QEIB: Using Phase Dynamics and a Model Experimental System to Understand the Effects of Extrinsic Variability on Predator and Prey Metapopulations

在大范围的地理区域内，人口密度的周期是同步的，或者说是同步的，这是人口生物学中最引人注目的现象。理论上，这种同步性要么是由广泛的气象因素造成的，要么是由种群之间的个体移动造成的。理论的捕食者-猎物的集合种群，扩展到群体的patchesalso链接同步区域持久性。对自然界中这些现象的研究由于难以确定种群周期的原因以及环境因素和斑块间运动在改变种群波动和同步性方面的作用而受到阻碍。这里探讨的集合种群的环境强迫与害虫物种的生物控制和保护有关。此外，由全球变暖引起的极端天气事件有可能使区域人口同步，这可能会缩短区域持续性。拟议的工作使用专注于相位动态的数学技术来分析同步性，并在环境变化，种群动态和灭绝之间建立精确的联系。相动力学已被广泛应用于神经生物学，但其在生态学中的潜力才刚刚开始实现。该项目为生态学观众开发了新的分析工具，并在实验室微观世界中使用了一个模型实验系统，细菌和原生动物，以弥合种群和集合种群理论之间的差距。这项工作从经典模型开始，然后发展更精确和生物学上更真实的模型，这反过来又将推动进一步的、更精确的实验测试。由随机扩散耦合的两斑块捕食者-猎物系统将提供一个与解析解的联系，数值模拟和实验可以建立在此基础上来考虑更复杂和现实的情况。两个斑块模型将被用来推导方程的关系相，在捕食者-食饵循环的点，人口动态过程。两个斑块之间的相位差的动力学将被导出并用作同步性的度量，这可以与区域持久性和斑块内捕食者-被捕食者动力学有关。相态动力学还可以区分持久性是否不是由确定性平衡动力学（大多数理论研究的焦点）控制的，而是由长寿命的瞬态动力学控制的，这可能在生态相关的时间尺度上占主导地位;特别是通过时间的相态差回归将用于计算瞬态动力学的持续时间，当相态差变为零时。在实验上，在两个相连的补丁的捕食者-猎物振荡的初始相位差将被操纵，在每个补丁中启动不同的捕食者和猎物密度的微观世界。统计将量化斑块之间的相位差，并测试其与区域持续时间的相关性。在微观世界中重复这一过程，在斑块之间具有不同的运动速率（走廊的长度），将测试斑块之间的运动速率增加将减少相位差和区域持续时间的预测。1-8块补丁的实验将通过温度波动来操纵环境变化，并控制这是在一个区域内均匀运行还是仅在单个补丁中运行。区域持续时间和斑块之间的相位差的量化将检验预测，局部变异增强区域持续性，但区域变异和增加的运动减少regionalvariability.这个项目将展示如何以及为什么环境变异影响区域分布的捕食者和猎物系统的dynamicsand灭绝。将向更广泛的生态学受众介绍阶段性生态学技术，并对两名研究生进行必要的数学、建模、统计和实验技术培训，以了解环境与人口之间的联系。这项工作将提供一个范例，在未来结合实验和理论研究的人口同步性和持久性可以建立。

Population density cycles that appear synchronous, or irin-phasel, over large geographic areasare some of the most striking phenomena in population biology. In theory, such synchrony iscaused either by widespread meteorological factors, or by movement of individuals betweenpopulations. Theory for predator-prey 'metapopulationsl' that extend over groups of patchesalso links synchrony to regional persistence. The study of these phenomena in nature has beenhampered by difficulty in identifying both the cause of population cycles and the roles ofenvironmental factors and interpatch movement in modifying population fluctuations andsynchrony. The environmental forcing of metapopulations which is explored here is relevant tobiological control of pest species and conservation. Additionally, extreme weather eventscaused by global warming have the potential to synchronize regional populations, which mightcut short regional persistence. The proposed work uses mathematical techniques focused onphase dynamics to analyze synchrony and build precise links among environmental variability,population dynamics and extinction. Phase dynamics have been widely used in neurobiology,but their potential in ecology is only just beginning to be realized. This project develops newanalytic tools for an ecological audience and uses a model experimental system, bacteria andprotozoa in laboratory microcosms, to bridge the gap between populations and metapopulationtheory. The work starts with a classic model and then develops more precise and biologicallyrealistic models, which in turn will fuel further, more precise, experimental tests.Two-patch predator-prey systems coupled by random dispersal will provide a link withanalytical solutions, which numerical simulations and experiments can build on to consider morecomplex and realistic situations. Two patch models will be used to derive equations which relatephase, the point in a predator-prey cycle, to population dynamic processes. The dynamics ofphase difference between two patches will be derived and used as a measure of synchrony,which can be related to regional persistence and within-patch predator-prey dynamics. Phasedynamics can also distinguish whether persistence is controlled not by deterministic equilibriumdynamics (the focus of most theoretical studies), but instead by long-lived transient dynamicswhich may dominate during ecologically relevant time scales; specifically regression of phasedifference through time will be used to calculate the duration of transient dynamics, when phasedifference becomes zero. Experimentally, the initial phase difference of predator-preyoscillations in two linked patches will be manipulated by starting microcosms with differentpredator and prey densities in each patch. Statistics will then quantify the phase differencebetween patches and test its correlation with regional persistence time. Repeating thisprocedure in microcosms with different movement rates between patches (lengths of corridors)will test the prediction that increased movement rate between patches will reduce phasedifferences and regional persistence time. Experiments with 1-8 patches will manipulateenvironmental variability through temperature fluctuations and control whether this operatesuniformly across a region or just in a single patch. Quantification of regional persistence timeand phase differences between patches will then test the predictions that local variabilityenhances regional persistence, but regional variability and increased movement reduce regionalvariability.This project will demonstrate how and why environmental variability influences dynamicsand extinction in regionally-distributed predator and prey systems. The techniques of phasedynamics will be brought to a broader ecological audience, and two graduate students will betrained with the necessary mathematical, modeling, statistical and experimental techniques thatare required to understand the links between the environment and populations. This work willprovide a paradigm on which future combined experimental and theoretical studies of populationsynchrony and persistence can build.