A probabilistic approach to large time behaviour of viscosity solutions of parabolic equations with Neumann boundary conditions

This paper is devoted to the study of the large time behaviour of viscosity solutions of parabolic equations with Neumann boundary conditions. This work is the sequel of [13] in which a probabilistic method was developped to show that the solution of a parabolic semilinear PDE behaves like a linear term $\lambda T$ shifted with a function $v$, where $(v,\lambda)$ is the solution of the ergodic PDE associated to the parabolic PDE. We adapt this method in finite dimension by a penalization method in order to be able to apply an important basic coupling estimate result and with the help of a regularization procedure in order to avoid the lack of regularity of the coefficients in finite dimension. The advantage of our method is that it gives an explicit rate of convergence

Sources, fate, and pathways of Leeuwin Current water in the Indian Ocean and Great Australian Bight: A Lagrangian study in an eddy-resolving ocean model

The Leeuwin Current is the dominant circulation feature in the eastern Indian Ocean, transporting tropical and subtropical water southward. While it is known that the Leeuwin Current draws its water from a multitude of sources, existing Indian Ocean circulation schematics have never quantified the fluxes of tropical and subtropical source water flowing into the Leeuwin Current. This paper uses virtual Lagrangian particles to quantify the transport of these sources along the Leeuwin Current's mean pathway. Here the pathways and exchange of Leeuwin Current source waters across six coastally bound sectors on the south-west Australian coast are analyzed. This constitutes the first quantitative assessment of Leeuwin Current pathways within an offline, 50 year integration time, eddy-resolving global ocean model simulation. Along the Leeuwin Current's pathway, we find a mean poleward transport of 3.7 Sv in which the tropical sources account for 60-78% of the transport. While the net transport is small, we see large transports flowing in and out of all the offshore boundaries of the Leeuwin Current sectors. Along the Leeuwin Current's pathway, we find that water from the Indonesian Throughflow contributes 50-66% of the seasonal signal. By applying conditions on the routes particles take entering the Leeuwin Current, we find particles are more likely to travel offshore north of 30°S, while south of 30°S, particles are more likely to continue downstream. We find a 0.2 Sv pathway of water from the Leeuwin Current's source regions, flowing through the entire Leeuwin Current pathway into the Great Australian Bight

Bistability induced by generalist natural enemies can reverse pest invasions

Reaction-diffusion analytical modeling of predator-prey systems has shown that specialist natural enemies can slow, stop and even reverse pest invasions, assuming that the prey population displays a strong Allee effect in its growth. Few additional analytical results have been obtained for other spatially distributed predator-prey systems, as traveling waves of non-monotonous systems are notoriously difficult to obtain. Traveling waves have indeed recently been shown to exist in predator-prey systems, but the direction of the wave, an essential item of information in the context of the control of biological invasions, is generally unknown. Preliminary numerical explorations have hinted that control by generalist predators might be possible for prey populations displaying logistic growth. We aimed to formalize the conditions in which spatial biological control can be achieved by generalists, through an analytical approach based on reaction-diffusion equations. The population of the focal prey - the invader - is assumed to grow according to a logistic function. The predator has a type II functional response and is present everywhere in the domain, at its carrying capacity, on alternative hosts. Control, defined as the invader becoming extinct in the domain, may result from spatially independent demographic dynamics or from a spatial extinction wave. Using comparison principles, we obtain sufficient conditions for control and for invasion, based on scalar bistable partial differential equations (PDEs). The searching efficiency and functional response plateau of the predator are identified as the main parameters defining the parameter space for prey extinction and invasion. Numerical explorations are carried out in the region of those control parameters space between the super-and subso-lutions, in which no conclusion about controllability can be drawn on the basis of analytical solutions. The ability of generalist predators to control prey populations with logistic growth lies in the bis-table dynamics of the coupled system, rather than in the bistability of prey-only dynamics as observed for specialist predators attacking prey populations displaying Allee effects. The consideration of space in predator-prey systems involving generalist predators with a parabolic functional response is crucial. Analysis of the ordinary differential equations (ODEs) system identifies parameter regions with monostable (extinction) and bistable (extinction or invasion) dynamics. By contrast, analysis of the associated PDE system distinguishes different and additional regions of invasion and extinction. Depending on the relative positions of these different zones, four patterns of spatial dynamics can be identified : traveling waves of extinction and invasion, pulse waves of extinction and heterogeneous stationary positive solutions of the Turing type. As a consequence, prey control is predicted to be possible when space is considered in additional situations other than those identified without considering space. The reverse situation is also possible. None of these considerations apply to spatial predator-prey systems with specialist natural enemies

Présidentielle : le logement est-il bien loti ?

La publication du rapport de la Fondation Abbé Pierre en janvier 2017 n’a pas fait exception : le mal-logement continue de progresser en France. Les prix immobiliers sont repartis à la hausse ces derniers trimestres et la publication des premiers résultats de l’Enquête nationale logement de l’INSEE de 2013 font apparaître une dégradation de la situation financière des ménages. Malgré tous ces éléments, la thématique du logement est apparue relativement tardivement dans les débats entourant l’élection présidentielle. Nous tentons ici d’esquisser un panorama des propositions émanant des principaux candidats à l’élection présidentielle sur ce sujet. [Premier paragraphe

Investissement des ménages : en attendant l’ELAN

Le 4 avril dernier a été présenté en Conseil des ministres le projet de loi « Évolution du logement et aménagement numérique » (ELAN). Depuis l’automne 2017, les thématiques de la construction et du logement sont réapparues dans le débat public lorsque le gouvernement a annoncé sa volonté de faire des économies budgétaires sur les aides à la personne et sur la politique du logement. Alors que l’analyse des déterminants structurels de l’investissement des ménages laissait présager son fort redressement en 2017, il semblerait que les déclarations du gouvernement aient provoqué un certain attentisme sur le marché de la construction. [Premier paragraphe

A slow-fast dynamic decomposition links neutral and non-neutral coexistence in interacting multi-strain pathogens

Understanding the dynamics of multi-type microbial ecosystems remains a challenge, despite advancing molecular technologies for diversity resolution within and between hosts. Analytical progress becomes difficult when modelling realistic levels of community richness, relying on computationally-intensive simulations and detailed parametrisation. Simplification of dynamics in polymorphic pathogen systems is possible usingaggregation methods and the slow-fast dynamics approach. Here we develop one new such framework, tailored to the epidemiology of an endemic multi-strain pathogen. We apply Goldstone’s idea of slow dynamics resulting from spontaneously broken symmetries, to study direct interactions in co-colonization, ranging from competition to facilitation between strains. The slow-fast dynamics approach interpolates between a neutral and non-neutral model for multi-strain coexistence, and quantifies the exact asymmetries that are important for the maintenance and stabilisation of diversity

Morphological variation of the spermatheca in the garden snail Cantareus aspersus - article in French with an abridged English version

articleSpermathecal morphology is known to play an important role in postcopulatory sexual selection of many invertebrates. In helicid land snails, the spermatheca is subdivided into tubules, whose number is sometimes subject to a strong inter-individual variation. Significance of this variation for postcopulatory sexual selection is unknown, but it might be related to cryptic female choice. In the present work, we have investigated the fine multi-tubular structure of the sperm storage organ in Cantareus aspersus. We found between 3 and 13 tubules per individual in a single population, which represents a degree of variation rarely observed in helicid land snails

Historical biogeography of the land snail Cornu aspersum: new insights into the scenario inferred from haplotype distribution in both Europe and North Africa.

International audienceBackground: Despite its key location between the rest of the continent and Europe, research on the phylogeography of north African species remains very limited compared to European and North American taxa. The Mediterranean land mollusc Cornu aspersum (= Helix aspersa) is part of the few species widely sampled in north Africa for biogeographical analysis. It then provides an excellent biological model to understand phylogeographical patterns across the Mediterranean basin, and to evaluate hypotheses of population differentiation. We investigated here the phylogeography of this land snail to reassess the evolutionary scenario we previously considered for explaining its scattered distribution in the western Mediterranean, and to help to resolve the question of the direction of its range expansion (from north Africa to Europe or vice versa). By analysing simultaneously individuals from 73 sites sampled in its putative native range, the present work provides the first broad-scale screening of mitochondrial variation (cyt b and 16S rRNA genes) of C. aspersum. Results: Phylogeographical structure mirrored previous patterns inferred from anatomy and nuclear data, since all haplotypes could be ascribed to a B (West) or a C (East) lineage. Alternative migration models tested confirmed that C. aspersum most likely spread from north Africa to Europe. In addition to Kabylia in Algeria, which would have been successively a centre of dispersal and a zone of secondary contacts, we identified an area in Galicia where genetically distinct west and east type populations would have regained contact. Conclusions: Vicariant and dispersal processes are reviewed and discussed in the light of signatures left in the geographical distribution of the genetic variation. In referring to Mediterranean taxa which show similar phylogeographical patterns, we proposed a parsimonious scenario to account for the "east-west" genetic splitting and the northward expansion of the western (B) clade which roughly involves (i) the dispersal of ancestral (eastern) types through Oligocene terranes in the Western Mediterranean (ii) the Tell Atlas orogenesis as gene flow barrier between future west and east populations, (iii) the impact of recurrent climatic fluctuations from mid-Pliocene to the last ice age, (iv) the loss of the eastern lineage during Pleistocene northwards expansion phases