Lecture 12: Effective Population Size and Gene Flow October 5, 2012.

Lecture 12: Effective Population Size and Gene Flow

October 5, 2012

Last Time

Interactions of drift and selection

Effective population size

Today

Effective population size calculations

Historical importance of drift: shifting balance or noise?

Population structure

Factors Reducing Effective Population Size

Unequal number of breeding males and females

Unequal reproductive success

Changes in population size through time

Bottlenecks

Founder Effects

Table courtesy of K. Ritland

Effective Population Size: Effects of Different Numbers of Males and Females

See Hedrick (2011) page 213 for derivation

Elephant Seals Practice extreme

polygyny: one male has a harem with many females

Examined reproductive success of males using paternity analysis on Falkland Islands

Results:

7 harems with 334 females

32 mating males detected

What is Ne?

What if sneaky males were unsuccessful?

Assumptions?

Fabiani et al. 2004: Behavioural Ecology 6: 961

Small population size in one generation can cause drastic reduction in diversity for many future generations

Effect is approximated by harmonic mean

Variation of population size in different generations

i

e

N

tN

1

te NNNNtN

1...

11111

321

See Hedrick (2011) page 219 for derivation

Example: Effect of Varying Population Size Through Time: Golden Lion Tamarins (Leontopithecus rosalia)

Native to coastal Brazilian Rainforests

Estimated Population Censuses:

1940: 10,000

1970: 200

2000: 2,000

What is current effective population size?

i

e

N

tN

1

http://en.wikipedia.org

http://nationalzoo.si.edu

Effective population size is drastically reduced

Effect persists for a very long time

Reduced allelic diversity

Reduced heterozygosity

Genetic Implications of Bottlenecks and Founder Effects

0)2

11( H

NH t

et

q

qqNqT e )1ln()1(4

)(

For small q

Populations Resulting from Founder Effects and Bottlenecks Have Elevated Heterozygosity

Heterozygosity recovers more quickly following bottleneck/founding event than number of alleles

Rare alleles are preferentially lost, but these don’t affect heterozygosity much

Bottleneck/founding event yields heterozygosity excess when taking number of alleles into account

Also causes enhanced genetic distance from source population

Calculated using Bottleneck program (Cornuet and Luikart 1996)

Historical View on Drift Fisher

Importance of selection in determining variation

Selection should quickly homogenize populations (Classical view)

Genetic drift is noise that obscures effects of selection

Wright

Focused more on processes of genetic drift and gene flow

Argued that diversity was likely to be quite high (Balance view)

Controversy raged until advent of molecular markers showed diversity was quite high

Neutral theory revived controversy almost immediately

Genotype Space and Fitness Surfaces All combinations of alleles at a locus is genotype space

Each combination has an associated fitness

A1

A2

A3

A4

A5

A1 A2 A3 A4 A5

A1A1 A1A2 A1A3 A1A4 A1A5

A1A2 A2A2 A2A3 A2A4 A2A5

A1A3 A2A3 A3A3 A3A4 A3A5

A1A4 A2A4 A3A4 A4A4 A4A5

A1A5 A2A5 A3A5 A4A5 A5A5

Fisherian View Fisher's fundamental

theorem: The rate of change in fitness of a population is proportional to the genetic variation present

Ultimate outcome of strong directional selection is no genetic variation

Most selection is directional

Variation should be minimal in natural populations

Wright's Shifting Balance Theory

Genetic drift within 'demes' to allow descent into fitness valleys

Mass selection to climb new adaptive peak

Interdeme selection allows spread of superior demes across landscape

Sewall WrightBeebe and Rowe 2004

Wright's Adaptive Landscape

Representation of two sets of genotypes along X and Y axis

Vertical dimension is relative fitness of combined genotype

Sewall WrightBeebe and Rowe 2004

Wright's Shifting Balance Theory Genetic drift within 'demes' to allow descent

into fitness valleys

Mass selection to climb new adaptive peak

Interdeme selection allows spread of superior demes across landscape

Can the shifting balance theory apply to real species?

How can you have demes with a widespread, abundant species?

What Controls Genetic Diversity Within Populations?

4 major evolutionary forces

Diversity

Mutation+

Drift-

Selection

+/-

Migration

+

Migration is a homogenizing force Differentiation is

inversely proportional to gene flow

Use differentiation of the populations to estimate historic gene flow

Gene flow important determinant of effective population size

Estimation of gene flow important in ecology, evolution, conservation biology, and forensics

Isolation by Distance Simulation

Random Mating: Neighborhood = 99 x 99

Isolation by Distance: Neighborhood = 3x3

Each square is a diploid with color determined by codominant, two-allele locuus

Random mating within “neighborhood”

Run for 200 generations

Wahlund Effect

Separate Subpopulations:

HE = 2pq = 2(1)(0) = 2(0)(1) = 0

HE depends on how you define populations

HE ALWAYS exceeds HO when randomly-mating, differentiated subpopulations are

merged: Wahlund Effect

ONLY if merged population is not randomly mating as a whole!

Merged Subpopulations:

HE = 2pq = 2(0.5)(0.5) = 0.5

Wahlund Effect

Trapped mice will always be homozygous even though HE = 0.5

Hartl and Clark 1997

What happens if you remove the cats and the mice begin randomly mating?

F-Coefficients

Quantification of the structure of genetic variation in populations: population structure

Partition variation to the Total Population (T), Subpopulations (S), and Individuals (I)

TS

F-Coefficients and Deviations from Expected Heterozygosity

FIS: deviation from H-W proportions in subpopulation

E

O

H

HF 1

Recall the fixation index from inbreeding lectures and lab:

)1( ISEO FHH Rearranging:

)1( ISSI FHH Within a subpopulation:

F-Coefficients and Deviations from Expected Heterozygosity

)1( ISSI FHH FIS: deviation from H-W proportions in

subpopulation

FST: genetic differention over subpopulations

)1( STTS FHH

FIT: deviation from H-W proportions in the total population

)1( ITTI FHH

F-Coefficients Combine different sources of reduction in

expected heterozygosity into one equation:

)1)(1(1 ISSTIT FFF Deviation due to subpopulation differentiation

Overall deviation from H-W expectations

Deviation due to inbreeding within populations