The comparison of genetic divergence or genetic distances, estimated by pairwise FST and related statistics, with geographical distances by Mantel test is one of the most popular approaches to evaluate spatial processes driving population structure. There have been, however, recent criticisms and discussions on the statistical performance of the Mantel test. Simultaneously, alternative frameworks for data analyses are being proposed. Here, we review the Mantel test and its variations, including Mantel correlograms and partial correlations and regressions. For illustrative purposes, we studied spatial genetic divergence among 25 populations of Dipteryx alata (“Baru”), a tree species endemic to the Cerrado, the Brazilian savannas, based on 8 microsatellite loci. We also applied alternative methods to analyze spatial patterns in this dataset, especially a multivariate generalization of Spatial Eigenfunction Analysis based on redundancy analysis. The different approaches resulted in similar estimates of the magnitude of spatial structure in the genetic data. Furthermore, the results were expected based on previous knowledge of the ecological and evolutionary processes underlying genetic variation in this species. Our review shows that a careful application and interpretation of Mantel tests, especially Mantel correlograms, can overcome some potential statistical problems and provide a simple and useful tool for multivariate analysis of spatial patterns of genetic divergence.

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Understanding the origins of biodiversity has been an aspiration since the days of early naturalists. The immense complexity of ecological, evolutionary, and spatial processes, however, has made this goal elusive to this day. Computer models serve progress in many scientific fields, but in the fields of macroecology and macroevolution, eco-evolutionary models are comparatively less developed. We present a general, spatially explicit, eco-evolutionary engine with a modular implementation that enables the modeling of multiple macroecological and macroevolutionary processes and feedbacks across representative spatiotemporally dynamic landscapes. Modeled processes can include species’ abiotic tolerances, biotic interactions, dispersal, speciation, and evolution of ecological traits. Commonly observed biodiversity patterns, such as α, β, and γ diversity, species ranges, ecological traits, and phylogenies, emerge as simulations proceed. As an illustration, we examine alternative hypotheses expected to have shaped the latitudinal diversity gradient (LDG) during the Earth’s Cenozoic era. Our exploratory simulations simultaneously produce multiple realistic biodiversity patterns, such as the LDG, current species richness, and range size frequencies, as well as phylogenetic metrics. The model engine is open source and available as an R package, enabling future exploration of various landscapes and biological processes, while outputs can be linked with a variety of empirical biodiversity patterns. This work represents a key toward a numeric, interdisciplinary, and mechanistic understanding of the physical and biological processes that shape Earth’s biodiversity.

Comparative methods have commonly been applied in macroecological research. However, few methods exist to map and analyze phylogenetic variation in geographical space. Here we develop a general analytical framework to partition the phylogenetic and ecological structures of macroecological patterns in geographic space. As an example, we apply the framework to evaluate interspecific patterns of body size geographic variation (Bergmann's rule) in European Carnivora. We model the components of variance attributable to ecological and phylogenetic effects, and to the shared influence of both factors. Spatial patterns in the ecological component are stronger than those in the original body size data. More importantly, the magnitude of intraspecific body size patterns (as measured by the correlation coefficient between body size and latitude) is significantly correlated with the ecological component across species, providing a unified interpretation for Bergmann's rule at multiple levels of biological hierarchy. This approach provides a better understanding of patterns in macroecological traits and allows improved understanding of their underlying ecological and evolutionary mechanisms.Macroecology has been developed as a unifying conceptual framework for understanding broad-scale patterns of abundance and diversity, incorporating methods and concepts from a range of areas of biological research, including biogeography, physiology, ecology, and evolutionary biology (Brown 1995,

Most evolutionary processes occur in a spatial context and several spatial analysis techniques have been employed in an exploratory context. However, the existence of autocorrelation can also perturb significance tests when data is analyzed using standard correlation and regression techniques on modeling genetic data as a function of explanatory variables. In this case, more complex models incorporating the effects of autocorrelation must be used. Here we review those models and compared their relative performances in a simple simulation, in which spatial patterns in allele frequencies were generated by a balance between random variation within populations and spatially-structured gene flow. Notwithstanding the somewhat idiosyncratic behavior of the techniques evaluated, it is clear that spatial autocorrelation affects Type I errors and that standard linear regression does not provide minimum variance estimators. Due to its flexibility, we stress that principal coordinate of neighbor matrices (PCNM) and related eigenvector mapping techniques seem to be the best approaches to spatial regression. In general, we hope that our review of commonly used spatial regression techniques in biology and ecology may aid population geneticists towards providing better explanations for population structures dealing with more complex regression problems throughout geographic space.