In Exercise 4.22 we saw the equation, due to Fisher et al (1943), S = ln

In Exercise 4.22 we saw the equation, due to Fisher et al (1943), S = α ln 

1 +

N

α



, where S is the number of species in a random sample from a population, N is the number of individuals in the sample, and

α is a constant. Experimental data, and a comparison to the theoretical equation, are shown in Fig. 4.13.

a. What is limN→∞ S? Does this make scientific sense?

b. What is limα→∞ α ln 1 +

N

α

? Does your answer agree with the curves shown in Fig. 4.13.

You should probably do Exercise 4.22 before doing this question.

c. From your answer in the last part, calculate limα→∞

1 +

N

α

α