We consider a class of haploid population models with nonoverlapping generations and fixed population size N assuming that the family sizes within a generation are exchangeable random variables. A… (More)

Polyploidy is an important speciation mechanism, particularly in land plants. Allopolyploid species are formed after hybridization between otherwise intersterile parental species. Recent theoretical… (More)

We consider a stochastic evolutionary model for a phenotype developing amongst n related species with unknown phylogeny. The unknown tree is modelled by a Yule process conditioned on n contemporary… (More)

A class of two-sex population models is considered with N females and equal number N of males constituting each generation. Reproduction is assumed to undergo three stages: 1) random mating, 2)… (More)

Populations can die out in many ways. We investigate one basic form of extinction, stable or intrinsic extinction, caused by individuals on the average not being able to replace themselves through… (More)

A simple way to model phenotypic evolution is to assume that after splitting, the trait values of the sister species diverge as independent Brownian motions. Relying only on a prior distribution for… (More)

This text contains my lecture notes for the graduate course “Weak Convergence” given in September-October 2013 and then in March-May 2015. The course is based on the book Convergence of Probability… (More)

We establish convergence to the Kingman coalescent for a class of age-structured population models with time-constant population size. Time is discrete with unit called a year. Offspring numbers in a… (More)

A population has two types of individuals, each occupying an island. One of those, where individuals of type 1 live, offers a variable environment. Type 2 individuals dwell on the other island, in a… (More)