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 NNNNtN1...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)211( HN

H t

et −=

qqqNqT e )1ln()1(4)( −−

−= T (p) ! 4Ne

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 Wright Beebe 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 Wright Beebe 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)

T S

F-Coefficients and Deviations from Expected Heterozygosity

  FIS: deviation from H-W proportions in subpopulation

E

O

HHF −=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