How to calculate species abundance and diversity

blicker

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

I like Serena

Hi blicker!

Can it be that your formula is actually:

where "ln" is the natural logarithm (and also a button on your calculator), and where n_i is the number of individuals of species i?

See: http://en.wikipedia.org/wiki/Shannon_index

blicker

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?

I like Serena

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]

blicker

so would the equation for ants look like this:
-(9/15)In(9/15)

I like Serena

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".

blicker

well thanks for your help anyway.