Stochastic dynamics of adaptive trait and neutral marker driven by eco-evolutionary feedbacks

How the neutral diversity is affected by selection and adaptation is investigated in an eco-evolutionary framework. In our model, we study a finite population in continuous time, where each individual is characterized by a trait under selection and a completely linked neutral marker. Population dynamics are driven by births and deaths, mutations at birth, and competition between individuals. Trait values influence ecological processes (demographic events, competition), and competition generates selection on trait variation, thus closing the eco-evolutionary feedback loop. The demographic effects of the trait are also expected to influence the generation and maintenance of neutral variation. We consider a large population limit with rare mutation, under the assumption that the neutral marker mutates faster than the trait under selection. We prove the convergence of the stochastic individual-based process to a new measure-valued diffusive process with jumps that we call Substitution Fleming-Viot Process (SFVP). When restricted to the trait space this process is the Trait Substitution Sequence first introduced by Metz et al. (1996). During the invasion of a favorable mutation, a genetical bottleneck occurs and the marker associated with this favorable mutant is hitchhiked. By rigorously analysing the hitchhiking effect and how the neutral diversity is restored afterwards, we obtain the condition for a time-scale separation; under this condition, we show that the marker distribution is approximated by a Fleming-Viot distribution between two trait substitutions. We discuss the implications of the SFVP for our understanding of the dynamics of neutral variation under eco-evolutionary feedbacks and illustrate the main phenomena with simulations. Our results highlight the joint importance of mutations, ecological parameters, and trait values in the restoration of neutral diversity after a selective sweep.Comment: 29 page

Slow and fast scales for superprocess limits of age-structured populations

International audienceA superprocess limit for an interacting birth-death particle system modelling a population with trait and physical age-structures is established. Traits of newborn offspring are inherited from the parents except when mutations occur, while ages are set to zero. Because of interactions between individuals, standard approaches based on the Laplace transform do not hold. We use a martingale problem approach and a separation of the slow (trait) and fast (age) scales. While the trait marginals converge in a pathwise sense to a superprocess, the age distributions, on another time scale, average to equilibria that depend on traits. The convergence of the whole process depending on trait and age, only holds for finite-dimensional time-marginals. We apply our results to the study of examples illustrating different cases of trade-off between competition and senescence

Nonlinear historical superprocess approximations for population models with past dependence

We are interested in the evolving genealogy of a birth and death process with trait structure and ecological interactions. Traits are hereditarily transmitted from a parent to its offspring unless a mutation occurs. The dynamics may depend on the trait of the ancestors and on its past and allows interactions between individuals through their lineages. We define an interacting historical particle process describing the genealogies of the living individuals; it takes values in the space of point measures on an infinite dimensional c\`adl\`ag path space. This individual-based process can be approximated by a nonlinear historical superprocess, under the assumptions of large populations, small individuals and allometric demographies. Because of the interactions, the branching property fails and we use martingale problems and fine couplings between our population and independent branching particles. Our convergence theorem is illustrated by two examples of current interest in biology. The first one relates the biodiversity history of a population and its phylogeny, while the second treats a spatial model with competition between individuals through their past trajectories.Comment: 31 page

La certification qualité est-elle un facteur de compétitivité pour les entreprises ? Le cas de la norme ISO 9001

si les normes ISO 9000 traduisent un consensus international quant auxcaractéristiques essentielles que doit posséder un système qualité pour garantir le fonctionnement efficace de toute organisation, il semblerait qu'après des années de certification, les responsables qualité doivent rendre compte des apports réels de lacertification au sein de leurs organisations. Or, l'analyse de l'impact de la certification ISO 9000 est relativement peu étudié au regard des investissements financiers et organisationnelsconsidérables déployés par les organisations pour répondre aux exigences de ce référentiel.Les résultats des études menées dans ce domaine sont loin d'être consensuels et sont souvent soumis à des conditions de mise en place de la certification ISO 9000 au sein de l'organisation. La question se pose alors de savoir dans quelle mesure la certification peut permettre à une organisation d'atteindre des objectifs d'efficacité et sous quelles conditions.Une première partie est consacrée à la revue des études académiques qui ont cherché à appréhender le lien entre la certification et la performance des entreprises. Ensuite, une seconde partie expose les résultats d'une étude empirique portant sur plus de 835 entreprises, de secteurs et de tailles représentatifs des entreprises certifiées en France. Il apparaît, dans la comparaison des résultats théoriques et empiriques, une cohérence quant au caractère contingent de la certification et de son impact sur la performance de l'entreprise.Certification, ISO 9001, performance, qualité

Limiting Feller diffusions for logistic populations with age-structure

http://www.isi2011.ie/content/access-congress-proceedings.htmlInternational audiencePopulation dynamics with age structure are very important in demography and ecology since the demographic parameters of most species change over their life (think of maturation and senescence) and many phenomena (\eg evolving life histories or kinship based social interactions such as cooperative breeding) require the introduction of age for their proper description. We consider here a long time scale diffusion limit for the dynamics of a large purely age structured population with closely matched birth an death rates. To this end we work out the technical details necessary to apply the general results in Méléard and Tran to this particular case. This way we derive, starting from a logistic age-structured birth and death process, a Feller diffusion with drift and diffusion coefficients that are averages over the age distribution

Dynamic modelling of hepatitis C virus transmission among people who inject drugs: a methodological review

Equipment sharing among people who inject drugs (PWID) is a key risk factor in infection by hepatitis C virus (HCV). Both the effectiveness and cost-effectiveness of interventions aimed at reducing HCV transmission in this population (such as opioid substitution therapy, needle exchange programs or improved treatment) are difficult to evaluate using field surveys. Ethical issues and complicated access to the PWID population make it difficult to gather epidemiological data. In this context, mathematical modelling of HCV transmission is a useful alternative for comparing the cost and effectiveness of various interventions. Several models have been developed in the past few years. They are often based on strong hypotheses concerning the population structure. This review presents compartmental and individual-based models in order to underline their strengths and limits in the context of HCV infection among PWID. The final section discusses the main results of the papers

Impact of a treatment as prevention strategy on hepatitis C virus transmission and on morbidity in people who inject drugs

Background: Highly effective direct-acting antiviral (DAA) regimens (90% efficacy) are becoming available for hepatitis C virus (HCV) treatment. This therapeutic revolution leads us to consider possibility of eradicating the virus. However, for this, an effective cascade of care is required. Methods: In the context of the incoming DAAs, we used a dynamic individual-based model including a model of the people who inject drugs (PWID) social network to simulate the impact of improved testing, linkage to care, and adherence to treatment, and of modified treatment recommendation on the transmission and on the morbidity of HCV in PWID in France. Results: Under the current incidence and cascade of care, with treatment initiated at fibrosis stage $\ge$F2, the HCV prevalence decreased from 42.8% to 24.9% [95% confidence interval 24.8%--24.9%] after 10 years. Changing treatment initiation criteria to treat from F0 was the only intervention leading to a substantial additional decrease in the prevalence, which fell to 11.6% [11.6%--11.7%] at 10 years. Combining this change with improved testing, linkage to care, and adherence to treatment decreased HCV prevalence to 7% [7%--7.1%] at 10 years and avoided 15.3% [14.0%-16.6%] and 29.0% [27.9%--30.1%] of cirrhosis complications over 10 and 40 years respectively. Conclusion: A high decrease in viral transmission occurs only when treatment is initiated before liver disease progresses to severe stages, suggesting that systematic treatment in PWID, where incidence remains high, would be beneficial. However, eradication will be difficult to achieve

Peripapillary choroidal neovascularization associated with melanocytoma of the optic disc: a clinicopathologic case report

Background: Melanocytoma of the optic disc is a benign melanocytic tumor that rarely causes visual impairment. We report a case of a melanocytoma of the optic disc with a decreased vision related to a peripapillary choroidal neovascular membrane (PCNVM) that was successfully treated by submacular surgery. Methods: A 45-year-old southern European patient had a melanocytoma of the optic disc in his left eye with vision of 20/100. Fluorescein angiography demonstrated a PCNVM impeding the fovea associated with a subretinal hemorrhage. Results: The patient underwent a complete vitrectomy and removal of the PCNVM. Subsequently, the subretinal hemorrhage disappeared and visual acuity improved to 20/25. Visual acuity remained good for a period of 14months' follow-up without any recurrence of neovascular membrane. Conclusions: Submacular surgery is a potentially effective treatment for large PCNVM associated with a melanocytoma of the optic dis