The effect of initial density and parasitoid intergenerational survival rate on classical biological control

Models of biological control have a long history of theoretical development that have focused on the interaction of a parasitoid and its host. The host-parasitoid systems have identified several important and general factors affecting the long-term dynamics of interacting populations. However, much less is known about how the initial densities of host-parasitoid populations affect the biological control as well as the stability of host-parasitoid systems. To do this, the classical Nicholson-Bailey model with host self-regulation and parasitoid intergenerational survival rate is used to uncover the effect of initial densities on the successful biological control. The results indicate that the simplest Nicholson-Bailey model has various coexistence with a wide range of parameters, including boundary attractors where the parasitoid population is absent and interior attractors where host-parasitoid coexists. The final stable states of host-parasitoid populations depend on their initial densities as well as their ratios, and those results are confirmed by basins of attraction of initial densities. The results also indicate that the parasitoid intergenerational survival rate increases the stability of the host-parasitoid systems. Therefore, the present research can help us to further understand the dynamical behavior of host-parasitoid interactions, to improve the classical biological control and to make management decisions.