One way to measure species diversity is to use the Shannon diversity index H. If a habitat consists of three species, A, B, and C, then its Shannon diversity index is

where x is the percent of species A in the habitat, y is the percent of species B in the habitat, and z is the percent of species C in the habitat. Use the fact that

to show that the maximum value of H occurs when x = y = z = 1/3. What is the maximum value of H?

Transcribed Image Text:

H = -x ln x - y lny - z ln z