The state-space modeling of partially observed dynamical systems generally requires estimates of unknown parameters. The dynamic state vector together with the static parameter vector can be considered as an augmented state vector. Classical filtering methods, such as the extended Kalman filter and the bootstrap particle filter, fail to estimate the augmented state vector. For these classical filters to handle the augmented state vector, a dynamic noise term should be artificially added to the parameter components or to the deterministic component of the dynamical system. However, this approach degrades the estimation performance of the filters. In this work, we propose a variant of the particle filter based on convolution kernel approximation techniques. This approach is tested on a simulated case study.

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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.

a b s t r a c tFinely tuned process-based tree-growth models are of considerable help in understanding the variations of biomass increments measured in the dendrochronological series. Using site and species parameters, as well as daily climate variables, the MAIDEN model computes the water balance at ecosystem level and the daily increment of carbon storage in the stem through photosynthesis processes to reproduce the structure of the tree-ring series. In this paper, we use three techniques to calibrate this model with Pinus halepensis data sampled in the Mediterranean part of France: a standard optimization (PEST), Monte Carlo Markov Chains (MCMC) and Particle Filtering (PF). Contrary to PEST, which tries to find an optimum fit (giving the lowest error between observations and simulations), the principle of MCMC and PF is to walk, from a priori distributions, in the parameter space according to particular statistical rules to compute each parameter distribution. The PEST and MCMC calibrations of our dendrochronological series lead to rather similar adjustments between simulations and observations. PF and MCMC calibrations give different parameter distributions, showing how complementary are these methods, with a better fit for MCMC. Yet, independent validations over 11 independent meteorological years show a higher efficiency of the recent PF method over the others.

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International audienceWe 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 on the bacteria are explicitly described (growth, division and washout). Bacteria interact via consumption. We set the exact Monte Carlo simulation algorithm of this model and its mathematical representation as a stochastic process. We prove the convergence of this process to the solution of an integro-differential equation when the population size tends to infinity. Finally, we propose several numerical simulation

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