Supplement 1. Artificial and real data sets, and R functions and scripts to perform canonical correspondence analysis using fuzzy-coded explanatory variables, with adjustment of the variance explained.

File List artificial.csv (md5: 2dcf93451985a5205c88df0f24dcc709) - abundance data for 300 samples on 5 species (A, B, C, D and E) and environmental data on 2 variables (X and Y). <br> BarentsFish.csv (md5: e61ef26ef9a7fec70f831535587a5966) - fish abundance data set ‘BarentsFish’, on 89 samples from the Barents Sea, along with longitude and latitude positions, depth and temperature<br> fuzzy.tri.R (md5: 0bf5013ae24752cd27ed48e585a53870) - R function fuzzy.tri for fuzzy coding into any number of categories using triangular membership functions<br> CCA.R (md5: c6b9a3207e7e3405545a673b5a536daa) - R function CCA for basic computations of a CCA<br> fuzzyscript.R (md5: 4ce442235d7d6e107ff498fc62cc1789) - R script illustrating several analyses from this report (see description below) Description The two data files used in the report are given in csv format. Two R functions are provided: (i) to fuzzy code continuous variables into a chosen number of fuzzy categories, or into categories based on user-defined hinge points: (ii) to compute a basic canonical correspondence analysis, using the singular-value decomposition, with output of the sample (row) principal coordinates and the variable (column) contribution coordinates, as well as parts of constrained and unconstrained inertia. This function is useful for computing the adjusted percentage of variance explained (see R script next). Finally an R script is provided illustrating the following analyses: (a) the computation of the adjusted <i>R</i>² values in CCA by the permutation procedure proposed by Peres-Neto et al. (2006), (b) the conversion of continuous environmental variables (including spatial ones) into fuzzy-coded variables, and (c) plotting the results of the ‘BarentsFish’ analysis.<br> <br> Reference: Peres-Neto, P. R., P. Legendre, S. Dray, and D. Borcard. 2006. Partitioning of species data matrices: estimation and comparison of fractions. Ecology 87:2614–2625.

文件列表：
artificial.csv（MD5：2dcf93451985a5205c88df0f24dcc709）：包含300个样本的5个物种（A、B、C、D、E）丰度数据，以及2个变量（X与Y）的环境数据。
BarentsFish.csv（MD5：e61ef26ef9a7fec70f831535587a5966）：鱼类丰度数据集"BarentsFish"，涵盖巴伦支海的89个样本，附带经纬度位置、水深与温度数据。
fuzzy.tri.R（MD5：0bf5013ae24752cd27ed48e585a53870）：用于基于三角隶属度函数将连续变量模糊编码为任意数量类别的R函数fuzzy.tri。
CCA.R（MD5：c6b9a3207e7e3405545a673b5a536daa）：用于完成典范对应分析（Canonical Correspondence Analysis, CCA）基础计算的R函数CCA，可借助奇异值分解（singular-value decomposition）实现计算，输出样本（行）主坐标与变量（列）贡献坐标，同时给出约束惯性与非约束惯性的相关分量。该函数可用于计算校正后的方差解释百分比（详见后续R脚本）。
fuzzyscript.R（MD5：4ce442235d7d6e107ff498fc62cc1789）：用于演示本报告中多项分析的R脚本（详见下文描述）。

数据集说明：本报告所用的两份数据文件均采用CSV格式。本次共提供两个R函数：其一，可将连续环境变量模糊编码为指定数量的模糊类别，或基于用户自定义的分界点完成类别划分；其二，可借助奇异值分解完成基础典范对应分析计算，输出样本（行）主坐标与变量（列）贡献坐标，同时给出约束惯性与非约束惯性的相关分量。该函数可用于计算校正后的方差解释百分比（详见后续R脚本）。最后提供的R脚本可演示以下三类分析：(a) 基于Peres-Neto等人（2006）提出的置换法，计算典范对应分析中的校正R²值；(b) 将连续环境变量（包括空间变量）转换为模糊编码变量；(c) 绘制"BarentsFish"分析结果的可视化图形。

参考文献：Peres-Neto, P. R.、P. Legendre、S. Dray 与 D. Borcard. 2006. 物种数据矩阵的分区：组分估算与比较. 《生态学》（Ecology）87卷：2614–2625.