Ranked Schröder Trees

08/25/2018
by   Olivier Bodini, et al.
0

In biology, a phylogenetic tree is a tool to represent the evolutionary relationship between species. Unfortu- nately, the classical Schröder tree model is not adapted to take into account the chronology between the branching nodes. In particular, it does not answer the question: how many different phylogenetic stories lead to the creation of n species and what is the average time to get there? In this paper, we enrich this model in two distinct ways in order to obtain two ranked tree models for phylogenetics, i.e. models coding chronology. For that purpose, we first develop a model of (strongly) increasing Schröder trees, symbolically de- scribed in the classical context of increasing labeling. Then we introduce a generalization for the labeling with some unusual order constraint in Analytic Combinatorics (namely the weakly increasing trees). Although these models are direct extensions of the Schröder tree model, it appears that they are also in one-to-one correspondence with several classical combinatorial objects. Through the paper, we present these links, exhibit some parameters in typical large trees and conclude the studies with efficient uniform samplers.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
05/13/2019

Counting and sampling gene family evolutionary histories in the duplication-loss and duplication-loss-transfer models

Given a set of species whose evolution is represented by a species tree,...
research
01/15/2014

The Ultrametric Constraint and its Application to Phylogenetics

A phylogenetic tree shows the evolutionary relationships among species. ...
research
06/04/2021

Statistical summaries of unlabelled evolutionary trees and ranked hierarchical clustering trees

Rooted and ranked binary trees are mathematical objects of great importa...
research
05/26/2020

Compaction for two models of logarithmic-depth trees: Analysis and Experiments

In this paper we are interested in the quantitative analysis of the comp...
research
05/10/2021

Distinct Fringe Subtrees in Random Trees

A fringe subtree of a rooted tree is a subtree induced by one of the ver...
research
06/18/2022

Parameter Identifiability of a Multitype Pure-Birth Model of Speciation

Diversification models describe the random growth of evolutionary trees,...
research
07/18/2017

Efficient and consistent inference of ancestral sequences in an evolutionary model with insertions and deletions under dense taxon sampling

In evolutionary biology, the speciation history of living organisms is r...

Please sign up or login with your details

Forgot password? Click here to reset