Some organisms exhibit a density-dependent mortality from one generation to the next....

Some organisms exhibit a density-dependent mortality from one generation to the next. Let R > 1 be the net reproductive rate (that is, the number of surviving offspring per parent), let x > 0 be the density of parents and y be the density of surviving offspring. The Beverton- Holt recruitment curve is

where K > 0 is the carrying capacity of the environment. Notice that if x = K, then y = K.

Show that if x> K, then K < y < x. Explain what this means about the population size over successive generations if the initial population is larger than the carrying capacity of the environment.