Integration of the priming effect (PE) in ecosystem models is crucial to better predict the consequences of global change on ecosystem carbon (C) dynamics and its feedbacks on climate. Over the last decade, many attempts have been made to model PE in soil. However, PE has not yet been incorporated into any ecosystem models. Here, we build plant/soil models to explore how PE and microbial diversity influence soil/plant interactions and ecosystem C and nitrogen (N) dynamics in response to global change (elevated CO 2 and atmospheric N depositions). Our results show that plant persistence, soil organic matter (SOM) accumulation, and low N leaching in undisturbed ecosystems relies on a fine adjustment of microbial N mineralization to plant N uptake. This adjustment can be modeled in the SYMPHONY model by considering the destruction of SOM through PE, and the interactions between two microbial functional groups: SOM decomposers and SOM builders. After estimation of parameters, SYMPHONY provided realistic predictions on forage production, soil C storage and N leaching for a permanent grassland. Consistent with recent observations, SYMPHONY predicted a CO 2 -induced modification of soil microbial communities leading to an intensification of SOM mineralization and a decrease in the soil C stock. SYMPHONY also indicated that atmospheric N deposition may promote SOM accumulation via changes in the structure and metabolic activities of microbial communities. Collectively, these results suggest that the PE and functional role of microbial diversity may be incorporated in ecosystem models with a few additional parameters, improving accuracy of predictions.
We consider the optimal control problem of feeding in minimal time a tank where several species compete for a single resource, with the objective being to reach a given level of the resource. We allow controls to be bounded measurable functions of time plus possible impulses. For the one-species case, we show that the immediate one-impulse strategy (filling the whole reactor with one single impulse at the initial time) is optimal when the growth function is monotonic. For nonmonotonic growth functions with one maximum, we show that a particular singular arc strategy (precisely defined in section 3) is optimal. These results extend and improve former ones obtained for the class of measurable controls only. For the two-species case with monotonic growth functions, we give conditions under which the immediate one-impulse strategy is optimal. We also give optimality conditions for the singular arc strategy (at a level that depends on the initial condition) to be optimal. The possibility for the immediate one-impulse strategy to be nonoptimal while both growth functions are monotonic is a surprising result and is illustrated with the help of numerical simulations.
SUMMARYFor nonlinear systems in R n which are observable but not uniformly, we study how to design explicitly exponential observers, after having the system immersed in R m with m > n: The central issue concerns the determination of a lipschitzian extension in R m of the dynamics, which is defined exclusively on a subset of empty interior. We propose some constructive tools and illustrate their utility on a biological example.
We study a chemostat model in which two microbial species grow on a single resource. We show that species coexistence is possible when the species which would normally win the exclusive competition aggregates in flocs. Our mathematical analysis exploits the fact that flocculation is fast compared to biological growth, a common hypothesis in floc models. A numerical study shows the validity of this approach in a large parameter range. We indicate how our model yields a mechanistic justification for the so-called density-dependent growth.
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