## Search

Now showing items 1-10 of 19

#### Computing the minimum number of hybridization events for a consistent evolutionary history

(University of Canterbury. Mathematics and Statistics., 2007)

It is now well-documented that the structure of evolutionary relationships between a set of present-day species is not necessarily tree-like. The reason for this is that reticulation events such as hybridizations mean that ...

#### Computing the distribution of a tree metric

(University of Canterbury. Mathematics and Statistics, 2009)

The Robinson-Foulds (RF) distance is by far the most widely used measure of dissimilarity between trees. Although the distribution of these distances has been investigated for twenty years, an algorithm that is explicitly ...

#### Coalescent experiments I: Unlabeled n-coalescent and the site frequency spectrum

(Department of Mathematics & StatisticsUniversity of Canterbury. Mathematics and Statistics, 2009)

We derive the transition structure of a Markovian lumping of Kingman’s n-coalescent [1, 2]. Lumping a Markov chain is meant in the sense of [3, def. 6.3.1]. The lumped Markov process, referred as the
unlabeled n-coalescent, ...

#### Expected Anomolies in the Fossil Record

(University of Canterbury. Mathematics and Statistics, 2008)

The problem of intermediates in the fossil record has been frequently discussed ever since Darwin. The extent of ‘gaps’ (missing transitional stages) has been used to argue against gradual evolution from a common ancestor. ...

#### Bounding the Number of Hybridisation Events for a Consistent Evolutionary History

(University of Canterbury. Mathematics and Statistics., 2005)

#### Coalescent experiments II: Markov bases of classical population genetic statistics

(Department of Mathematics & StatisticsUniversity of Canterbury. Mathematics and Statistics, 2009)

Evaluating the likelihood function of parameters in complex population genetic models from extant deoxyribonucleic acid (DNA) sequences is computationally prohibitive. In such cases, one may approximately infer the parameters ...

#### A unified multi-resolution coalescent: Markov lumpings of the Kingman-Tajima n-coalescent

(Department of Mathematics & StatisticsUniversity of Canterbury. Mathematics and Statistics, 2009)

In this paper, we formulate six different resolutions of a continuous-time approximation of the Wright-Fisher sample genealogical process. We derive Markov chains for the six different approximations in the spirit of J.F.C. ...

#### Counting consistent phylogenetic trees is #P-complete

(University of Canterbury. Mathematics and Statistics., 2004)

Reconstructing phylogenetic trees is a fundamental task in evolutionary biology. Various algorithms exist for this purpose, many of
which come under the heading of `supertree methods'. These methods
amalgamate a collection ...

#### Special Section: Phylogenetics.

(University of Canterbury. Mathematics and Statistics, 2009)

Phylogenetics is the reconstruction and analysis of trees and networks to describe and understand the evolution of species, populations, and individuals. It is fundamental to evolutionary biology and finds applications in ...

#### Distributions of gene tree branch lengths under coalescence

(University of Canterbury. Mathematics and Statistics, 2008)

In Bayesian phylogenetic inference, commonly used prior distributions for branch lengths are the uniform, exponential, and gamma distributions. We derive the exact distributions of branch lengths of gene trees under a fixed ...