Question

10 The Allee effect: For a sexually reproducing population, very small poppulation size hinders the growth of a population because it becomes difficult to find mates. Suppose that individ the probability finding a mate is proportional to N2(t) where N (t) is the population at time t. Thus, the births per unit time is proportional to N2 (t). Also assume that the deaths per unit time is propotional to N(t) Develop an ordinary differential equation model, and show that there ex ists a threshold population size N" such that, if the initial population size N(0) E (0, N*), then N(t) 0 as t - oo; if N(0) > N°, then N(t)o as too uals are random mixed, i.e., 7 00

Answer 1