似Allee效应对2-物种集合种群竞争动态的影响

集合种群具有与局域种群Allee效应相似的现象被称为似Allee效应.将似Allee效应引入2-竞争物种集合种群系统,建立了具有似Allee效应的2-物种集合种群演化动态模型.大量的数值模拟表明:(1)似Allee效应导致集合种群水平上两竞争物种构成的系统具有多个平衡态;(2)似Allee效应使竞争共存物种无法续存甚至全部灭绝,即使种群具有很高的初始斑块占有率,并且最终平衡态随初始斑块占有率变化而改变;(3)似Allee效应可能使竞争排斥物种共同灭绝,且效应越强,物种存活时间越短;但似Allee效应不会增强强物种对弱物种的排斥强度,反而可能使强物种变为弱物种,弱物种变为强物种,其具有与栖息地毁坏类似的影响种群竞争等级排序的作用;(4)似Allee效应对竞争集合种群续存是一个不稳定的干扰因素,微小的变化都将引起系统平衡态的剧变.但对于已经达到平衡态的集合种群系统,似Allee效应对强弱种群多度起到调节与制约的作用,有助于平衡态集合种群的稳定与共存,这一结论更完整的揭示了似Allee效应在竞争集合种群系统发展的不同阶段所起的不同作用.以上这些结论对物种保护及集合群落的管理具有重要的指导意义.     

Allee效应对具有生境恢复的集合种群的影响

Allee效应与种群的灭绝密切相关,其研究对生态保护和管理至关重要。Allee效应对物种续存是潜在的干扰因素,濒危物种更容易受其影响,可能会增加生存于生境破碎化斑块的濒危物种的死亡风险,因此研究Allee效应对种群的动态和续存的影响是必要的。从包含由生物有机体对环境的修复产生的Allee效应的集合种群模型出发,引入由其他机制形成的Allee效应,建立了常微分动力系统模型和基于网格模型的元胞自动机模型。通过理论分析和计算机模拟表明:(1)强Allee效应不利于具有生境恢复的集合种群的续存;(2)生境恢复有利于种群续存;(3)局部扩散影响了集合种群的空间结构、动态行为和稳定性,生境斑块之间的局部作用将会减缓或消除集合种群的Allee效应,有利于集合种群的续存。     

捕食系统时空动态对非对称的Allee效应的响应

虽然具有Allee效应的捕食系统动态已得到了广泛的研究,但很少有研究关注同一系统中不同种群受Allee效应影响情况.本文将考虑捕食、食饵种群分别受.Allee效应的影响,利用常微分方程与元胞自动机建立空间隐含(非空间)与显含的捕食模型,并讨论了Allee效应对捕食、食饵种群相互作用的非对称影响.空间隐含模型的模拟结果显示,捕食系统的稳定性与哪一个种群受Allee效应影响有关.当食饵种群受到中等强度Allee效应影响时,系统从稳定变为振荡状态.然而,捕食种群受Allee效应影响可使系统振动减弱并迅速达到稳定.空间显含模型的模拟结果表明,在概率转化模式下Allee效应可促使空间异质化,而捕食种群受Allee效应影响时空间异质化比食饵种群受影响时更强.此外,考虑统计随机性后发现两种群分别受Allee效应影响时种群呈现出两种分布模式:聚集型和界限型.特别当食饵受Allee效应,加之空间结构及统计随机性的作用,捕食系统出现一种矛盾的现象.     

具有Allee效应的合作进化

Allee效应对物种的续存是潜在的干扰因素,在很大程度上将增加种群局部甚至全局灭绝的可能性。对许多物种,尤其是濒临物种更容易受其影响。将Allee效应引入囚徒困境博弈模型,通过理论分析与数值模拟相结合的方法分析讨论了Allee效应对合作进化的影响。研究结果表明:在恶劣的环境条件下,Allee效应极易使物种灭绝,不利于合作进化;在相对优越的环境条件下(死亡率较低),Allee效应促进合作进化,且Allee效应强度越强,更有利于合作进化,不过种群的空间斑块占有率也会随着Allee效应强度的增强而降低,使物种最终灭绝。     

Allee效应对单种群模型动力学行为影响研究

提出具有Allee效应的抽象的单种群模型,证得如果原系统有唯一的全局稳定的正平衡点,则具有Allee效应的单种群模型仍然具有唯一的全局稳定的正平衡点.Allee效应并不改变种群的平衡位置和稳定性;其后,针对具有Allee效应的对数种群模型,食物有限的单种群模型,Ayala型单种群模型分别进行了数值模拟,数值模拟表明随着Allee效应增大,系统的解需要更久的时间才能趋于正平衡点,从这一角度讲,Allee效应不利于系统的稳定,种群在受到外界干扰时,可能种群密度更容易出现剧烈波动.     

人类活动影响下具有Allee效应的非自治种群演化模式的研制及其应用——以丹顶鹤为例

提出“中国的丹顶鹤是否是一活着的灭绝物种(活死者) ?”这一重大科学问题。要回答这个问题,首先必须建立有关丹顶鹤种群演化与人类活动、栖息地斑块平均面积和斑块数关系的动力学模式,其次必须对丹顶鹤种群的大小进行动力学预测。前者涉及到所谓的“相互作用的标度理论”,后者则属于“物种多样性动力学预测”这一崭新的研究领域。首次应用标度理论,阐述了单个物种环境容量(K)与斑块数(P)的标度性质,并用实测的小三江平原的丹顶鹤资料进行了验证发现,K∝P0 .7。同时,在对logistic模式改进的基础上,引进人类活动累积效应及其作用的时间因素,首次提出了人类活动影响下具有Allee效应的非自治种群演化模式。并以丹顶鹤为例,模拟了其种群演化特征,预测了其灭绝时间。模拟结果发现:对于我国的珍稀物种丹顶鹤,其繁殖率的相对高低对物种灭绝的影响并不显著,但Allee效应对其物种灭绝的影响却是明显的,Allee效应越弱,物种灭绝时间越长。如果小三江平原湿地的生境质量得不到有效的恢复和提高,该区丹顶鹤将有可能会在330～4 2 8a后走向灭绝,即丹顶鹤的灭绝对现有栖息地毁坏的响应具有330～4 2 8a的时间滞后性。因此,认为丹顶鹤是一种典型的“活着的灭绝物种”,这一点必须引起政府、科学家和公众的高度重视。     

集合种群的Allee效应研究进展

随着全球环境破坏的加剧,物种丧失的速度加快,人们日益关注生物多样性的保护。种群生物学和自然保护生物学的一些研究表明,如果一个局域种群受到Allee效应的影响,最终可能走向灭绝。从物种保护的角度考虑,分别介绍了集合种群水平上的Allee效应的和似Allee效应,比较了集合种群的Allee效应和似Allee效应产生的原因,以及集合种群的Allee效应和局域种群的Allee效应之间的关系、集合种群的似Allee效应和局域种群的Allee效应之间的关系,并提出集合种群的Allee效应还需要进一步的研究。     

具有Allee效应的食饵-捕食者模型的稳定性分析

建立了具有Allee效应的食饵—捕食者模型,讨论了强Allee效应和弱Allee效应对食饵种群的影响以及模型解的有界性和各平衡点的存在性,分析了各平衡点的局部渐近稳定性,进一步通过构造Lyapunov函数分析了正平衡点的全局渐近稳定性.     

滨海湿地植物种群Allee效应驱动机制研究进展

Allee效应是指生物个体适应度与种群规模或密度之间呈正向关联的现象,因与植物种群动态和种群灭绝密切相关而受到生态学家的普遍重视。阐释多重胁迫下滨海湿地植物种群响应机制,从保护生物多样性和维持生态系统稳定性层面发展系统性生态修复措施成为相关研究关注的重点。本研究分别从遗传过程、花粉扩散过程和生物互作关系不同层面,总结分析了植物种群Allee效应驱动机制的研究进展。一方面,植物因遗传过程中近交衰退、遗传变异丧失、有害突变累积等遗传结构改变造成繁殖失败而引发Allee效应;另一方面,植物花粉扩散过程和动植物互作关系影响下的花粉限制也通过影响植物种群繁殖力成为驱动Allee效应的关键因素。滨海湿地水盐梯度变异及格局破碎化影响下,植物种群遭受Allee效应的风险需引起关注,维持滨海湿地植物种群适宜分布格局和生物连通过程成为缓解Allee效应的重要手段。结合生理学与化学生态学研究手段和长时间尺度动态监测技术,有助于进一步阐释环境及生物等多重胁迫下Allee效应的非线性驱动机制。     

生境丧失对具有似Allee效应集合种群的影响及对策——以江苏盐城为例

似Allee效应对物种续存是潜在的扰动因素,稀有物种更易受其影响,可能增加生存于破碎化栖息地中的珍稀物种的死亡风险;但似Allee效应对多物种集合种群续存的影响及其在珍稀物种保护中的应用未能引起足够重视。将似Allee效应引入集合种群动力模式,建立了生境丧失下具有似Allee效应的n-珍稀物种的集合种群模式,并以江苏盐城滩涂湿地中的29种珍稀物种为研究实例。研究结果表明:(1)似Allee效应导致n-物种集合种群多度作长期变周期振荡,原本竞争共存物种可能无法继续共存,甚至灭绝。(2)似Allee效应增强对次强种及劣势种的生存极为不利,导致次强物种由强至弱灭绝,劣势物种由弱至强依次灭绝。(3)盐城天然湿地丧失29%后,11种劣势物种的集合种群由弱到强将最终依次灭绝,灭绝迟豫时间为304～890a,这些物种即Hanski所指的"活死者"。(4)适度增加栖息地面积是保护珍稀物种多样性的有效方法之一,在盐城现存3200km2的天然湿地基础上适度增加1801～2064km2左右栖息地面积,可以有效保护29种濒危物种的多样性,同时应注意结合针对具体物种的保护措施来提高濒危物种多度。研究结果对物种多样性保护及自然保护区建设具有重要的理论指导意义。     

The stability of predator-prey systems subject to the Allee effects

In recent years, many theoreticians and experimentalists have concentrated on the processes that affect the stability of predator-prey systems. But few papers have addressed the Allee effect with focus on the their stability. In this paper, we select two classical models describing predator-prey systems and introduce the Allee effects into the dynamics of both the predator and prey populations in these models, respectively. By combining mathematical analysis with numerical simulation, we have shown that the Allee effect may be a destabilizing force in predator-prey systems: the equilibrium point of the system could be changed from stable to unstable or otherwise, the system, even when it is stable, will take much longer time to reach the stable state. We also conclude that the equilibrium of the prey population will be enlarged due to the Allee effect of the predator, but the Allee effects of the prey may decrease the equilibrium value of the predator, or that of both the predator and prey. It should also be pointed out that the impact of the Allee effects of predator and prey due to different mechanisms on different predator-prey systems could also vary.     

A mechanistic model for interference and Allee effect in the predator population

We present the results of simulations in an individual-based model describing spatial movement and predator-prey interaction within a closed rectangular habitat. Movement of each individual animal is determined by local conditions only, so any collective behavior emerges owing to self-organization. It is shown that the pursuit of prey by predators entails predator interference, manifesting itself at the population level as the dependency of the trophic function (individual ration) on predator abundance. The stabilizing effect of predator interference on the dynamics of a predator-prey system is discussed. Inclusion of prey evasion induces apparent cooperation of predators and further alters the functional response, giving rise to a strong Allee effect, with extinction of the predator population upon dropping below critical numbers. Thus, we propose a simple mechanistic interpretation of important but still poorly understood behavioral phenomena that underlie the functioning of natural trophic systems.     

Impact of Allee effect on an eco-epidemiological system

In this paper, we propose a general ratio-dependent prey-predator model with disease in predator subject to the strong Allee effect in prey. We obtain the complete dynamics of both models: (a) full model with Allee effect; (b) full model without Allee effect. Model (a) may have more than one interior equilibrium point, but model (b) has only one interior equilibrium point. Numerical results reveal that the coexistence of all the populations at the endemic state is possible for both the models. But for the model with Allee effect, the coexistence can be destroyed by an increased supply of alternative food for the predators. It can also be proved that for the full model with Allee effect, the disease can be suppressed under certain parametric conditions. Also by comparing models (a) and (b), we conclude that Allee effect can create or destroy the interior attractor. Finally, we have studied the disease free-submodel (prey and susceptible predator model) with and without Allee effect. The comparative study between these two submodels leads to the following conclusions: 1) In the presence of Allee effect, the number of interior equilibrium points can change from zero to two whereas the submodel without Allee effect has unique interior equilibrium point; 2) Both with and without Allee effect, initial conditions play an important role on the survival and extinction of prey as well as its corresponding predator; 3) In the presence of Allee effect, bi-stability occurs with stable or periodic coexistence of prey and susceptible predator and the extinction of prey and susceptible predator; 4) Allee effect can generate or destroy the interior equilibrium points.     

Modeling the Effect of Prey Refuge on a Ratio-Dependent Predator–Prey System with the Allee Effect

The extinction of species is a major threat to the biodiversity. The species exhibiting a strong Allee effect are vulnerable to extinction due to predation. The refuge used by species having a strong Allee effect may affect their predation and hence extinction risk. A mathematical study of such behavioral phenomenon may aid in management of many endangered species. However, a little attention has been paid in this direction. In this paper, we have studied the impact of a constant prey refuge on the dynamics of a ratio-dependent predator–prey system with strong Allee effect in prey growth. The stability analysis of the model has been carried out, and a comprehensive bifurcation analysis is presented. It is found that if prey refuge is less than the Allee threshold, the incorporation of prey refuge increases the threshold values of the predation rate and conversion efficiency at which unconditional extinction occurs. Moreover, if the prey refuge is greater than the Allee threshold, situation of unconditional extinction may not occur. It is found that at a critical value of prey refuge, which is greater than the Allee threshold but less than the carrying capacity of prey population, system undergoes cusp bifurcation and the rich spectrum of dynamics exhibited by the system disappears if the prey refuge is increased further.     

Bistability and an Allee effect as emergent consequences of stage-specific predation

The Allee effect, a reduction of individual fitness at low population density that can lead to sudden and unannounced extinctions, has been shown to come about through a number of mechanisms, usually associated with group behavior or mate search. Recent papers show that it may arise through size-selective predation, without explicit assumptions relating individual fitness to population density. It arises from the shift that a predator induces in the population stage distribution of its prey. We study the parameter conditions that lead to such an emergent Allee effect. The emergent Allee effect occurs under fairly broad conditions. We show that stage-specific predation can also induce bistability between alternative states where both prey and predator are present. A perturbation analysis on the equilibria shows that all equilibria are highly robust to changes in predator density. Our work shows that when size-specific interactions are taken into account, bistabilities and catastrophic collapses are possible even in purely exploitative food webs, which has substantial implications for questions related to food web theory and conservation issues.     

局域种群的Allee效应和集合种群的同步性

从包含Allee效应的局域种群出发,建立了耦合映像格子模型,即集合种群模型.通过分析和计算机模拟表明:(1)当局域种群受到Allee效应强度较大时,集合种群同步灭绝;(2)而当Allee效应强度相对较弱时,通过稳定局域种群动态(减少混沌)使得集合种群发生同步波动,而这种同步波动能够增加集合种群的灭绝风险;(3)斑块间的连接程度对集合种群同步波动的发生有很大的影响,适当的破碎化有利于集合种群的续存.全局迁移和Allee效应结合起来增加了集合种群同步波动的可能,从而增加集合种群的灭绝风险.这些结果对理解同步性的机理、利用同步机理来制定物种保护策略和害虫防治都有重要的意义.     

The effects of interacting species on predator-prey coevolution

Simple optimization models are used to explore the effects that an additional species has on predator-prey coevolution. The additional species is either an alternative prey or a higher-level predator that consumes the first predator species. Results indicate that a variety of effects on predator-prey coevolution are possible. In general, the additional species does not decouple evolutionary changes in the predator and the prey, and often leads to stronger coupling. The manner in which predator and prey adaptations combine to determine the predator's capture rate has a major effect on how an additional species influences the coevolutionary responses of the original pair of species.     

Influence of density dependence on predator-prey seabird interactions at large spatio-temporal scales

Theoretical investigations of competitive dynamics have noted that numbers of predator and prey influence each other. However, few empirical studies have demonstrated how a life-history trait of the prey (such as fecundity) can be affected simultaneously by its own density and the density of predators. For instance, density dependence can reduce fecundity with increasing number of prey, while inverse density dependence or Allee effects may occur especially when the prey is a social organism. Here we analysed an intraguild predator-prey system of two seabird species at a large spatio-temporal scale. As expected, we found that fecundity of prey was negatively affected by predator density. Nevertheless, fecundity of prey also increased nonlinearly with its own density and strikingly with the prey-predator ratio. Small groups of prey were probably not able to defend their nests especially against large number of predators. At the highest prey densities (i.e. when anti-predator strategies should be most efficient), prey fecundity also lowered, suggesting the appearance of density dependence mediated by food competition. Allee effects and density dependence occurred across a broad range of population sizes of both the prey and the predator at several local populations facing different ecological environments.     

Should "handled" prey be considered? Some consequences for functional response, predator-prey dynamics and optimal foraging theory

Predator-prey models consider those prey that are free. They assume that once a prey is captured by a predator it leaves the system. A question arises whether in predator-prey population models the variable describing prey population shall consider only those prey which are free, or both free and handled prey together. In the latter case prey leave the system after they have been handled. The classical Holling type II functional response was derived with respect to free prey. In this article we derive a functional response with respect to prey density which considers also handled prey. This functional response depends on predator density, i.e., it accounts naturally for interference. We study consequences of this functional response for stability of a simple predator-prey model and for optimal foraging theory. We show that, qualitatively, the population dynamics are similar regardless of whether we consider only free or free and handled prey. However, the latter case may change predictions in some other cases. We document this for optimal foraging theory where the functional response which considers both free and handled prey leads to partial preferences which are not observed when only free prey are considered.     

Predator overcomes the Allee effect due to indirect prey–taxis

A mathematical model for spatiotemporal dynamics of prey–predator system was studied by means of linear analysis and numerical simulations. The model is a system of PDEs of taxis–diffusion–reaction type, accounting for the ability of predators to detect the locations of higher prey density, which is formalized as indirect prey–taxis, according to hypothesis that the taxis stimulus is a substance being continuously emitted by the prey, diffusing in space and decaying with constant rate in time (e.g. odour, pheromone, exometabolit). The local interactions of the prey and predators are described by the classical Rosenzweig – MacArthur system, which is modified in order to take into account the Allee effect in the predator population. The boundary conditions determine the absence of fluxes of population densities and stimulus concentration through the habitat boundaries. The obtained results suggest that the prey–taxis activity of the predator can destabilize both the stationary and periodic spatially-homogeneous regimes of the species coexistence, causing emergence of various heterogeneous patterns. In particular, it is demonstrated that formation of local dense aggregations induced by prey–taxis allows the predators to overcome the Allee effect in its population growth, avoiding the extinction that occurs in the model in the absence of spatial effects.