Simple signaling games of sexual selection (Grafen’s revisited)

International audienceWe investigate several versions of a simple game of sexual selection, to explore the role of secondary sexual characters (the "handicap paradox") with the tools of signaling theory. Our models admit closed form solutions. They are very much inspired by Grafen's (J Theor Biol 144:517-546, 1990a; J Theor Biol 144:473-516, 1990b) seminal companion papers. By merging and simplifying his two approaches, we identify a not so minor artifact in the seminal study. We propose an alternative model to start with Grafen's sexual selection theory, with several similarities with Getty (Anim Behav 56:127-130, 1998)

Uncoupling Isaacs’equations in nonzero-sum two-player differential games : The example of conflict over parental care

International audienceWe use a recently uncovered decoupling of Isaacs PDE’s of some mixed closed loop Nash equilibria to give a rather complete analysis of the classical problem of conflict over parental care in behavioural ecology, for a more general set up than had been considered heretofore.On utilise un découplage récemment mis en évidence des équations d’Isaacs d’un jeu différentiel pour des stratégies mixtes singulières particulières pour donner une analyse assez complète d’un problème classique en écologie comportementale concernant le conflit à propos des soins parentaux

Diagnostic des systèmes dynamiques linéaires sans modèle explicite

International audienceWe propose a diagnosis approach of sensor and actuator modeled as structured signals acting on a particular class of uncertain linear dynamical systems. The main advantage of this approach is that it is possible under certain assumptions, to detect, isolate and identify faults using only input and output measurements without having to identify model parameters. The method is based on the generation and analysis of analytical redundancy relations and exploits the fact that a structured signal satisfies a differential equation. The decision rule is based entirely on the temporal behaviour of the estimates of some fault characteristics. A numerical example is provided and discussed to illustrate the proposed approach.Nous proposons une méthode de diagnostic des défauts actionneur et capteur modélisés au travers de signaux structurés sur une classe particulière de systèmes dynamiques linéaires incertains. Le principal atout de cette approche est qu'il est possible, sous certaines hypothèses, de détecter, localiser et identifier les défauts à l'aide des seules mesures de la commande et de la sortie sans avoir à identifier les paramètres du modèle. La méthode est fondée sur la génération et l'analyse de relations de redondance analytique et exploite le fait qu'un signal structuré satisfait une équation différentielle. La prise de décision est entièrement fondée sur l'évolution temporelle des estimations de certaines caractéristiques des défauts. Un exemple numérique est fourni et commenté afin d'illustrer l'approche proposée

Une méthode algébrique de diagnostic de défauts.

6 pagesInternational audienceCet article présente une reformulation et extension au diagnostic des méthodes algébrique développées pour l'identification des systèmes linéaires (Fliess and Sira-Ramirez [2003]). En exploitant les outils et résultats de l'analyse pseudo-spectrale, une approche est proposée pour la génération d'indicateurs de défaut. Le principal atout de cette approche est qu'il est possible, sous certaines hypothèses, de détecter, localiser et identifier les défauts uniquement à partir des mesures de la commande et celles de la sortie sans identifier explicitement un modèle. Un exemple numérique est fourni et commenté afin d'illustrer l'approche proposée

A robust algebraic approach to fault diagnosis of uncertain linear systems

International audienceThis article proposes an algebraic method to fault diagnosis for uncertain linear systems. The main advantage of this new approach is to realize fault diagnosis only from knowledge of input and output measurements without identi- fying explicitly model parameters. Using tools and results of algebraic identification and pseudospectra analysis, the issues of robustness of the proposed approach compared to the model order and noise measurement are examined. Numerical examples are provided and discussed to illustrate the efficiency of the proposed fault diagnosis method

Observability, Identifiability and Epidemiology -- A survey

In this document we introduce the concepts of Observability and Iden-tifiability in Mathematical Epidemiology. We show that, even for simple and well known models, these properties are not always fulfilled. We also consider the problem of practical observability and identi-fiability which are connected to sensitivity and numerical condition numbers

Seasonality and the evolutionary divergence of plant parasites

The coexistence of closely related plant parasites is widespread. Yet, understanding the ecological determinants of evolutionary divergence in plant parasites remains an issue. Niche differentiation through resource specialization has been widely researched, but it hardly explains the coexistence of parasites exploiting the same host plant. Time-partitioning has so far received less attention, although in temperate climates, parasites may specialize either in the early or in the late season. Accordingly we investigated whether seasonality can also promote phenotypic divergence. For plant parasites, seasonality generally engenders periodic host absence. To account for abrupt seasonal events, we made use of an epidemic model that combines continuous and discrete dynamics. Based on the assumption there is a trade-off between in-season transmission and inter-season survival, we found out through an 'evolutionary invasion analysis' that evolutionary divergence of the parasite phenotype can occur. Since such a trade-off has been reported, this study provides further ecological bases for the coexistence of closely related plant parasites. Moreover, this study provides original insights into the coexistence of sibling plant pathogens which perform either a single or several infection cycles within a season (mono- and poly-cyclic diseases, or uni- and multi-voltine life cycles)

Stability analysis for unknown delayed systems controlled by model-free control

International audienceUnknown delayed systems are present in many domains and control this kind of systems remains a difficult problem. Indeed, we can find theses systems in physics, chemistry, aeronautics, etc. The main problem is that the delay is unknown, and so the model is not exactly well-known. By the way, the use of model-free control (MFC) remains a suitable solution to tackle this problem. This paper deals with a stability analysis to show the influence of a parameter on the stability of the systems regarding to the delay

Epidemiological and ecological consequences of virus manipulation of host and vector in plant virus transmission.

Many plant viruses are transmitted by insect vectors. Transmission can be described as persistent or non-persistent depending on rates of acquisition, retention, and inoculation of virus. Much experimental evidence has accumulated indicating vectors can prefer to settle and/or feed on infected versus noninfected host plants. For persistent transmission, vector preference can also be conditional, depending on the vector's own infection status. Since viruses can alter host plant quality as a resource for feeding, infection potentially also affects vector population dynamics. Here we use mathematical modelling to develop a theoretical framework addressing the effects of vector preferences for landing, settling and feeding-as well as potential effects of infection on vector population density-on plant virus epidemics. We explore the consequences of preferences that depend on the host (infected or healthy) and vector (viruliferous or nonviruliferous) phenotypes, and how this is affected by the form of transmission, persistent or non-persistent. We show how different components of vector preference have characteristic effects on both the basic reproduction number and the final incidence of disease. We also show how vector preference can induce bistability, in which the virus is able to persist even when it cannot invade from very low densities. Feedbacks between plant infection status, vector population dynamics and virus transmission potentially lead to very complex dynamics, including sustained oscillations. Our work is supported by an interactive interface https://plantdiseasevectorpreference.herokuapp.com/. Our model reiterates the importance of coupling virus infection to vector behaviour, life history and population dynamics to fully understand plant virus epidemics