PC-ORD 生态多元统计分析系统

生态数据多元分析软件（适用于 Windows 98, 00, ME, NT, XP, Vista, 7, 8, 10 和 11 系统）

PC-ORD 用于对电子表格中输入的生态数据进行多元分析。我们的侧重在于非参数工具、图形化表示、随机化检验以及用于分析群落数据的自举置信区间。

除了数据转换和文件管理实用程序外，PC-ORD 还提供了许多主流统计软件包中不具备的排序和分类技术，包括：

• 典范对应分析 (CCA)、除趋势对应分析 (DCA)
• 指示物种分析
• Mantel 检验及偏 Mantel 检验
• 多响应置换过程 (MRPP)
• 主坐标分析 (PCoA)
• 多变量方差置换分析 (perMANOVA)
• 冗余分析 (RDA)
• 双向聚类
• TWINSPAN 分类
• Beals 平滑
• 多样性指数计算
• 物种列表生成
• 多种排序叠加方法（定量叠加、符号编码、颜色编码、网格叠加、联合图、双序图、演替向量）
• 多种旋转方法
• 三维排序图形
• Bray-Curtis 排序
• 街区距离度量
• 种-面积曲线
• 树木数据汇总
• 可用于发表的树状图
• 自动导航模式的非度量多维尺度分析 (NMS 或 NMDS)

该软件可分析超大型数据集。在计算机内存充足的情况下，大多数运算可处理高达 32,000 行或 32,000 列、顶多 536,848,900 个元素的矩阵。

软件术语专为生态学家量身定制。完整的用户手册已集成在软件中，作为上下文相关的帮助系统。

性状

PC-ORD 7 提供了将物种性状数据（性状矩阵）与群落样本数据（主矩阵）和环境数据（第二矩阵）相关联的方法。虽然其中许多操作可以在 PC-ORD 的其他菜单项中完成，但“性状”菜单专门提供了几项针对此类数据的操作。

功能多样性

功能多样性分析结合了样方×物种矩阵和物种×性状矩阵。功能多样性度量旨在描述样方单元中所体现的物种功能性状的多样性，而非简单的物种多样性。例如，一个包含三个物种的样地，如果这三个物种都具有相同的性状，则其功能多样性被认为并不比单个物种高。同样，两个功能性状差异很大的物种比两个功能性状相似的物种贡献了更高的功能多样性。举例来说，如果一个样地中有两个物种，一个是喜光的杂草型先锋植物物种，另一个是耐荫且定殖能力差的物种，那么该样地的功能多样性就高于两个都是耐荫、定殖能力差的物种。

第四角分析

通过样方×物种矩阵将物种性状与环境变量联系起来的方法学问题，被称为第四角问题。这是由于四个基本矩阵的排列方式（参见 Dray 和 Legendre (2008, Fig. 1a) 以及 McCune 和 Grace (2002, Fig. 2.1) 中性状×环境的位置）。第四角分析提供了检验这些矩阵之间联系强度的统计方法。关于第四角分析理论和数学的详细解释，请参阅 Legendre 等人 (1997), Dray 和 Legendre (2008), Ter Braak 等人 (2012), 以及 Dray 等人 (2014)。

分类变量转二进制

对于给定的分类变量，如果存在 n 个惟一类别（即具有惟一值标签的分类水平），则将生成 n 个新的二进制（0/1）变量。每个新变量将被指定为 Q 变量，其值为 0 或 1。

创建性状组合

通过组合两个现有变量的类别来创建一个新的分类变量。从所选两个变量的类别中提取的每种组合都将作为新变量中的一个新类别。生成的新变量始终是分类变量。现有变量保持不变，但您可以使用“修改 | 删除列”(Modify | Delete Columns) 轻松移除它们。

例如，假设您有两个分类变量，一个用于编码本地种与非本地种，另一个用于编码一年生植物与多年生植物。这种编码在分析中可能适用，但如果某些物种具有这些性状的特定组合（例如非本地一年生植物）在生态上与所有其他物种存在显著差异呢？因此，您可能希望创建一个包含所有这些性状类别所有四种组合的新分类变量：(1)本地一年生植物，(2)本地多年生植物，(3)非本地一年生植物，(4)非本地多年生植物。

计算样方×性状矩阵 

计算样方×性状矩阵为分析物种性状与解释变量之间的关系提供了一个灵活的第①步。该矩阵通过样方×物种矩阵乘以物种×性状矩阵获得，但所得矩阵的内容取决于性状是否以及如何进行标准化，以及乘法之后是否进行加权平均步骤（McCune 2015）。为了大限度地提高样方×性状矩阵的通用性，包括性状之间的可比性以及与多种距离度量的适用性，我们建议首先对性状进行min-to-max标准化，然后计算每个样方单元内的丰度加权性状平均值。

性状空间中的物种距离 

物种之间可以通过基于物种×性状矩阵计算物种间的距离矩阵来进行性状比较。在数学上，这与在物种空间中计算样方单元之间的距离矩阵相同，区别在于此处的对象是物种，其属性是性状，而不是对象为样方单元且属性为物种。在性状菜单中提供的距离度量与在物种空间中计算样方单元间距离时提供的度量相同。

【英文介绍】

PC-ORD performs multivariate analysis of ecological data entered in spreadsheets. Our emphasis is on nonparametric tools, graphical representation, randomization tests, and bootstrapped confidence intervals for analysis of community data. In addition to utilities for transforming data and managing files, PC-ORD offers many ordination and classification techniques not available in major statistical packages including: CCA, DCA, Indicator Species Analysis, Mantel tests and partial Mantel tests, MRPP, PCoA, perMANOVA, RDA, two-way clustering, TWINSPAN, Beals smoothing, diversity indices, species lists, many ordination overlay methods (quantitative, symbol-coding, color-coding, grid, joint plot, biplot, successional vector), various rotation methods, 3-D ordination graphics, Bray-Curtis ordination, city-block distance measures, species-area curves, tree data summaries, publication-quality dendrograms, and autopilot mode nonmetric multidimensional scaling (NMS or NMDS). Very large data sets can be analyzed. Most operations accept a matrix up to 32,000 rows or 32,000 columns and up to 536,848,900 matrix elements, provided that you have adequate memory in your computer. The terminology is tailored for ecologists. The full manual is included as a context-sensitive help system.

Traits

PC-ORD 7 provides ways to relate data on species traits (trait matrix) to community samples (main matrix) and environmental data (second matrix).  While many of these operations can be done in the other PC-ORD menu items, the Traits menu provides several operations specific to this kind of data.

Functional Diversity

Functional diversity analyzes the combination of the sample unit x species matrix with a species x trait matrix.  Functional diversity measures attempt to describe the diversity of species functional traits represented in a sample unit, rather that simply species diversity.  For example, a plot containing three species, all having the same traits, are considered no more diverse than a single species.  Similarly, two species with very different functional traits contribute more functional diversity than two species that are similar in their functional traits.  For example, if we have two species in a plot and one is a weedy sun-loving pioneer plant species, and the other is a shade tolerant species with poor colonizing ability, that plot would have more functional diversity than two different species that were both shade tolerant poor colonizers.

Fourth Corner Analysis

The methodological question of linking species traits to environmental variables, via the sample unit x species matrix, is called the fourth corner problem because of the arrangement of four basic matrices (see the traits x environment positions in Dray and Legendre (2008, Fig. 1a) and McCune and Grace (2002, Fig. 2.1).  Fourth Corner Analysis provides statistical tests of the strength of the links between these matrices.   For a detailed explanation of the theory and mathematics of fourth corner analysis see Legendre et al. (1997), Dray and Legendre (2008), Ter Braak et al, (2012), and Dray et al. (2014).

Categorical to Binary

If, for a given variable, there are n unique categories (i.e., class levels with unique value labels), then n new binary (0/1) variables will be generated.  Each new variable will be designated as a Q variable with value 0 or 1.

Create Trait Combinations

Create one new categorical variable by combining categories from two existing variables.  Each combination of categories from the two selected variables is taken as a new category in the new variable.  The resulting new variable is always categorical.  The existing variables are left intact, but you can easily remove them with Modify | Delete Columns.

For example, say you had two categorical variables, one coding for native vs. non-native species, and one coding for annuals vs. perennials.  That might work well in the analyses, but what if species having a combinations of those, for example the non-native annuals, is particularly different ecologically from all remaining species?  You might, therefore, wish to create a new categorical variable with all four combinations of those trait categories: (1) native annuals, (2) native perennials, (3) non-native annuals, (4) non-native perennials.

Calculate SU x Traits Matrix

Calculating a sample unit x trait matrix provides a flexible first step in analyzing the relationships between species traits and explanatory variables.  This matrix is obtained by multiplying a sample unit x species matrix by a species x trait matrix, but the content of the resulting matrix depends on whether and how traits are standardized and whether or not the multiplication is followed by a weighted averaging step (McCune 2015).  To maximize versatility of the SU x trait matrix, including comparability among traits, and usability with a wide range of distance measures, we recommend first standardizing traits by min-to-max, then calculating abundance-weighted trait averages in each sample unit.

Species Distances in Trait Space

Species can be compared in their traits by calculating a distance matrix among species, starting with a species x trait matrix.  Mathematically this is the same as calculating a distance matrix among sample units in species space, except that in this case the objects are species and their attributes are traits, rather than objects being sample units and the attributes species.  The same distance measures are offered from the traits menu as for distances between sample units in species space.