How to calculate species abundance and diversity

  1. 1. The problem statement, all variables and given/known data
    This is the sample population taken along a 5m transect:
    ants:9
    grasshoppers:1
    pill bugs:4
    spiders:1


    2. Relevant equations
    What formulas would i use to calculate the species abundance and diversity?


    3. The attempt at a solution
    I only know this formula H'=-[itex]\Sigma[/itex] (n[itex]_{}i[/itex]/N)xIn(n[itex]_{}i[/itex]/N) and i dont know what to do with this formula.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. I like Serena

    I like Serena 6,194
    Homework Helper

    Hi blicker! :smile:

    Can it be that your formula is actually:
    [​IMG]
    where "ln" is the natural logarithm (and also a button on your calculator), and where ni is the number of individuals of species i?

    See: http://en.wikipedia.org/wiki/Shannon_index
     
  4. yes thats it! but i dont know what numbers go where or how to calculate it. like would i include the sigma symbol and the letters above and below it?
     
  5. I like Serena

    I like Serena 6,194
    Homework Helper

    The sigma symbol indicates that you have to sum.
    So:
    [tex]H'=-\sum_{i=1}^S {n_i \over N} \ln {n_i \over N} = -({n_1 \over N} \ln {n_1 \over N} + {n_2 \over N} \ln {n_2 \over N} + {n_3 \over N} \ln {n_3 \over N} + {n_4 \over N} \ln {n_4 \over N})[/tex]

    From wiki:
    * ni The number of individuals in species i; the abundance of species i.
    * S The number of species. Also called species richness.
    * N The total number of all individuals
    * pi The relative abundance of each species, calculated as the proportion of individuals of a given species to the total number of individuals in the community: [itex]n_i\over N[/itex]
     
  6. so would the equation for ants look like this:
    -(9/15)In(9/15)
     
  7. I like Serena

    I like Serena 6,194
    Homework Helper

    Well, Shannon's index specifies to sum all the terms.
    So what you mention is only part of H'.

    Btw, it is [itex]ln[/itex] ("logarithmus naturalis").


    But I can't really tell you what your problem asks.
    I'm not studying whatever science you're studying - I'm a mathematician.

    I did find this article about diversity: http://en.wikipedia.org/wiki/Diversity_Index
    And apparently [itex]n_i[/itex] is the "species abundance".
    Furthermore [itex]p_i={n_i \over N}[/itex] is the "relative species abundance".
     
  8. well thanks for your help anyway.
     
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