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The freshwater red algal genus Batrachospermum has been shown to be paraphyletic since the first molecular studies of the Batrachospermales. Previous research, along with this study, provides strong support for the clade Batrachospermum section Helminthoidea. This study has found that heterocortication, the presence of both cylindrical and bulbous cells on the main axis, is an underlying synapomorphy of this clade. Based on support from DNA sequences of the rbcL gene, the COI barcode region and the rDNA ITS 1 and 2, along with morphological studies, the new genus Sheathia is proposed. Seven heterocorticate species were recognized from the molecular clades. Sheathia boryana and S. exigua sp. nov. appear to be restricted to Europe, whereas S. confusa occurs in Europe and New Zealand. Sheathia involuta is widespread in the USA and reported for the first time from Europe. Sheathia americana sp. nov., has been collected in the USA and Canada, and S. heterocortica and S. grandis sp. nov. have been collected only in the USA. Sheathia confusa and S. grandis can be distinguished based on morphological characters, whereas DNA sequence data are required to conclusively distinguish the other species. Sheathia fluitans and S. carpoinvolucra also are placed within this genus based on the presence of heterocortication. These data also hint at greater diversity among non-heterocorticate Sheathia than is recognized by the single species name S. arcuata.

Species level taxonomy and phylogeographical distribution patterns in the freshwater rhodophyte Sirodotia are resolved through phylogenetic inferences based on rbcL and cox2-3 sequence data. Previous studies focused on the taxonomy of specific Sirodotia species or the distributions across a limited geographical region. Our molecular phylogenies included samples attributable to five recognized Sirodotia species and include collections from Australia, Brazil, Costa Rica, Canada, Finland, Mexico, New Zealand, South Africa and the United States. Both rbcL and cox2-3 phylogenies inferred S. suecica, S. tenuissima and S. goebelii as a monophyletic group with little sequence divergence. This result supports the synonymy of S. tenuissima and S. goebelii with S. suecica (the species name with priority). Within this clade, samples collected from Australia and New Zealand formed a monophyletic group with no other discernible phylogeographical patterns within S. suecica. This result seems to be somewhat unusual in the Batrachospermales, as other species have shown greater genetic variation among geographically distant locations. As in previous studies, S. huillensis and S. delicatula were inferred as a separate species based on the rbcL phylogeny, supporting the current taxonomy. A specimen of S. aff. huillensis from South Africa, may represent a new species but further research is necessary before it can be designated as such.

Of the total number of freshwater red algae (ca. 180 taxa), one third are found in Europe (ca. 60 taxa). Over one third (24 taxa) of European taxa have been found at only one single location or at very few locations. The majority of taxa live in running waters, but some occur in lakes, on wet ground, in hot springs or in garden ponds. Diversity in the Nordic countries of Sweden and Finland seems to be somewhat higher (27 and 28 taxa, respectively) than in the central and southern parts of Europe (e.g.

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