Modelling pollen dispersal is essential to make predictions of cross-pollination rates in various environmental conditions between plants of a cultivated species. An important tool for studying this problem is the "individual pollen dispersal function" or "kernel dispersal". Various models for airborne pollen dispersal are developed. These models are based on assumptions about wind directionality, gravity, settling velocity and may integrate other biological or external parameters. Some previous approaches have used Brownian Motions with drift for modelling pollen trajectories. However, models for pollen transport used in aerobiology are often based on the Lagrangian Stochastic approach: velocities of pollen grains satisfy stochastic differential equations or Langevin equations and pollen trajectories are obtained by integrating these velocities. New models based on this approach are introduced. A model where the vertical component is driven by an integrated Ornstein-Uhlenbeck process is studied here. Cross-pollination rates data were obtained from large field experiments of maize using the colour of grains as a phenotypic marker of pollen dispersal. We first studied the various individual dispersal functions associated with these models. Second, a thorough statistical framework was developed in order to estimate and compare their performances on data sets. This framework is quite general and can be used to study many other cross-pollination data. Previous and new models were successively analysed using this framework. This new statistical analysis improved significantly former results which had been obtained on the previous models with other statistical methods. The statistical analyses showed that the performances of Lagrange Stochastic models were good, but not better than the previous mechanistic models analysed using this new statistical framework. These results however might be due to some specific environmental conditions in this experiment. Comparisons withth e external parameters were quite good, proving that these models can be used in other environmental conditions. All these results show that mechanistic models are good models for predicting short or medium range pollen dispersal and cross-pollination rates.

La premiere partie de cette these est consacree a l'etude de la dispersion du pollen de mais. Le grain de pollen est vu comme une particule soumise a un champ de forces et sa trajectoire est modelisee a l'aide de differents processus de diffusion. Lorsque deux champs sont contigus (milieu homogene), differentes fonctions de dispersion individuelles parametriques sont alors obtenues, differentes hypotheses etant faites sur des temps d'atteinte de processus stochastiques. A partir d'experiences, les parametres sont alors estimes en considerant un modele de regression non lineaire. Le choix du modele le mieux adapte se fait a l'aide d'un critere de type Akaike et de methodes graphiques. Par ailleurs ces modeles permettent d'effectuer des predictions. Les resultats sont alors appliques lorsque deux champs sont separes par une autre culture (milieu heterogene), afin d'etudier l'effet d'une discontinuite sur la dispersion. Dans la seconde partie, on s'interesse a des modeles a volatilite stochastique «mean-reverting», souvent utilises en economie. Le processus observe est fonction d'une diffusion non observable dont on souhaite estimer les parametres. Une methode d'estimation a deux pas basee sur la structure ARMA(1,1) du processus est proposee, en utilisant un estimateur de moments et un contraste de Whittle. Des simulations sont realisees afin de comparer cette methode avec d'autres methodes existantes. Ensuite un parametre dit «leverage» est ajoute et un modele discretise est etudie. Un critere auxiliaire est propose pour estimer les parametres a l'aide d'une methode d'inference indirecte. Enfin des simulations sont realisees pour evaluer leurs performances.

Precise control of chromosome pairing is vital for conferring meiotic, and hence reproductive, stability in sexually reproducing polyploids. Apart from the Ph1 locus of wheat that suppresses homeologous pairing, little is known about the activity of genes that contribute to the cytological diploidization of allopolyploids. In oilseed rape (Brassica napus) haploids, the amount of chromosome pairing at metaphase I (MI) of meiosis varies depending on the varieties the haploids originate from. In this study, we combined a segregation analysis with a maximum-likelihood approach to demonstrate that this variation is genetically based and controlled mainly by a gene with a major effect. A total of 244 haploids were produced from F(1) hybrids between a high- and a low-pairing variety (at the haploid stage) and their meiotic behavior at MI was characterized. Likelihood-ratio statistics were used to demonstrate that the distribution of the number of univalents among these haploids was consistent with the segregation of a diallelic major gene, presumably in a background of polygenic variation. Our observations suggest that this gene, named PrBn, is different from Ph1 and could thus provide complementary information on the meiotic stabilization of chromosome pairing in allopolyploid species.