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

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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.