Asymptotic frequency of shapes in supercritical branching trees
TLDR
In this paper, the authors used the general Crump-Mode-Jagers branching process to model an outbreak of an infectious disease under mild assumptions, and derived a formula for the limit of the frequency of the occurrences of a given shape in a general tree.Abstract:
The shapes of branching trees have been linked to disease transmission patterns. In this paper we use the general Crump‒Mode‒Jagers branching process to model an outbreak of an infectious disease under mild assumptions. Introducing a new class of characteristic functions, we are able to derive a formula for the limit of the frequency of the occurrences of a given shape in a general tree. The computational challenges concerning the evaluation of this formula are in part overcome using the jumping chronological contour process. We apply the formula to derive the limit of the frequency of cherries, pitchforks, and double cherries in the constant-rate birth‒death model, and the frequency of cherries under a nonconstant death rate.read more
Citations
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Journal ArticleDOI
A Metric on Phylogenetic Tree Shapes.
TL;DR: This work presents a full characterization of the shapes of rooted branching trees in a form that lends itself to natural tree comparisons, and uses this characterization to define a metric, in the sense of a true distance function, on tree shapes.
Journal ArticleDOI
Phylogenies from dynamic networks.
TL;DR: The effects of mis-specification of the underlying network and its parameters have a strong adverse effect on the ability to estimate the transmission parameter, and the results point to the importance of correctly estimating and modelling contact networks with dynamics when using phylodynamic tools to estimate epidemiological parameters.
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Analyzing Phylogenetic Trees with a Tree Lattice Coordinate System and a Graph Polynomial.
TL;DR: This paper introduces representation and comparison methods for rooted unlabelled phylogenetic trees based on a tree lattice that serves as a coordinate system for rooted binary trees with branch lengths and a graph polynomial that fully characterizes tree shapes.
Posted ContentDOI
Polynomial Phylogenetic Analysis of Tree Shapes
TL;DR: This paper uses tree-defining polynomials to compare tree shapes randomly generated by simulations and tree shapes reconstructed from data and shows that the comparisons can be used to estimate parameters and to select the best-fit model that generates specific tree shapes.
Journal ArticleDOI
On asymptotic joint distributions of cherries and pitchforks for random phylogenetic trees.
TL;DR: In this paper, two subtree counting statistics for random phylogenetic trees generated by two widely used null tree models: the proportional to distinguishable arrangements (PDA) and the Yule-Harding-Kingman (YHK) models were studied.
References
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BEAST: Bayesian evolutionary analysis by sampling trees
TL;DR: BEAST is a fast, flexible software architecture for Bayesian analysis of molecular sequences related by an evolutionary tree that provides models for DNA and protein sequence evolution, highly parametric coalescent analysis, relaxed clock phylogenetics, non-contemporaneous sequence data, statistical alignment and a wide range of options for prior distributions.
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Stochastic partial differential equations
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On incomplete sampling under birth–death models and connections to the sampling-based coalescent
TL;DR: The density of the bifurcation events for trees on n leaves which evolved under this birth-death-sampling process is derived and is used for calculating prior distributions in Bayesian inference programs and for efficiently simulating trees.