On the overconvergence of certain series

In this work, we consider certain class of exponential series with polynomial coefficients and study the properties of convergence of such series. Then we consider a subclass of this class and prove certain theorems on the overconvergence of such a series, which allow us to determine the conditions under which the boundary of the region of convergence of this series is a natural boundary for the function f defined by this series

Genetic diversity and population divergences of an indigenous tree (Coffea mauritiana) in Reunion Island: role of climatic and geographical factors

International audienceOceanic islands are commonly considered as natural laboratories for studies on evolution and speciation. The evolutionary specificities of islands associated with species biology provide unique scenarios to study the role of geography and climate in driving population divergence. However, few studies have addressed this subject in small oceanic islands with heterogeneous climates. Being widely distributed in Reunion Island forest, Coffea mauritiana represents an interesting model case for investigating patterns of within-island differentiation at small spatial scale. In this study, we examined the genetic diversity and population divergences of C. mauritiana using SNP markers obtained from 323 individuals across 34 locations in Reunion Island. Using redundancy analysis, we further evaluated the contribution of geographic and climatic factors to shaping genetic divergence among populations. Genetic diversity analyses revealed that accessions clustered according to the source population, with further grouping in regional clusters. Genetic relationships among the regional clusters underlined a recent process of expansion in the form of step-by-step colonization on both sides of the island. Divergence among source populations was mostly driven by the joint effect of geographic distance and climatic heterogeneity. The pattern of isolation-by-geography was in accordance with the dispersal characteristics of the species, while isolation-by-environment was mostly explained by the heterogeneous rainfall patterns, probably associated with an asynchronous flowering among populations. These findings advance our knowledge on the patterns of genetic diversity and factors of population differentiation of species native to Reunion Island, and will also usefully guide forest management for conservation