生态学统计基础及简单分析

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1 Analytical Methods in Community Ecology 刘金亮浙江大学生命科学学院

2 What is statistics for? To find patterns in your data To detect relations between variables To detect difference among groups of data

3 基本概念数据类型 : 二元数据连续数据分类数据频度分布平均值与中位数总体与样本方差 variance(var) 标准差 standard deviation (SD) 标准误 standard error(se)

4 样本特征数总体和样本平均数算数平均数加权平均数中位数众数等差数列和正态分布, 平均数 = 中位数

5 样本特征数样本方差标准差和标准误方差标准差 SD 标准误 SE 标准差是表示个体间变异大小的指标, 是衡量数据精密程度的指标 ; 标准误是反映样本均数对总体均数的变异程度, 是度量结果精密度的指标变异系数 CV: CV=SD/Mean

6 样本特征数平均数 :5 中位数 :5 众数 :NA 方差 :7.5 标准差 : 2.74 标准误 : 平均数 :5 中位数 :2 众数 :1 方差 :75.5 标准差 : 8.69 标准误 :2.90 EXCEL 练习 : 中位数 :median() 众数 :mode() 平均数 :average() 标准差 :STDEVA() 方差 :var() 标准误 :SD/sqrt(N)

7 数据校对和纠错数据之间建立联系 Data exploration using Excel Excel 练习 : 排序筛选表 ( 列表 ) If() 函数等 Excel 练习 :vlookup() 函数 Concatenate() 函数等数据格式转变 ( 列表 ~ 矩阵 ) Excel 练习 : 数据透视表的应用

8 描述统计绘图 Data exploration using Excel Excel 练习 : 数据数据分析 ( 需要安装 ) 描述统计 Excel 练习 : 数据数据分析直方图插入散点图 / 柱状图

9 探索性分析 Data exploration using Excel 画图, 看数据的分布, 适合哪种统计方法分类数据条形图数据分布的形状直方图, 散点图数据分布的大致状况箱线图正态分布

10 Frequency 异常值上边缘上四分位数中位数下四分位数下边缘 DBH 直方图箱线图

11 Y X Y: dependent variable, or, response variable, the outcome we measured. X: independent variable, the factor presumed to affect the values of Y. 散点图

12 Exploring data Choosing your analytical method Four classes of experimental and sampling design Independent variable (X) Dependent variable (Y) Continuous Continuous Regression Categorical ANOVA Categorical Logistic regression Tabular (X 2 )

13 Exploring data Choosing your analytical method Hypothesis test 两组数据平均数比较参数检验 Parameter test t-test 非参数检验 Non-parameter test Wilcoxon rank sum test (Mann-Whitney U-test) 多组数据平均数比较 ANOVA Kruskal-Wallis test 两组变量比较 F test Mood test 多组变量比较 Bartlerr test Fligner test

14 ANOVA Multiple two-sample t-tests would result in an increased chance of committing a statistical type I error. ANOVAs are useful in comparing (testing) three or more means (groups or variables) for statistical significance.

15 P-Value P 0.01 : very strong presumption against null hypothesis 0.01<P 0.05 : strong presumption against null hypothesis 0.05<P 0.1 : low presumption against null hypothesis P >0.1: no presumption against the null hypothesis

16 Normal test Q-Q plot Shapiro-Wilk test

17 相关分析协方差相关系数 : 中心化和标准化的协方差, 表示两组数据之间是否有某种关系

18 相关分析植物多样性与动物多样性物种多样性与岛屿生境特征物种多样性与功能特征 Pearson 相关 Spearman 相关例子 Table Pearson correlation coefficients among island attributes PAR SI I A -0.21** 0.79*** PAR -0.38*** SI A: area, PAR: P/A, SI: shape index, I: islation

19 Regression analysis 线性回归 y=a+bx 非线性回归 : 通过数据转化, 部分可以变换成线性回归, 例如物种面积关系 (SAR) Y=aX b lny=lna+b lnx

20 Regression analysis Stepwise regression A common problem is that there is a large set of candidate predictor variables. 土壤节肢动物多样性 ~ 岛屿面积岛屿形状隔离度 Goal is to choose a small subset from the larger set so that the resulting regression model is simple, yet have good predictive ability. 土壤节肢动物多样性 ~ 隔离度

21 多元统计分析排序排序 (Ordination): 研究群落之间群落与环境之间的相互关系 PCA RDA CA CCA NMDS 在 RDA 排序图内, 环境因子一般用箭头表示, 箭头连线的长度代表某个环境因子与群落分布和种类分布间相关程度的大小, 连线越长, 说有相关性越大, 反之越小 ; 箭头连线和排序轴的夹角代表某个环境因子与排序轴的相关性大小, 夹角越小, 相关性越高, 反之越低.

Exploring data Choosing your analytical method Analytical methods for community studies Species richness Diversity similarity Similarity Hierarchical clustering Presence

22 Exploring data Choosing your analytical method Analytical methods for community studies Species richness Diversity similarity Similarity Hierarchical clustering Presence or Absence Community data Abundance Hierarchical clustering Association Association Ordination Desprication or classification Indicator species Desprication or classification

23 Species diversity α diversity:species biodiversity of a local community β diversity:change (or turnover) in species composition between two local sites γ diversity:total species richness in a region α α α α α α α β γ

24 Measurement of species diversity

25 Area A Area B Which one is more diverse? Purvis & Hector, 2000.

26 Measurement of Species diversity α diversity: 群落内物种多样性 Simpson 指数 Shannon-Winner 指数 Pielou 均匀度指数 P i 可用相对多度 ( 如鸟类土壤动物群落 ) 或重要值 ( 植物群落 ) 计算 β diversity: 沿环境梯度物种组成差异 Jaccard Sorsen 相似性指数 Whittaker 指数 γ diversity: 多个样方的物种数量 γ = a + β

27 重要值木本植物 : 重要值 IV=( 相对多度 + 相对频度 + 相对显著度 )/3 相对多度 =( 某种植物的个体数 / 全部植物的个体数 ) 100% 频度 : 是指一个种在所做的全部样方中出现的频率相对频度 =( 该种的频度 / 所有种的频度总和 ) 100% 显著度 : 指样方内某种植物的胸高断面积除以样地面积相对显著度 =( 样方中该种个体胸面积和 / 样方中全部个体胸面积总和 ) 100% 草本植物 :IV=( 相对多度 + 相对盖度 + 相对高度 )/3

28 Similarity-based beta diversity indices

29 Table and figure in papers 1. 使文章更加简洁明了 2. 图表具有自明性 3. 尽可能的使用图 Liu et al., Wetland Science, 2014

30 李等, 生物多样性, 2011 Yu, et al., Biol Invasions, 2011

31 Qian et al. science, 2012

33 生境片段化对植物多样性的影响以千岛湖为例 Hu et al., Landscape Ecol, 2011

34 岛屿设置个数 29个面积 0.08~1155 ha 最大岛界首岛 JSE 浙江省大陆 JSE

35 Habitat loss and fragmentation Habitat loss + no fragmentation Habitat loss +fragmentation No habitat loss +fragmentation Habitat loss +fragmentation +change in habitat quality Franklin et al., 2002

36 Extent of fragmentation None area Fragmentation Edge Shape Isolation Matrix Species diversity --Species richness --Species composition --Community assembly High Curtis, 1956

37 Islands attributes Island area (A) and perimeter (P) : calculated through analysis of maps in ArcGIS 9.3 for when the water level reaches 105 m a.s.l. Perimeter/area ratio (PAR): indicative of the relative amount of edge habitat on an island Shape index (SI= P/[2 (π A) 0.5 ]): the island shape complexity Island isolation(i): the shortest straight-line distance from the edge of a study island to the edge of mainland

38 Species richness stepwise linear regression Main factors affecting species richness Hu et al., 2011

39 Nestedness: the species composition of small assemblages is a nested subset of the species composition of large assemblages. Area Shape complex isolation

40 Nestedness in TIL: Results: larger islands and islands with more complex shapes tend to host richer species communities

41 Species composition RDA analysis Figure Species composition of plants on 41 study islands in the Thousand Island Lake, China, in relation to five island attributes as characterized by redundancy analyses (RDA). Figures show species composition of (a) all plant species, (b) shade-intolerant plants, (c) shade-tolerant plants. The size of the points varies in relation to log island size. The lengths and angles of the arrows represent the explanatory power of the island attributes along each axis; that is, the explanatory power is higher when the length is longer and the angle is smaller. Yu et al,. 2012

42 Species composition beta diversity analysis 岛屿面积决定藤本和灌木的 beta 多样性岛屿间距离决定乔木的 beta 多样性 Peng et al,. 2014

43 Edge effects Perimeter-area ratio the changes in population or community structures that occur at the boundary of two habitats. changing abiotic conditions direct biotic effects indirect biological effects

44 Su et al., 2014

45 Su et al., 2014

46 Main conclusion Species richness: Islands area (Main), shape complex, PAR Species composition: Isolation

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.. 1. 2. ) () () Pilot test () 1. 2. 3. 4. Scale (1). (nominal scale) 1. 2. 3. (1,2,3) (scale value) (arithmetic mean) (median) (mode) (chi-square test) (2). (ordinal scale) 5 1 A>B>C>D>E A B C D (non-parametric