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When dissimilarity matrices of faunistic and phylogenetic beta-diversity turnover indices are projected in dendrograms, a high frequency of ties and zero values produces trees whose topology and bootstrap support are affected by the order of areas in the original presence–absence matrix. We tested the magnitude of this bias and developed R functions to obtain consensus trees after shuffling of matrix row order and applied this algorithm to a multiscale bootstrap procedure. Our functions not only solve the bias of row order but, owing to varying support for different bootstrap scales, reveal fundamental characteristics about the structure of species assemblages.