[organism]

[biofilms & biodiversity]

How To Calculate Biodiversity?

The Steps To Follow | More About Measuring Biodiversity | Some Examples



The Steps To Follow

1. Identify the number of different organisms present.

[circle with area formula]

How we did it . . .

A stereomicroscope was used to identify the organisms found on the plexiglass discs (check out Featured Creatures to learn about what these organisms are and why they are found on the discs). An area on the disc was selected at random for biodiversity analysis before it was viewed under the stereoscope (check out Random Sampling to learn how it is done).

The total area of the field of view (diagram w/formula for area of circle) analyzed was 1.5 cm2 at a magnification of 15 (x) times. This technique was used for each sample to keep the data consistent.

2. Count the total number of each organism.

3. Use the numbers to estimate various measures of biodiversity.

Species Richness (S) - the total number of different organisms present. It does not take into account the proportion and distribution of each species within the local aquatic community.

Simpson Index (D) - a measurement that accounts for the richness and the percent of each species from a biodiversity sample within a local aquatic community. The index assumes that the proportion of individuals in an area indicate their importance to diversity.

Shannon-Wiener index (D) - Similar to the Simpson's index, this measurement takes into account species richness and proportion of each species within the local aquatic community. The index comes from information science. It has also been called the Shannon index and the Shannon-Weaver index in the ecological literature.

A comparison of one or all of these measures of biodiversity can illustrate changes in water quality conditions within a local community. Water quality parameters like light penetration, dissolved oxygen and salinity can have dramatic impacts on levels of biodiversity.

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More About Measuring Biodiversity

When measuring diversity it is good to remember that what we are trying to describe is the relationship of individuals of varying categories within a community. These categories can be species, genera, families, or any other categories that you consider to be important. In our biofilm research, we use the number of individuals in each species observed (e.g., found on each acrylic disc).

There are some underlying assumptions that all the measures of biodiversity have in common:

  1. The categories are well known.
    In most cases, such as with our biofilm study, this assumption is not violated since the taxonomic classification of organisms that we use is accepted world-wide. However, this may be difficult if everyone does not use the same classification system (e.g., some people may put similar individuals into several categories while others use one category). This can happen when species are regrouped into new species, genera or families.

  2. All categories are equally different.
    Categories are equally different from each other category. This is not always true since two species from the same genera are treated the same as two species from different families.

  3. Use a measure of species importance.
    Usually, one uses the number of individuals, percent coverage, relative density or biomass. The choice usually depends on the ease of measurement. In our case, we use the number of individuals in each species observed. .

  4. The community under study is well defined.
    The relative importance of an individual category will vary greatly depending on the definition of the extent and makeup of the community. The community in our biofilm studies is the local aquatic community near the pier.

The most common measures of biodiversity are species richness, Simpson's index and Shannon-Wiener index.

  • Species Richness

    This is the simplest of all the measures of species diversity. All you do is count of the number of species found in a community (e.g., the number of the species found on a biofilm plate).

    However, this does not indicate how the diversity of the population is distributed or organized among those particular species. For example, if there were 4 different species on a plate from the Marina and a plate from Pier 4 the richness would be equal. This does not indicate what % of each species there were of the 4 species identified. At the Marina 80% of the total number of species could have been stentor while at Pier 4 there could have been an even 25% of each species.

  • Simpson's Index

    A measure that accounts for both richness and proportion (percent) of each species is the Simpson's diversity index. It has been a useful tool to terrestrial and aquatic ecologists for many years and will help us understand the profile of biofilm organisms and their colonization pattern in the Inner Harbor. The index, first developed by Simpson in 1949, has been defined three different ways in published ecological research. The first step for all three is to calculate Pi, which is the number of a given species divided by the total number of organisms observed.

    1. Simpson's index: D = sum(Pi2)
      The probability that two randomly selected individuals in the community belong to the same category (e.g., species).

    2. Simpson's index of diversity: 1 - D
      The probability that two randomly selected individuals in a community belong to different categories (e.g., species).

    3. Simpson's reciprocal index: 1/D
      The number of equally common categories (e.g., species) that will produce the observed Simpson's index. D is influenced by two parameters - the equitability of percent of each species present and richness. For a given species richness, D will decrease as the percent of the species becomes more equitable. The examples illustrate how these three indices are influenced by these two parameters. The researcher must observe the species patterns carefully to interpret the values effectively. The number of equally common categories (e.g., species) that will produce the observed Simpson's index.

      Critical Thinking:

      a. What are the minimum and maximum values for each of the three Simpson indices? (if you need some help, please see(if you need some help, please see Some Examples.)

    4. Shannon-Wiener Index

      This diversity measure came from information theory and measures the order (or disorder) observed within a particular system. In ecological studies, this order is characterized by the number of individuals observed for each species in the sample plot (e.g., biofilm on a acrylic disc). It has also been called the Shannon index and the Shannon-Weaver index. Similar to the Simpson index, the first step is to calculate Pi for each category (e.g., species). You then multiply this number by the log of the number. While you may use any base, the natural log is commonly used (ln). The index is computed from the negative sum of these numbers. In other words, the Shannon-Wiener index is defined as:

      H = -sum(Pilog[Pi]) (for any base)

      H = -sum(Piln[Pi]) (natural log)


      Using species richness (S) and the Shannon-Wiener index (H), you can also compute a measure of Evenness. Evenness (E) is a measure of how similar the abundance of different species are. When there are similar proportions of all species then evenness is one, but when the abundance are very dissimilar (some rare and some common species) then the value increases. Using the same log base as with H, evenness is defined as:

      E = H/log(S) (for any base)

      E = H/ln(S) (natural log)

      Critical Thinking:

      b. Why do you take the negative of the sum(Pilog[Pi])? (if you need some help, please see some examples.)

      c. What are the minimum and maximum values for the Shannon-Wiener index? (if you need some help, please see some examples.)

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Some Examples

The following tables illustrate how the various indices change as the relative number of each species change. In the first three examples, there are a total of 200 organisms. The number of organisms are equal in the first example. There is one dominant species in the second and third example.

Please compare the indices computed for the three examples. To help you gain an intuitive understanding of the indices, you can enter your own number found for each species in the last table.

  1. All the same

    Species Name
    # Found
    Pi
    Pi2
    Piln[Pi]

    Measure
    Value
    Species 1
    40
    0.200
    0.040
    -0.322
    S
    5
    Species 2
    40
    0.200
    0.040
    -0.322
    D
    0.200
    Species 3
    40
    0.200
    0.040
    -0.322
    1 - D
    0.800
    Species 4
    40
    0.200
    0.040
    -0.322
    1/D
    5.000
    Species 5
    40
    0.200
    0.040
    -0.322
    H
    1.609
    Totals
    200
    1.000
     
     
    E
    1.000


  2. One dominate species

    Species Name
    # Found
    Pi
    Pi2
    Piln[Pi]

    Measure
    Value
    Species 1
    1
    0.005
    0.000
    -0.026
    S
    5
    Species 2
    1
    0.005
    0.000
    -0.026
    D
    0.960
    Species 3
    196
    0.980
    0.961
    -0.020
    1 - D
    0.040
    Species 4
    1
    0.005
    0.000
    -0.026
    1/D
    1.041
    Species 5
    1
    0.005
    0.000
    -0.026
    H
    0.126
    Totals
    200
    1.000
     
     
    E
    0.078


  3. Only one species

    Species Name
    # Found
    Pi
    Pi2
    Piln[Pi]

    Measure
    Value
    Species 1
    0
    0.000
    0.000
    0.000
    S
    1
    Species 2
    0
    0.000
    0.000
    0.000
    D
    1.000
    Species 3
    200
    1.000
    1.000
    0.000
    1 - D
    0.000
    Species 4
    0
    0.000
    0.000
    0.000
    1/D
    1.000
    Species 5
    0
    0.000
    0.000
    0.000
    H
    0.000
    Totals
    200
    1.000
     
     
    E
    0.000


  4. Try it yourself

    Species Name
    # Found
    Pi
    Pi2
    Piln[Pi]

    Measure
    Value
    Species 1




    S

    Species 2




    D

    Species 3




    1 - D

    Species 4




    1/D

    Species 5




    H

    Totals


      
    E

    See what happens when you change the number of organisms for each of the species. Enter your own counts and press the 'Compute' button to find out what effect your changes have on the various biodiversity measures. Remember, counts are integers.

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Critical Thinking Answers

When you examine the equations or the examples, you will see the answers to the questions posed above.

a. What are the minimum and maximum values for each of the three Simpson indices?

  1. Simpson's index: D = sum(Pi2)
    Minimum value: 1/(# of categories)
    Maximum value: 1

  2. Simpson's index of diversity: 1 - D
    Minimum value: 0
    Maximum value: 1 - 1/(# of categories), approaches 1 as the number of categories increase.

  3. Simpson's reciprocal index: 1/D
    Minimum value: 1
    Maximum value: # of categories

b. Why do you take the negative of the sum(Pilog[Pi])?

Since Pi is the proportion of a given category, its maximum value is 1 and its minimum approaches 0. For any base, the log of 1 is 0 and the log of any value between 0 and 1 is a negative number. By reversing the sign, the index becomes positive and is easier to understand.

c. What are the minimum and maximum values for the Shannon-Wiener index?

Minimum value: 0
Maximum value: log(1/# of categories)

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