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Swap and fill algorithms in null model analysis: rethinking the knight's tour
Nicholas J Gotelli1, Gary L Entsminger2
1Department of Biology, University of Vermont, 05405, Burlington, VT, USA.
Oecologia
|May 27, 2017
Summary
Null model algorithms for presence-absence matrices are crucial for ecological studies. This research reveals the Knight's Tour algorithm is biased, unlike the more reliable Sequential Swap, ensuring accurate ecological community assembly analysis.
Area of Science:
- Ecology
- Computational Biology
- Statistical Modeling
Background:
- Community assembly rules are often inferred from presence-absence matrices.
- Devising null model algorithms for random matrices with fixed row and column sums is challenging.
- Previous algorithms like Sequential Swap and Knight's Tour have been used with varying success.
Purpose of the Study:
- To evaluate the statistical properties of the Knight's Tour algorithm for generating null model matrices.
- To introduce and validate an unbiased Random Knight's Tour algorithm.
- To compare the performance of the Random Knight's Tour and Sequential Swap algorithms.
Main Methods:
- Analysis of presence-absence matrices using probability calculations.
- Introduction of an unbiased Random Knight's Tour algorithm.
- Comparison of Random Knight's Tour and Sequential Swap algorithms on ecological datasets.
Main Results:
- The Knight's Tour algorithm was found to be biased, not sampling unique matrices equiprobably.
- The Random Knight's Tour algorithm appears to sample unique matrices with equal frequency.
- The Sequential Swap algorithm produced results similar to the unbiased Random Knight's Tour and showed no evidence of Type I errors.
Conclusions:
- The Knight's Tour algorithm generates high variance and is not suitable for null model generation.
- The Sequential Swap algorithm is a reliable method for generating null model matrices.
- Future null model algorithm development should include rigorous statistical property examination and comparison with artificial datasets.
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