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DIVERSITY INDICES: SHANNON'S H AND E
Introduction: A diversity index is a mathematical measure of species diversity in a community. Diversity indices provide more information about community composition than simply species richness (i.e., the number of species present); they also take the relative abundances of different species into account (for an illustration of this point, see below, or introduction to SIMPSON'S D AND E).
Importance: Diversity indices provide important information about rarity and commonness of species in a community. The ability to quantify diversity in this way is an important tool for biologists trying to understand community structure.
Question: How do we measure diversity?
Variables:
HShannon's diversity indexStotal number of species in the community (richness)piproportion of S made up of the ith speciesEHequitability (evenness)Methods: The Shannon diversity index (H) is another index that is commonly used to characterize species diversity in a community. Like Simpson's index, Shannon's index accounts for both abundance and evenness of the species present. The proportion of species i relative to the total number of species (pi) is calculated, and then multiplied by the natural logarithm of this proportion (lnpi). The resulting product is summed across species, and multiplied by -1:
INCLUDEPICTURE "http://www.tiem.utk.edu/~gross/bioed/bealsmodules/shannonDI.eqn1.gif" \* MERGEFORMATINET
Shannon's equitability (EH) can be calculated by dividing H by Hmax (here Hmax = lnS). Equitability assumes a value between 0 and 1 with 1 being complete evenness.
INCLUDEPICTURE "http://www.tiem.utk.edu/~gross/bioed/bealsmodules/shannonDI.eqn2.gif" \* MERGEFORMATINET
Example: The graph below shows H and EH for four hypothetical communities, each consisting of 100 individuals. The communities are composed of 5, 10, 20 and 50 species, respectively. For each community H and EH have been calculated for the case in which individuals are distributed evenly among the different species (i.e., each species makes up an equal proportion of S), and for the case in which one species has 90% of the individuals, and the remaining individuals are distributed evenly. For example, in a community with 10 species in which the species contain equal numbers of individuals, p = 0.1 for each species. In a community with 10 species in which one species has 90% of the individuals, p = 0.9 for the dominant species, and p = 0.01 for the other nine species. The diamonds represent H and EHvalues for the first case (equal proportions), and the triangles represent values for H and EH for the second case (unequal proportions).
INCLUDEPICTURE "http://www.tiem.utk.edu/~gross/bioed/bealsmodules/shannonDI.gph.gif" \* MERGEFORMATINET
For the first case, EH is always equal to one (complete evenness, or equitability), but H increases dramatically as the number of species increases, as we would expect. For the second case, in which one species makes up 90% of the community, the picture is a little different. Here we can see that although H does increase with increasing numbers of species, it does so much more slowly than in the first case. Additionally, EH decreases as species number increases (since one species always makes up 90% of the community in the second case of this hypothetical example, the remaining species make up some fraction of 10% of the community; as species number increases this fraction becomes smaller and evenness decreases). H and EH clearly give more information about these communities than would species number (richness) alone.
The following table contains data from a study of Costa Rican ant diversity (Roth et al. 1994). The authors measured diversity in four different habitats ranging very low levels of human disturbance (primary rain forest) to very high levels of human disturbance (banana plantations) to assess the impacts of different levels of disturbance on biological diversity. For each habitat studied we will use data collected from one site within that habitat. The numbers below represent relative proportions of each species (from Roth et al. 1994 [family names have been omitted]).
Interpretation: We can see from our results that the diversity and evenness in this site from the undisturbed habitat (primary rain forest) are much higher than in the site from the highly disturbed habitat (banana plantation). The primary rain forest not only has a greater number of species present, but the individuals in the community are distributed more equitably among these species. In the banana plantation there are 23 fewer species and over 80% of the individuals belong to one species, Solenopsis geminata (the most common species in the primary rain forest, on the other hand, makes up about 16% of the community [Pheidole sp. 15]).
Conclusions: Different levels of disturbance have different effects on ant diversity. If our goal is to preserve biodiversity in a given area, we need to be able to understand how diversity is impacted by different management strategies. Because diversity indices provide more information than simply the number of species present (i.e., they account for some species being rare and others being common), they serve as valuable tools that enable biologists to quantify diversity in a community and describe its numerical structure
DIVERSITY INDICES: SIMPSON'S D AND E
Introduction: A diversity index is a mathematical measure of species diversity in a community. Diversity indices provide more information about community composition than simply species richness (i.e., the number of species present); they also take the relative abundances of different species into account. Consider two communities of 100 individuals each and composed of 10 different species. One community has 10 individuals of each species; the other has one individual of each of nine species, and 91 individuals of the tenth species. Which community is more diverse? Clearly the first one is, but both communities have the same species richness. By taking relative abundances into account, a diversity index depends not only on species richness but also on the evenness, or equitability, with which individuals are distributed among the different species.
Importance: Diversity indices provide important information about rarity and commonness of species in a community. The ability to quantify diversity in this way is an important tool for biologists trying to understand community structure.
Question: How do we measure diversity?
Variables:
DSimpson's diversity indexStotal number of species in the community (richness)piproportion of S made up of the ith speciesEDequitability (evenness)Methods: Simpson's diversity index (D) is a simple mathematical measure that characterizes species diversity in a community. The proportion of species i relative to the total number of species (pi) is calculated and squared. The squared proportions for all the species are summed, and the reciprocal is taken:
INCLUDEPICTURE "http://www.tiem.utk.edu/~gross/bioed/bealsmodules/simpsonDI.eqn1.gif" \* MERGEFORMATINET
For a given richness (S), D increases as equitability increases, and for a given equitability D increases as richness increases. Equitability (ED) can be calculated by taking Simpson's index (D) and expressing it as a proportion of the maximum value D could assume if individuals in the community were completely evenly distributed (Dmax, which equals S-- as in a case where there was one individual per species). Equitability takes a value between 0 and 1, with 1 being complete evenness.
INCLUDEPICTURE "http://www.tiem.utk.edu/~gross/bioed/bealsmodules/simpsonDI.eqn2.gif" \* MERGEFORMATINET
Siemann et al. (1997) collected the following data on oak savanna arthropod communities to investigate the effects of prescribed burning on arthropods. The abundance data below represent the number of individuals per family (rather than per species) collected in sweep-net sampling during a two year period (1992-1993) (from Siemann et al. 1997).
Although we do not have species data, we can calculate family diversity and equitability using these data. The proportions (pi values) have been calculated by dividing the number of individuals in a given family by the total number of individuals collected in a year (8,561 in 1992 and 1,379 in 1993). To calculate Simpson's D, we square each proportion (pi), sum these squared values, and take the reciprocal (divide one by the sum). For example, for the 1992 data, Simpson's D is calculated (1 / [0.0132 + 0.0082 + 0.0002 + 0.0152 + ... + 0.0072]) = 8.732. We could then calculate the equitability (ED) quite easily using the second equation above (ED = D / Dmax, with Dmax = S). Here, we will use the number of families in place of S, so that E = 8.732 / 31 = 0.2817.
Interpretation: What we have calculated is an index of family diversity and evenness, rather than the standard index of species diversity and evenness. Based on the value of 0.2817 calculated for ED, we could describe the equitability, or evenness of individuals' distributions among families, in this community as relatively low (recall that ED assumes a value between 0 and 1, and 1 is complete equitability).
Conclusions: Simpson's D is one of many diversity indices used by biologists. Others include the Shannon index (H), the Berger-Parker index (d), Hill's N1, and Q-statistics. Each of these indices has strengths and weaknesses. An ideal index would discriminate clearly and accurately between samples, not be greatly affected by differences in sample size, and be relatively simple to calculate. Biologists often use a combination of several indices to take advantages of the strengths of each and develop a more complete understanding of community structure.
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