A parasitism-mutualism-predation model consisting of crows, cuckoos and cats with stage-structure and maturation delays on crows and cuckoos

JOURNAL OF THEORETICAL BIOLOGY

卷:446

Article

Luo, Yantao¹  Zhang, Long¹  Teng, Zhidong¹  DeAngelis, Donald L.² 

[1] Xinjiang Univ, Coll Math & Syst Sci, Urumqi 830046, Peoples R China

[2] Univ Miami, Dept Biol, US Geol Survey, Coral Gables, FL 33124 USA

关键词: Stage-structure;    Global stability;    Threshold dynamics;    Coexistence;    Weak persistence;   

DOI  :  10.1016/j.jtbi.2018.02.028

来源: Elsevier

【 摘 要 】

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 Hulling-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. (C) 2018 Elsevier Ltd. All rights reserved.

【 授权许可】

Free