[论文解读] Bistability induced by generalist natural enemies can reverse pest invasions

Sten Madec, Jérôme Casas+2 more|arXiv (Cornell University)|Sep 7, 2015

Mathematical and Theoretical Epidemiology and Ecology ModelsMedicine参考文献 43被引用 17

一句话总结

本文通过反应-扩散模型证明，在具有逻辑斯蒂猎物增长的空间显式捕食者-猎物系统中，泛化性天敌可通过捕食者搜索效率和功能性反应驱动的双稳态动力学，逆转害虫入侵，即使不存在阿列效应亦可实现空间控制，揭示了超越经典模型的生物防治新条件。

ABSTRACT

Reaction-diffusion analytical modeling of predator-prey systems has shown that specialist natural enemies can slow, stop and even reverse pest invasions, assuming that the prey population displays a strong Allee effect in its growth. Few additional analytical results have been obtained for other spatially distributed predator-prey systems, as traveling waves of non-monotonous systems are notoriously difficult to obtain. Traveling waves have indeed recently been shown to exist in predator-prey systems, but the direction of the wave, an essential item of information in the context of the control of biological invasions, is generally unknown. Preliminary numerical explorations have hinted that control by generalist predators might be possible for prey populations displaying logistic growth. We aimed to formalize the conditions in which spatial biological control can be achieved by generalists, through an analytical approach based on reaction-diffusion equations. The population of the focal prey - the invader - is assumed to grow according to a logistic function. The predator has a type II functional response and is present everywhere in the domain, at its carrying capacity, on alternative hosts. Control, defined as the invader becoming extinct in the domain, may result from spatially independent demographic dynamics or from a spatial extinction wave. Using comparison principles, we obtain sufficient conditions for control and for invasion, based on scalar bistable partial differential equations (PDEs). The searching efficiency and functional response plateau of the predator are identified as the main parameters defining the parameter space for prey extinction and invasion. Numerical explorations are carried out in the region of those control parameters space between the super-and subso-lutions, in which no conclusion about controllability can be drawn on the basis of analytical solutions. The ability of generalist predators to control prey populations with logistic growth lies in the bis-table dynamics of the coupled system, rather than in the bistability of prey-only dynamics as observed for specialist predators attacking prey populations displaying Allee effects. The consideration of space in predator-prey systems involving generalist predators with a parabolic functional response is crucial. Analysis of the ordinary differential equations (ODEs) system identifies parameter regions with monostable (extinction) and bistable (extinction or invasion) dynamics. By contrast, analysis of the associated PDE system distinguishes different and additional regions of invasion and extinction. Depending on the relative positions of these different zones, four patterns of spatial dynamics can be identified : traveling waves of extinction and invasion, pulse waves of extinction and heterogeneous stationary positive solutions of the Turing type. As a consequence, prey control is predicted to be possible when space is considered in additional situations other than those identified without considering space. The reverse situation is also possible. None of these considerations apply to spatial predator-prey systems with specialist natural enemies.

研究动机与目标

• 研究在具有逻辑斯蒂猎物增长的空间分布系统中，泛化性捕食者是否能够逆转害虫入侵。
• 确定在猎物不表现出阿列效应的情况下，空间生物防治可能成立的条件。
• 分析捕食者扩散、功能性反应和搜索效率在决定入侵或灭绝结果中的作用。
• 识别除经典单稳态或双稳态动力学外，出现的特定空间模式——如行进波、脉冲波和图灵型模式。
• 比较泛化性与特化性捕食者系统在空间控制背景下的动力学，突出空间在泛化性系统中的关键作用。

提出的方法

• 使用反应-扩散模型形式化该系统，其中猎物具有逻辑斯蒂增长，泛化性捕食者采用Ⅱ型功能性反应。
• 应用比较原理，通过标量双稳态PDE推导出猎物灭绝与入侵的充分条件。
• 分析相关常微分方程（ODE）系统，以识别单稳态（灭绝）与双稳态（灭绝或入侵）的参数区域。
• 将分析扩展至PDE系统，以检测额外的空间动力学，包括灭绝与入侵的行进波、脉冲波以及异质性静止解。
• 在解析结论不明确的上下解之间的参数空间区域进行数值探索。
• 运用行进波理论、稳定性分析和图灵不稳定性检测等数学工具，对空间模式进行分类。

实验结果

研究问题

• RQ1 当猎物呈逻辑斯蒂增长且无强烈阿列效应时，泛化性捕食者能否逆转害虫入侵？
• RQ2 决定控制或入侵结果的关键捕食者参数是什么？特别是搜索效率和功能性反应平台值。
• RQ3 与非空间或特化性捕食者系统相比，空间结构如何改变泛化性捕食者系统中捕食者-猎物的动力学？
• RQ4 在PDE系统中会涌现出哪些类型的空间模式（如行进波、脉冲波、图灵模式），它们对生物防治有何含义？
• RQ5 为何如先前模拟与田间观察所示，具有更高扩散系数的泛化性捕食者反而无法控制猎物？

主要发现

• 只要捕食者的搜索效率和功能性反应平台值足够高，泛化性捕食者即可在具有逻辑斯蒂猎物增长的系统中逆转害虫入侵。
• 实现控制的关键机制是捕食者-猎物耦合系统中的双稳态动力学，而非特化性捕食者系统中所见的仅由猎物引起的阿列效应。
• 四种不同的空间动力学被识别：灭绝与入侵的行进波、灭绝的脉冲波，以及图灵型异质性静止解。
• 考虑空间因素后，控制的参数空间显著扩大，揭示了非空间模型中不存在的新灭绝条件。
• 在中间参数区域（上下解之间）的数值探索证实了复杂空间模式的存在，这些模式无法仅通过ODE分析预测。
• 本研究证实，捕食者扩散速率相对于猎物扩散速率是关键因素，更高的捕食者扩散会降低控制效果——与先前的田间观察和模拟结果一致。