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

N=16 N=16 N=16

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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

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i

e

N

tN 1

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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)