Your comment "Furthermore, both Gotelli  and Fayle & Manica  explored type II error rates using only highly structured, biologically unrealistic test matrices." is incorrect. In Fayle and Manica (2010) we used matrices with a range of strengths of structuring, from completely structured to those with completely random co-occurrence of species. In fact I am not sure how one would explore type 2 error rates without having variation in the strength of matrix structuring. I should also point out, in relation to the statement "For co-occurrence null models, Fayle & Manica  explored matrices ranging from 10 × 10 up to 100 × 100; however, they relied on the sequential swap algorithm, which is vulnerable to serial correlation ." that one of the main findings of our paper was that that the sequential swap is very vulnerable to serial correlation, and that is why, if you choose to use it, you need to use a large number of randomisations. We found that the more randomisations you use, the less biased the sequential swap becomes. As it stands, the citation makes it sound like we were completely unaware that this was a problem, despite it being a major focus of our paper!
Fayle T.M. & Manica A. (2010). Reducing over-reporting of deterministic co-occurrence patterns in biotic communities. Ecological Modelling 221: 2237-2242. doi:10.1016/j.ecolmodel.2010.06.013