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Calculate the index of diversity for this site using the formula: d = \frac{N(N-1)}{\Sigma(n(n-1))} Where: - N = Total number of individuals - n = Number of individuals of each species - AQA - A-Level Biology - Question 4 - 2017 - Paper 3

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Calculate-the-index-of-diversity-for-this-site-using-the-formula:--d-=-\frac{N(N-1)}{\Sigma(n(n-1))}--Where:---N-=-Total-number-of-individuals---n-=-Number-of-individuals-of-each-species-AQA-A-Level Biology-Question 4-2017-Paper 3.png

Calculate the index of diversity for this site using the formula: d = \frac{N(N-1)}{\Sigma(n(n-1))} Where: - N = Total number of individuals - n = Number of indivi... show full transcript

Worked Solution & Example Answer:Calculate the index of diversity for this site using the formula: d = \frac{N(N-1)}{\Sigma(n(n-1))} Where: - N = Total number of individuals - n = Number of individuals of each species - AQA - A-Level Biology - Question 4 - 2017 - Paper 3

Step 1

Calculate Total Number of Individuals (N)

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Answer

The total number of individuals (N) can be calculated from the table:

Hydrocotyle vulgaris: 3 Plantago maritima: 19 Ranunculus acris: 3 Hieracium pilosellum: 3 Calligonum cuspidatum: 10 Prunella vulgaris: 16 Pseudoscleropodium purum: 6

Thus,
N=3+19+3+3+10+16+6=59N = 3 + 19 + 3 + 3 + 10 + 16 + 6 = 59

Step 2

Calculate \Sigma(n(n-1))

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Answer

Now calculate \Sigma(n(n-1)) for each species:

  • For Hydrocotyle vulgaris: 3(3−1)=3×2=63(3-1) = 3 \times 2 = 6
  • For Plantago maritima: 19(19−1)=19×18=34219(19-1) = 19 \times 18 = 342
  • For Ranunculus acris: 3(3−1)=63(3-1) = 6
  • For Hieracium pilosellum: 3(3−1)=63(3-1) = 6
  • For Calligonum cuspidatum: 10(10−1)=9010(10-1) = 90
  • For Prunella vulgaris: 16(16−1)=24016(16-1) = 240
  • For Pseudoscleropodium purum: 6(6−1)=306(6-1) = 30

Adding these together: Σ(n(n−1))=6+342+6+6+90+240+30=720\Sigma(n(n-1)) = 6 + 342 + 6 + 6 + 90 + 240 + 30 = 720

Step 3

Calculate the Index of Diversity (d)

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Answer

Plugging the values into the formula gives: d=59(59−1)720=59×58720=3422720≈4.92d = \frac{59(59-1)}{720} = \frac{59 \times 58}{720} = \frac{3422}{720} \approx 4.92 Therefore, the index of diversity for this site is approximately 4.92.

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