@inproceedings{719a837dafab444eaf438379aa742dc1,

title = "One dimensional maps as population and evolutionary dynamic models",

abstract = "I discuss one dimensional maps as discrete time models of population dynamics from an extinction-versus-survival point of view by means of bifurcation theory. I extend this approach to a version of these population models that incorporates the dynamics of a single phenotypic trait subject to Darwinian evolution. This is done by proving a fundamental bifurcation theorem for the resulting two dimensional, discrete time model. This theorem describes the bifurcation that occurs when an extinction equilibrium destabilizes. Examples illustrate the application of the theorem. Included is a short summary of generalizations of this bifurcation theorem to the higher dimensional maps that arise when modeling the evolutionary dynamics of a structured population.",

keywords = "Allee effects, Bifurcations, Difference equations, Discrete time dynamics, Equilibria, Evolutionary dynamics, Population dynamics, Stability",

author = "Cushing, {Jim M.}",

note = "Funding Information: The author gratefully acknowledges the support of the National Science Foundation (Mathematical Biology Program in the Division of Mathematical Sciences and the Population & Community Ecology Program in the Division of Environmental Biology) under NSF grant DMS 0917435. Publisher Copyright: {\textcopyright} Springer India 2016.; International Conference on Recent Advances in Mathematical Biology, Analysis and Applications, ICMBAA 2015 ; Conference date: 25-05-2016 Through 29-05-2016",

year = "2016",

doi = "10.1007/978-81-322-3640-5_3",

language = "English (US)",

isbn = "9788132236382",

series = "Springer Proceedings in Mathematics and Statistics",

publisher = "Springer New York LLC",

pages = "41--62",

editor = "Cushing, {Jim M.} and M. Saleem and Khan, {Mumtaz Ahmad} and M. Merajuddin and H.M. Srivastava",

booktitle = "Applied Analysis in Biological and Physical Sciences - ICMBAA 2015",

}