Dynamics of a predator-prey system with prey subject to Allee effects and disease
Dynamics of a predator-prey system with prey subject to Allee effects and disease
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DOI：
10.3934/mbe.2014.11.877
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发表时间：
2014-03
影响因子：
2.6
通讯作者：
Yun Kang;S. K. Sasmal;Amiya Ranjan Bhowmick;J. Chattopadhyay
中科院分区：
文献类型：
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作者：
Yun Kang;S. K. Sasmal;Amiya Ranjan Bhowmick;J. Chattopadhyay
在本文中，我们提出了一种一般的捕食者-食饵系统，其中食饵受到Allee效应和疾病的影响，具有以下独特的特征：(i)食饵繁殖过程中存在Allee效应，其中感染的食饵（i类）没有贡献；（二）与食用易感猎物（s类）相比，食用受感染猎物对捕食者（p类）增长率的贡献较小或为负。本文给出了这一通用模型的基本动力学性质，并对具体模型（SIP-Allee模型）以及无Allee效应时的相应模型（SIP-no-Allee模型）进行了详细分析；(a) SIP-Allee模型可能只有一个吸引子（所有物种灭绝），两个吸引子（由疾病和捕食者的繁殖数量小或竞争排斥引起的双稳定），或三个吸引子（三稳定）；(b) SIP-no-Allee模型可以有一个吸引子（只有S类存活或S和i类的持久性或S和p类的持久性）或两个吸引子（S和i类的持久性或S和p类的持久性的双稳定性）。最有趣的发现之一是，两种模型都不能支持S、I、p三种等级的共存。这是由假设（ii）造成的，其生物学含义是，I类和p类对s类存在剥削性竞争，而I类不可能优于p类，p类不可能从消耗I类中获得显著收益。此外，SIP-Allee模型与SIP-no-Allee模型的动态对比研究得出以下结论：1)存在Allee效应时，物种容易灭绝，初始条件对猎物及其捕食者的生存起着重要作用；(2)在Allee效应存在的情况下，疾病可以拯救被捕食者免于捕食驱动的灭绝，导致S类和i类共存，而捕食者不能拯救疾病驱动的灭绝。这些发现可能在保护生物学中具有潜在的应用价值。
In this article, we propose a general predator-prey system where prey is subject to Allee effects and disease with the following unique features: (i) Allee effects built in the reproduction process of prey where infected prey (I-class) has no contribution; (ii) Consuming infected prey would contribute less or negatively to the growth rate of predator (P-class) in comparison to the consumption of susceptible prey (S-class). We provide basic dynamical properties for this general model and perform the detailed analysis on a concrete model (SIP-Allee Model) as well as its corresponding model in the absence of Allee effects (SIP-no-Allee Model); we obtain the complete dynamics of both models: (a) SIP-Allee Model may have only one attractor (extinction of all species), two attractors (bi-stability either induced by small values of reproduction number of both disease and predator or induced by competition exclusion), or three attractors (tri-stability); (b) SIP-no-Allee Model may have either one attractor (only S-class survives or the persistence of S and I-class or the persistence of S and P-class) or two attractors (bi-stability with the persistence of S and I-class or the persistence of S and P-class). One of the most interesting findings is that neither models can support the coexistence of all three S, I, P-class. This is caused by the assumption (ii), whose biological implications are that I and P-class are at exploitative competition for S-class whereas I-class cannot be superior and P-class cannot gain significantly from its consumption of I-class. In addition, the comparison study between the dynamics of SIP-Allee Model and SIP-no-Allee Model lead to the following conclusions: 1) In the presence of Allee effects, species are prone to extinction and initial condition plays an important role on the surviving of prey as well as its corresponding predator; 2) In the presence of Allee effects, disease may be able to save prey from the predation-driven extinction and leads to the coexistence of S and I-class while predator can not save the disease-driven extinction. All these findings may have potential applications in conservation biology.