Point pattern sets arise in many different areas of physical, biological, and applied research, representing many random realizations of underlying pattern formation mechanisms. These pattern sets can be heterogeneous with respect to underlying spatial processes, which may not be visually distiguishable. This heterogeneity can be elucidated by looking at statistical measures of the patterns sets and using these measures to divide the pattern set into distinct groups representing like spatial processes. We introduce here a numerical procedure for sorting point pattern sets into spatially homogenous groups using Functional Principal Component Analysis (FPCA) applied to the approximated Minkowski functionals of each pattern. We demonstrate that this procedure correctly sorts pattern sets into similar groups both when the patterns are drawn from similar processes and when the 2nd-order characteristics of the pattern are identical. We highlight this routine for distinguishing the molecular patterning of fluorescently labeled cell membrane proteins, a subject of much interest in studies investigating complex spatial signaling patterns involved in the human immune response.

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Background Snake venoms are trophic adaptations that represent an ideal model to examine the evolutionary factors that shape polymorphic traits under strong natural selection. Venom compositional variation is substantial within and among venomous snake species. However, the forces shaping this phenotypic complexity, as well as the potential integrated roles of biotic and abiotic factors, have received little attention. Here, we investigate geographic variation in venom composition in a wide-ranging rattlesnake (Crotalus viridis viridis) and contextualize this variation by investigating dietary, phylogenetic, and environmental variables that covary with venom. Results Using shotgun proteomics, venom biochemical profiling, and lethality assays, we identify 2 distinct divergent phenotypes that characterize major axes of venom variation in this species: a myotoxin-rich phenotype and a snake venom metalloprotease (SVMP)-rich phenotype. We find that dietary availability and temperature-related abiotic factors are correlated with geographic trends in venom composition. Conclusions Our findings highlight the potential for snake venoms to vary extensively within species, for this variation to be driven by biotic and abiotic factors, and for the importance of integrating biotic and abiotic variation for understanding complex trait evolution. Links between venom variation and variation in biotic and abiotic factors indicate that venom variation likely results from substantial geographic variation in selection regimes that determine the efficacy of venom phenotypes across populations and snake species. Our results highlight the cascading influence of abiotic factors on biotic factors that ultimately shape venom phenotype, providing evidence for a central role of local selection as a key driver of venom variation.

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