To find the measure of diversity H for the following proportions of each

Wribreeminsl

Wribreeminsl

Answered question

2021-09-13

To find the measure of diversity H for the following proportions of each:
hemlock, 0.521; beech, 0.324; birch, 0.081; maple, 0.074.

Answer & Explanation

Jayden-James Duffy

Jayden-James Duffy

Skilled2021-09-14Added 91 answers

Modeling diversity of species:
One measure of the diversity of the species in an ecological community is modeled by the formula,
H=[P1log2P1+P2log2P2++Pnlog2Pn]..(1)
Where P1,P2,,Pn are the proportions of sample that belong to the each of n species found in the sample.
Given that P1=0.521,P2=0.324,P3=0.081 and P4=0.074
Substitute these values in equation (1) to get the following,
H=[0.521log20.521+0.324log20.324+0.081log20.081+0.074log20.074]..(2)
Change-of -Base theorem:
For any positive real numbers x, a and b, where aq1 and bq1, the following holds.
logax=logbxlogba
By using the change of base theorem the terms in the equation (2) becomes the following.
log20.521=log0.521log2
=0.28320.3010
=0.9406
log20.324=log0.324log2
=0.48950.3010
=1.6259
log20.081=log0.081log2
=1.09150.3010
=3.6259
log20.074=log0.074log2
=1.13080.3010
=3.7563
Substitute in equation (2) to get the following,
H=[0.521(0.9406)+0.324(1.6259)+0.081(3.6259)+0.074(3.7563)]
=[0.49007590.526802710.293700680.27796849]
=[1.5886]
=1.5886
1.589
So, the measure of diversity H is 1.589.
Final statement:
The measure of diversity H is 1.589.

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