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 …

To learn about the past from a sample of genomic sequences, one needs to understand how
evolutionary processes shape genetic diversity. Most population genetics inferences are …

We investigate the effect of spatial range expansions on the evolution of fitness when
beneficial and deleterious mutations cosegregate. We perform individual‐based simulations …

These notes attempt to provide an elementary introduction to the one-dimensional discrete-
time branching random walk and to exploit its spinal structure. They begin with the case of …

Given a sample of genome sequences from an asexual population, can one predict its
evolutionary future? Here we demonstrate that the branching patterns of reconstructed …

The genetic diversity of a species is shaped by its recent evolutionary history and can be
used to infer demographic events or selective sweeps. Most inference methods are based …

Characterizing the mode—the way, manner or pattern—of evolution in tumours is important
for clinical forecasting and optimizing cancer treatment. Sequencing studies have inferred …

Traveling waves are ubiquitous in nature and control the speed of many important
dynamical processes, including chemical reactions, epidemic outbreaks, and biological …

We investigate analytically and numerically eigenfunction statistics in a disordered system
on a finite Bethe lattice (Cayley tree). We show that the wave-function amplitude at the root …

Epidemics, flame propagation, and cardiac rhythms are classic examples of reaction–
diffusion waves that describe a switch from one alternative state to another. Only two types of …