2. Currently there is a debate on the importance of preserving large tracts of land to maintain biodiversity. Many of the arguments for setting aside large tracts are based on studies of biodiversity on islands. In this problem you apply the power rule to determine the number of species of herpetofauna (amphibians and reptiles) as a function of island area for the given Caribbean islands. You are given the following data [1]:
|
Island
|
Area
(mi2)
|
Species
|
|
|
Redunda
|
1
|
3
| |
|
Montserrat
|
33
|
10
| |
|
Jamaica
|
4,411
|
38
| |
|
Cuba
|
46,736
|
97
|
a. Let N be the number of species and A be the area of the island, then the power law expression relating the number of species to the area of the island is given by
Use the power law under Excel's trendline to best fit the data above. Plot the data and the best power law fit, then have Excel write the formula on your graph. How well does the graph match the data?
b. As in the previous problem, we want to fit a straight line to the logarithms of the data. From the allometric model above, we obtain the formula ln(N) = ln(k) + a ln(A). In the table above, take the logarithm of the Number of Species (ln(N)) and the logarithm of the Island Area (ln(A)). Use Excel's scatter plot and linear fit under trendline to see how this fits the data. Plot a graph of the logarithm of the data and the best straight line fit to these data. Show the formula for this straight line on your graph. Compare the coefficients obtained in this manner to the ones found in Part a. How well does the graph match the data?
c. From your calculations above give estimates to fill in the table below.
|
Island
|
Area (mi
2)
|
Species
|
|
Saba
|
5
|
|
|
Puerto
Rico
|
|
40
|
|
Saint
Croix
|
80
|
|
|
Hispaniola
|
|
88
|
