Analytic Expressions for Stochastic Distances Between Relaxed Complex Wishart Distributions

The scaled complex Wishart distribution is a widely used model for multilook full polarimetric SAR data whose adequacy has been attested in the literature. Classification, segmentation, and image analysis techniques which depend on this model have been devised, and many of them employ some type of dissimilarity measure. In this paper we derive analytic expressions for four stochastic distances between relaxed scaled complex Wishart distributions in their most general form and in important particular cases. Using these distances, inequalities are obtained which lead to new ways of deriving the Bartlett and revised Wishart distances. The expressiveness of the four analytic distances is assessed with respect to the variation of parameters. Such distances are then used for deriving new tests statistics, which are proved to have asymptotic chi-square distribution. Adopting the test size as a comparison criterion, a sensitivity study is performed by means of Monte Carlo experiments suggesting that the Bhattacharyya statistic outperforms all the others. The power of the tests is also assessed. Applications to actual data illustrate the discrimination and homogeneity identification capabilities of these distances.Comment: Accepted for publication in the IEEE Transactions on Geoscience and Remote Sensing journa

Hox3 duplication and divergence in the Lepidoptera

Using the Speckled Wood Butterfly Pararge aegeria as the model species, this thesis presents the possible evolutionary significance of a set of duplications found in the Hox cluster of the Lepidoptera, called the Special Homeobox genes. An annotation of this duplicated cluster across a wide number of Lepidoptera was performed in order to assess patterns of duplication and loss across the order. The sequences recovered revealed a large amount of variation associated with the duplicate genes, indicating these are evolving very rapidly in different lineages. Patterns of sequence variation were examined to ascertain whether the observed variation was maintained due to selection at three separate levels of divergence: within the Ditrysia, within the more recently diverged Heliconius genus, and at the intraspecific level by quantifying nucleotide polymorphism within Pararge aegeria. Selective pressures were found to be operating between paralogous and orthologous genes, suggesting these have evolved, in part, under positive selection. The potential function of the duplicates was examined by means of CRISPR/Cas9 geneome editing, but revealed inconclusive results. Genome editing, however, was shown to be largely applicable to P. aegeria, and resulted in consistent mutations associated with wing patterning genes. The potential significance of the duplications for Lepidopeteran biology are discussed, as well as future applications for genome editing techniques in P. aegeria

Variation within and between Closely Related Species Uncovers High Intra-Specific Variability in Dispersal

Mounting evidence shows that contrasting selection pressures generate variability in dispersal patterns among individuals or populations of the same species, with potential impacts on both species dynamics and evolution. However, this variability is hardly considered in empirical works, where a single dispersal function is considered to adequately reflect the species-specific dispersal ability, suggesting thereby that within-species variation is negligible as regard to inter-specific differences in dispersal abilities. We propose here an original method to make the comparison of intra- and inter-specific variability in dispersal, by decomposing the diversity of that trait along a phylogeny of closely related species. We used as test group European butterflies that are classic study organisms in spatial ecology. We apply the analysis separately to eight metrics that reflect the dispersal propensity, the dispersal ability or the dispersal efficiency of populations and species. At the inter-specific level, only the dispersal ability showed the signature of a phylogenetic signal while neither the dispersal propensity nor the dispersal efficiency did. At the within-species level, the partitioning of dispersal diversity showed that dispersal was variable or highly variable among populations: intra-specific variability represented from 11% to 133% of inter-specific variability in dispersal metrics. This finding shows that dispersal variation is far from negligible in the wild. Understanding the processes behind this high within-species variation should allow us to properly account for dispersal in demographic models. Accordingly, to encompass the within species variability in life histories the use of more than one value per trait per species should be encouraged in the construction of databases aiming at being sources for modelling purposes