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Index of Diversity

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Species diversity is described as the number of species in a community. The more species, the higher the diversity. What if there are two separate communities like this:

 

Community #1 has 150 individuals per each of 20 different species (3000 individuals in total)
Community #2 has 10 individuals per each of 19 species, and 2990 individuals of the last species (3000 individuals in total)

 

It doesn’t take a complex formula to figure out that community #1 is far more diverse compared to community #2, despite them having the same number of species and individuals. The distribution of individuals to species is important in determining a community’s diversity.

 

The above example is easy enough, but for most purposes a formula is needed. This formula measures the index of diversity, which is simply a measure of diversity in a community. By calculating it and obtaining a numerical value, different communities can be easily compared.

 

Right, here it comes…

 

 

No, don’t run away yet! Wait and see how easy it is to work out.

 

D = Diversity index

N = total number of all organisms

n = total number of organisms of each species

Σ = sum of

 

Now it’s simply a matter of replacing numbers. Look, I made it all purple so you would enjoy looking at it. Let’s work out the index of diversity for community #1 (from above).

 

Firstly, we need a value for N. What’s the total number of organisms? 3000. Sorted.

 

Next, we need a value for N – 1. No calculators! …2999, sorted.

 

Finally, we need a value for n and n – 1. n = 150, while n – 1 = 149.

 

Drawing up a table helps:
 
 species n n – 1 n(n – 1)
 a 150 149  22350
 b 150 149  22350
 c 150 149  22350
 d 150 149  22350
 e 150 149  22350
 f 150 149  22350
 g 150 149  22350
 h 150 149  22350
 i 150 149  22350
 j 150 149  22350
 k 150 149 22350
 l 150 149 22350
 m 150 149 22350
 n 150 149 22350
 o 150 149 22350
 p 150 149 22350
 q 150 149 22350
 r 150 149 22350
 s 150 149 22350
 t 150 149   22350
Total  3000  2980 447000
 
 
                3000*2999      8,997,000
So, D = —————– =  ————— = 20
                  447000            447000

20 in this case is maximum diversity (there are 20 different species). If the index was 1, then diversity would have been non-existent. An index of 10 would indicate moderate diversity.

 

Now work out the index of diversity for community #2 using the table above and the walk through as a guide. You should get a pretty low value. I know it’s a bit confusing that the above numbers are identical in all the columns, but if you work out community #2 then the values for 1 species should be different to the other 19.

 

Most of the time all species will have different values. The working of it is the same though.

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