A5076221761- Mathematical and Theoretical Epidemiology and Ecology Models
- Evolution and Genetic Dynamics
- Evolutionary Game Theory and Cooperation
- Plant and animal studies
- Mathematical Biology Tumor Growth
- Nonlinear Differential Equations Analysis
- Nonlinear Dynamics and Pattern Formation
- Ecology and Vegetation Dynamics Studies
- Species Distribution and Climate Change
- Animal Behavior and Reproduction
- Avian ecology and behavior
- Genetic diversity and population structure
- Mycorrhizal Fungi and Plant Interactions
- Insect and Arachnid Ecology and Behavior
- Plant Parasitism and Resistance
- Aquatic Ecosystems and Phytoplankton Dynamics
- Stochastic processes and statistical mechanics
- Numerical methods in inverse problems
- Plant and Fungal Interactions Research
- Cooperative Studies and Economics
- Reproductive biology and impacts on aquatic species
- Fish Ecology and Management Studies
- Ecosystem dynamics and resilience
- Diatoms and Algae Research
- Nonlinear Partial Differential Equations
Laboratoire d’Analyse et de Mathématiques Appliquées
2016-2025
Université Savoie Mont Blanc
2016-2025
Laboratoire de Mathématiques
2014-2025
Centre National de la Recherche Scientifique
2013-2024
Université Grenoble Alpes
2021-2024
Sorbonne Université
2001-2016
Milieux environnementaux, transferts et interactions dans les hydrosystèmes et les sols
2001-2016
Biostatistique et Processus Spatiaux
2011-2014
Laboratoire de Probabilités et Modèles Aléatoires
2011-2012
Aix-Marseille Université
2011-2012
Most mathematical studies on expanding populations have focused the rate of range expansion a population. However, genetic consequences population remain an understudied body theory. Describing as traveling wave solution derived from classical reaction-diffusion model, we analyze spatio-temporal evolution its structure. We show that presence Allee effect (i.e., lower per capita growth at low densities) drastically modifies diversity, both in colonization front and behind it. With pushed...
In this paper, we study the spreading properties of solutions an integro-differential equation form $u_t=J\ast u-u+f(u)$. We focus on equations with slowly decaying dispersal kernels $J(x)$ which correspond to models population dynamics long-distance events. prove that for J, decrease 0 slower than any exponentially function, level sets solution u propagate infinite asymptotic speed. Moreover, obtain lower and upper bounds position set u. These allow us estimate how accelerates, depending...
Abstract The Paris Agreement is a multinational initiative to combat climate change by keeping global temperature increase in this century 2°C above preindustrial levels while pursuing efforts limit the 1.5°C. Until recently, ensembles of coupled simulations producing temporal dynamics en route stable mean at 1.5 and were not available. Hence, few studies that have assessed ecological impact used ad‐hoc approaches. development new specific mitigation now provides an unprecedented opportunity...
We study the asymptotic behavior of solutions to a monostable integro-differential Fisher-KPP equation, that is, where standard Laplacian is replaced by convolution term, when dispersal kernel fat-tailed. focus on two different regimes. First, we long time/long range scaling limit introducing relevant rescaling in space and time prove sharp bound (superlinear) spreading rate Hamilton--Jacobi sense means sub- supersolutions. Second, investigate time/small mutation regime for which, after...
We study the asymptotic behavior of stationary solutions to a quantitative genetics model with trait-dependent mortality and sexual reproduction. The infinitesimal accounts for mixing parental phenotypes at birth.Our analysis encompasses case when deviations between offspring mean trait are typically small. Under suitable regularity growth conditions on rate, we prove existence local uniqueness profile that get concentrated around optimum mortality, Gaussian shape having small variance. Our...
The notion of inside dynamics traveling waves has been introduced in the recent paper [14]. Assuming that a wave u(t,x) = U(x − c t) is made several components υi ≥ 0 (i ∈ I ⊂ N), then given by spatio-temporal evolution densities υi. For reaction-diffusion equations form ∂tu(t,x) ∂xxu(t,x) + f(u(t,x)), where f monostable or bistable type, results [14] show can be classified into two main classes: pulled and pushed waves. Using same framework, we study pulled/pushed nature solutions delay
In this paper, we investigate the inside dynamics of positive solutions integro-differential equations \begin{equation*} \partial_t u(t,x)= (J\star u)(t,x) -u(t,x) + f(u(t,x)), \ t>0 \hbox{ and } x\in\mathbb{R}, \end{equation*} with both <em>thin-tailed</em> <em>fat-tailed</em> dispersal kernels $J$ a monostable reaction term $f.$ The notion has been introduced to characterize traveling waves some reaction-diffusion [23]. Assuming that solution is made several fractions $\upsilon^i\ge 0$...
We consider a general form of reaction-dispersion equations with non-local or nonlinear dispersal operators and local reaction terms. Under some conditions, we prove the non-existence transition fronts, as well stretching properties at large time for solutions Cauchy problem. These conditions are satisfied in particular when is monostable operator either fractional Laplacian, convolution fat-tailed kernel fast diffusion operator.
In this paper, we prove a uniqueness result in the inverse problem of determining several non-constant coefficients one-dimensional reaction-diffusion equations. Such equations include classical model Kolmogorov, Petrovsky and Piskunov as well more sophisticated models from biology. When reaction term contains an unknown polynomial part degree $N,$ with $\mu_k(x),$ our gives sufficient condition for determination part. This only involves pointwise measurements solution $u$ equation its...
Biodiversity is an important component of healthy ecosystems, and thus understanding the mechanisms behind species coexistence critical in ecology conservation biology. In particular, few studies have focused on dynamics resulting from co-occurrence mutualistic competitive interactions within a group species. Here we build mathematical model to study guild competitors who are also engaged with common partner. We show that as well exclusion can occur depending competition strength...