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

University Of California-Davis, Davis CA

Investigators

Abstract

Population density cycles that appear synchronous, or irin-phasel, over large geographic areas are some of the most striking phenomena in population biology. In theory, such synchrony is caused either by widespread meteorological factors, or by movement of individuals between populations. Theory for predator-prey 'metapopulationsl' that extend over groups of patches also links synchrony to regional persistence. The study of these phenomena in nature has been hampered by difficulty in identifying both the cause of population cycles and the roles of environmental factors and interpatch movement in modifying population fluctuations and synchrony. The environmental forcing of metapopulations which is explored here is relevant to biological control of pest species and conservation. Additionally, extreme weather events caused by global warming have the potential to synchronize regional populations, which might cut short regional persistence. The proposed work uses mathematical techniques focused on phase 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 new analytic tools for an ecological audience and uses a model experimental system, bacteria and protozoa in laboratory microcosms, to bridge the gap between populations and metapopulation theory. The work starts with a classic model and then develops more precise and biologically realistic models, which in turn will fuel further, more precise, experimental tests. Two-patch predator-prey systems coupled by random dispersal will provide a link with analytical solutions, which numerical simulations and experiments can build on to consider more complex and realistic situations. Two patch models will be used to derive equations which relate phase, the point in a predator-prey cycle, to population dynamic processes. The dynamics of phase 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. Phase dynamics can also distinguish whether persistence is controlled not by deterministic equilibrium dynamics (the focus of most theoretical studies), but instead by long-lived transient dynamics which may dominate during ecologically relevant time scales; specifically regression of phase difference through time will be used to calculate the duration of transient dynamics, when phase difference becomes zero. Experimentally, the initial phase difference of predator-prey oscillations in two linked patches will be manipulated by starting microcosms with different predator and prey densities in each patch. Statistics will then quantify the phase difference between patches and test its correlation with regional persistence time. Repeating this procedure in microcosms with different movement rates between patches (lengths of corridors) will test the prediction that increased movement rate between patches will reduce phase differences and regional persistence time. Experiments with 1-8 patches will manipulate environmental variability through temperature fluctuations and control whether this operates uniformly across a region or just in a single patch. Quantification of regional persistence time and phase differences between patches will then test the predictions that local variability enhances regional persistence, but regional variability and increased movement reduce regional variability. This project will demonstrate how and why environmental variability influences dynamics and extinction in regionally-distributed predator and prey systems. The techniques of phase dynamics will be brought to a broader ecological audience, and two graduate students will be trained with the necessary mathematical, modeling, statistical and experimental techniques that are required to understand the links between the environment and populations. This work will provide a paradigm on which future combined experimental and theoretical studies of population synchrony and persistence can build.