Randomization of Presence–absence Matrices: Comments and New Algorithms

Randomization of presence–absence data matrices with fixed row and column totals is an important tool in ecological research wherever the significance of data-based statistics (e.g., species association measures) is to be evaluated. In the current literature of numerical ecology, however, there has been no algorithm that randomizes moderately large matrices in short time such that equidistribution of results is guaranteed. We show that a simple modification of the swap algorithm, called here the “trial-swap method,” satisfies the requirement for equidistribution. Since this is relatively slow, we suggest two fast algorithms that, combined with the trial-swap method, produce all possible results with equal chance. The three procedures are illustrated using actual examples taken from bird biogeography and vegetation ecology.