Null models for species co-occurrence patterns: assessing bias and minimum iteration number for the sequential swap

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Disentangling community patterns of nestedness and species co‐occurrence (2007, background): “It has a small bias against finding species segregation patterns (Miklós and Podani 2004, Lehsten and Harmand 2006), but has lower type I and type II error probabilities than other randomization algorithms (Gotelli 2000, Gotelli and Entsminger 2001, Ulrich and Gotelli 2007).”
Phylogenetic diversity, trait diversity and niches: species assembly of ferns along a tropical elevational gradient (2011, background): “…generated null assemblage (30,000) exceeds the number of filled cells within the original matrices (c. 2000 for terrestrial species, c. 4200 for epiphytic species), in order to ensure that the resulting randomized matrix is sufficiently different from the empirical one (Lehsten & Harmand, 2006).”
A probabilistic model for analysing species co-occurrence (2013, background): “This issue of biased randomizations has recently attracted the attention of ecologists and statisticians (Zaman & Simberloff, 2002; Miklós & Podani, 2004; Lehsten & Harmand, 2006; Navarro-Alberto & Manly, 2009; Sanderson et al., 2009; Fayle & Manica, 2010; Gotelli & Ulrich, 2011).”