Éditeur(s) : HAL CCSD
Résumé : 28 pages, 6 figures
We study a universal object for the genealogy of a sample in populations with mutations: the critical birth-death process with Poissonian mutations, conditioned on its population size at a fixed time horizon. We show how this process arises as the law of the genealogy of a sample in a large class of critical branching populations with mutations at birth, namely populations converging, in a large population asymptotic, towards the continuum random tree. We extend this model to populations with random foundation times, with (potentially improper) prior distributions g_i: xmapsto x^{-i}, iinZ_+, including the so-called uniform (i=0) and log-uniform (i=1) priors. We first investigate the mutational patterns arising from these models, by studying the site frequency spectrum of a sample with fixed size, i.e. the number of mutations carried by k individuals in the sample. Explicit formulae for the expected frequency spectrum of a sample are provided, in the cases of a fixed foundation time, and of a uniform and log-uniform prior on the foundation time. Second, we establish the convergence in distribution, for large sample sizes, of the (suitably renormalized) tree spanned by the sample genealogy with prior g_i on the time of origin. We finally prove that the limiting genealogies with different priors can all be embedded in the same realization of a given Poisson point measure.
https://hal.archives-ouvertes.fr/hal-01053343

hal-01053343
https://hal.archives-ouvertes.fr/hal-01053343
ARXIV : 1407.7720

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
A comprehensive inventory of global biodiversity would be greatly improved by automating methods for species delimitation. The Automatic Barcode Gap Discovery method, the Poisson tree processes algorithm and the Generalized mixed Yule coalescent model have been proposed as means of increasing the rate of biodiversity description using single locus data. We applied these methods to explore the diversity within the Aglaopheniidae, a hydrozoan family with many species widely distributed across tropical and tem perate oceans. Our analyses revealed widespread cryptic diversity in this family, almost half of the morpho species presenting several independent evolutionary lineages, as well as support for cases of synonymy. For two common species of this family, Lytocarpia brevirostris and Macrorhynchia phoenicea, we compared the outputs to clustering analyses based on microsatellite data and to nuclear gene phylo genies. For L. brevirostris, microsatellite data were congruent with results of the species delimitation methods, revealing the existence of two cryptic species with Indo Pacific distribution. For M. phoenicea, all analyses confirmed the presence of two cryptic species within the South Western Indian Ocean. Our study suggests that the diversity of Aglaopheniidae might be much higher than assumed, likely related to low dispersal capacities. Sequence based species delimitation methods seem highly valuable to reveal cryptic diversity in hydrozoans; their application in an integrative framework will be very useful in describing the phyletic diversity of these organisms.
ISSN: 1055-7903

hal-01359407
https://hal.archives-ouvertes.fr/hal-01359407
https://hal.archives-ouvertes.fr/hal-01359407/document
https://hal.archives-ouvertes.fr/hal-01359407/file/Postaire-etal2016MolPhylEvol_sp_delim_hydraires_HAL.pdf
DOI : 10.1016/j.ympev.2016.08.013

Éditeur(s) : HAL CCSD
Résumé : For ecology scientists, spatial statistics are a set of tools allowing characterization of the structure of a point set, for instance a map of trees in a forest plot. This structure is defined implicitly as a departure from complete spatial randomness (CSR), the result of a Poisson point process. Inhomogeneity of the process and non-independence of points are its causes. As they cannot be disentangled by analyzing the data, so-called "spatial concentration" or "aggregation" (evenness due to repulsion also exists but is actually rare) usually concerns non-independence while intensity is assumed as known. The literature of point processes and measures of spatial structures is reviewed to clarify concepts and choices. The purpose of this thesis was to produce methodological enhancements. Its main results are: * A test for the most used statistic, Ripley's K function, against the null hypothesis of CSR. It can replace Monte-Carlo simulations used until now in the literature. * An extension of K to inhomogeneous processes, within a typology of available statistics (absolute, relative and topographic measures). When data is available as number of objects per zones (say a number of tree in each forest plot) rather than their exact position, information theory is used to define a general framework allowing to characterize spatial structure (of species) and diversity (of plots) as two aspects of a single measure of inequality. This framework is applied to Shannon's index of biodiversity to derive a self-sufficient definition of beta diversity, its calculation independently from the difference between gamma and alpha diversity, and a statistical test of significance against the null hypothesis that plots are samples of the same community. The way is paved for other applications to measures of diversity and spatial structures. As a conclusion, it appears clear that pattern characterization tools are a first step to deal with ecological questionings. Their development is still a matter of research. Yet, they are far from sufficient to address ecological processes as point processes ignore the temporal aspect of object locations.
Les statistiques spatiales sont pour les écologues un ensemble d'outils permettant de caractériser la structure d'un semis de points, par exemple une carte représentant des emplacements des arbres dans une parcelle de forêt. Cette structure est définie implicitement comme un écart à semis complètement aléatoire, résultat d'un processus de Poisson. L'hétérogénéité du processus ponctuel dont le semis de points est une réalisation et la non-indépendance des points en sont les causes indiscernables, ce qui amène généralement à supposer l'intensité du processus connu et nommer " concentration spatiale " ou " agrégation " (la régularité spatiale est possible, mais rare en pratique) la non-indépendance. Une revue de la littérature des processus ponctuels et des mesures de structures spatiales est fournie pour clarifier les concepts et les choix. L'objectif de ce travail de thèse était de produire des améliorations méthodologiques. Ses résultats principaux sont : * L'établissement d'un test pour la principale statistique utilisée, la fonction K de Ripley, permettant de s'affranchir de la méthode de Monte-Carlo utilisée dans la littérature pour rejeter l'hypothèse nulle d'un processus complètement aléatoire. * L'extension de K aux processus hétérogènes, dans le cadre d'une typologie claire des statistiques (absolues, relatives, topographiques). Lorsque la position exacte des objets n'est pas connue, mais que des effectifs par zone sont disponibles (par exemple des nombres d'arbres par parcelle), la théorie de l'information est utilisée pour définir un cadre général permettant de caractériser la structure spatiale (des espèces dans les parcelles) et la diversité (des parcelles, en termes d'espèces) comme deux aspects d'une même mesure d'inégalité. Ce cadre est appliqué à l'indice de biodiversité de Shannon pour définir clairement la mesure de diversité bêta, son calcul direct indépendamment de la différence entre diversités gamma et alpha, et fournir un test statistique de non nullité. La voie est ouverte pour l'application à d'autres mesures de diversité et de structure spatiale. En conclusion, il semble clair que ces outils de caractérisation sont un premier pas pour traiter les questions écologiques, leur développement étant toujours du domaine de la recherche. Ils sont cependant très insuffisants pour répondre à des questions liées aux processus écologiques, assez éloignés des processus ponctuels qui ignorent l'aspect temporel de l'installation des objets.
https://pastel.archives-ouvertes.fr/pastel-00540327

NNT : 2010AGPT0075
pastel-00540327
https://pastel.archives-ouvertes.fr/pastel-00540327
https://pastel.archives-ouvertes.fr/pastel-00540327/document
https://pastel.archives-ouvertes.fr/pastel-00540327/file/13_Marcon2010.pdf