Exact enumeration of cherries and pitchforks in ranked trees under the coalescent model

2011/12/06 by Filippo Disanto, Thomas Wiehe, Disanto, Filippo +1
Biochemistry, Genetics and Molecular Biology · Computer Science · Decision Sciences · Economics, Econometrics and Finance · Mathematics · #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Biological sciences #FOS: Computer and information sciences #FOS: Mathematics #Game Theory and Applications #Game Theory and Voting Systems #Populations and Evolution (q-bio.PE) #Sports Analytics and Performance #cs.DM #math.CO #q-bio.PE

paper · pdf · doi:10.48550/arxiv.1112.1295

openalex publication_date 2011/12/06 · arxiv created 2012/08/19 · arxiv updated 2012/08/21 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28

Abstract

We consider exact enumerations and probabilistic properties of ranked trees when generated under the random coalescent process. Using a new approach, based on generating functions, we derive several statistics such as the exact probability of finding k cherries in a ranked tree of fixed size n. We then extend our method to consider also the number of pitchforks. We find a recursive formula to calculate the joint and conditional probabilities of cherries and pitch- forks when the size of the tree is fixed.

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