Abstract:
We study a non-local parabolic Lotka-Volterra type equation describing a population structured by a space variable x 2 Rd and a phenotypical trait 2 . Considering diffusion, mutations and space-local competition between the individuals, we analyze the asymptotic (long- time/long-range in the x variable) exponential behavior of the solutions. Using some kind of real phase WKB ansatz, we prove that the propagation of the population in space can be described by a Hamilton-Jacobi equation with obstacle which is independent of . The effective Hamiltonian is derived from an eigenvalue problem. The main difficulties are the lack of regularity estimates in the space variable, and the lack of comparison principle due to the non-local term.

Abstract:
In this paper, we study propagation in a nonlocal reaction-diffusion-mutation model describing the invasion of cane toads in Australia. The population of toads is structured by a space variable and a phenotypical trait and the space-diffusivity depends on the trait. We use a Schauder topological degree argument for the construction of some travelling wave solutions of the model. The speed $c^*$ of the wave is obtained after solving a suitable spectral problem in the trait variable. An eigenvector arising from this eigenvalue problem gives the flavor of the profile at the edge of the front. The major difficulty is to obtain uniform $L^\infty$ bounds despite the combination of non local terms and an heterogeneous diffusivity.

Abstract:
We introduce various models for cellulose bio-degradation by micro-organisms. Those models rely on complex chemical mechanisms, involve the structure of the cellulose chains and are allowed to depend on the phenotypical traits of the population of micro-organisms. We then use the corresponding models in the context of multiple-trait populations. This leads to classical, logistic type, reproduction rates limiting the growth of large populations but also, and more surprisingly, limiting the growth of populations which are too small in a manner similar to the effects seen in populations requiring cooperative interactions (or sexual reproduction). This study hence offers a striking example of how some mechanisms resembling cooperation can occur in structured biological populations, even in the absence of any actual cooperation.

Abstract:
The evolution of dispersal is a classical question in evolutionary ecology, which has been widely studied with several mathematical models. The main question is to define the fittest dispersal rate for a population in a bounded domain, and, more recently, for traveling waves in the full space. In the present study, we reformulate the problem in the context of adaptive evolution. We consider a population structured by space and a genetic trait acting directly on the dispersal (diffusion) rate under the effect of rare mutations on the genetic trait. We show that, as in simpler models, in the limit of vanishing mutations, the population concentrates on a single trait associated to the lowest dispersal rate. We also explain how to compute the evolution speed towards this evolutionary stable distribution. The mathematical interest stems from the asymptotic analysis which requires a completely different treatment of the different variables. For the space variable, the ellipticity leads to the use the maximum principle and Sobolev-type regularity results. For the trait variable, the concentration to a Dirac mass requires a different treatment. This is based on the WKB method and viscosity solutions leading to an effective Hamiltonian (effective fitness of the population) and a constrained Hamilton-Jacobi equation.

Abstract:
We are interested in a stochastic model of trait and age-structured population undergoing mutation and selection. We start with a continuous time, discrete individual-centered population process. Taking the large population and rare mutations limits under a well-chosen time-scale separation condition, we obtain a jump process that generalizes the Trait Substitution Sequence process describing Adaptive Dynamics for populations without age structure. Under the additional assumption of small mutations, we derive an age-dependent ordinary differential equation that extends the Canonical Equation. These evolutionary approximations have never been introduced to our knowledge. They are based on ecological phenomena represented by PDEs that generalize the Gurtin-McCamy equation in Demography. Another particularity is that they involve a fitness function, describing the probability of invasion of the resident population by the mutant one, that can not always be computed explicitly. Examples illustrate how adding an age-structure enrich the modelling of structured population by including life history features such as senescence. In the cases considered, we establish the evolutionary approximations and study their long time behavior and the nature of their evolutionary singularities when computation is tractable. Numerical procedures and simulations are carried.

Abstract:
In linear regression problems with related predictors, it is desirable to do variable selection and estimation by maintaining the hierarchical or structural relationships among predictors. In this paper we propose non-negative garrote methods that can naturally incorporate such relationships defined through effect heredity principles or marginality principles. We show that the methods are very easy to compute and enjoy nice theoretical properties. We also show that the methods can be easily extended to deal with more general regression problems such as generalized linear models. Simulations and real examples are used to illustrate the merits of the proposed methods.

Abstract:
This research was conducted with the main purpose to evaluate the level of genetic similarities among an olive population situated in Djebel Ouslet (central east of Tunisia). Morphological characters and phenological growth stages of four olive cultivars Ousleti, Brahmi, Chaibi and Jeli were described during 2004-2006. Morphological classification used, was based on tree, leaf, inflorescence, fruit and endocarp characteristics. Technological characters of the fruits concerned the oil content and their chemical composition. Floral phenology, flowering and pistil abortion rates of the cultivars were recorded at full bloom. Also, a pollen monitoring survey for each cultivar was investigated. This study shows the relative differences between cultivars in flowering, fruiting patterns, oil yield and fatty acid contents of the fruits. Under the conditions of Djebel Ouslet, the flowering period of the cultivars was similar and covered each other but little differences were recorded in the duration and the onset of flowering. The evaluation of self-fertility showed that all cultivars can be considered self-compatible and fruiting rates were higher under free-pollination than under self-pollination. The results obtained are consistent with the high pollen capacity of the cultivars, suggesting their use as pollinizers in the cross-pollination assays to improve productivity. Large differences in oil content and in fatty acid profiles were observed in the cultivars examined. But their olive oil are conform to international standards. The ranges of fatty acid for all the cultivars fall within the accepted limits for fatty acid composition of Virgin olive oil. This database of the most representative cultivars grown in Djebel Ouslet concerning their agronomic and chemical characteristics could be exploited for screening synonyms within this olive population and could provide information for cultural purposes and breeding programs.

Abstract:
A fundamental goal in biology is to achieve a mechanistic understanding of how and to what extent ecological variation imposes selection for distinct traits and favors the fixation of specific genetic variants. Key to such an understanding is the detailed mapping of the natural genomic and phenomic space and a bridging of the gap that separates these worlds. Here we chart a high-resolution map of natural trait variation in one of the most important genetic model organisms, the budding yeast Saccharomyces cerevisiae, and its closest wild relatives and trace the genetic basis and timing of major phenotype changing events in its recent history. We show that natural trait variation in S. cerevisiae exceeds that of its relatives, despite limited genetic variation, and follows the population history rather than the source environment. In particular, the West African population is phenotypically unique, with an extreme abundance of low-performance alleles, notably a premature translational termination signal in GAL3 that cause inability to utilize galactose. Our observations suggest that many S. cerevisiae traits may be the consequence of genetic drift rather than selection, in line with the assumption that natural yeast lineages are remnants of recent population bottlenecks. Disconcertingly, the universal type strain S288C was found to be highly atypical, highlighting the danger of extrapolating gene-trait connections obtained in mosaic, lab-domesticated lineages to the species as a whole. Overall, this study represents a step towards an in-depth understanding of the causal relationship between co-variation in ecology, selection pressure, natural traits, molecular mechanism, and alleles in a key model organism.

Abstract:
In this paper I prove the existence of a positive stationary solution for a generic quasilinear model of structured population. The existence is proved using Schauder's fixed point theorem. The theorem is applied to a hierarchically size-structured population model.

Abstract:
We address the evolution of entanglement in bimodal continuous variable quantum systems interacting with two independent structured reservoirs. We derive an analytic expression for the entanglement of formation without performing the Markov and the secular approximations and study in details the entanglement dynamics for various types of structured reservoirs and for different reservoir temperatures, assuming the two modes initially excited in a twin-beam state. Our analytic solution allows us to identify three dynamical regimes characterized by different behaviors of the entanglement: the entanglement sudden death, the non-Markovian revival and the non-secular revival regimes. Remarkably, we find that, contrarily to the Markovian case, the short-time system-reservoir correlations in some cases destroy quickly the initial entanglement even at zero temperature.