Simpson's Index of Diversity | 辛普森多样性指数

📚 Simpson’s Index of Diversity | 辛普森多样性指数

Simpson’s Index of Diversity is a quantitative measure used in A-Level Biology to describe the biodiversity of a habitat. It takes into account both species richness and species evenness, producing a value between 0 and 1.

辛普森多样性指数是 A-Level 生物课程中用于定量描述栖息地生物多样性的指标。它同时考虑物种丰富度和物种均匀度，得出一个介于 0 和 1 之间的数值。

For Cambridge International A-Level Biology, you are expected to calculate the index using the formula D = 1 − ∑(n/N)² and to interpret what the result tells you about community structure.

在剑桥国际 A-Level 生物考试中，你需要使用公式 D = 1 − ∑(n/N)² 计算该指数，并解释结果所反映的群落结构特征。

1. Defining Simpson’s Index of Diversity | 辛普森多样性指数的定义

Simpson’s Index of Diversity, usually written as D, is a single numerical value that summarises the diversity of a biological community. It ranges from 0 to 1, where higher values indicate greater diversity.

辛普森多样性指数通常写作 D，是一个用来概括生物群落多样性的单一数值。它的取值范围为 0 到 1，数值越高表示多样性越大。

The index is based on the probability that two organisms chosen at random from a sample belong to the same species. A high probability of picking the same species means low diversity, so the formula subtracts this probability from 1.

该指数基于从样本中随机选取两个个体属于同一物种的概率。选中同一物种的概率越高，多样性就越低，因此公式用 1 减去这个概率。

Unlike simply counting the number of species, Simpson’s Index also reflects how evenly individuals are distributed among those species. This makes it a more informative measure of community structure.

与单纯统计物种数目不同，辛普森指数还能反映个体在各物种之间分布的均匀程度。因此它能更全面地说明群落结构。

2. Why Biodiversity Is Measured | 为什么要测量生物多样性

Biodiversity is a key concept in ecology and conservation. Measuring it allows scientists to compare habitats, monitor environmental change, and assess the impact of human activities such as deforestation, farming, or pollution.

生物多样性是生态学和保护生物学中的核心概念。测量生物多样性有助于科学家比较不同栖息地、监测环境变化，并评估森林砍伐、农业活动或污染等人类活动的影响。

A habitat with high biodiversity is generally more stable and resilient to disturbance because it contains a wider range of species with different ecological roles. If one species declines, others may fill similar roles.

生物多样性高的栖息地通常更稳定、对干扰的恢复能力更强，因为它包含具有不同生态功能的更多物种。如果某一物种数量下降，其他物种可以承担相似的功能。

Conservation projects often use Simpson’s Index to decide which areas should be protected. A higher D value can indicate a habitat that supports many species in balanced proportions, making it a priority for conservation.

保护项目经常使用辛普森指数来决定哪些区域需要保护。较高的 D 值说明栖息地以较均衡的比例支持许多物种，因此应优先加以保护。

3. The Formula and Its Components | 公式及其组成部分

D = 1 − ∑ (n ÷ N)²

In this formula, n represents the total number of individuals of a particular species, and N represents the total number of individuals of all species in the sample. The symbol ∑ means ‘sum of’.

在这个公式中，n 表示某一特定物种的个体总数，N 表示样本中所有物种的个体总数。符号 ∑ 表示“求和”。

For each species, you divide n by N to obtain the proportion of the community made up by that species. You then square this proportion and add the squared values for all species. Finally, you subtract the total from 1.

对每个物种，你用 n 除以 N，得到该物种占整个群落的比例。然后将这个比例平方，再把所有物种的平方值相加。最后用 1 减去这个总和。

The subtraction step is important because ∑(n/N)² on its own is a measure of dominance. If one species dominates, this sum is close to 1; subtracting from 1 converts it into a diversity measure where high values mean high diversity.

减法这一步很重要，因为 ∑(n/N)² 本身表示优势度。如果某一物种占绝对优势，这个总和接近 1；用 1 减去它之后，就转换成多样性指标，数值越高代表多样性越高。

4. Step-by-Step Worked Example | 分步计算示例

The table below shows the number of individuals of four plant species recorded in a quadrat sample from a meadow.

下表显示了在一块草地的样方中记录到的四种植物个体数量。

Species	Number (n)	n ÷ N	(n ÷ N)²
A	12	0.375	0.1406
B	8	0.250	0.0625
C	6	0.1875	0.0352
D	6	0.1875	0.0352
Total	N = 32		∑ = 0.2735

Step 1: Calculate N by adding all individual counts: 12 + 8 + 6 + 6 = 32.

步骤 1：将所有个体数相加得到 N：12 + 8 + 6 + 6 = 32。

Step 2: For each species, divide n by N to get the proportion. For species A this is 12 ÷ 32 = 0.375.

步骤 2：对每个物种，用 n 除以 N 得到比例。例如物种 A 为 12 ÷ 32 = 0.375。

Step 3: Square each proportion. For species A, 0.375² = 0.1406.

步骤 3：将每个比例平方。例如物种 A 为 0.375² = 0.1406。

Step 4: Add all squared values: 0.1406 + 0.0625 + 0.0352 + 0.0352 = 0.2735.

步骤 4：将所有平方值相加：0.1406 + 0.0625 + 0.0352 + 0.0352 = 0.2735。

Step 5: Apply the formula D = 1 − 0.2735 = 0.7265. This value indicates a reasonably high level of diversity.

步骤 5：套用公式 D = 1 − 0.2735 = 0.7265。这个数值表明该群落具有较高的多样性。

5. Interpreting D Values | 解释 D 值

A D value of 0 means there is no diversity; the community consists of only one species. This occurs because ∑(n/N)² equals 1 when all individuals belong to the same species.

D 值为 0 表示没有多样性，群落只由一个物种组成。这是因为当所有个体都属于同一物种时，∑(n/N)² 等于 1。

A D value close to 1 indicates high diversity. In practice, D never reaches exactly 1 because that would require an infinite number of species each with a very small proportion of the total. However, values above about 0.7 usually suggest a diverse and evenly distributed community.

D 值接近 1 表示多样性很高。实际上，D 永远不会正好等于 1，因为这需要无限多个物种且每个物种只占总数的极小比例。但通常 D 值大于约 0.7 就说明群落多样且分布较均匀。

Between these extremes, higher D values mean more species or a more even distribution of individuals among species, or both. You should always relate the numerical value to the ecological context of the habitat.

在这两个极端之间，D 值越高意味着物种越多或个体在物种间分布越均匀，或两者兼有。你应始终将数值与栖息地的生态背景联系起来解释。

6. Species Richness vs Evenness | 物种丰富度与均匀度

Species richness is simply the number of different species present in a sample. It does not consider how many individuals belong to each species.

物种丰富度只是样本中出现的不同物种的数目。它不考虑每个物种有多少个体。

Species evenness describes how equal the population sizes of the different species are. A community where all species have similar numbers of individuals has high evenness.

物种均匀度描述不同物种种群大小的相近程度。如果所有物种的个体数量都相近，则该群落具有高均匀度。

Simpson’s Index combines richness and evenness into one value. Two communities can have the same species richness but very different D values if one is dominated by a single species and the other is evenly balanced.

辛普森指数将丰富度和均匀度结合为一个数值。两个群落可能具有相同的物种丰富度，但如果一个由单一物种占优势，而另一个分布均匀，它们的 D 值会大不相同。

This is why Simpson’s Index is often preferred over simply counting species. It gives a more complete picture of community structure.

这就是为什么辛普森指数通常比单纯统计物种数目更受青睐。它能更全面地反映群落结构。

7. Comparing Habitats Using D | 使用 D 值比较栖息地

Simpson’s Index is especially useful for comparing the biodiversity of two or more habitats. For a fair comparison, samples must be collected using the same method and similar sampling effort.

辛普森指数特别适用于比较两个或多个栖息地的生物多样性。为了公平比较，必须使用相同的方法和相似的采样力度收集样本。

For example, a woodland with D = 0.82 and a grassland with D = 0.61 indicates that the woodland has higher species diversity. You should then suggest reasons, such as more layers of vegetation, more food sources, or less disturbance.

例如，某林地 D = 0.82，某草地 D = 0.61，说明林地的物种多样性更高。你接着应提出可能的原因，如植被层次更多、食物来源更丰富或干扰更少。

When comparing D values, avoid saying a habitat is ‘better’ without justification. In A-Level answers, link the difference to measurable ecological factors such as light availability, soil pH, moisture, or human impact.

在比较 D 值时，避免在没有依据的情况下说某个栖息地“更好”。在 A-Level 答案中，应把差异与可测量的生态因子联系起来，如光照、土壤 pH、湿度或人类影响。

8. Sampling Methods and Data Reliability | 取样方法与数据可靠性

To calculate Simpson’s Index, you first need reliable abundance data for each species. For plants and slow-moving organisms, random quadrats are commonly used. For mobile animals, pitfall traps, sweep nets, or mark-release-recapture may be needed.

要计算辛普森指数，首先需要每个物种可靠的丰度数据。对于植物和移动缓慢的生物，通常使用随机样方。对于活动性强的动物，可能需要陷阱、扫网或标记重捕法。

Random sampling reduces bias, but the sample size must be large enough to be representative. If too few quadrats are taken, rare species may be missed and D may be overestimated or underestimated.

随机取样可以减少偏差，但样本量必须足够大才能具有代表性。如果样方太少，稀有物种可能被漏掉，导致 D 值被高估或低估。

Identification errors also affect the result. If two similar species are recorded as one, the number of species appears lower and the index becomes less accurate.

物种鉴定错误也会影响结果。如果两个相似物种被记录为同一种，物种数目就会看起来更少，指数也就不准确。

Repeating samples at different times or in different seasons can improve reliability. It also helps to calculate a mean D value rather than relying on a single sample.

在不同时间或不同季节重复取样可以提高可靠性。计算平均 D 值也比只依赖单次样本更好。

9. Limitations and Assumptions | 局限性与假设

Simpson’s Index assumes that all individuals in the sample have been counted accurately and that the sample is representative of the whole habitat. In reality, sampling always involves some error.

辛普森指数假设样本中的所有个体都被准确计数，并且样本能代表整个栖息地。实际上，取样总会有一定误差。

The index is also sensitive to the most abundant species. Because proportions are squared, common species contribute much more to the sum than rare species. This can mask the presence of rare species.

该指数对数量最多的物种较为敏感。由于比例被平方，常见物种对总和的贡献远大于稀有物种。这可能掩盖稀有物种的存在。

Furthermore, D does not tell you which species are present or whether they are native or invasive. A high D value could include several non-native species, which may not indicate a healthy natural ecosystem.

此外，D 值不能告诉你存在哪些物种，也无法区分本地种和入侵种。高 D 值可能包含若干非本地物种，这并不一定代表自然生态系统健康。

Therefore, Simpson’s Index should be used alongside other data, such as species lists, abundance curves, and environmental measurements, before drawing conservation conclusions.

因此，在得出保护结论之前，辛普森指数应与其他数据一起使用，如物种名录、丰度曲线和环境测量数据。

10. Exam Tips and Common Errors | 考试技巧与常见错误

In A-Level exams, you may be asked to calculate D from a table of species abundances. Always show every step of your working, including the sum of squared proportions, because marks are often given for method as well as the final answer.

在 A-Level 考试中，你可能会被要求根据物种丰度表计算 D 值。一定要写出每一步计算过程，包括比例平方的总和，因为分数通常会给在方法和最终答案上。

A common mistake is to forget to square the n/N values before adding them. Another is to forget to subtract the sum from 1, or to use percentages instead of decimal proportions.

一个常见错误是在相加之前忘记将 n/N 值平方。另一个错误是忘记用 1 减去总和，或使用百分数而不是小数比例。

Do not confuse n and N. N is the total number of all individuals from all species, while n is the number of individuals of one species. Many students use N for a single species and obtain an incorrect result.

不要混淆 n 和 N。N 是所有物种全部个体的总数，而 n 是某一物种的个体数。许多学生把 N 当成某一物种的个体数，导致结果错误。

When interpreting a calculated D value, state clearly what the number means, for example ‘D = 0.73 indicates high diversity because it is close to 1’. Then link this to species richness or evenness and to ecological factors.

解释计算出的 D 值时，要清楚说明数字的含义，例如“D = 0.73 表明多样性高，因为它接近 1”。然后将其与物种丰富度或均匀度以及生态因子联系起来。

Finally, quote your final answer to an appropriate number of significant figures, usually two or three decimal places, unless the question states otherwise.

最后，除非题目另有说明，否则最终答案通常保留两到三位小数。

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Simpson’s Index of Diversity | 辛普森多样性指数