Is the Distribution of Species Consistent?

The distribution of species also follows a ziff's law kind of a thing and or the infinite. And maybe other areas in nature will come up with this, too. So it's like given the exponent, what does it converge to? Obviously, if the exponent is infinite, then it just converges to one because all the other terms except for one go to zero. The Riemann zeta function is really important in pure mathematics.