1. Extensions to Basic Coalescent Chapter 4, Part 2

2. Extension 2 Relax another assumption – > Coalescent with population structure 3/3/2009COMP 790-Extensions to Basic Coalescent2

3. Extension 2 Finite island model Assume population is divided into d islands (demes) of equal size 2N, with total population of 2 N d genes. Each island contributes with a fraction m to a pool of migrants from which the island in return receives an equal proportion of migrants. Thus all demes can be treated equally 3/3/2009COMP 790-Extensions to Basic Coalescent3

4. Extension 2 Coalescent process with time scaled in units of 2 N d generations. Time until first coalescent event is exponentially distributed with parameter 3/3/2009COMP 790-Extensions to Basic Coalescent4

5. Extension 2 Migration rate 3/3/2009COMP 790-Extensions to Basic Coalescent5

6. Extension 2 In total this leads to a rate of I coal + I migr until the first event. This event is coalescent with probability And migration event with probability 3/3/2009COMP 790-Extensions to Basic Coalescent6

7. Extension 2 If coalescent event occurs, deme j is chosen with probability 3/3/2009COMP 790-Extensions to Basic Coalescent7

8. Extension 2 Sample genealogy 3/3/2009COMP 790-Extensions to Basic Coalescent8

9. Extension 2 Coalescent tree in finite island model T(2,0) is the time for two genes in two different demes to find a MRCA T(0,1) is the time for two genes in the same demes to find MRCA Two genes cannot find a MRCA until they are in the same deme and they must do so before one of them migrates 3/3/2009COMP 790-Extensions to Basic Coalescent9

10. Extension 2 Thus 3/3/2009COMP 790-Extensions to Basic Coalescent10

11. Extension 2 When these equations are solved we have Variances 3/3/2009COMP 790-Extensions to Basic Coalescent11

12. Extension 2 3/3/2009COMP 790-Extensions to Basic Coalescent12

13. Extension 2 3/3/2009COMP 790-Extensions to Basic Coalescent13

14. Extension 2 3/3/2009COMP 790-Extensions to Basic Coalescent14

15. Extension 2 3/3/2009COMP 790-Extensions to Basic Coalescent15 Basic coalescent (multimodal)

16. Extension 2 General models of subdivision 1. Stepping stone models Island model assume that a gene from one island or deme is equally likely to migrate to any other island In stepping stone models Equally sized demes are repplaces by demes of arbitrary sizes and rate of migration from deme I to deme j is given 3/3/2009COMP 790-Extensions to Basic Coalescent16

18. Extension 2 3/3/2009COMP 790-Extensions to Basic Coalescent18

19. Extension 2 Splitting of populations 3/3/2009COMP 790-Extensions to Basic Coalescent19

20. Extension 2 3/3/2009COMP 790-Extensions to Basic Coalescent20

21. Thank you 3/3/2009COMP 790-Extensions to Basic Coalescent21