This work deals with the approximate reduction of a nonautonomous two time scales ordinary differential equations system with periodic fast dynamics. We illustrate this technique with the analysis of two models belonging to different fields in ecology. On the one hand, we deal with a two patches periodic predator-prey model with a refuge for prey. Considering migrations between patches to be faster than local interaction allows us to study a three-dimensional system by means of a two-dimensional one. On the other hand, a two time scales periodic eco-epidemic model is addressed by considering two competing species, one of them being affected by a periodic SIR epidemic process which is faster than inter-species interactions. The difference between time scales allows us to study the asymptotic behavior of the four-dimensional system by means of a planar, reduced one. Furthermore, we propose a methodology straightforwardly applicable to a very large class of two time scales periodic systems.

This article is a review of spatial aggregation of variables for time continuous models. Two cases are considered. The first case corresponds to a discrete space, i.e. a set of discrete patches connected by migrations, which are assumed to be fast with respect to local interactions. The mathematical model is a set of coupled ordinary differential equations (O.D.E.). The spatial aggregation allows one to derive a global model governing the time variation of the total numbers of individuals of all patches in the long term. The second case considers a continuous space and is a set of partial differential equations (P.D.E.). In that case, we also assume that diffusion is fast in comparison with local interactions. The spatial aggregation allows us again to obtain an O.D.E. governing the total population density, which is obtained by integration all over the spatial domain, at the slow time scale. These aggregations of variables are based on time scales separation methods which have been presented largely elsewhere and we recall the main results. We illustrate the methods by examples in population dynamics and prey–predator models.

Enhancingthepredictivepowerofmodelsinbiologyisachallengingissue.Amongthemajor difficultiesimpedingmodeldevelopmentandimplementationarethesensitivityofoutcomesto variationsinmodelparameters,theproblemofchoosingofparticularexpressionsfortheparametriza- tion offunctionalrelations,anddifficultiesinvalidatingmodelsusinglaboratorydataand/orfield observations.Inthispaper,werevisitthephenomenonwhichisreferredtoasstructuralsensitivityofa model. Structuralsensitivityarisesasaresultoftheinterplaybetweensensitivityofmodeloutcomesto variationsinparametersandsensitivitytothechoiceofmodelfunctions,andthiscanbesomewhatofa bottleneckinimprovingthemodelspredictivepower.Weprovidearigorousdefinitionofstructural sensitivityandweshowhowwecanquantifythedegreeofsensitivityofamodelbasedonthe Hausdorffdistanceconcept.Weproposeasimplesemi-analyticaltestofstructuralsensitivityinanODE modelingframework.Furthermore,weemphasizetheimportanceofdirectlylinkingthevariabilityof field/experimentaldataandmodelpredictions,andwedemonstrateawayofassessingtherobustness of modelingpredictionswithrespecttodatasamplingvariability.Asaninsightfulillustrativeexample, we testoursensitivityanalysismethodsonachemostatpredator–preymodel,whereweuselaboratory data onthefeedingofprotozoatoparameterizethepredatorfunctionalresponse.

This article is a review of spatial aggregation of variables for time continuous models. Two cases are considered. The first case corresponds to a discrete space, i.e. a set of discrete patches connected by migrations, which are assumed to be fast with respect to local interactions. The mathematical model is a set of coupled ordinary differential equations (O.D.E.). The spatial aggregation allows one to derive a global model governing the time variation of the total numbers of individuals of all patches in the long term. The second case considers a continuous space and is a set of partial differential equations (P.D.E.). In that case, we also assume that diffusion is fast in comparison with local interactions. The spatial aggregation allows us again to obtain an O.D.E. governing the total population density, which is obtained by integration all over the spatial domain, at the slow time scale. These aggregations of variables are based on time scales separation methods which have been presented largely elsewhere and we recall the main results. We illustrate the methods by examples in population dynamics and prey-predator models.

Dissolved organic carbon (DOC) can be mineralized into CO2 through bacterial respiration, reenter the trophic chain if bacterial biomass is grazed, or be partly stored in a recalcitrant form for millennia in the deep ocean by bacterial production during DOC degradation. This review compares mathematical models used to represent these pathways in the context of the current knowledge of bacterial metabolism, and examines how they may be related to the biological carbon pump and the microbial carbon pump. In view of the ever-changing environments in which bacteria exist, the authors propose that models of DOC degradation should be based on data from experiments in which bacteria are subjected to external constraints, such as DOC availability, temperature, and ocean depth. Further, the need for combining experimental and mechanistic modeling approaches to advance our understanding of the factors that affect oceanic DOC cycling and organic carbon storage is discussed.

Enhancing the predictive power of models in biology is a challenging issue. Among the major difficulties impeding model development and implementation are the sensitivity of outcomes to variations in model parameters, the problem of choosing of particular expressions for the parametrization of functional relations, and difficulties in validating models using laboratory data and/or field observations. In this paper, we revisit the phenomenon which is referred to as structural sensitivity of a model. Structural sensitivity arises as a result of the interplay between sensitivity of model outcomes to variations in parameters and sensitivity to the choice of model functions, and this can be somewhat of a bottleneck in improving the models predictive power. We provide a rigorous definition of structural sensitivity and we show how we can quantify the degree of sensitivity of a model based on the Hausdorff distance concept. We propose a simple semi-analytical test of structural sensitivity in an ODE modeling framework. Furthermore, we emphasize the importance of directly linking the variability of field/experimental data and model predictions, and we demonstrate a way of assessing the robustness of modeling predictions with respect to data sampling variability. As an insightful illustrative example, we test our sensitivity analysis methods on a chemostat predator-prey model, where we use laboratory data on the feeding of protozoa to parameterize the predator functional response.

The semi-enclosed nature of the Mediterranean Sea, together with its smaller inertia due to the relative short residence time of its water masses, make it highly reactive to external forcings, in particular variations of water, energy and matter fluxes at the interfaces. This region, which has been identified as a "hotspot" for climate change, is therefore expected to experience environmental impacts that are considerably greater than those in many other places around the world. These natural pressures interact with the increasing demographic and economic developments occurring heterogeneously in the coastal zone, making the Mediterranean even more sensitive. This review paper aims to provide a review of the state of current functioning and responses of Mediterranean marine biogeochemical cycles and ecosystems with respect to key natural and anthropogenic drivers and to consider the ecosystems' responses to likely changes in physical, chemical and socio-economical forcings induced by global change and by growing anthropogenic pressure at the regional scale. The current knowledge on and expected changes due to single forcing (hydrodynamics, solar radiation, temperature and acidification, chemical contaminants) and combined forcing (nutrient sources and stoichiometry, extreme events) affecting the biogeochemical fluxes and ecosystem functioning are explored. Expected changes in biodiversity resulting from the combined action of the different forcings are proposed. Finally, modeling capabilities and necessity for modeling are presented. A synthesis of our current knowledge of expected changes is proposed, highlighting relevant questions for the future of the Mediterranean ecosystems that are current research priorities for the scientific community. Finally, we discuss how these priorities can be approached by national and international multi-disciplinary research, which should be implemented on several levels, including observational studies and modeling at different temporal and spatial scales. (C) 2011 Elsevier Ltd. All rights reserved.