Species-area relation: Ecologists have studied the relationship between the number S of species of a given taxonomic group within a given habitat (often an island) and the area A of the habitat.34...

Species-area relation: Ecologists have studied the relationship between the number S of species of a given taxonomic group within a given habitat (often an island) and the area A of the habitat.34 They have discovered a consistent relationship: Over similar habitats, S is approximately a power function of A, and for islands the powers fall within the range 0.2 to 0.4. Table 5.9 gives, for some islands in the West Indies, the area in square miles and the number of species of amphibians and reptiles.

a. Find a formula that models S as a power function of A.

b. Is the graph of S against A concave up or concave down? Explain in practical terms what your answer means.

c. The species-area relation for the West Indies islands can be expressed as a rule of thumb: If one island is 10 times larger than another, then it will have times as many species. Use the homogeneity property of the power function you found in part a to fill in the blank in this rule of thumb.

d. In general, if the species-area relation for a group of islands is given by a power function, the relation can be expressed as a rule of thumb: If one island is 10 times larger than another, then it will have times as many species. How would you fill in the blank? (Hint: The answer depends only on the power.)