A goal of fishery scientists has been to determine the relationship between the size of a fish population and the number of offspring from it that survive to enter the fishery. Fishery scientists refer to a population of a fish as a stock, and the process of entering the fishery as recruitment. The relationship, called the stock-recruitment relationship, is often obtained by empirical fitting of the data to an analytic function. The Beverton-Holt stock recruitment is governed by the difference equation:
Nn+1 = RNn/1 + R-1/K Nn, R > 1
A. Find the equilibria and determine their stability.
B. Find an exact, closed form solution in terms of the first population N1.