Department of Applied Mathematics, University of Washington, Seattle, WA, USA.
J Biol Dyn. 2020 Dec;14(1):479-514. doi: 10.1080/17513758.2020.1783005.
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.
我们对四个离散时间的宿主-寄生模型进行了系统的比较和分析。对于每个模型，我们都指定在宿主生命周期中，密度依赖效应先于寄生发生。我们比较了由 Beverton-Holt 和 Ricker 映射产生的密度依赖性增长函数，以及假设寄生攻击服从泊松或负二项分布的寄生函数。我们表明，过补偿密度依赖性会导致倍周期分岔，可能是超临界或亚临界的。来自泊松分布的更强的寄生作用通过 Neimark-Sacker 分岔导致共存平衡点的失稳，从而导致种群循环。我们的分析结果还揭示了我们的一个模型的动态，这些动态是以前通过进行数值研究的作者所没有发现的。最后，我们强调了在促进交流和更广泛的理解方面，清晰呈现离散时间模型结构中固有的生物学假设的重要性。
