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

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

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 eigenpr...

Random and deterministic fragmentation models

Random and deterministic fragmentation models are considered. Their relationship is studied by deriving different forms of the kinetic fragmentation equation from the corresponding stochastic models. Results related to the problem of non-conservation of mass (phase transition into dust) are discussed. Illustrative examples are given and some open problems are mentioned.

Stochastic versus Deterministic Approaches

Spatial models: stochastic and deterministic

Theoretical studies of biological populations via analysis and/or simulation of deterministic and stochastic systems sometimes end up drawing conflicting conclusions. Papers purporting to investigate the same dynamics, albeit through different methods, often cannot agree on essential properties of the system being modeled. This problem often arises when trying to compare results that were obtai...

Comparison between stochastic and deterministic selection-mutation models.

We present a deterministic selection-mutation model with a discrete trait variable. We show that for an irreducible selection-mutation matrix in the birth term the deterministic model has a unique interior equilibrium which is globally stable. Thus all subpopulations coexist. In the pure selection case, the outcome is known to be that of competitive exclusion, where the subpopulation with the l...