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Eléments D'interface Entre Analyses Multivariées, Systèmes D

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Eléments D'interface Entre Analyses Multivariées, Systèmes D N° d’ordre 03-2003 Année 2003 THESE présentée devant l’UNIVERSITE CLAUDE BERNARD - LYON 1 pour l’obtention du DIPLOME DE DOCTORAT (arrêté du 30 mars 1992) présentée et soutenue publiquement le 06 janvier 2003 par Stéphane DRAY Eléments d’interface entre analyses multivariées, systèmes d’information géographique et observations écologiques Directeur de thèse : Daniel CHESSEL JURY : M. Antoine GUISAN, Rapporteur M. Francis LALOË, Rapporteur M. Daniel CHESSEL M. Jean-Dominique LEBRETON M. Alain PAVE Mme Dominique PONTIER AVANT-PROPOS Cette thèse a été préparée au sein de l’équipe d’Ecologie Statistique du laboratoire de Biométrie et Biologie Evolutive (UMR CNRS 5558). Elle se caractérise par l’étude et la mise en relation de plusieurs domaines de compétences. Ceci s’est traduit notamment par la mise en œuvre de multiples collaborations avec des écologues. En biométrie, et plus particulièrement dans le cadre de cette thèse, ces diverses relations constituent l’essence du travail. Je tiens à remercier l’ensemble des personnes ayant participé de près ou de loin à ce travail et particulièrement : - Raphaël Pélissier, Pierre Couteron, Clémentine Gimaret-Carpentier, Jean-Pierre Pascal, Nathalie Pettorelli, Jean-Michel Gaillard, Jean-François Michel qui m’ont permis de mettre des images de forêts, de chevreuils ou de mouches sur des tableaux de nombres. Leurs connaissances biologiques, leur intérêt méthodologique et leurs qualités humaines ont permis l’établissement de collaborations fructueuses. Rolland Alemand, Philippe Richoux et Joël Clary qui sont à l’origine de mon sujet de DEA et donc indirectement, de cette thèse. L’ensemble des organismes qui ont accepté de mettre leurs précieuses données à ma disposition. - Les membres du Jury : Françis Laloë et Antoine Guisan pour avoir accepter de juger ce travail en tant que rapporteur, pour leur intérêt, leurs remarques et leurs questions précises et très pertinentes. Jean-Dominique Lebreton, Alain Pavé et Dominique Pontier qui ont accepté de parcourir de (très) grandes distances pour participer à ce jury, pour la qualité de leurs remarques et les discussions que nous avons eues. Daniel Chessel pour avoir accepté de diriger cette thèse, pour sa confiance, sa passion, son intérêt, son écoute, son expérience et ses conseils, qu’il a su me transmettre depuis le DEA. Ces quatre années de collaboration ont été très très enrichissantes. - Jean Thioulouse et Anne-Béatrice Dufour de m’avoir accueilli dans leur équipe…et dans leur bureau. J’ai ainsi pu bénéficier d’un voisinage et d’un cadre de travail très agréable et d’une structure satisfaisant l’ensemble de mes demandes. Misou, Sophie (puis Anne-Lucie, puis Dominique) de m’avoir faciliter les différentes démarches administratives et Marie-Hélène pour, notamment, la préparation du pot. « Soit A un succès dans la vie. Alors A = x + y + z, où x = travailler, y = s'amuser, z = se taire.» (A . Einstein) - A tous les amis de Lyon, du Jura, de Montpellier ou d’ailleurs… pour le y. « C'est le devoir de chaque homme de rendre au monde au moins autant qu'il en a reçu. » (A . Einstein) - A ma famille, A Emeraude. A ma mère, mon père et mon frère qui m’ont beaucoup donné. Eléments d’interface entre analyses multivariées, systèmes d’information géographique et observations écologiques Résumé Dans une approche pluridisciplinaire basée sur 1) le contenu de méthodes statistiques multivariées et spatiales, 2) l'usage d’un système d’information géographique et 3) les objectifs expérimentaux définis par des écologues, cette thèse fournit des éléments nouveaux pour l’analyse de données écologiques multivariées et spatialisées. La première partie présente les différents éléments du dialogue. Il y figure 1) une synthèse, basée sur l’utilisation du schéma de dualité, des principales méthodes d’analyse de données, 2) une description des interfaces écrites entre trois logiciels largement utilisés (R, ADE-4 et ArcView), 3) une présentation des collaborations entreprises avec des écologues, en particulier N. Pettorelli, qui, au delà des prestations de la consultation statistique, permet d'accéder à des questions méthodologiques ouvertes. La seconde partie présente les résultats obtenus lors de ces collaborations sous la forme de publications en anglais (6 acceptées et 4 soumises). L’utilisation de l’analyse canonique des corrélations sur des listes d’occurrences a permis d’étudier la structuration spatiale de peuplement forestier à une échelle locale ou régionale. Une modélisation de la prévalence d’une maladie à transmission vectorielle fondée sur des méthodes statistiques et des analyses spatiales est proposée. Les travaux sur la dynamique d’une population de chevreuils en relation avec l’habitat a conduit à définir deux nouvelles méthodes d’analyse multivariée. La première (analyse RLQ spatialisée) permet de coupler deux tableaux de données provenant de deux plans d’échantillonnage distincts d'un même espace, la seconde (analyse NIPALS spatialisée) permet de faire l'ACP de données provenant de k plans d’échantillonnage distincts d'un même espace. Enfin, un compromis entre analyse de co-inertie et rotation procustéenne a été introduit dans l'étude de la co-structure de deux tableaux. Elements of interface between multivariate analyses, geographic information systems and ecological observations. Abstract Adopting a multidisciplinary approach based on 1) the content of spatial and multivariate analyses, 2) the use of a geographic information system, 3) experimental objectives defined by ecologists, this thesis gives new elements for the analysis of spatially referenced and multivariate ecological data. The first part presents the elements of the dialogue. It consists of 1) a synthesis, based on the duality diagram, of the main methods of multivariate analysis, 2) a description of written interfaces between three widely used software (R, ADE-4 and ArcView), 3) a presentation of the collaborations with ecologists, particularly N. Pettorelli, which, more than a simple statistical consulting, offers a number of methodological problems. In the second part, the results obtained in these collaborations are presented with English publications (6 accepted and 4 submitted). The use of canonical correlation analysis of occurrences lists allows studying the spatial structure of forests at regional or local scale. Modeling the prevalence of a vector-transmitted disease, with statistical methods and spatial analyses, is proposed. The study of roe-deer population dynamic in relation with habitat leads to develop two new methods of data analysis. The first one (spatial RLQ analysis) links two datasets recorded from two different samplings of the same area, the second one (spatial NIPALS analysis) consists in PCA of data from k different samplings of the same area. Lastly, a compromise between co-inertia analysis and procrustean rotation is introduced for studying the co-structure of two datasets. SOMMAIRE Introduction _____________________________________________________________1 Partie I : Les composantes du dialogue _______________________________________5 Chapitre I : Théorie de l’analyse de données __________________________________7 I.1. Schéma de dualité __________________________________________________7 I.1.1. Diagonalisation d’un schéma de dualité______________________________8 I.1.2. Critères d’optimalité____________________________________________11 I.1.3. Inertie d’un triplet______________________________________________11 I.1.4. Reconstitution de données _______________________________________12 I.1.5. Diagonalisation d’un schéma dissymétrique _________________________13 I.1.6. Exemples de schéma de dualité ___________________________________13 I.2. Couplage ________________________________________________________14 I.2.1. Analyse canonique des corrélations ________________________________15 I.2.2. Analyses sur variables instrumentales ______________________________17 I.2.3. Analyse de co-inertie ___________________________________________19 I.3. Correspondances et analyses canoniques _______________________________20 I.3.1. Analyses des correspondances ____________________________________22 I.3.2. Tableaux des correspondances ____________________________________24 I.3.3. Analyses canoniques ___________________________________________26 Chapitre II : Supports du savoir-faire _______________________________________31 II.1. ADE-4 _________________________________________________________31 II.2. R______________________________________________________________39 II.3. ArcView________________________________________________________46 Chapitre III : La consultation des écologues __________________________________53 III.1. Les listes d’occurrences ___________________________________________53 III.2. Maladie à transmission vectorielle ___________________________________57 III.3. Dynamique de population__________________________________________59 Partie II : Résultats ______________________________________________________63 Chapitre IV : L’analyse des listes d’occurrences ______________________________65 C. Gimaret-Carpentier, S. Dray, J.-P. Pascal : Large-scale biodiversity pattern analyses of the endemic tree flora of the western Ghats (India) using canonical correlation analysis of point data (accepté dans Ecography) ............................................................................................................... 67 R. Pélissier, S. Dray and D. Sabatier : Within-plot relationships between tree species occurrences and hydrological soil constraints: an example
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