Abstract
In this chapter further developments of the conditioning and projection matrix method are presented. In the following section, the discussion of the metapopulation Moran model is completed by adding mutation. Following this, a more detailed comparison of the two reduction methods is conducted. Finally, in the third section, the projection matrix method is applied to a new system, the Lotka-Volterra competition model of two interacting populations.
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Notes
- 1.
The matrix \(\Xi \) is the covariance matrix for the Gaussian PDF \(p(\varvec{\xi }_{z},\varvec{\xi }_{w},t)\) described by the linear FPE. It is not to be confused with the diffusion matrix \(B(\varvec{x})\) which describes the covariance of the noise terms, \(\kappa _{i}(t)\), in the SDE.
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Constable, G.W.A. (2015). Further Developments. In: Fast Variables in Stochastic Population Dynamics. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-21218-0_6
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DOI: https://doi.org/10.1007/978-3-319-21218-0_6
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