Global priorities for conservation across multiple dimensions of mammalian diversity

Conservation priorities that are based on species distribution, endemism, and vulnerability may underrepresent biologically unique species as well as their functional roles and evolutionary histories. To ensure that priorities are biologically comprehensive, multiple dimensions of diversity must be considered. Further, understanding how the different dimensions relate to one another spatially is important for conservation prioritization, but the relationship remains poorly understood. Here, we use spatial conservation planning to (i) identify and compare priority regions for global mammal conservation across three key dimensions of biodiversity-taxonomic, phylogenetic, and traits-and (ii) determine the overlap of these regions with the locations of threatened species and existing protected areas. We show that priority areas for mammal conservation exhibit low overlap across the three dimensions, highlighting the need for an integrative approach for biodiversity conservation. Additionally, currently protected areas poorly represent the three dimensions of mammalian biodiversity. We identify areas of high conservation priority among and across the dimensions that should receive special attention for expanding the global protected area network. These high-priority areas, combined with areas of high priority for other taxonomic groups and with social, economic, and political considerations, provide a biological foundation for future conservation planning efforts

Laplacian Coarse Graining in Complex Networks

Complex networks can model a range of different systems, from the human brain to social connections. Some of those networks have a large number of nodes and links, making it impractical to analyze them directly. One strategy to simplify these systems is by creating miniaturized versions of the networks that keep their main properties. A convenient tool that applies that strategy is the renormalization group (RG), a methodology used in statistical physics to change the scales of physical systems. This method consists of two steps: a coarse grain, where one reduces the size of the system, and a rescaling of the interactions to compensate for the information loss. This work applies RG to complex networks by introducing a coarse-graining method based on the Laplacian matrix. We use a field-theoretical approach to calculate the correlation function and coarse-grain the most correlated nodes into super-nodes, applying our method to several artificial and real-world networks. The results are promising, with most of the networks under analysis showing self-similar properties across different scales.Comment: 14 pages, 7 figure