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The data used in this publication uses highly selective terms to add up the data. Without repeating the entire study, a simple search in Google Scholar can produce radically different results just by using the plural of a term. As of 9.30 am GMT 08/03/16 there are 835 hits for Euglenid and 2420 hits for Euglenids for example.
The webpages that are noted in table 2 as using the botanical terms include Wikipedia, which has pages entitled Euglenozoa and Euglenid, which are annotated as zoological terms and the botanical terms redirect to these. The Euglenoid Project has "Euglenoid" in the title and hence uses zoological terms, against the data in table 2.
However in support of the thesis a quick repetition of the searches performed in Web of Science shows that Euglenophyta is far in the lead with 8139 hits in the topic search, with the other terms in table 1 summing to 3070. I have not checked for duplications in this data.
Overall I agree with the idea of using botanical naming conventions, but don't think this paper is rigorous enough to definitively show this.
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