TY  - INPR
A1  - Méléard, Sylvie
A1  - Roelly, Sylvie
T1  - Evolutive two-level population process and large population approximations
N2  - We are interested in modeling the Darwinian evolution of a population described by two levels of biological parameters: individuals characterized by an heritable phenotypic trait submitted to mutation and natural selection and cells in these individuals influencing their ability to consume resources and to reproduce. Our models are rooted in the microscopic description of a random (discrete) population of individuals characterized by one or several adaptive traits and cells characterized by their type. The population is modeled as a stochastic point process whose generator captures the probabilistic dynamics over continuous time of birth, mutation and death for individuals and birth and death for cells. The interaction between individuals (resp. between cells) is described by a competition between individual traits (resp. between cell types). We are looking for tractable large population approximations. By combining various scalings on population size, birth and death rates and mutation step, the single microscopic model is shown to lead to contrasting nonlinear macroscopic limits of different nature: deterministic approximations, in the form of ordinary, integro- or partial differential equations, or probabilistic ones, like stochastic partial differential equations or superprocesses.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 2 (2013) 8 
KW  - Two-level interacting process
KW  - birth-death-mutation-competition point process
KW  - non-linear integro-differential equations
Y1  - 2013
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/6229
UR  - https://nbn-resolving.org/urn:nbn:de:kobv:517-opus-64604
SN  - 2193-6943
ER  -