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.

Infectious diseases are often regarded as possible explanations for the sudden collapse of biological invasions. This phenomenon is characterized by a host species, which firstly can successfully establish in a nonnative habitat, but then spontaneously disappears again. This study proposes a reaction-diffusion model consisting of a simple SI disease with vital dynamics of Allee effect type. By way of travelling wave analysis, conditions are derived under which the invasion of the host population is slowed down, stopped or reversed as a consequence of a subsequently introduced disease. Hence, pathogens can dramatically control the rate of spread of invasive species.

We analyze a time-discrete mathematical model of host-parasite population dynamics with harvesting, in which the host can be regarded as a pest. We harvest a portion of the host population at a moment in each parasitism season. The principal target of the harvesting is the host; however, the parasite population may also be affected and reduced by a portion. Our model involves the Beverton-Holt type density effect on the host population. We investigate the condition in which the harvesting of the host results in an eventual increase of its equilibrium population size, analytically proving that the paradoxical increase could occur even when the harvesting does not directly affect the parasite population at all. We show that the paradox of pest control could be caused essentially by the interspecific relationship and the intraspecific density effect.

The version presented here may differ from the published version or from the version of the record. Please see the repository URL above for details on accessing the published version and note that access may require a subscription.

No abstract