Related papers: Diversity, disparity, and evolutionary rate estima…
A phylogenetic tree is an important way in Bioinformatics to find the evolutionary relationship among biological species. In this research, a proposed model is described for the estimation of a phylogenetic tree for a given set of data. To…
The ongoing explosion of genome sequence data is transforming how we reconstruct and understand the histories of biological systems. Across biological scales, from individual cells to populations and species, trees-based models provide a…
Understanding the processes that give rise to quantitative measurements associated with molecular sequence data remains an important issue in statistical phylogenetics. Examples of such measurements include geographic coordinates in the…
The Yule (pure-birth) model is the simplest null model of speciation; each lineage gives rise to a new lineage independently with the same rate $\lambda$. We investigate the expected length of an edge chosen at random from the resulting…
Tree-based networks are a class of phylogenetic networks that attempt to formally capture what is meant by "tree-like" evolution. A given non-tree-based phylogenetic network, however, might appear to be very close to being tree-based, or…
Many biological studies involve inferring the evolutionary history of a sample of individuals from a large population and interpreting the reconstructed tree. Such an ascertained tree typically represents only a small part of a…
Given a gene-tree labeled topology $G$ and a species tree $S$, the "ancestral configurations" at an internal node $k$ of $S$ represent the combinatorially different sets of gene lineages that can be present at $k$ when all possible…
In evolutionary studies it is common to use phylogenetic trees to represent the evolutionary history of a set of species. However, in case the transfer of genes or other genetic information between the species or their ancestors has…
Phylogenetic tree shapes capture fundamental signatures of evolution. We consider ``ranked'' tree shapes, which are equipped with a total order on the internal nodes compatible with the tree graph. Recent work has established an elegant…
We use a classical combinatorial inequality to establish a Markov inequality for multivariate binary Markov processes on trees. We then apply this result, alongside with the FKG inequality, to compare the expected loss of biodiversity under…
An ongoing debate in evolutionary biology is whether phenotypic change occurs predominantly around the time of speciation or whether it instead accumulates gradually over time. In this work I propose a general framework incorporating both…
We study maximal clades in random phylogenetic trees with the Yule-Harding model or, equivalently, in binary search trees. We use probabilistic methods to reprove and extend earlier results on moment asymptotics and asymptotic normality. In…
Phylogenetic trees and networks are leaf-labelled graphs used to model evolution. Display graphs are created by identifying common leaf labels in two or more phylogenetic trees or networks. The treewidth of such graphs is bounded as a…
Recently, much attention has been given to understanding recombination events along a chromosome in a variety of field. For instance, many population genetics problems are limited by the inaccuracy of inferred evolutionary histories of…
Phylogenetic comparative analysis is an approach to inferring evolutionary process from a combination of phylogenetic and phenotypic data. The last few years have seen increasingly sophisticated models employed in the evaluation of more and…
Phylogenetic comparative methods (PCMs) are widely used to study trait evolution. However, many evolutionary histories involve reticulate evolutionary scenarios, such as hybridization, that violate core assumptions of these methods. In this…
In mathematical phylogenetics, evolutionary relationships are often represented by trees and networks. The latter are typically used whenever the relationships cannot be adequately described by a tree, which happens when so-called…
Inferring concerted changes among biological traits along an evolutionary history remains an important yet challenging problem. Besides adjusting for spurious correlation induced from the shared history, the task also requires sufficient…
Determination of functions for poorly characterized genes is crucial for understanding biological processes and studying human diseases. Functionally associated genes are often gained and lost together through evolution. Therefore…
Comparative analyses of phylogenetic trees typically require identical taxon sets, however, in practice, trees often include distinct but overlapping taxa. Pruning non-shared leaves discards phylogenetic signal, whereas tree completion can…