Ancestral Features of Multitype Branching Trees

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" summary

Analyzes multitype Galton–Watson trees by embedding the full genealogy to produce a coalescent point process and encoding the reduced phylogeny as a sequence-valued Markov chain on spines whose transitions track surviving offspring counts and types. Shows multi-type linear-fractional offspring laws make consecutive coalescence depths i.i.d., compares symmetric vs asymmetric two-type cases (stochastic dominance of same-type coalescence depths), and in continuous-time Yule limits derives linear equations so one can recover rates from cherry and pendant frequencies in the long-time, time-homogeneous case.

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" chapters (14)

1. 0:00Start
2. 0:33Motivation: phylogenies with marked phenotypes
3. 2:26Discrete multi-type Galton-Watson tree
4. 11:18Single-type coalescent results (Lambert-Popovic AOAP'13)
5. 15:44Multi-type coalescent point process. Notation
6. 17:30Multi-type coalescent theorem (Popovic-Rivas SPA14)
7. 19:51Construction of 2-type G-W trees (by example)
8. 21:41MRCA of same type individuals
9. 23:52MRCA of consecutive individuals (Coalescence times)
10. 24:19Special case: Linear fractional offspring distribution
11. 25:43G-W population in Linear fractional case
12. 28:38Comparison of ancestral features (using same type MRCA)
13. 29:39Comparison for two-type symmetric vs asymmetric model
14. 31:01Statistics on multi-type phylogenetic trees

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