Bi-dimensional null model analysis of presence-absence binary matrices

Comparing the structure of presence/absence (i.e. binary) matrices with those of randomized counterparts is a common practice in ecology. However, differences in the randomization procedures (null models) can affect the results of the comparisons, leading matrix structural patterns to appear either ‘random’ or not depending on the procedure adopted. Subjectivity in the choice of one particular randomization approach over another makes it often advisable to compare the results obtained using several different null models. Yet, available algorithms to randomize binary matrices differ substantially in respect to the constraints they impose on the discrepancy between observed and randomized row and column marginal totals, which complicates the interpretation of contrasting patterns. This calls for new strategies both to explore intermediate scenarios of restrictiveness in-between extreme constraint assumptions, and to properly synthesize the resulting information. Here we introduce a new flexible algorithm, named the ‘Tuning Peg’ algorithm, and a new null modeling framework based on it, that permit to tackle both issues. The algorithm consists of a modified swap procedure in which the discrepancy between the row and column marginal totals of the target matrix and those of its randomized counterpart can be ‘tuned’ in a continuous way by two parameters (controlling, respectively, row and column discrepancy). The application of the algorithm across the range of both parameters permits to explore the complete null space embraced by existing algorithms, allowing researchers to visualize matrix structural patterns in an innovative bi-dimensional landscape of significance/effect size. We demonstrate the rational and potential of our approach with a set of simulated and real matrices, showing how the simultaneous investigation of a comprehensive (and continuous) portion of the null space can be extremely informative, and possibly key to resolving longstanding debates in the analysis of ecological matrices.

STRONA Giovanni;  ULRICH Werner;  GOTELLI Nicholas; 

2018-02-19

WILEY-BLACKWELL

JRC107276

0012-9658,   

http://onlinelibrary.wiley.com/doi/10.1002/ecy.2043/full,    https://publications.jrc.ec.europa.eu/repository/handle/JRC107276,   

10.1002/ecy.2043,