Biogeographical regions (geographically distinct assemblages of species and communities) constitute a cornerstone for ecology, biogeography, evolution and conservation biology. Species turnover measures are often used to quantify spatial biodiversity patterns, but algorithms based on similarity can be sensitive to common sampling biases in species distribution data. Here we apply a community detection approach from network theory that incorporates complex, higher-order presence-absence patterns. We demonstrate the performance of the method by applying it to all amphibian species in the world (c. 6,100 species), all vascular plant species of the USA (c. 17,600) and a hypothetical data set containing a zone of biotic transition. In comparison with current methods, our approach tackles the challenges posed by transition zones and succeeds in retrieving a larger number of commonly recognized biogeographical regions. This method can be applied to generate objective, data-derived identification and delimitation of the world's biogeographical regions.

Structural controllability has been proposed as an analytical framework for making predictions regarding the control of complex networks across myriad disciplines in the physical and life sciences (Liu et al., Nature:473(7346):167–173, 2011). Although the integration of control theory and network analysis is important, we argue that the application of the structural controllability framework to most if not all real-world networks leads to the conclusion that a single control input, applied to the power dominating set, is all that is needed for structural controllability. This result is consistent with the well-known fact that controllability and its dual observability are generic properties of systems. We argue that more important than issues of structural controllability are the questions of whether a system is almost uncontrollable, whether it is almost unobservable, and whether it possesses almost pole-zero cancellations.

In addition to their devastating effects on global biodiversity, mass extinctions have had a long-term influence on the history of life by eliminating dominant lineages that suppressed ecological change. Here, we test whether the end-Permian mass extinction (252.3 Ma) affected the distribution of tetrapod faunas within the southern hemisphere and apply quantitative methods to analyze four components of biogeographic structure: connectedness, clustering, range size, and endemism. For all four components, we detected increased provincialism between our Permian and Triassic datasets. In southern Pangea, a more homogeneous and broadly distributed fauna in the Late Permian (Wuchiapingian, ∼257 Ma) was replaced by a provincial and biogeographically fragmented fauna by Middle Triassic times (Anisian, ∼242 Ma). Importantly in the Triassic, lower latitude basins in Tanzania and Zambia included dinosaur predecessors and other archosaurs unknown elsewhere. The recognition of heterogeneous tetrapod communities in the Triassic implies that the end-Permian mass extinction afforded ecologically marginalized lineages the ecospace to diversify, and that biotic controls (i.e., evolutionary incumbency) were fundamentally reset. Archosaurs, which began diversifying in the Early Triassic, were likely beneficiaries of this ecological release and remained dominant for much of the later Mesozoic.biogeography | complex networks | macroevolution | biotic recovery | paleoecology M ass extinctions are thought to reshape the composition and ecological structure of communities on a scale unparalleled by background extinction (1, 2). Within the terrestrial realm, the replacement of dinosaur-dominated communities by those of mammals after the end-Cretaceous extinction is perhaps the best-known example of such wholesale faunal reshuffling. By contrast, understanding the effects of the more massive endPermian extinction on terrestrial community structure has been hampered by the paucity of high-quality geographic data, with nearly all studies restricted to sequences from single basins in Russia (3, 4) or South Africa (5-8). Although some broad similarities have emerged, such as the progressive aridification of the two basins (3, 8) and a heightened diversity of temnospondyl amphibians in the recovery interval (9), limited geographic sampling in each hemisphere constrains the ability of paleontologists to distinguish regional patterns from those characteristic of the individual basins. Moreover, these broadly separated areas are uninformative regarding large-scale (i.e., continentlevel) patterns of faunal evolution.Here we examine tetrapod faunal composition in five fossiliferous areas in southern Pangea approximately 5 million years before and 10 million years after the end-Permian mass extinction. We analyze changes in biogeographic structure with four metrics of taxon occurrence data. First, biogeographic connectedness (BC) quantifies the proportion of taxon-locality occurrences relative to the maximum number of such occurrences possible. Thus...

Inference of past and present global biodiversity requires enough global data to distinguish biological pattern from sampling artifact. Pertinently, many studies have exposed correlated relationships between richness and sampling in the fossil record, and methods to circumvent these biases have been proposed. Yet, these studies often ignore paleobiogeography, which is undeniably a critical component of ancient global diversity. Alarmingly, our global analysis of 481,613 marine fossils spread throughout the Phanerozoic reveals that where localities are and how intensively they have been sampled almost completely determines empirical spatial patterns of richness, suggesting no separation of biological pattern from sampling pattern. To overcome this, we analyze diversity using occurrence records drawn from two discrete paleolatitudinal bands which cover the bulk of the fossil data. After correcting the data for sampling bias, we find that these two bands have similar patterns of richness despite markedly different spatial coverage. Our findings suggest that i) long-term diversity trends result from large-scale tectonic evolution of the planet, ii) short-term diversity trends are region-specific, and iii) paleodiversity studies must constrain their analyses to well-sampled regions to uncover patterns not driven by sampling.