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

1 4G

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.

Panthera pardus nimr

Example

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.

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.

Effective population size

When the number of individual vary through the time

generation 1 = 10,000 individualsgeneration 2 = 10,000 individualsgeneration 3 = 100 individuals (bottleneck)generation 4 = 10,000 individualsgeneration 5 = 10,000 individuals

Examples when Ne and N differ

Bottleneck

B

B

b

Bb

b

b

b

b

b

b

b

B

B

B

b

b

b

b bb

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.

The effective size of the population is closer to 100 individuals than to 1,000.

When the number of individual vary through the time

generation 1 = 10,000 individualsgeneration 2 = 10,000 individualsgeneration 3 = 100 individuals (bottleneck)generation 4 = 10,000 individualsgeneration 5 = 10,000 individuals

Bottleneck

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 2

1 2 0

1 1 1'( ) (1 ) '( 1) (1 )(1 ) '( 2)

2 2 2

1 1 1'( ) (1 )(1 ) (1 ) '(0)

2 2 2

t t t

t t

H t H t H tN N N

H t HN N N

When size varies

1 1'( 1) (1 ) '( )

2 21

'( 1) (1 ) '( )2

1'( ) '(0)(1 )

2t

G t G tN N

H t H tN

H t HN

Derivation of Ne when population size varies

2

1 1(1 ) 1 ( )

2 2t t

ON N N

1'( ) '(0)(1 )

2tH t H

N

1 2 0

1 1 1'( ) (1 )(1 ) (1 ) '(0)

2 2 2t t

H t HN N N

Approximations

21 2 0 0 1

1 1 1 1 1 1(1 )(1 ) (1 ) 1 ( ) ( )

2 2 2 2 2t t t

ON N N N N N

1 2 0

1 1 1 1(1 ) (1 )(1 ) (1 )

2 2 2 2t

t tN N N N

Derivation of Ne when population size varies

0 1

0 1

0 1

1 11 1 ( )

2 2 2

1 1

2 2

1 1 1 1( )2 2

t

t

t

t

N N N

t

N N N

N t N N

N is big, 1/N2 is small…

21 2 0 0 1

1 1 1 1 1 1(1 )(1 ) (1 ) 1 ( ) ( )

2 2 2 2 2t t t

ON N N N N N

1 2 0

1 1 1 1(1 ) (1 )(1 ) (1 )

2 2 2 2t

t tN N N N

2

1 1(1 ) 1 ( )

2 2t t

ON N N

Derivation of Ne when population size varies

0 1

1 1 1 1( )2 2e tN t N N

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’.

In lions Nm< Nf

Examples when Ne and N differ

When the number of breeding male Nm and breeding female Nf differ.

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.

Lion group structure

Ne is the effective population sizeNf is the number of femalesNm is the number of males

fm

fme NN

NNN

4

Drift and sex ratio: the formula

(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 of

Females

sex ratio

4NmNf Nm+Nf Ne

m/f

100100140000200200

901100.81818239600200198

801200.66666738400200192

701300.53846236400200182

601400.42857133600200168

501500.33333330000200150

401600.2525600200128

301700.17647120400200102

201800.1111111440020072

101900.052632760020038

51950.025641390020019.5

11990.0050257962003.98

2: Population genetics

Conservation BiologyWhich 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]

Dasypus novemcinctus (nine banded armadillo)

Armadillo founder effect

Armadillo founder effect

•The expansion of the range of the nine-banded 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 effectThe 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).

2 haplotypes

10 haplotypes

greatest distance between two captured armadillos was 32 km

greatest distance between two captured armadillos was 1,026 km

outgroupUSA armadillo are significantly less diversed than those of French Guiana

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