Coralie Fritsch

National Institute for Research in Computer Science and Control | INRIA · BIGS - Biology, Genetics and Statistics Research Team

In this work we study the bisexual Galton-Watson process with a finite number of types, where females and males mate according to a ''mating function'' and form couples of different types. We assume that this function is superadditive, which in simple words implies that two groups of females and males will form a larger number of couples together r...

The Crump-Young model consists of two fully coupled stochastic processes modeling the substrate and microorganisms dynamics in a chemostat. Substrate evolves following an ordinary differential equation whose coefficients depend of microorganisms number. Microorganisms are modeled though a pure jump process whose the jump rates depend on the substra...

Body size or mass is one of the main factors underlying food webs structure. A large number of evolutionary models have shown that indeed, the adaptive evolution of body size (or mass) can give rise to hierarchically organised trophic levels with complex between and within trophic interactions. However, these models generally make strong arbitrary...

Body size or mass is generally seen as one of the main factors which structure food webs. A large number of evolutionary models have shown that indeed, the evolution of body size (or mass) can give rise to hierarchically organized trophic levels with complex between and within trophic interactions. However, because these models have often very diff...

In a chemostat, bacteria live in a growth container of constant volume in which liquid is injected continuously. Recently, Campillo and Fritsch introduced a mass-structured individual-based model to represent this dynamics and proved its convergence to a more classic partial differential equation. In this work, we are interested in the convergence...

We study the variations of the principal eigenvalue associated to a growth-fragmen- tation-death equation with respect to a parameter acting on growth and fragmentation. To this aim, we use the probabilistic individual-based interpretation of the model. We study the variations of the survival probability of the stochastic model using a generation b...

We propose a general numerical approach that can be used to study the invasion fitness of a mutant in evolutionary models and to determine evolutionary singular strategies when the competitive exclusion principle holds. We illustrate this method with a mass-structured individual-based chemostat model. We assume that the mutations are rare and that...

We present two approaches to study invasion in growth-fragmentation-death mod- els. 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 p...

We study the variations of the principal eigenvalue associated to a growth-fragmentation-death equation with respect to a parameter. To this aim, we use the probabilistic individual-based interpretation of the model. We study the variations of the survival probability of the stochastic model, using a generation by generation approach. Then, making...

We propose a model of chemostat where the bacterial population is individually-based, each bacterium is explicitly represented and has a mass evolving continuously over time. The substrate concentration is represented as a conventional ordinary differential equation. These two components are coupled with the bacterial consumption. Mechanisms acting...

In the first part, we propose a new chemostat model in which the bacterial population is mass structured and individual-based and the substrate dynamics are modelized by an ordinary differential equation. We obtain a Markov process which we describe as random measures. We determine, under a certain normalization of the process, a result of converge...

Dans une première partie, nous proposons un nouveau modèle de chemostat dans lequel la population bactérienne est représentée de manière individu-centrée, structurée en masse, et la dynamique du substrat est modélisée par une équation différentielle ordinaire. Nous obtenons un processus markovien que nous décrivons à l'aide de mesures aléatoires. N...

Population dynamics and in particular microbial population dynamics, though they are complex but also intrinsically discrete and random, are conventionally represented as deterministic differential equations systems. We propose to revisit this approach by complementing these classic formalisms by stochastic formalisms and to explain the links betwe...

We propose a model of chemostat where the bacterial population is individually-based, each bacterium is explicitly represented and has a mass evolving continuously over time. The substrate concentration is represented as a conventional ordinary differential equation. These two components are coupled with the bacterial consumption. Mechanisms acting...