Question

Which sample has a higher diversity?

Each of 100 individuals of a mammal species was placed in enclosure containing equal amount of each of five different foods. The frequency with which the animals chose each of the foods was: (15 pts) Food item Sample 1 Sample 2 18 7. 20 20 46 17 21 24

Describe a sample frequency (of n=100) that achieve the highest diversity. Please show all the steps and work.

Answer 1

Solution: The shannon - Wiener diveesity index is broadly a measure o uncertainty in the Ecological terms. thigh uncertainly would mean a high live esily. It accounts for both species sichnen & Evennes. It has a range of about 1.5 to 3.5 0 Given shannon Wienes divessily index for Samplefi stept sum of all free ğ fir: 18 +20 +19+21 +24 Stepa: . 100 calculate Hi Pi 0.18 pie Sample Sum: . 0.30 0-17 0.21 0.24 steps: - calculate ln (pi): en(pi) In(0.18) : -1.714 en (0-) : -1.609 In (0.17) : -1.77 In Co-ai) = -1.56 en (0-24): -1.427 stopy: calculate pi x ln (Pi) Pillow) 0.18 -1.914 0.2 -1.609 0-17 o al -1.56 0.04 -1.407 Pi x ln(pi) -0.308 -0.328 • 0-3009 -0.3776 -0.3424 -1.6007

.: Shannon - Wiened diverisily Index W) : -1.6009 Hmax = ln (N) in(5) 34.61 € venne H #man 1.6007 Hman : 1.6007 1.61 -0.99 Shanmon- Wience divcesily fell sample o 11i) Wod sample vi - Sample Sum Pix en cpi) -0.1855 0.07 e nepi -2.65 -1.60 -0.77 - 2.40 -191 -0.32 -0-35 46 0.46 0.9 -0.2) -0.30 0.18 - 1.3655 Therefore it a shammon inden= 101 Hman = ln(n) = ln(5) = 161 Evenen = H +18655 Aman 1.61 :+0.8981 sample À has highes Shannon Inden value of H= 1.6. Therefore sample A has higher diversity than sample B. In sample B highest diversity is shown by n: 46 and in sample. A highest divesity is shown by n= 24. b - (0)