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)

README
======

本数据集包含的数据与代码用于评估嵌套性指标（nestedness measures）与零模型（null models）（Beckett与Williams，已投稿）。

我们采用拉丁超立方抽样（Latin hypercube sampling）选取行数区间[5,60]、列数区间[5,60]与曲率参数，生成了500个初始“完美嵌套（perfectly nested）”矩阵。

我们对每个初始矩阵进行“重连（rewiring）”操作，以探究嵌套性显著性检验在高度嵌套（低重连水平）与低度嵌套（高重连水平）网络间的差异。重连过程中，为矩阵内每个元素分配一个重连发生概率：若判定某存在边的矩阵元素（值为1）需要重连，则移除该边（将其置为0），随后将其随机重定位至一个空位置（将其中一个0置为1），以此保证总边数守恒。

我们设置了6种重连水平，对应的重连概率分别为0.01、0.05、0.1、0.15、0.2与0.5。针对每种重连水平，我们对初始的500个矩阵各生成10个重复样本，因此整体集成网络总数为500×10×6=30000个。

随后，我们使用FALCON（Beckett等，2014）对这30000个网络的嵌套性进行分析，共采用6种嵌套性指标与5种零模型。相关分析细节可参见Beckett与Williams（已投稿）的研究。

本数据集包含以下内容：
代码：用于构建人工集成网络的MATLAB代码
- SHAPE_MATRIX.m：MATLAB函数，用于生成具有指定行数、列数与曲率参数的“完美嵌套”二分网络（bipartite network）。
- makeBenchmarkEnsemble.m：MATLAB函数，用于基于初始矩阵以指定重连概率P生成X个重连后的矩阵集合。
- randomiseMatrix.m：MATLAB函数，用于以指定重连概率P对给定输入矩阵进行重连操作。

网络数据：人工集成网络的集合
- 共30000个二值矩阵（binary matrices），每个矩阵保存为一个独立的csv文件。

输出结果：各嵌套性指标的分析输出数据
- 5个csv文件，分别对应5种零模型（SS、FF、CC、DD、EE）的分析输出。
- 针对每种指标（NODF、MD、SR、JDM、BR、NTC），均提供了指标得分、p值、z得分与校正归一化温度（AnT）得分。

参考文献：
Beckett S.J.、Williams H.T.P. 《关于嵌套性的思考：嵌套性分析易受测量选择与网络属性的敏感性干扰》，已投稿。

Beckett SJ、Boulton CA与Williams HTP. FALCON：二分网络嵌套性分析软件包[v1；引用状态：已索引，http://f1000r.es/3z8] F1000Research 2014, 3:185（doi: 10.12688/f1000research.4831.1）