Statistics 简明教程
Statistics - Shannon Wiener Diversity Index
在文献中，“物种丰富度”和“物种多样性”这两个术语有时可以互换使用。我们建议至少，作者应该定义他们所说的这两个术语的含义。在文献中使用的众多物种多样性指数中，香农指数可能是使用最广泛的。有时它被称为香农 - 维纳指数，有时被称为香农 - 韦弗指数。我们建议对这种双重术语解释一下，同时我们向已故的克劳德·香农（于 2001 年 2 月 24 日去世）致敬。
In the literature, the terms species richness and species diversity are sometimes used interchangeably. We suggest that at the very least, authors should define what they mean by either term. Of the many species diversity indices used in the literature, the Shannon Index is perhaps most commonly used. On some occasions it is called the Shannon-Wiener Index and on other occasions it is called the Shannon-Weaver Index. We suggest an explanation for this dual use of terms and in so doing we offer a tribute to the late Claude Shannon (who passed away on 24 February 2001).
香农 - 维纳指数的定义和函数如下：
Shannon-Wiener Index is defined and given by the following function:
其中——
Where −
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${p_i}$ = proportion of total sample represented by species ${i}$. Divide no. of individuals of species i by total number of samples.
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${S}$ = number of species, = species richness
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${H_{max} = ln(S)}$ = Maximum diversity possible
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${E}$ = Evenness = ${\frac{H}{H_{max}}}$
Example
Problem Statement:
Problem Statement:
5 个物种的样本为 60、10、25、1、4。对于这些样本值，计算香农多样性指数和均匀度。
The samples of 5 species are 60,10,25,1,4. Calculate the Shannon diversity index and Evenness for these sample values.
样本值 (S) = 60、10、25、1、4 物种数量 (N) = 5
Sample Values (S) = 60,10,25,1,4 number of species (N) = 5
首先，让我们计算给定值的总和。
First, let us calculate the sum of the given values.
总和 = (60 + 10 + 25 + 1 + 4) = 100
sum = (60+10+25+1+4) = 100
Species ${(i)}$ |
No. in sample |
${p_i}$ |
${ln(p_i)}$ |
${p_i \times ln(p_i)}$ |
Big bluestem |
60 |
0.60 |
-0.51 |
-0.31 |
Partridge pea |
10 |
0.10 |
-2.30 |
-0.23 |
Sumac |
25 |
0.25 |
-1.39 |
-0.35 |
Sedge |
1 |
0.01 |
-4.61 |
-0.05 |
Lespedeza |
4 |
0.04 |
-3.22 |
-0.13 |
S = 5 |
Sum = 100 |
Sum = -1.07 |