Synthetic matrix ensemble for nestedness analysis

README
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The data and code in this dataset was used to evaluate nestedness measures and null models (Beckett and Williams, submitted).

500 initial 'perfectly nested' matrices were created using Latin hypercube sampling to choose the number of rows [5,60] , columns [5,60] and curvature.

We 'rewired' each of these matrices to evaluate how significance testing of nestedness alters between highly nested (low rewiring) and less nested (high rewiring) networks. In rewiring, a probability of rewiring occuring is assigned to each element in a matrix. If rewiring is judged to occur in a matrix element that has an edge (is a 1) - this edge is removed (turned to 0) and then randomly repositioned in one of the empty positions (one of the 0's becomes a 1), such that the number of total edges is conserved.

We used 6 rewiring levels, such that the probability of rewiring was 0.01, 0.05, 0.1, 0.15, 0.2 and 0.5 . Ten replicates of the initial 500 matrices were made for each rewiring level. The entire ensemble is then 500x10x6 = 30,000 networks.

Each of these 30,000 networks was then analysed for nestedness using FALCON (Beckett et al., 2014). Six nestedness measures and five null models were used. Details of these analyses can be found in Beckett and Williams (submitted).

The dataset contains:
code: MATLAB code used to create the synthetic ensemble.
- SHAPE_MATRIX.m a MATLAB function for creating a 'perfectly nested' bipartite network with given rows, columns and curvature parameters.
- makeBenchmarkEnsemble.m a MATLAB function for creating a set of X matrices rewired from an initial matrix with probability P.
- randomiseMatrix.m a MATLAB function for rewiring a given input matrix with probability P.

networks: The set of networks used in the synthetic ensemble.
- A total of 30,000 binary matrices each saved as a separate csv file.

output: The output data from nestedness analysis for each measure.
- Five csv files corresponding to output from the five null models used (SS,FF,CC,DD,EE).
- For each measure (NODF, MD, SR, JDM, BR, NTC) the measure score, p-value, z-score and adjusted normalised temperature(AnT) scores are given.

Beckett S.J., Williams H.T.P. Brooding on nestedness: nestedness analyses are confounded by sensitivity to measurement choices and network properties. submitted.

 

Beckett SJ, Boulton CA and Williams HTP. FALCON: a software package for analysis of nestedness in bipartite networks [v1; ref status: indexed, http://f1000r.es/3z8] F1000Research 2014, 3:185 (doi: 10.12688/f1000research.4831.1)