Abstract:
: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. Subjectivity in the choice of one particular null model over another makes it often advisable to compare the results obtained using several different approaches. 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 modeling framework based on a flexible matrix randomization algorithm (named the "Tuning Peg" algorithm) that addresses 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). We show how combining the Tuning Peg with a wise random walk procedure makes it possible to explore the complete null space embraced by existing algorithms. This exploration allows 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.
journal_name
Ecologyjournal_title
Ecologyauthors
Strona G,Ulrich W,Gotelli NJdoi
10.1002/ecy.2043subject
Has Abstractpub_date
2018-01-01 00:00:00pages
103-115issue
1eissn
0012-9658issn
1939-9170journal_volume
99pub_type
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