On joint subtree distributions under two evolutionary models

Taoyang Wu and Kwok Pui Choi

Theoretical Population Biology, 2016, vol. 108, issue C, 13-23

Abstract: In population and evolutionary biology, hypotheses about micro-evolutionary and macro-evolutionary processes are commonly tested by comparing the shape indices of empirical evolutionary trees with those predicted by neutral models. A key ingredient in this approach is the ability to compute and quantify distributions of various tree shape indices under random models of interest. As a step to meet this challenge, in this paper we investigate the joint distribution of cherries and pitchforks (that is, subtrees with two and three leaves) under two widely used null models: the Yule–Harding–Kingman (YHK) model and the proportional to distinguishable arrangements (PDA) model. Based on two novel recursive formulae, we propose a dynamic approach to numerically compute the exact joint distribution (and hence the marginal distributions) for trees of any size. We also obtained insights into the statistical properties of trees generated under these two models, including a constant correlation between the cherry and the pitchfork distributions under the YHK model, and the log-concavity and unimodality of the cherry distributions under both models. In addition, we show that there exists a unique change point for the cherry distributions between these two models.

Keywords: Phylogenetic tree; Subtree distribution; Yule–Harding–Kingman model; PDA model; Tree indices; Joint distribution (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0040580915001215
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:thpobi:v:108:y:2016:i:c:p:13-23

DOI: 10.1016/j.tpb.2015.11.004

Access Statistics for this article

Theoretical Population Biology is currently edited by Jeremy Van Cleve

More articles in Theoretical Population Biology from Elsevier
Bibliographic data for series maintained by Catherine Liu ().