Neutral dynamics operate among the species of each guild in patchy habitats
The variation partitioning based on canonical analysis (i.e. redundancy analysis; Borcard, Legendre, & Gillet 2011; Peres-Neto & Legendre, 2010) and the autocorrelation method (Diniz-Filho et al., 2012) were also used to infer the relative roles of alternative processes. In general, the applications followed Yunoki & Torres (2016); Yunoki, Torres, Pouilly, & Hablützel (2017); Yunoki, Torres, & Cholima (2018); Yunoki, Torres, & Cholima (2019).
The variation partitioning was applied for the model communities at convergence time. In model communities, the species response curves might be often unimodal, so that the species abundances data was Hellinger transformed prior to analysis and the first and second-order orthogonal environmental variables were used (Borcard et al., 2011; Gilbert & Bennett, 2010). The standard forward selection procedure was used because the habitat associations among the species of each guild were equivalent and these species might have similarities regarding their environmental and spatial associations (Borcard et al., 2011; Peres-Neto & Legendre, 2010). If more than two guilds were coexisted in model communities and if the pure environmental component was significant, the hierarchical guild structure was identified by thek -means partitioning of linear combination scores (scaling 1) and simple structure index criterion. If the hierarchical guild structure was significant, the principal coordinates of neighbour matrices (PCNM) were constructed to model the spatial structures within and among patchy habitats in the residual variation of species composition between sites. The portion explained by each component was obtained by the adjusted coefficient of determination in overall and hierarchical models, and its significance was estimated by a randomization test applying an alpha of 0.05.
The functional uniqueness and redundancy of model communities were compared to the relative portions explained by environmental and pure spatial components in the total explaind variation of overall model; then, the total explained variation and these relative portions were compared between overall and hierarchical models. Furthermore, the number of guilds coexisted in model communities was compared to the number of habitat types identified by hierarchical guild structure.
In the model communities resulted with only one guild, the autocorrelation method was applied for the species abundances predicted by true spatial and false environmental components. In the model communities resulted with more than two guilds, this method was applied for the true environmental component of overall model, and the spatial structures found by hierarchical model in each environmental context. The correlograms were calculated using the number of distance classes computed by Sturges method in overall model; while, three or two distance classes in each environmental context. In all cases, the Mantel correlation between matrices of correlation coefficients and correlogram distances among species was tested against the null hypothesis of less than zero applying an alpha of 0.05. Appendix A presents the summary statics of scenarios.