Bayesian Reconstruction of Coevolutionary Histories

Slides for the presentation that I gave at the George Washington University for the National Finals of the Siemens Competition. I earned second place in the individual category and a $50,000 scholarship for my project. A video recording of my talk is available at the following link. http://youtu.be/a3aAQ8sUJMY

Transcript

1. Introduction Methods Simulation Results Closing Remarks Bayesian Reconstruction of Coevolutionary Histories Arman Bilge Lexington High School Lexington, Massachusetts December 9, 2013 x Bayesian Reconstruction of Coevolutionary Histories Arman Bilge
2. Introduction Methods Simulation Results Closing Remarks Symbiotic Interactions are Fundamental to Life Bayesian Reconstruction of Coevolutionary Histories Arman Bilge
3. Introduction Methods Simulation Results Closing Remarks Pocket Gophers and Chewing Lice Thomomys bottae Botta’s Pocket Gopher Thomomydoecus sp. Bayesian Reconstruction of Coevolutionary Histories Arman Bilge
4. Introduction Methods Simulation Results Closing Remarks Phylogenetic Trees are Evolutionary Models Bayesian Reconstruction of Coevolutionary Histories Arman Bilge
5. Introduction Methods Simulation Results Closing Remarks Phylogenetic Trees are Evolutionary Models Bayesian Reconstruction of Coevolutionary Histories Arman Bilge
6. Introduction Methods Simulation Results Closing Remarks Phylogenetic Trees are Evolutionary Models Bayesian Reconstruction of Coevolutionary Histories Arman Bilge
7. Introduction Methods Simulation Results Closing Remarks Coevolution is a Complex Process Hafner & Nadler (1988), Nature 332: 258–259 Bayesian Reconstruction of Coevolutionary Histories Arman Bilge
8. Introduction Methods Simulation Results Closing Remarks Coevolution is Event-Driven Bayesian Reconstruction of Coevolutionary Histories Arman Bilge
9. Introduction Methods Simulation Results Closing Remarks Reconstruction Methods Make Several Assumptions Bayesian Reconstruction of Coevolutionary Histories Arman Bilge
10. Introduction Methods Simulation Results Closing Remarks Evolutionary Processes are Studied Probabilistically Molecular Evolution Felsenstein (1981) Population Genetics Kingman (1982) Gene Evolution Arvestad et al. (2003) Biogeography Lemey et al. (2009, 2010) Speciation Yang & Rannala (2010) Bayesian Reconstruction of Coevolutionary Histories Arman Bilge
11. Introduction Methods Simulation Results Closing Remarks Evolutionary Processes are Studied Probabilistically Molecular Evolution Felsenstein (1981) Population Genetics Kingman (1982) Gene Evolution Arvestad et al. (2003) Biogeography Lemey et al. (2009, 2010) Speciation Yang & Rannala (2010) Coevolution? Bayesian Reconstruction of Coevolutionary Histories Arman Bilge
12. Introduction Methods Simulation Results Closing Remarks A Bayesian Formulation for Coevolution probability of reconstruction P H, S, R | D H = host tree, S = symbiont tree, R = reconciliation, θ = coevolutionary rates, D, dH, dS = sequence data Bayesian Reconstruction of Coevolutionary Histories Arman Bilge
13. Introduction Methods Simulation Results Closing Remarks A Bayesian Formulation for Coevolution probability of reconstruction P H, S, R | D ∝ θ likelihood P dH, dS | H, S, R, θ prior P (H, S, R, θ) dθ H = host tree, S = symbiont tree, R = reconciliation, θ = coevolutionary rates, D, dH, dS = sequence data Bayesian Reconstruction of Coevolutionary Histories Arman Bilge
14. Introduction Methods Simulation Results Closing Remarks A Bayesian Formulation for Coevolution probability of reconstruction P H, S, R | D ∝ θ likelihood P dH, dS | H, S, R, θ prior P (H, S, R, θ) dθ Likelihood P dH, dS | H, S, R, θ = P dH | H, S, R, θ P dS | H, S, R, θ H = host tree, S = symbiont tree, R = reconciliation, θ = coevolutionary rates, D, dH, dS = sequence data Bayesian Reconstruction of Coevolutionary Histories Arman Bilge
15. Introduction Methods Simulation Results Closing Remarks A Bayesian Formulation for Coevolution probability of reconstruction P H, S, R | D ∝ θ likelihood P dH, dS | H, S, R, θ prior P (H, S, R, θ) dθ Likelihood P dH, dS | H, S, R, θ = P dH | H, S, R, θ P dS | H, S, R, θ = P dH | H tree likelihood P dS | S tree likelihood H = host tree, S = symbiont tree, R = reconciliation, θ = coevolutionary rates, D, dH, dS = sequence data Bayesian Reconstruction of Coevolutionary Histories Arman Bilge
16. Introduction Methods Simulation Results Closing Remarks A Bayesian Formulation for Coevolution probability of reconstruction P H, S, R | D ∝ θ likelihood P dH, dS | H, S, R, θ prior P (H, S, R, θ) dθ Prior P (H, S, R, θ) = P S | H, R, θ P (H, R, θ) H = host tree, S = symbiont tree, R = reconciliation, θ = coevolutionary rates, D, dH, dS = sequence data Bayesian Reconstruction of Coevolutionary Histories Arman Bilge
17. Introduction Methods Simulation Results Closing Remarks A Bayesian Formulation for Coevolution probability of reconstruction P H, S, R | D ∝ θ likelihood P dH, dS | H, S, R, θ prior P (H, S, R, θ) dθ Prior P (H, S, R, θ) = P S | H, R, θ P (H, R, θ) = P S | H, R, θ ? P (H) P (R) P (θ) existing/trivial priors H = host tree, S = symbiont tree, R = reconciliation, θ = coevolutionary rates, D, dH, dS = sequence data Bayesian Reconstruction of Coevolutionary Histories Arman Bilge
18. Introduction Methods Simulation Results Closing Remarks Approximating the Symbiont Tree Prior, P S | H, R, θ Cannot be calculated easily because of infinite permutations of unobserved events Bayesian Reconstruction of Coevolutionary Histories Arman Bilge
19. Introduction Methods Simulation Results Closing Remarks Approximating the Symbiont Tree Prior, P S | H, R, θ Cannot be calculated easily because of infinite permutations of unobserved events Approximation by considering only observed events Bayesian Reconstruction of Coevolutionary Histories Arman Bilge
20. Introduction Methods Simulation Results Closing Remarks Approximating the Symbiont Tree Prior, P S | H, R, θ Cannot be calculated easily because of infinite permutations of unobserved events Approximation by considering only observed events Observation of duplication, host-switch, and loss events are modeled as independent Poisson processes Bayesian Reconstruction of Coevolutionary Histories Arman Bilge
21. Introduction Methods Simulation Results Closing Remarks Approximating the Symbiont Tree Prior, P S | H, R, θ Cannot be calculated easily because of infinite permutations of unobserved events Approximation by considering only observed events Observation of duplication, host-switch, and loss events are modeled as independent Poisson processes Cospeciation assumed to occur whenever host speciates Bayesian Reconstruction of Coevolutionary Histories Arman Bilge
22. Introduction Methods Simulation Results Closing Remarks Approximating the Symbiont Tree Prior, P S | H, R, θ Cannot be calculated easily because of infinite permutations of unobserved events Approximation by considering only observed events Observation of duplication, host-switch, and loss events are modeled as independent Poisson processes Cospeciation assumed to occur whenever host speciates Algorithm identifies between 7 cases to calculate probability of observation Bayesian Reconstruction of Coevolutionary Histories Arman Bilge
23. Introduction Methods Simulation Results Closing Remarks Approximating the Symbiont Tree Prior, P S | H, R, θ Cannot be calculated easily because of infinite permutations of unobserved events Approximation by considering only observed events Observation of duplication, host-switch, and loss events are modeled as independent Poisson processes Cospeciation assumed to occur whenever host speciates Algorithm identifies between 7 cases to calculate probability of observation Any uncertainties are integrated out Bayesian Reconstruction of Coevolutionary Histories Arman Bilge
24. Introduction Methods Simulation Results Closing Remarks The Cases x x x x Host / Symbiont Bayesian Reconstruction of Coevolutionary Histories Arman Bilge
25. Introduction Methods Simulation Results Closing Remarks An Example Case x Host / Symbiont Bayesian Reconstruction of Coevolutionary Histories Arman Bilge
26. Introduction Methods Simulation Results Closing Remarks An Example Case x Host / Symbiont Bayesian Reconstruction of Coevolutionary Histories Arman Bilge
27. Introduction Methods Simulation Results Closing Remarks An Example Case x Host / Symbiont Bayesian Reconstruction of Coevolutionary Histories Arman Bilge
28. Introduction Methods Simulation Results Closing Remarks An Example Case x Host / Symbiont Bayesian Reconstruction of Coevolutionary Histories Arman Bilge
29. Introduction Methods Simulation Results Closing Remarks An Example Case x x Host / Symbiont Bayesian Reconstruction of Coevolutionary Histories Arman Bilge
30. Introduction Methods Simulation Results Closing Remarks An Example Case x Host / Symbiont Bayesian Reconstruction of Coevolutionary Histories Arman Bilge
31. Introduction Methods Simulation Results Closing Remarks Bayesian MCMC Implementation Probability of a reconstruction cannot be determined analytically Bayesian Reconstruction of Coevolutionary Histories Arman Bilge
32. Introduction Methods Simulation Results Closing Remarks Bayesian MCMC Implementation Probability of a reconstruction cannot be determined analytically Approximated using Markov chain Monte Carlo (MCMC) MCMC uses a random walk to explore the parameter-space Bayesian Reconstruction of Coevolutionary Histories Arman Bilge
33. Introduction Methods Simulation Results Closing Remarks Bayesian MCMC Implementation Probability of a reconstruction cannot be determined analytically Approximated using Markov chain Monte Carlo (MCMC) MCMC uses a random walk to explore the parameter-space Algorithm implemented as a Java plug-in for BEAST, an existing program for evolutionary analysis via Bayesian MCMC Bayesian Reconstruction of Coevolutionary Histories Arman Bilge
34. Introduction Methods Simulation Results Closing Remarks Bayesian MCMC Implementation Probability of a reconstruction cannot be determined analytically Approximated using Markov chain Monte Carlo (MCMC) MCMC uses a random walk to explore the parameter-space Algorithm implemented as a Java plug-in for BEAST, an existing program for evolutionary analysis via Bayesian MCMC All parameters estimated simultaneously host tree symbiont tree reconciliation Bayesian Reconstruction of Coevolutionary Histories Arman Bilge
35. Introduction Methods Simulation Results Closing Remarks Simulation Results simulation 1 simulation 2 Rate Actual Estimated Actual Estimated duplication 0.0 6.418 × 10−2 1.0 1.419 host-switch 0.0 6.295 × 10−2 1.0 2.471 loss 0.0 5.416 × 10−2 1.0 1.606 Bayesian Reconstruction of Coevolutionary Histories Arman Bilge
36. Introduction Methods Simulation Results Closing Remarks Simulation Results simulation 1 simulation 2 Rate Actual Estimated Actual Estimated duplication 0.0 6.418 × 10−2 1.0 1.419 host-switch 0.0 6.295 × 10−2 1.0 2.471 loss 0.0 5.416 × 10−2 1.0 1.606 0 0 0.998 1 1 1 1 1 symbiont4.1 symbiont8.1 symbiont2.1 symbiont3.1 symbiont1.1 symbiont7.1 symbiont6.1 symbiont5.1 0.079 0.053 0.365 symbiont5.1 0.615 0.079 0.984 0.053 0.365 0.366 symbiont3.3 symbiont7.1 symbiont8.1 symbiont5.1 symbiont5.2 symbiont3.1 0.607 symbiont8.2 Bayesian Reconstruction of Coevolutionary Histories Arman Bilge
37. Introduction Methods Simulation Results Closing Remarks Contributions Formulated an expression for the probability of a coevolutionary reconstruction Bayesian Reconstruction of Coevolutionary Histories Arman Bilge
38. Introduction Methods Simulation Results Closing Remarks Contributions Formulated an expression for the probability of a coevolutionary reconstruction Developed an algorithm to approximate the probability of symbiont tree for a reconstruction Bayesian Reconstruction of Coevolutionary Histories Arman Bilge
39. Introduction Methods Simulation Results Closing Remarks Contributions Formulated an expression for the probability of a coevolutionary reconstruction Developed an algorithm to approximate the probability of symbiont tree for a reconstruction Implemented the algorithm in a popular, widely-used phylogenetics program Bayesian Reconstruction of Coevolutionary Histories Arman Bilge
40. Introduction Methods Simulation Results Closing Remarks Future Work Analysis of real datasets Bayesian Reconstruction of Coevolutionary Histories Arman Bilge
41. Introduction Methods Simulation Results Closing Remarks Future Work Analysis of real datasets Model for preferential host-switching Bayesian Reconstruction of Coevolutionary Histories Arman Bilge
42. Introduction Methods Simulation Results Closing Remarks Future Work Analysis of real datasets Model for preferential host-switching Integration with other evolutionary models (e.g., biogeography) Bayesian Reconstruction of Coevolutionary Histories Arman Bilge
43. Introduction Methods Simulation Results Closing Remarks Future Work Analysis of real datasets Model for preferential host-switching Integration with other evolutionary models (e.g., biogeography) Hypothesis-testing of coevolutionary theories Bayesian Reconstruction of Coevolutionary Histories Arman Bilge
44. Introduction Methods Simulation Results Closing Remarks Acknowledgements My mentors, Dr. Yi-Chieh Jessica Wu, Rachel Sealfon, and Prof. Mukul Bansal Andrew Brownjohn, Jon Sanders, Prof. Ran Libeskind-Hadas, Hayden Metsky, and Prof. Manolis Kellis, for their support Dr. Susan Offner, for inspiring me My family Siemens Foundation and College Board George Washington University Bayesian Reconstruction of Coevolutionary Histories Arman Bilge
45. Introduction Methods Simulation Results Closing Remarks References Baum, D. A. & Offner, S. (2008). The American Biology Teacher, 70(4), 222–229. Bayes, T. & Price, R. (1763). Phil. Trans. 53, 370–418. Charleston, M. A. (2009). A new likelihood method for cophylogenetic analysis. Drummond, A. J., et al. (2012). Mol. Biol. Evol. 29(8), 1969–1973. Faria, N. R., et al. (2013). Phil. Trans. R. Soc. B, 368(1614). Felsenstein, J. (1981). J. Mol. Evol. 17(6), 368–376. Felsenstein, J. (2004). Inferring phylogenies. Sunderland, MA: Sinauer. Hafner, M. S. & Nadler, S. A. (1988). Nature, 332(6161), 258–259. Huelsenbeck, J. P., Rannala, B., & Larget, B. (2000). Evolution, 54(2), 352–364. Kingman, J. F. C. (1982). Stochastic Processes and their Applications, 13(3), 235–248. Segraves, K. A. (2010). Evo. Edu. Outreach, 3(1), 62–70. Sj¨ ostrand, J., et al. (In prep.). A Bayesian method for analyzing lateral gene transfer. Bayesian Reconstruction of Coevolutionary Histories Arman Bilge