Question

2.         Suppose that wildlife workers capture 328 penguins on an island, mark them, and allow them to mix with the rest of the population. Later, they capture 200 penguins, 64 of which are marked.What is the estimate for the number of penguins on the island?

3.         You have been tasked to estimate the number of rattlesnakes using a series of hibernacula along a ridge in western Texas. To accomplish your assigned task, you capture 37 rattlesnakes and mark them with tags. You return to the site one week later and resample the population by capturing 52 rattlesnakes. Of the 52, 30 are marked from your first sample. How many rattlesnakes are in the population?

Example 1: Using the data from Communities 1 and 2 above and calculate Simpson’s Index.

For Community 1: 18 of 20 individuals are Species A So for Species A, (pi)2 = (18/20)2= 0.81

         1 of 20 individuals are Species B For Species B, (pi)2 = (1/20)2= 0.025

         1 of 20 individuals are Species C For Species C, (pi)2 = (1/20)2 = 0.025

         ? (pi)2 = 0.815?

Simpson's Index is 1 - 0.815, or 0.185 for Community 1

For Community 2:

D = 1 - [ (7/20)2 + (8/20)2 + (5/20)2] Simpson's Index = 1 - [0 .1225 + 0.16 + 0.0625 ]

Simpson's Index = 1 - [0.345]? =  0.655

So Community 2 has a higher biodiversity.

Now, compare the diversity of these two kinds of mixed nuts using Simpson’s Index:

Species	Number in “Mixed Nuts”	Number in “Deluxe Mixed Nuts”
Brazil nut	1	8
Cashew	8	15
Pecan	1	7
Almond	15	18
Peanut	85	0

We will set up a table to record the calculations:

Species	Number in “Mixed Nuts”	(pi)2	Species	Number in “Deluxe Mixed Nuts”	(pi)2
Brazil nut	1		Brazil nut	8
Cashew	8		Cashew	15
Pecan	1		Pecan	7
Almond	15		Almond	18
Peanut	85		Peanut	0
Total			Total

“Mixed Nuts”:        ? (pi)2   =    ______________     and           1- ? (pi)2 ___________

                        So D = ______________

“Deluxe Mixed Nuts”:       ? (pi)2   =    ______________     and           1- ? (pi)2 __________

So D = ______________

1.         Which of the “populations” of nuts has the higher biodiversity?

Answer 1

Answer:

2) Based on the given information:

• Number of penguins captured and marked initially (M) = 328
• Number of penguins recaptured (n) = 200
• Number of recaptured penguins that are marked (m) = 64
• Number of penguins on the island can be determined using mark and capture formula: N = M*n / m
• N = 328*200 / 64 = 1025

3)

• Number of rattlesnakes captured and marked initially (M) = 37  
• Number of rattlesnakes recaptured (n) = 52 rattlesnakes.
• Number of rattlesnakes that are recaptured and are marked (m) = 30.  
• N = M*n / m
• N = 37*52/30 = 64

4)

Species	Number in “Mixed Nuts”	(pi)2	Species	Number in “Deluxe Mixed Nuts”	(pi)2
Brazil nut	1	=(1/110)^2	Brazil nut	8	=(8/48)^2
Cashew	8	=(8/110)^2	Cashew	15	=(15/48)^2
Pecan	1	=(1/110)^2	Pecan	7	=(7/48)^2
Almond	15	=(15/110)^2	Almond	18	=(18/48)^2
Peanut	85	=(85/110)^2	Peanut	0	0.000
Total	=(1+8+1+15+85)		Total	=(8+15+7+18+0)

Species	Number in “Mixed Nuts”	(pi)2	Species	Number in “Deluxe Mixed Nuts”	(pi)2
Brazil nut	1	0.000083	Brazil nut	8	0.027778
Cashew	8	0.005289	Cashew	15	0.097656
Pecan	1	0.000083	Pecan	7	0.021267
Almond	15	0.018595	Almond	18	0.140625
Peanut	85	0.597107	Peanut	0	0.000000
Total	110	0.621	Total	48	0.287

For Mixed Nuts, sum(pi^2) = 0.621, 1 - sum(pi^2) = 1 - 0.621 = 0.379  and  

For Delux Mixed Nuts, sum(pi^2) = 0.287, 1 - sum(pi^2) = 1 - 0.287 = 0.713

So population of Delux Mixed Nuts has higher biodiversity.