Lecture 11: Genetic Drift and Effective Population Size. October 1, 2012

Transcription

1 Lecture 11: Genetic Drift and Effective Population Size October 1, 2012

2 Last Time Introduction to genetic drift Fisher-Wright model of genetic drift Diffusion model of drift Effects within and among subpopulations

3 Simple Model of Genetic Drift Many independent subpopulations Subpopulations are of constant size Random mating within subpopulations

4 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)

5 Today Interactions of drift and selection Effective population size Exams!

6 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

7 Example: Drift and Flour Beetle Color N=10 Tribolium castaneum experiment with lab populations of different sizes N=20 N=50 N=100 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

8 Effects of Selection on Allele Frequency Distributions N=20 No Selection s=0.1, h=0.5 Selection pushes A 1 toward fixation A 2 still becomes fixed by chance 3.1% of the time

9 Genetic drift versus directional selection s=0.1,h=0.5, p 0 =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?

10 Fixation as a Function of Ns and Starting Allele Frequency N=100, s=0.25 Drift can counter selection in very small populations N=10, s=0.25 Problem 4 in Wednesday s lab exercise contrasts two cases that fall on the middle curve

11 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

12 Size of nuclear genomes varies tremendously among organisms: C-value paradox Nuclear Genome Size 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

13 Noncoding DNA is part of Answer Human: 3500 Mbp Fugu: 365 Mbp

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15 wheat ~ 80% corn ~ 70% barley ~ 55% opossum ~ 52% Arabidopsis ~ 14% pufferfish ~ mouse ~ 40% Drosophila ~ rice ~ 35% Human ~

16 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?

17 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 Lynch and Conery 2004 Science 302:1401 Transposable elements and introns eliminated from finely-tuned populations, persist where drift can overwhelm selection

18 Fisher Historical View on Drift 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

19 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

20 Factors Reducing Effective Population Size Unequal number of breeding males and females Unequal reproductive success Changes in population size through time Bottlenecks Founder Effects

21 Effective Population Size: Effects of Different Numbers of Males and Females See Hedrick (2011) page 213 for derivation Table courtesy of K. Ritland

22 Effect of Proportion of Males in the Population on Effective Population Size

23 Variation of population size in different generations Small population size in one generation can cause drastic reduction in diversity for many future generations Effect is approximated by harmonic mean N e 1 N = = 1 t t 1 N i 1 N + 1 N + 1 N e N t 1 See Hedrick (2011) page 219 for derivation

24 Effective Population Size: The bottleneck effect Alleles in original population Alleles remaining after bottleneck

25 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

26 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)