 MacArthur and Wilson formulated a mathematical model with these assumptions (Wilson &amp; Bossert 1971). Suppose \(P\) is a parameter representing a pool of species. Let the total immigration rate \(\lambda_{S}\) be the number of new species colonizing an island per unit time. Let the total extinction rate \(\mu_{S}\) be the number of species on the island going extinct per unit time. Thus, the instantaneous rate of change of species on the island is,