The Projection Matrix Method

  • George William Albert ConstableEmail author
Part of the Springer Theses book series (Springer Theses)


In this section, a second method of fast variable elimination in stochastic systems will be introduced. This method aims to remove the problems encountered in the conditioning method when the noise matrix is singular (see Sect.  3.5). The essential idea is to explicitly remove any contribution to the dynamics from the fast directions and retain only the slow degrees of freedom. Since the methodology follows in a straightforward way from the conditioning method, a verbal description of the method is given in the following section, along with applications to some of the models encountered in Chap.  3. The method is later applied to a Moran model with migration, however for clarity some of the history of models of population genetics featuring migration is given in Sect. 4.2, while the model pertaining to later work is introduced in Sect. 4.3.


Effective Population Size Centre Manifold Diffusion Matrix Deterministic Dynamic Neutral Case 
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© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of Ecology and Evolutionary BiologyPrinceton UniversityPrincetonUSA

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