The exact taxonomic identity of Nitzschia sigma (Kützing) W.Smith remained an enigma. The species was originally described as Synedra sigma Kützing from Denmark, but the type material and the original Kützing slide from 'Ostsee bei Hofmannsgave' could no longer be found. A minority of authors, however, follow William Smith who in 1853 discussed and depicted a marine and brackish water specimen based on material from Pevensey Beach (south-east England between Hastings and Brighton, UK) as Nitzschia sigma. Kützing (1849) had listed in addition to the locality in Denmark, two other samples where he found N. sigma: the English Channel and material he received from his friend Alphonse de Brébisson from the Calvados region. This latter material is present in Meise and London and can be used to choose a neotype for this species. Based on the accompanying diatom flora in the sample, N. sigma is a typical marine species, making observations in freshwater samples doubtful.
The general confusion is due to two largely overlooked taxa, now almost forgotten. The first, Nitzschia sigma var. rigida Grunow in Van Heurck, was originally described as Amphipleura rigida Kützing, an illegitimate name however, by Kützing (1844). Grunow also described N. sigma var. rigidula Grunow to Van Heurck, from a sample collected by Charles-Henri Delogne in Brussels. While the var. rigida can be considered a slightly brackish taxon, var. rigidula is a typical freshwater species.
The poster discusses the taxonomic history of this Nitzschia sigma complex illustrating the different populations used to disentangle this problematic group.

Kützing, F.T. (1844). Die Kieselschaligen. Bacillarien oder Diatomeen. Nordhausen. 152 pp., 30 pls., available online at https://doi.org/10.5962/bhl.title.64360
Kützing, F.T. (1849). Species Algarum. F. A. Brockhaus: Lipsiae (Leipzig). VI-922 pp. (look up in IMIS), available online at https://doi.org/10.5962/bhl.title.60464