A paradox in discrete single species population dynamics with harvesting/thinning

We analyze a general time-discrete mathematical model of single species population dynamics with the intraspecific density effect and the harvesting/thinning effect. We harvest a portion of the population at a moment in each year. We investigate the condition under which the harvesting/thinning causes an eventual increase of its population at the equilibrium, and show that such a paradoxical increase could occur for the discrete single species population dynamics with a large family of density effect functions. Some typical models are analyzed in detail according to the possibility of the paradox emergence. Our result implies that the contest competition would never cause the paradox, while the scramble competition would be likely to cause it.