The aim of this article is to provide a simple method for obtaining data to teach how to calculate basic indexes of alpha diversity. Data were collected during an undergraduate class laboratory exercise using automobiles in parking lots, considering the brand as the “genus” and the model as the “species”. The alpha diversity measures calculated were species richness, Chao1 index, Simpson Index and Shannon Index. The data collection method was efficient for producing quantitative data adequate for the pretended analyses.

Keywords: alpha diversity indices, chao1, Simpson, Shannon, teaching methods

Diversity indexes are important tools in ecological science incorporating data on species richness and evenness. Their introduction into ecological research began in the middle of the 20^th century.^1–4 There are many publications explaining the importance of knowledge about ecological diversity and the application of these indices can be found in many different areas of study. There is a recent publication that summarizes many aspects related to the importance and use of diversity indexes in ecology.⁵

Ecological diversity can be estimated in different scales and the types of analyses used are varied.⁶ Alpha diversity (a diversity) is a measure of the species diversity within a particular community or habitat, for example the community of trees in your local park. There is no exact number of published alpha diversity indices, but several are more commonly used than others.⁷ Beta diversity (b diversity) is a measure of the similarity or dissimilarity between two communities in the same region or between the same type of community in different regions, for example a comparison of the composition of beetle communities in a meadow and nearby forest or the species of fish in two lakes. Gamma diversity (g diversity) is a measure of total species diversity along an environmental gradient at the landscape level, for example a study of bird communities along an altitudinal transect or coral species with depth.

The collection of data for calculating ecological diversity usually involves excursions to field sites which are expensive and time consuming in many cases. The inspiration for this exercise was based on a publication on species packing of fast-food restaurants in shopping malls⁸ and objective of this paper is to provide a simple method for collecting data for teaching ecological diversity indexes without the need for expensive field excursions.

Data collection

The data presented here were collected by the students during a laboratory exercise in an undergraduate course in general ecology during the first semester of 2019. All data were collected during one afternoon in different parking lots on the University campus (Figure 1). The class was divided into different groups and each group collected data on the cars parked in the different areas. The data were collected using an accumulation curve by walking along a line of the parking spots and annotating the brand (“genus”) and model (“species”) of the first 100 parked cars found in the selected area.

Figure 1 An example of one of the sampling locations on the University campus.

Calculation of diversity measures

After collection of the data four basic measures of alpha diversity were calculated in the classroom or at home. These were:

1. Richness – defined as the number of species present in the sample
2. Chao1 – an estimate or species richness that includes species that were not sampled but are likely to be present. The bias-corrected formula used for calculating this index is:

${\widehat{S}}_{Chao1} = S_{obs}+ \frac{f_1\left(f_1-1\right)}{2\left(f_2+2\right)}$       (1)

Where:   S_obs = the number of observed species

f₁ = the number of singletons in the sample (species with only 1 occurrence in the whole data set)

f₂ = the number of doubletons in the sample (species with only 2 occurrences in the whole data set, that in this case could be one occurrence in each of two different groups or two occurrences in the same group)

Simpson – there are three variants of this index, Simpson’s Dominance Index (D), Simpson’s Diversity Index (1-D) and Inverse Simpson’s Index (1/D).⁹ Calculation in this exercise was done using the Simpson’s Diversity Index. This index varies from 0 to 1 where a value of 0 indicates total dominance (only one species) and higher values indicate increasing species diversity by estimating the probability that two randomly selected (or sampled) individuals belong to different categories (or species). The formula used for calculating this index was:

$D_s=1-{\displaystyle \sum }_{i=1}^S\frac{n_1\left(n_1-1\right)}{N\left(N-1\right)}$ (2)

Where:   S = the total number of species

                n_i = the number of individuals in the i^th species

                N = the total number of individuals

Shannon (H) – varies from 0 when only one species is present to an upper bound that is based on the number of species. This index is also cited as the Shannon-Weiner index.⁹ The original calculation of this index was done using natural logarithms, but any base can be used. The formula used for calculating this index in this exercise was:

$H= -{\displaystyle \sum }_{i=1}^S{p}_{i}log\left(p_i\right)$ (3)

Where:   S = the total number of species

                p_i = the proportion of individuals belonging to species i

                log is in base 10

It is also possible to calculate the maximum obtainable values and degree of evenness for the Simpson and Shannon index. Evenness represents the similarity in number of individuals in each species.

The formulae for calculating these values for the Simpson index are:

$D_{max}= \left(\frac{s-1}{s}\right)\left(\frac{N}{N-1}\right) and E= \left(\frac{D}{D_{max}}\right)*100$    (4)

Where    D_max = the maximum value based on the particular data set

                s = the number of species

                N = the number of individuals

                E = the evenness of the distribution of individuals among species and for the Shannon index are

$H_{max}= \log s and J= \left(\frac{H}{H_{max}}\right)*100$    (5)

Where    H_max = the maximum value based on the particular data set

                s = the number of species

                J = the evenness of the distribution of individuals among species

All calculations were done using simple functions in EXCEL or with a hand calculator.

The time necessary for data collection was relatively quick, with all groups finishing within 1 ½ hours. A total 595 individuals were counted, and 18 “genera” and 98 “species” were recorded by the six groups varying from 36 to 51 (Table 1). Although each group collected data on 100 individuals some of the identifications were incorrect and these data were omitted from the analyses. Of the 98 “species” there were 32 singletons and 18 doubletons and the calculation for richness using the Chao1 estimate was approximately 111. The calculation of the Simpson and Shannon indices for the whole data set were D = 0.973 and H = 1.713 respectively and the maximum values and evenness for each index were D_max = 0.991 and 98.1% for the Simpson index and H_max = 1.99 and J = 86.0% for the Shannon index.

In this laboratory exercise each group also did other analyses using the data from their group. These analyses were:

1. Calculation of the maximum possible values for the Simpson and Shannon indices and the evenness for each group
2. Making a density-dominance graph
3. Making a species-area curve after separating the data into contiguous blocks of 10 cars.

The use of these alpha diversity indices in common in ecology, but there have been critiques of them.^10,11 It is also important to remember that the values produced by these indices are not significant by themselves and that they should be used in comparison with other studies where the data were collected using the same methodology and the same base for logarithms when comparing Shannon indexes. It is also important to note that the maximum values are dependent upon the sample size and the number of species found.

There are too many texts, laboratory manuals, software and apps that have been published to calculate these and other diversity indices to cite them all. A search in Google Scholar using “alpha diversity indices” as the search term returned 24100 results but using “teaching alpha diversity” returned no (zero) results. One of the most frequently used methods in current research for calculating alpha diversity in communities is the vegan R package available at https://CRAN.R-project.org/package=vegan.¹²

Although the calculations done in this text are for the basic diversity indices shown in the Methods section the collected data can be used for teaching other analytical techniques. These could include calculations of beta diversity (similarity or dissimilarity indexes) by comparing the data from different groups of students or different methods of multivariate analyses to compare differences among sampling sites. In my opinion, this type of collection does not provide data for analysis of gamma diversity.

As a final note, the brands and models observed in this study are representative of the time when the data were collected and of the country where the data were collected and the same study done in another country or more recently on the same campus would have a different collection of “genera” and “species”.

Although the data were collected using artificial species the collection procedure used was simple and efficient to furnish data for teaching how to calculate basic alpha diversity indices. There are many different methods to calculate alpha diversity of ecological communities, but the methods described in this manuscript are widely used. Using the data collected with this method it would also be possible for teachers to show their classes how to use other more advanced methods in ecological research in analysis of communities such as different types of multivariate analyses.

To all the students who participated in the data collection and to an anonymous reviewer for helpful comments.

None.

The author declares that there is no conflict of interests.

1. MacArthur RH. Fluctuations of animal populations and a measure of community stability. Ecology. 1955;36:533–536.
2. Margalef R. Information and specific diversity in communities of organisms. Invest Pesg. 1956;3:99–106.
3. Simpson EH. Measurement of diversity. Nature. 1949;163:688.
4. Chao A. Estimating population size for capture-recapture data with unequal catchability. Biometrics. 1987;43(4):783–791.
5. Magurran AE. Measuring biological diversity. 2nd edn. Oxford: Blackwell; 2013. ISBN: 978-1-118-68792-5.
6. Whittaker RH. Evolution and measurement of species diversity. Taxon. 1972;21:213–251.
7. Morris EK, Caruso T, Buscot F, et al. Choosing and using diversity indices: insights for ecological applications from the German Biodiversity Exploratories. Ecol Evol. 2014;4(18):3514–3524.
8. Kangas PC, Risser PG. Species packing in the fast-food restaurant guild. Bull Ecol Soc Amer. 1979;60(3):143–148.
9. Brower JE, Zar JH, von Ende CN. Field and laboratory methods for general ecology. 8th edn. Boston: WCB McGraw-Hill; 1997. ISBN: 0-697-24358-3.
10. Hurlbert SH. The non-concept of species diversity: a critique and alternative parameters. Ecology. 1971;52:577–586.
11. Roswell M, Dushoff J, Winfree R. A conceptual guide to measuring species diversity. 2021;130:321–338.
12. Oksanen J, Blanchet FG, Kindt R, et al. vegan: Community ecology package. R package version. 2025.