1 / 23

Exploring Genetic Diversity with Coalescent Theory

Dive into the world of population genetics and natural selection with an introductory guide to coalescent theory. Learn how heritable variation, differential reproductive success, and causal connections shape genealogies. Discover the significance of demography, molecular events, and natural selection in generating and maintaining genetic diversity. Uncover the concepts of Muller, Dobzhansky, Lewontin-Hubby, and Kimura, including the neutral theory and sampling with replacement. Explore the coalescent theory and its application in modeling genealogical history and genetic evolution. Understand the importance of inferring underlying processes and estimating parameters in shaping genetic diversity. Delve into tests of neutrality, purifying selection, balancing selection, and the structured coalescent in studying population structures and geography. Explore the challenges and solutions of coalescent simulations for realistic genetic modeling. Unravel the complex yet fascinating world of genetic diversity with coalescent theory.

jkersh
Download Presentation

Exploring Genetic Diversity with Coalescent Theory

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. Genealogies I:Introduction to Coalescent Theory Jon Wilkins Santa Fe Institute wilkins@santafe.edu Beijing CSSS 2008

  2. Ingredients of Natural Selection • Heritable variation • Differential reproductive success • Causal connection between the two

  3. Population Genetics • How is variation generated and maintained in a population? • What can patterns of genetic diversity tell us about the history of a population? • Demography (migration, reproduction, etc.) • Molecular events (mutation, recombination, etc.) • Natural selection (directional, purifying, etc.)

  4. Why diversity? • Muller - mutation drives deviations from the optimal phenotype • Dobzhansky - heterogeneous environments / frequency dependent effects • Lewontin-Hubby experiments (mid 1960s) • Too much variation for either explanation • Kimura - neutral theory

  5. Neutral Theory • Selective neutrality • All alleles are equally good • Genetic variation does not lead to (relevant) functional variation • Creates a statistically tractable null model • Basis for various “tests of neutrality”

  6. Sampling with Replacement • Some alleles pass on no copies to the next generation, while some pass on more than one • All that we care about are the ancestors of sequences present in our dataset Past Present

  7. The Coalescent ACTT • Homologous genes share a common ancestor • DNA sequence diversity is shaped by genealogical history • Genealogies are shaped by chance, demography, selection T G G C ACGT ACGT ACTT ACTT AGTT

  8. Balls in Boxes • The coalescent models genealogies backwards in time • Follow ancestral lineages back until the most recent common ancestor (MRCA) is reached Probability = 1/2N * (1-1/2N)3 Probability = 1/2N * (1-1/2N)2 Model genealogies back in time Probability = 1/2N * (1-1/2N) Probability = 1/2N Present

  9. The Shapes of Genealogies • Time to the MRCA of a pair of sequences is exponentially distributed with mean time of 2N generations • Time to the next coalescent event for a sample of n sequences is exponential with mean 2N/ generations E[T2] = 2N E[T3] = 2N/3 E[T4] = 2N/6 E[T5] = 2N/10

  10. Genealogies are highly variable • The variance on the length of each portion of the genealogy is large, on the order of N2 • Variation in topology as well • Mutations are random on top of the genealogy

  11. The problem • Want to infer the underlying processes that have shaped genetic diversity, but • The inherent stochasticity means that any given genealogy is consistent with a wide range of demographic processes • How do we estimate parameters, and how do we know how good our estimates are?

  12. Estimating N • Expected pairwise distance () • 2N times 2 (= ) • Expected number of polymorphisms (S)

  13. Tests of neutrality • Deviations from the neutral model affect these summary statistics differently • Tajima’s D

  14. Purifying Selection Shrinks internal branches more than external D < 0

  15. Balancing Selection Extends internal branches D > 0

  16. The Structured Coalescent • With geographically structured populations, all topologies are not equally likely Location Location

  17. The Structured Coalescent • The relationship between genealogy and geography can be used to make inferences Low Migration High Migration

  18. The Island Model N N N N N N • Each migrant is equally likely to come from any deme • Population structure, but no geography

  19. A finite, linear habitat MRCA past present

  20. The Solution Not trivial to extend to > 1 dimension Not trivial to extend to > 2 sequences

  21. Realistic Geography

  22. Coalescent Simulations • In most systems of interest, analytic solutions are too cumbersome • The coalescent provides an efficient framework in which to do simulations • Must understand how to relate the forward-time system to a corresponding backward-time process

  23. Take-home messages • The coalescent provides a convenient approach to modeling evolutionary processes • Well suited to dealing with data • Analytic results are accessible only for very simple models • In other cases, it produces efficient simulations • Leaves the question of how to make inferences • Come back on Friday

More Related