Luo Yantao, Zhang Long, Teng Zhidong, DeAngelis Donald L
College of Mathematics and Systems Science, Xinjiang University, Urumqi 830046, PR China.
College of Mathematics and Systems Science, Xinjiang University, Urumqi 830046, PR China.
J Theor Biol. 2018 Jun 7;446:212-228. doi: 10.1016/j.jtbi.2018.02.028. Epub 2018 Feb 27.
In this paper, a parasitism-mutualism-predation model is proposed to investigate the dynamics of multi-interactions among cuckoos, crows and cats with stage-structure and maturation time delays on cuckoos and crows. The crows permit the cuckoos to parasitize their nestlings (eggs) on the crow chicks (eggs). In return, the cuckoo nestlings produce a malodorous cloacal secretion to protect the crow chicks from predation by the cats, which is apparently beneficial to both the crow and cuckoo population. The multi-interactions, i.e., parasitism and mutualism between the cuckoos (nestlings) and crows (chicks), predation between the cats and crow chicks are modeled both by Holling-type II and Beddington-DeAngelis-type functional responses. The existence of positive equilibria of three subsystems of the model are discussed. The criteria for the global stability of the trivial equilibrium are established by the Krein-Rutman theorem and other analysis methods. Moreover, the threshold dynamics for the coexistence and weak persistence of the model are obtained, and we show, both analytically and numerically, that the stabilities of the interior equilibria may change with the increasing maturation time delays. We find there exists an evident difference in the dynamical properties of the parasitism-mutualism-predation model based on whether or not we consider the effects of stage-structure and maturation time delays on cuckoos and crows. Inclusion of stage structure results in many varied dynamical complexities which are difficult to encompass without this inclusion.
本文提出了一个寄生 - 互利共生 - 捕食模型，以研究杜鹃、乌鸦和猫之间具有阶段结构以及杜鹃和乌鸦成熟时间延迟的多相互作用动态。乌鸦允许杜鹃将其雏鸟（卵）寄生在乌鸦雏鸟（卵）上。作为回报，杜鹃雏鸟会分泌一种恶臭的泄殖腔分泌物，以保护乌鸦雏鸟免受猫的捕食，这显然对乌鸦和杜鹃种群都有益。杜鹃（雏鸟）与乌鸦（雏鸟）之间的多相互作用，即寄生和互利共生，以及猫与乌鸦雏鸟之间的捕食，均通过Holling - II型和Beddington - DeAngelis型功能反应进行建模。讨论了该模型三个子系统正平衡点的存在性。利用Krein - Rutman定理和其他分析方法建立了平凡平衡点全局稳定性的判据。此外，得到了该模型共存和弱持续性的阈值动态，并且我们通过解析和数值方法表明，内部平衡点的稳定性可能会随着成熟时间延迟的增加而变化。我们发现，基于是否考虑杜鹃和乌鸦的阶段结构以及成熟时间延迟的影响，寄生 - 互利共生 - 捕食模型的动力学性质存在明显差异。包含阶段结构会导致许多不同的动力学复杂性，如果不包含这一点则难以涵盖这些复杂性。
