NDLI: Links between deterministic and stochastic approaches for invasion in growth-fragmentation-death models

Content Provider	Springer Nature Link
Author	Campillo, Fabien Fritsch, Coralie Champagnat, Nicolas
Copyright Year	2016
Abstract	We present two approaches to study invasion in growth-fragmentation-death models. The first one is based on a stochastic individual based model, which is a piecewise deterministic branching process with a continuum of types, and the second one is based on an integro-differential model. The invasion of the population is described by the survival probability for the former model and by an eigenproblem for the latter one. We study these two notions of invasion fitness, giving different characterizations of the growth of the population, and we make links between these two complementary points of view. In particular we prove that the two approaches lead to the same criterion of possible invasion. Based on Krein-Rutman theory, we also give a proof of the existence of a solution to the eigenproblem, which satisfies the conditions needed for our study of the stochastic model, hence providing a set of assumptions under which both approaches can be carried out. Finally, we motivate our work in the context of adaptive dynamics in a chemostat model.
Ending Page	1821
Page Count	41
Starting Page	1781
File Format	PDF
ISSN	03036812
e-ISSN	14321416
Journal	Journal of Mathematical Biology
Issue Number	6-7
Volume Number	73
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2016-04-23
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	PDEs in connection with biology and other natural sciences Population dynamics (general) Bacterial population Mathematical and Computational Biology Branching processes (Galton-Watson, birth-and-death, etc.) Growth-fragmentation-death model Invasion fitness Piecewise-deterministic Markov process Eigenvalue problems Individual-based model Applications of branching processes Infinite dimensional branching process Eigenproblem Integro-differential equation Applications of Mathematics Continuous-time Markov processes on general state spaces
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Agricultural and Biological Sciences Modeling and Simulation

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