Appendix D. The extraction of spatial variables from the distance matrices and the selection of spatial and environmental variables as input for the variation partitioning.
We extracted distance variables (coordinates) from the distance matrices of the Land model and the Water model with Principle Coordinate Analyses using the DistPCoA freeware tool (Legendre and Anderson 1998). We did not include the Neighboring model since this model cannot be properly summarized into a restricted number of coordinates. The Land distance model was summarized into two axes (X, Y) in both pond groups, but the more complex Water model resulted in 7 and 11 axes in pond groups 1 and 2, respectively. We used these newly extracted axes to construct two distance matrices for each pond group: one matrix consisting of a third degree polynomial of X and Y, and another including the axes and their quadratic terms extracted from the water model. These data matrices were used in a forward selection Redundancy Analysis (RDA) procedure with as dependent matrix the macroinvertebrate abundances. The number of selected axes ranged from 1–3 for group 1, and from 1–4 for group 2. In RDA, the sum of explanatory variables and covariates (environmental + spatial) cannot exceed the number of samples (ponds) -1. Therefore only the first two axes were used in the spatial explanatory matrix [S] for group 1. For group 2, the first three axes were included. Matrices of the full set of environmental variables were used as input in 48 forward selection RDAs (distance model[2] × pond group[2] × dispersal mode[2]/ generation time class[2] × year[3]). The number of selected environmental variables ranged from 1 to 5 for group 1, and from 2 to 5 for group 2. For group 2, the first five environmental variables were included in the environmental matrix [E]. To keep the sum of variables in [E+S] lower than the number of ponds -1, the first four environmental variables were included for group 1.
LITERATURE CITED
Legendre, P., and M. J. Anderson. 1998. Program DISTPCOA. Département de sciences biologiques, Université de Montréal, Montréal, Canada.