.052632
7600
200
38
5
195
0.025641
3900
200
19.5
1
199
0.005025
796
200
3.98
2: Population genetics
Conservation Biology
Which species to protect?
(species that lost a lot of diversity
or more variable species)
Where to place natural reserves?
(should we consider areas that have a lot of
species, or areas that have genetically
different individuals)
What should be the size of reserves?
(a too small reserve will not protect against
drift)
2: Population genetics
Example of founder effect
[Huchon et al. 1999 Molecular Ecology 8, 1743–1748]
Armadillo founder effect
Dasypus novemcinctus (nine banded armadillo)
Armadillo founder effect
•The expansion of the range of the ninebanded armadillo into the USA is unique
among placental mammals in that it has been
occurring since the mid-19th century at a
mean rate of 10 km a year.
•This fast migration may have resulted from a
low predation on adults, a lack of natural
competitors, a weak homing ability (although
it is rather sedentary with small home
ranges), and human-induced translocations.
Armadillo founder effect
Armadillo founder effect
The researchers compared the genetic
diversity of the North-America armadillo
population to that of French Guiana
Haplotype
They compared the number of haplotypes =
combinations of one or more alleles (e.g., in
a sequence, each unique set of SNPs is
considered an haplotype).
They sequenced the mitochondrial
control region (which is relatively highly
variable).
outgroup
USA armadillo
are significantly
less diversed
than those of
French Guiana
2 haplotypes
greatest distance between
two captured armadillos
was 1,026 km
10 haplotypes
greatest distance between
two captured armadillos was 32 km
2: Population genetics
Speciation and geographical distribution
•Populations that are at the limit of the species
range tend to be slightly different from the rest of
the populations.
•New species have higher chances to appear
from these populations.
2: Population genetics