ABSTRACT

We present a systematic comparison and analysis of four discrete-time, host–parasitoid models. For each model, we specify that density-dependent effects occur prior to parasitism in the life cycle of the host. We compare density-dependent growth functions arising from the Beverton–Holt and Ricker maps, as well as parasitism functions assuming either a Poisson or negative binomial distribution for parasitoid attacks. We show that overcompensatory density-dependence leads to period-doubling bifurcations, which may be supercritical or subcritical. Stronger parasitism from the Poisson distribution leads to loss of stability of the coexistence equilibrium through a Neimark–Sacker bifurcation, resulting in population cycles. Our analytic results also revealed dynamics for one of our models that were previously undetected by authors who conducted a numerical investigation. Finally, we emphasize the importance of clearly presenting biological assumptions that are inherent to the structure of a discrete-time model in order to promote communication and broader understanding.

摘要

我们对四个离散时间的宿主-寄生物模型进行了系统的比较和分析。对于每个模型，我们指定在宿主的生命周期中寄生之前发生依赖密度的效应。我们比较了由Beverton-Holt和Ricker映射产生的依赖密度的增长函数，以及假定寄生虫发作的泊松分布或负二项式分布的寄生函数。我们表明，过度补偿的密度依赖性导致倍增的分叉，这可能是超临界或亚临界的。泊松分布中更强的寄生性通过Neimark-Sacker分叉导致共存均衡稳定性的损失，从而导致种群周期。我们的分析结果还揭示了我们其中一种模型的动力学，此前进行过数值研究的作者没有发现这种动力学。最后，我们强调清楚呈现离散时间模型结构所固有的生物学假设的重要性，以促进交流和更广泛的理解。