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Efficient Coalescent Simulation and Genealogical Analysis for Large Sample Sizes
Sparse trees and coalescence records are introduced as the key units of genealogical analysis and exact simulation of the coalescent with recombination for chromosome-sized regions over hundreds of thousands of samples is possible, and substantially faster than present-day approximate methods. Expand
An introduction to superprocesses
Superprocesses as diffusion approximations Qualitative behaviour I The Le Gall representation The relationship between our two classes of superprocesses A countable representation QualitativeExpand
A course in financial calculus
Finance provides a dramatic example of the successful application of advanced mathematical techniques to the practical problem of pricing financial derivatives. This self-contained 2002 text isExpand
Some Mathematical Models from Population Genetics
This work provides a rapid introduction to a range of mathematical models that have their origins in theoretical population genetics and falls into two classes: forwards in time models for the evolution of frequencies of different genetic types in a population; and backwards in time model that trace out the genealogical relationships between individuals in a sample from the population. Expand
Neutral evolution in spatially continuous populations.
We introduce a general recursion for the probability of identity in state of two individuals sampled from a population subject to mutation, migration, and random drift in a two-dimensional continuum.Expand
We consider a single genetic locus which carries two alleles, labelled P and Q. This locus experiences selection and mutation. It is linked to a second neutral locus with recombination rate r . If rExpand
A coalescent dual process in a Moran model with genic selection, and the lambda coalescent limit.
It is shown that in the limit of infinite population size the non-neutral Moran models converge to a Markov jump process which is called the lamda-Fleming-Viot process with viability selection and a coalescent dual is derived for this process directly from the generator and as a limit from the Moran models. Expand
Alpha-Stable Branching and Beta-Coalescents
We determine that the continuous-state branching processes for which the genealogy, suitably time-changed, can be described by an autonomous Markov process are precisely those arising fromExpand
The infinitesimal model: Definition, derivation, and implications.
It is proved in particular that, within each family, the genetic components of the individual trait values in the current generation are indeed normally distributed with a variance independent of ancestral traits, up to an error of order 1∕M. Expand