Lecture 11: Genetic Drift and Effective Population Size
October 1, 2012
Last Time Introduction to genetic drift
Fisher-Wright model of genetic drift
Diffusion model of drift
Effects within and among subpopulations
Simple Model of Genetic Drift
Many independent subpopulations
Subpopulations are of constant size
Random mating within subpopulations
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Effects of Drift
Within subpopulations
Changes allele frequencies Degrades diversity Reduces variance Does not cause deviations from HWE
Among subpopulations (if there are many)
Does NOT change allele frequencies Does NOT degrade diversity Increases variance in allele frequencies Causes a deficiency of heterozygotes compared to Hardy-
Weinberg expectations (if the existence of subpopulations is ignored) (to be covered in more detail later)
Today
Interactions of drift and selection
Effective population size
Exams!
Effects of Drift Simulation of 4 subpopulations with 20 individuals, 2 alleles
Random changes through time
Fixation or loss of alleles
Little change in mean frequency
Increased variance among subpopulations
Example: Drift and Flour Beetle Color Tribolium castaneum
experiment with lab populations of different sizes
Frequency of body color polymorphisms: single locus, black, red, brown
Why does frequency of wild-type allele increase over time?
Why does this depend on population size?
Conner and Hartl 2004
N=10
N=20
N=50
N=100
Effects of Selection on Allele Frequency Distributions
No Selection N=20
s=0.1, h=0.5
Selection pushes A1 toward fixation
A2 still becomes fixed by chance 3.1% of the time
Genetic drift versus directional selection s=0.1,h=0.5, p0=0.5
Drift eventually leads to fixation and loss of alleles
Drift and selection combined push fit alleles to fixation more quickly than drift or selection alone
Some “unfit” alleles do become fixed
What happens
without drift?
No populations are fixed for A1 after 20 generations
How long until these become fixed?
Drift can counter selection in very small populations
Problem 4 in Wednesday’s lab exercise contrasts two cases that fall on the middle curve
N=10, s=0.25
N=100, s=0.25
Fixation as a Function of Ns and Starting Allele Frequency
Combined Effects of Drift and Selection
Probability of fixation of a favorable allele will be a function of initial allele frequency, selection coefficient, heterozygous effect, and population size
Favorable alleles won’t necessarily go to fixation when drift is involved
Drift reduces efficiency of selection in the sense that unfavorable alleles may not be purged from population
Favorable alleles do increase in frequency more quickly when drift is involved over ALL subpopulations
Can be simulated by allowing selection to alter allele frequencies prior to effects of drift
Nuclear Genome Size Size of nuclear
genomes varies tremendously among organisms: C-value paradox
No association with organismal complexity, number of chromosomes, or number of genes Arabidopsis thaliana 120 Mbp
Poplar 460 Mbp Rice 450 Mbp Maize 2,500 Mbp Barley 5,000 Mbp Hexaploid wheat 16,000 Mbp Fritillaria (lilly family) >87,000 Mbp
Noncoding DNA is part of Answer
Fugu: 365 Mbp Human: 3500 Mbp
opossum ~ 52% rice ~ 35%
Arabidopsis ~ 14% Drosophila ~ 15%
pufferfish ~ 2%
barley ~ 55%
wheat ~ 80% corn ~ 70%
Human ~ 45%
mouse ~ 40%
Why is there so much variation in genome size? Why do microbes have so much simpler genomes than eukaryotes? Why do trees have such huge genomes?
The importance of Genetic Drift and Selection in Determining Genome Size
Large effective population sizes mean selection more effective at wiping out variations with even minor effects on fitness
Transposable elements and introns eliminated from finely-tuned populations, persist where drift can overwhelm selection Lynch and Conery 2004 Science 302:1401
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
Effective Population Size
Census population size often inappropriate for population genetics calculations
Breeding population size often smaller
For genetic drift, historical events or nonrandom mating patterns might reduce EFFECTIVE size of the population
Effective Population Size is an ideal population of size N in which all parents have an equal probability of being the parents of any individual progeny.
also
The size of a theoretically ideal population that would have the same observed level of genetic drift
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
Effect of Proportion of Males in the Population on Effective Population Size
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
Effective Population Size: The bottleneck effect
“Alleles” in original population
“Alleles” remaining after bottleneck
The Founder effect Outlying populations
founded by a small number of individuals from source population
Analogous to bottleneck
Expect higher drift, lower diversity in outlying populations
Exam Issues
Genotype frequency versus allele frequency (problem 2A, 7)
Meaning of the chi-square: larger than critical value, reject null hypothesis
Recessive alleles and fitness (Multiple choice problem 3; problem 5)