Coalescent theory is the study of random processes where particles may join each other to
form clusters as time evolves. These notes provide an introduction to some aspects of the …

Three series of lectures were given at the 32nd Probability Summer School in Saint-Flour
(July 7–24, 2002), by the Professors Pitman, Tsirelson and Werner …

Our basic question is: Given a collection of DNA sequences, what underlying forces are
responsible for the observed patterns of variability? To approach this question we introduce …

This work reflects sixteen hours of lectures delivered by the author at the 2009 St Flour
summer school in probability. It provides a rapid introduction to a range of mathematical …

We report a complex set of scaling relationships between mutation and reproduction in a
simple model of a population. These follow from a consideration of patterns of genetic …

We consider the space of complete and separable metric spaces which are equipped with a
probability measure. A notion of convergence is given based on the philosophy that a …

We consider a system of particles which perform branching Brownian motion with negative
drift and are killed upon reaching zero, in the near-critical regime where the total population …

We investigate a new model for populations evolving in a spatial continuum. This model can
be thought of as a spatial version of the Lambda-Fleming-Viot process. It explicitly …

The ability of the site-frequency spectrum (SFS) to reflect the particularities of gene
genealogies exhibiting multiple mergers of ancestral lines as opposed to those obtained in …

We prove several limit theorems that relate coalescent processes to continuous-state
branching processes. Some of these theorems are stated in terms of the so-called …