Abstract
In what follows I am going to explore how concepts and mathematical tools originally developed within physics can be applied to a variety of other fields. These can include, but are not limited to, population genetics, evolution, opinion dynamics, epidemiology and ecology. This thesis will focus primarily on models with an interpretation in population genetics, however models with an ecological and epidemiological flavour will also be explored. With this in mind, let us begin by discussing the questions, ‘what do we mean by a model?’ and ‘what makes a good model?’. The answers to these questions are by no means unarguable, but rather serve to give the reader an impression of the philosophy to which I attempt to adhere.
Essentially, all models are wrong, but some are useful.
George Box [3]
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References
L. Arnold, P. Imkeller, Normal forms for stochastic differential equations. Probab. Theory Relat. Fields 110, 559–588 (1998)
A.J. Black, A.J. McKane, Stochastic formulation of ecological models and their applications. Trends Ecol. Evol. 27, 337–345 (2012)
G.E.P. Box, N.R. Draper, Empirical Model-Building and Response Surfaces (Wiley, New York, 1987)
M.G. Bulmer, Principles of Statistics (Dover, New York, 1979)
W.J. Ewens, Mathematical Population Genetics, 2nd edn. (Springer, Berlin, 2004)
R.A. Fisher, The Genetical Theory of Natural Selection (Clarendon Press, Oxford, 1930)
C.W. Gardiner, Adiabatic elimination in stochastic systems. I. Formulation of methods and application to few-variable systems. Phys. Rev. A 29, 2814–2822 (1984)
C.W. Gardiner, Handbook of Stochastic Methods (Springer, Berlin, 2009)
A.V. Holden, Chaos (Manchester University Press, Manchester, 1986)
L.E. Reichl, A Modern Course in Statistical Physics (Wiley, New York, 1998)
S.H. Rice, Evolutionary Theory (Sinauer Associates, Sunderland, 2004)
G. Schöner, H. Haken, The slaving principle for Stratanovich stochastic differential equations. Z. Phys. B 63, 493–504 (1986)
S. Wright, Evolution in Mendelian populations. Genetics 16, 97–159 (1931)
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Constable, G.W.A. (2015). Introduction. In: Fast Variables in Stochastic Population Dynamics. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-21218-0_1
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DOI: https://doi.org/10.1007/978-3-319-21218-0_1
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