Modern attempts to produce biogeographic maps focus on the distribution of species, and the maps are typically drawn without phylogenetic considerations. Here, we generate a global map of zoogeographic regions by combining data on the distributions and phylogenetic relationships of 21,037 species of amphibians, birds, and mammals. We identify 20 distinct zoogeographic regions, which are grouped into 11 larger realms. We document the lack of support for several regions previously defined based on distributional data and show that spatial turnover in the phylogenetic composition of vertebrate assemblages is higher in the Southern than in the Northern Hemisphere. We further show that the integration of phylogenetic information provides valuable insight on historical relationships among regions, permitting the identification of evolutionarily unique regions of the world.

Aim This research aims to understand the factors that shape elevational diversity gradients and how those factors vary with spatial grain. Specifically, we test the predictions of the species-productivity hypothesis, species-temperature hypothesis, the metabolic theory of ecology and the mid-domain effects null model. We also examine how the effects of productivity and temperature on richness depend on spatial grain. Location Deciduous forests along an elevational gradient in Great Smoky MountainsNational Park, USA. MethodsWe sampled 22 leaf litter ant assemblages at three spatial grains, from 1-m 2 quadrats to 50 × 50 m plots using Winkler samplers.Results Across spatial grains, warmer sites had more species than did cooler sites, and primary productivity did not predict ant species richness. We found some support for the predictions of the metabolic theory of ecology, but no support for the mid-domain effects null model. Thus, our data are best explained by some version of a species-temperature hypothesis. Main conclusionsOur results suggest that temperature indirectly affects ant species diversity across spatial grains, perhaps by limiting access to resources. Warmer sites support more species because they support more individuals, thereby reducing the probability of local extinction. Many of our results from this elevational gradient agree with studies at more global scales, suggesting that some mechanisms shaping ant diversity gradients are common across scales.

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One of the most efficient methods for determining the equilibria of a continuous parameterized family of differential equations is to use predictor-corrector continuation techniques. In the case of partial differential equations this procedure must be applied to some finite dimensional approximation which of course raises the question of the validity of the output. We introduce a new technique that combines the information obtained from the predictor-corrector steps with ideas from rigorous computations and verifies that the numerically produced equilibrium for the finite dimensional system can be used to explicitly define a set which contains a unique equilibrium for the infinite dimensional partial differential equation. Using the Cahn-Hilliard and Swift-Hohenberg equations as models we demonstrate that the cost of this new validated continuation is less than twice the cost of the standard continuation method alone.

There is a long tradition in ecology of evaluating the relative contribution of the regional species pool and local interactions on the structure of local communities. Similarly, a growing number of studies assess the phylogenetic structure of communities, relative to that in the regional species pool, to examine the interplay between broad-scale evolutionary and fine-scale ecological processes. Finally, a renewed interest in the influence of species source pools on communities has shown that the definition of the source pool influences interpretations of patterns of community structure. We use a continent-wide dataset of local ant communities and implement ecologically explicit source pool definitions to examine the relative importance of regional species pools and local interactions for shaping community structure. Then we assess which factors underlie systematic variation in the structure of communities along climatic gradients. We find that the average phylogenetic relatedness of species in ant communities decreases from tropical to temperate regions, but the strength of this relationship depends on the level of ecological realism in the definition of source pools. We conclude that the evolution of climatic niches influences the phylogenetic structure of regional source pools and that the influence of regional source pools on local community structure is strong.

Th e species pool concept has played a central role in the development of ecological theory for at least 60 yr. Surprisingly, there is little consensus as to how one should defi ne the species pool, and consequently, no systematic approach exists. Because the defi nition of the species pool is essential to infer the processes that shape ecological communities, there is a strong incentive to develop an ecologically realistic defi nition of the species pool based on repeatable and transparent analytical approaches. Recently, several methodological tools have become available to summarize repeated patterns in the geographic distribution of species, phylogenetic clades and taxonomically broad lineages. Here, we present three analytical approaches that can be used to defi ne what we term ' the biogeographic species pool ' : distance-based clustering analysis, network modularity analysis, and assemblage dispersion fi elds. Th e biogeographic species pool defi nes the pool of potential community members in a broad sense and represents a fi rst step towards a standardized defi nition of the species pool for the purpose of comparative ecological, evolutionary and biogeographic studies.

In this paper we extend the ideas of the so-called validated continuation technique to the context of rigorously proving the existence of equilibria for partial differential equations defined on higherdimensional spatial domains. For that effect we present a new set of general analytic estimates. These estimates are valid for any dimension and are used, together with rigorous computations, to construct a finite number of radii polynomials. These polynomials provide a computationally efficient method to prove, via a contraction argument, the existence and local uniqueness of solutions for a rather large class of nonlinear problems. We apply this technique to prove existence and local uniqueness of equilibrium solutions for the Cahn-Hilliard and the Swift-Hohenberg equations defined on two-and three-dimensional spatial domains.

In this paper, we use rigorous numerics to compute several global smooth branches of steady states for a system of three reaction-diffusion PDEs introduced by Iida et al. [J. Math. Biol., 53, 617-641 (2006)] to study the effect of cross-diffusion in competitive interactions. An explicit and mathematically rigorous construction of a global bifurcation diagram is done, except in small neighborhoods of the bifurcations. The proposed method, even though influenced by the work of van den Berg et al. [Math. Comp., 79, 1565-1584], introduces new analytic estimates, a new gluing-free approach for the construction of global smooth branches and provides a detailed analysis of the choice of the parameters to be made in order to maximize the chances of performing successfully the computational proofs.