A population subject to the Allee effect will decreasewhen population numbers are either very low (due to inability tofind a mate) or very high (due to overcrowding), but will increasewhen population numbers are at intermediate levels (due tosuccessful reproduction and not too much overcrowding). A model fora population subject to an Allee effect is given by
xt+1=(4x2t)/(3+x2t),xt is greater than and equal to 0
where ?t is the population number in year t (measuredin hundreds of individuals.
(a) Determine the equilibria.
(b) Use the Stability Criterion to classify the equilibria asasymptotically stable or unstable.
(c) Use cobwebbing to illustrate the dynamics of the differenceequation for ?0=0.5, ?0=0.5,?0=1.5 and ?0=4(it is OK to plot all three onthe same diagram).
(d) Explain the significance of all equilibria and theirstability in terms of the population size in the long run.
