Metric trees of generalized roundness one

Every finite metric tree has generalized roundness strictly greater than one. On the other hand, some countable metric trees have generalized roundness precisely one. The purpose of this paper is to identify some large classes of countable metric trees that have generalized roundness precisely one. At the outset we consider spherically symmetric trees endowed with the usual combinatorial metric (SSTs). Using a simple geometric argument we show how to determine decent upper bounds on the generalized roundness of finite SSTs that depend only on the downward degree sequence of the tree in question. By considering limits it follows that if the downward degree sequence $(d_{0}, d_{1}, d_{2}...)$ of a SST $(T,\rho)$ satisfies $|\{j \, | \, d_{j} > 1 \}| = \aleph_{0}$, then $(T,\rho)$ has generalized roundness one. Included among the trees that satisfy this condition are all complete $n$-ary trees of depth $\infty$ ($n \geq 2$), all $k$-regular trees ($k \geq 3$) and inductive limits of Cantor trees. The remainder of the paper deals with two classes of countable metric trees of generalized roundness one whose members are not, in general, spherically symmetric. The first such class of trees are merely required to spread out at a sufficient rate (with a restriction on the number of leaves) and the second such class of trees resemble infinite combs.Comment: 14 pages, 2 figures, 2 table

The Global Soil Mycobiome consortium dataset for boosting fungal diversity research.

Fungi are highly important biotic components of terrestrial ecosystems, but we still have a very limited understanding about their diversity and distribution. This data article releases a global soil fungal dataset of the Global Soil Mycobiome consortium (GSMc) to boost further research in fungal diversity, biogeography and macroecology. The dataset comprises 722,682 fungal operational taxonomic units (OTUs) derived from PacBio sequencing of full-length ITS and 18S-V9 variable regions from 3200 plots in 108 countries on all continents. The plots are supplied with geographical and edaphic metadata. The OTUs are taxonomically and functionally assigned to guilds and other functional groups. The entire dataset has been corrected by excluding chimeras, index-switch artefacts and potential contamination. The dataset is more inclusive in terms of geographical breadth and phylogenetic diversity of fungi than previously published data. The GSMc dataset is available over the PlutoF repository

Global patterns in endemicity and vulnerability of soil fungi.

Fungi are highly diverse organisms, which provide multiple ecosystem services. However, compared with charismatic animals and plants, the distribution patterns and conservation needs of fungi have been little explored. Here, we examined endemicity patterns, global change vulnerability and conservation priority areas for functional groups of soil fungi based on six global surveys using a high-resolution, long-read metabarcoding approach. We found that the endemicity of all fungi and most functional groups peaks in tropical habitats, including Amazonia, Yucatan, West-Central Africa, Sri Lanka, and New Caledonia, with a negligible island effect compared with plants and animals. We also found that fungi are predominantly vulnerable to drought, heat and land-cover change, particularly in dry tropical regions with high human population density. Fungal conservation areas of highest priority include herbaceous wetlands, tropical forests, and woodlands. We stress that more attention should be focused on the conservation of fungi, especially root symbiotic arbuscular mycorrhizal and ectomycorrhizal fungi in tropical regions as well as unicellular early-diverging groups and macrofungi in general. Given the low overlap between the endemicity of fungi and macroorganisms, but high conservation needs in both groups, detailed analyses on distribution and conservation requirements are warranted for other microorganisms and soil organisms