Advertisement

Further Developments

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

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.

Keywords

Master Equation Projection Matrix Centre Manifold Diffusion Matrix Drift Term 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    R. Halliburton, Introduction to Population Gentetics (Pearson Press, New Jersey, 2004)Google Scholar
  2. 2.
    M. Lax, Fluctuations from the nonequilibrium steady state. Rev. Mod. Phys. 32, 25–64 (1960)ADSCrossRefzbMATHGoogle Scholar
  3. 3.
    C.C. Li, Population Genetics (The University of Chicago Press, Chicago, 1955)Google Scholar
  4. 4.
    Y.T. Lin, H. Kim, C.R. Doering, Demographic stochasticity and evolution of dispersion I. Spatially homogeneous environments. J. Math. Biol. 70, 647 (2015)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Y.T. Lin, H. Kim, C.R. Doering, Demographic stochasticity and evolution of dispersion II. Spatially inhomogeneous environments. J. Math. Biol. 70, 679 (2015)MathSciNetCrossRefGoogle Scholar
  6. 6.
    C.D. Meyer, Matrix Analysis and Applied Linear Algebra (SIAM, Philadelphia, 2000)CrossRefzbMATHGoogle Scholar
  7. 7.
    A.E. Noble, A. Hastings, W.F. Fagan, Multivariate Moran process with Lotka-Volterra phenomenology. Phys. Rev. Lett. 107, 228101 (2011)ADSCrossRefGoogle Scholar
  8. 8.
    M.A. Nowak, Evolutionary Dynamics: Exploring the Equations of Life (Harvard University Press, Cambridge, 2006)Google Scholar
  9. 9.
    M.A. Nowak, A. Sasaki, C. Taylor, D. Fudenberg, Emergence of cooperation and evolutionary stability in finite populations. Nature 428, 646–650 (2004)ADSCrossRefGoogle Scholar
  10. 10.
    T. Parsons, C. Quince, Fixation in haploid populations exhibiting density dependence I: the non-neutral case. Theor. Pop. Biol. 72, 121–135 (2007)CrossRefzbMATHGoogle Scholar
  11. 11.
    E.C. Pielou, Mathematical Ecology (Wiley, New York, 1977)Google Scholar
  12. 12.
    N. Rohner, D.F. Jarosz, J.E. Kowalko, M. Yoshizawa, W.R. Jeffery, R.L. Borowsky, S. Lindquist, C.J. Tabin, Cryptic variation in morphological evolution: Hsp90 as a capacitor for loss of eyes in cavefish. Science 342, 1372–1375 (2013)ADSCrossRefGoogle Scholar
  13. 13.
    J. Roughgarden, Theory of Population Genetics and Evolutionary Ecology: An Introduction (Macmillan, New York, 1979)Google Scholar
  14. 14.
    A. Traulsen, J.C. Claussen, C. Hauert, Coevolutionary dynamics: from finite to infinite populations. Phys. Rev. Lett. 95, 238701 (2005)ADSCrossRefGoogle Scholar
  15. 15.
    D. Waxman, A unified treatment of the probability of fixation when population size and the strength of selection change over time. Genetics 188, 907–913 (2011)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of Ecology and Evolutionary BiologyPrinceton UniversityPrincetonUSA

Personalised recommendations