The bootstrapped ordination re-examined

A method is described to determine the number of significant dimensions in metric ordination of a sample. The method is probabilistic, based on bootstrap resampling. An iterative algorithm takes bootstrap samples with replacement from the sample. It finds in each bootstrap sample ordination coordinates and computes, after Procrustean adjustments, the correlation between observed and bootstrap ordination scores. It compares this correlation to the same parameter generated in a parallel bootstrapped ordination of randomly permuted data, which uponmany iterations will generate a probability. The method is assessed in principal coordinates analysis of simulated data sets that have varying number of variables and correlation levels, uniform or patterned correlation structure. The results suggest the method is more reliable than other available methods in recovering the true intrinsic dimensionality. Examples with grassland data illustrate utility. [ABSTRACT FROM AUTHOR]