1 / 26

Modeling Evolution: The Wright-Fisher Model

Modeling Evolution: The Wright-Fisher Model. Rick Stuart and Samantha Biehl. Introduction to Evolution. Change over time Natural Selection Variation Inheritance Differential Survival Alleles Dominant Recessive. Introduction to Evolution. Genetic Drift Extinction Fixation

raja
Télécharger la présentation

Modeling Evolution: The Wright-Fisher Model

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Modeling Evolution: The Wright-Fisher Model Rick Stuart and Samantha Biehl

  2. Introduction to Evolution • Change over time • Natural Selection • Variation • Inheritance • Differential Survival • Alleles • Dominant • Recessive

  3. Introduction to Evolution • Genetic Drift • Extinction • Fixation • Increasing variability • Migration • Mutation • Fitness

  4. The Basic Wright-Fisher Model • Stochastic model • Genetic drift • Finite population • Allele frequencies • Two or more alleles

  5. Definition of Variables • Number of individuals • Number of alleles (type A and B) • Number of type A alleles at step • Number of type B alleles at step • Number of type A alleles at step • Probability of getting type A allele • Probability of getting type B allele

  6. The Basic Wright-Fisher Model • Probability of having A alleles • Markov Chain • The transition matrix T

  7. The Basic Wright-Fisher Model • Absorbing States • All type B • All type A • Once in absorbing state, will stay in that state • Given enough time, will enter one of the absorbing states • Extinction • Fixation

  8. The Basic Wright-Fisher Model • Binomial distribution • By induction it can be shown , for all

  9. The Basic Wright-Fisher Model • This makes the process a bounded martingale • Bounded martingale property, converges as

  10. The Basic Wright-Fisher Model • simulations • trials • , (A allele) • Expect number of A alleles to fixate • Simulations results • Mean of fixations per trials

  11. The Basic Wright-Fisher Model • Assumptions • Generations do not overlap • Population size remains constant • No mutation or recombination occurring • Gender of individuals ignored • Familial ties ignored • No selection pressure acting

  12. The Basic Wright-Fisher Model Individuals or Alleles Randomly choose A B B A B A B A B B B A A A A A B B B A A

  13. The Basic Wright-Fisher Model Individuals or Alleles Alleles from step are randomly chosen to produce alleles in step A B B A B A B A B B B A A A A A B B B A A A A B B A A A B A B A B A A A A B B B

  14. The Basic Wright-Fisher Model1 Simulation, 2N=20

  15. The Basic Wright-Fisher Model10 Simulations, 2N=20

  16. The Basic Wright-Fisher Model10 Simulations, 2N=1000

  17. The Basic Wright-Fisher Model5 Simulations, 2N=100,000

  18. The Wright-Fisher Model with Fitness Individuals or Alleles A B B A B A B A B B B A A A A A B B B A 0 1 CRV

  19. The Wright-Fisher Model with Fitness10 Simulations, 2N=20 wa=1.0 wb=0.9

  20. The Wright-Fisher Model with FitnessSimulations, wa=1.00 wb=0.95

  21. The Wright-Fisher Model with FitnessSimulations, wa=1.00 wb=0.95

  22. Wright-Fisher with Fitness and Mutation • Wright-Fisher model with fitness • Mutation rate • Mutation fitness • Unique, random • Simple model of natural selection

  23. Wright-Fisher with Fitness and Mutation Individuals or Alleles A B B A B A H A B B B A A A D D B B B A 0 1 CRV

  24. Wright-Fisher with Fitness and Mutation10 Simulations, 2N=100

  25. Conclusion • Objective • Study a stochastic model and report findings • Basic Wright-Fisher Model • Genetic drift • Modifications • Fitness • Competition of alleles • Mutation • Natural selection • Variation

  26. References • “Genetic Drift.” Wikipedia: The Free Encyclopedia. 3 May 2013. Web. http://en.wikipedia.org/wiki/Genetic_drift • "Martingale Convergence Theorem.” Planetmath.org. N.p., n.d. Web. 06 May 2013. http://planetmath.org/martingaleconvergencetheorem • Mitrofanova, Antonina. "Lecture 2: Absorbing States in Markov Chains. Mean Time to Absorption. Wright-Fisher Model. Moran Model." Lecture. Lecture Notes. NYU, Department of Computer Science, New York. 18 Dec. 2007. Web. http://cs.nyu.edu/mishra/COURSES/09.HPGP/scribe2

More Related