A fast and unbiased procedure to randomize ecological binary matrices with fixed row and column totals

Area of Science:

• Numerical ecology
• Ecological modeling
• Computational biology

Background:

• Recombining ecological matrices while preserving row and column totals is a persistent challenge.
• Existing methods for matrix randomization suffer from issues with statistical robustness and computational performance.
• Accurate randomization is crucial for null model analysis in ecology.

Purpose of the Study:

• To introduce a new algorithm, the 'Curveball algorithm', for randomizing presence-absence matrices.
• To address the limitations of existing methods in terms of statistical robustness and computational efficiency.
• To enable uniform sampling of all possible matrix configurations.

Main Methods:

• The Curveball algorithm focuses on matrix information content rather than matrix structure for randomization.
• It generates different matrix configurations with the same probability, ensuring statistical robustness.
• The algorithm's computational efficiency allows for rapid randomization of large matrices.

Main Results:

• The Curveball algorithm samples uniformly from the set of all possible matrix configurations.
• It requires computational effort orders of magnitude lower than existing methods.
• The algorithm successfully randomizes matrices larger than 10^8 cells.

Conclusions:

• The Curveball algorithm offers a statistically robust and computationally efficient solution for randomizing ecological matrices.
• It overcomes the limitations of previous methods, facilitating more reliable null model analyses.
• This advancement enables the analysis of larger and more complex ecological datasets.