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
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