Functional biogeography of oceanic islands and the scaling of functional diversity in the Azores

Analyses of species-diversity patterns of remote islands have been crucial to the development of biogeographic theory, yet little is known about corresponding patterns in functional traits on islands and how, for example, they may be affected by the introduction of exotic species. We collated trait data for spiders and beetles and used a functional diversity index (FRic) to test for nonrandomness in the contribution of endemic, other native (also combined as indigenous), and exotic species to functional-trait space across the nine islands of the Azores. In general, for both taxa and for each distributional category, functional diversity increases with species richness, which, in turn scales with island area. Null simulations support the hypothesis that each distributional group contributes to functional diversity in proportion to their species richness. Exotic spiders have added novel trait space to a greater degree than have exotic beetles, likely indicating greater impact of the reduction of immigration filters and/or differential historical losses of indigenous species. Analyses of species occurring in native-forest remnants provide limited indications of the operation of habitat filtering of exotics for three islands, but only for beetles. Although the general linear (not saturating) pattern of trait-space increase with richness of exotics suggests an ongoing process of functional enrichment and accommodation, further work is urgently needed to determine how estimates of extinction debt of indigenous species should be adjusted in the light of these findings.

Mapping stability : real rational maps of degree zero

In memory of our beloved Professor José Rodrigues Santos de Sousa Ramos (1948-2007), who João Cabral, one of the authors of this paper, had the honor of being his student between 2000 and 2006, we wrote this paper following the research by experimentation, using the new technologies to capture a new insight about a problem, as him so much love to do it. His passion was to create new relations between different fields of mathematics. He was a builder of bridges of knowledge, encouraging the birth of new ways to understand this science. One of the areas that Sousa Ramos researched was the iteration of maps and the description of its behavior, using the symbolic dynamics. So, in this issue of this journal, honoring his memory, we use experimental results to find some stable regions of a specific family of real rational maps, the ones that he worked with João Cabral. In this paper we describe a parameter space (a,b) to the real rational maps fa,b(x) = (x2 −a)/(x2 −b), using some tools of dynamical systems, as the study of the critical point orbit and Lyapunov exponents. We give some results regarding the stability of these family of maps when we iterate it, specially the ones connected to the order 3 of iteration. We hope that our results would help to understand better the behavior of these maps, preparing the ground to a more efficient use of the Kneading Theory on these family of maps, using symbolic dynamics.