A Pseudopolynomial Algorithm for Alexandrov's Theorem

Alexandrov's Theorem states that every metric with the global topology and local geometry required of a convex polyhedron is in fact the intrinsic metric of a unique convex polyhedron. Recent work by Bobenko and Izmestiev describes a differential equation whose solution leads to the polyhedron corresponding to a given metric. We describe an algorithm based on this differential equation to compute the polyhedron to arbitrary precision given the metric, and prove a pseudopolynomial bound on its running time. Along the way, we develop pseudopolynomial algorithms for computing shortest paths and weighted Delaunay triangulations on a polyhedral surface, even when the surface edges are not shortest paths.Comment: 25 pages; new Delaunay triangulation algorithm, minor other changes; an abbreviated v2 was at WADS 200

Environmental DNA COI barcoding for quantitative analysis of protists communities: A test using the <i>Nebela collaris</i> complex (Amoebozoa;Arcellinida; Hyalospheniidae)

Environmental DNA surveys are used for screening eukaryotic diversity. However, it is unclear how quantitative this approach is and to what extent results from environmental DNA studies can be used for ecological studies requiring quantitative data. Mitochondrial cytochrome oxidase (COI) is used for species-level taxonomic studies of testate amoebae and should allow assessing the community composition from environmental samples, thus bypassing biases due to morphological identification. We tested this using a COI clone library approach and focusing on the Nebela collaris complex. Comparisons with direct microscopy counts showed that the COI clone library diversity data matched the morphologically identified taxa, and that community com-position estimates using the two approaches were similar. However, this correlation was improved when microscopy counts were corrected for biovolume. Higher correlation with biovolume-corrected community data suggests that COI clone library data matches the ratio of mitochondria and that within closely-related taxa the density of mitochondria per unit biovolume is approximately constant. Further developments of this metabarcoding approach including quantifying the mitochondrial density among closely-related taxa, experiments on other taxonomic groups and using high throughput sequencing should make if possible to quantitatively estimate community composition of different groups, which would be invaluable for microbial food webs studies

Impact of two hot and dry summers on the community structure and functional diversity of testate amoebae in an artificial bog, illustrating their use as bioindicators of peatland health

Ongoing climate warming threatens the survival of bogs at the warm/dry limit of their distribution (e.g. in central Europe), and jeopardises the restoration of damaged bogs even more. Because vegetation changes can be slow, early indicators of hydrological change such as testate amoebae are useful. We used testate amoeba community structure and community weighted mean of functional traits to monitor the impact of two very hot and dry summers on a small (around 100 m2) artificial peatland constructed in the botanic garden of Neuchâtel, Switzerland. We collected analogous samples in a naturally regenerating cutover peatland at 1000 m a.s.l. in the Jura Mountains as a reference. The comparison of living and dead assemblages in the botanic garden showed an increased representation of smaller testate amoeba taxa (Corythion dubium, small Euglypha sp.) with a small pseudostome (indicative of dry conditions) and a loss of mixotrophy in 2015, followed by a weaker further shift in 2016. Nevertheless, the testate amoeba community structure in 2016 still indicated a dry Sphagnum bog. Testate amoeba analysis allows rapid assessment of peatland health and/or restoration success. The comparison of living and dead assemblages makes it possible to observe changes within a season in a single sampling campaign

The Phanerozoic diversification of silica-cycling testate amoebae and its possible links to changes in terrestrial ecosystems

The terrestrial cycling of Si is thought to have a large influence on the terrestrial and marine primary production, as well as the coupled biogeochemical cycles of Si and C. Biomineralization of silica is widespread among terrestrial eukaryotes such as plants, soil diatoms, freshwater sponges, silicifying flagellates and testate amoebae. Two major groups of testate (shelled) amoebae, arcellinids and euglyphids, produce their own silica particles to construct shells. The two are unrelated phylogenetically and acquired biomineralizing capabilities independently. Hyalosphenids, a group within arcellinids, are predators of euglyphids.We demonstrate that hyalosphenids can construct shells using silica scales mineralized by the euglyphids. Parsimony analyses of the current hyalosphenid phylogeny indicate that the ability to “steal” euglyphid scales is most likely ancestral in hyalosphenids, implying that euglyphids should be older than hyalosphenids. However, exactly when euglyphids arose is uncertain. Current fossil record contains unambiguous euglyphid fossils that are as old as 50 million years, but older fossils are scarce and difficult to interpret. Poor taxon sampling of euglyphids has also prevented the development of molecular clocks. Here, we present a novel molecular clock reconstruction for arcellinids and consider the uncertainties due to various previously used calibration points. The new molecular clock puts the origin of hyalosphenids in the early Carboniferous (~370 mya). Notably, this estimate coincides with the widespread colonization of land by Si-accumulating plants, suggesting possible links between the evolution of Arcellinid testate amoebae and the expansion of terrestrial habitats rich in organic matter and bioavailable Si