Formulation and Analysis of Deterministic Models of Predation Among Acarine Populations

点击翻译按钮获取中文摘要

Gardner The investigator develops and analyzes models of persistentbehavior of locally self-annihilating populations of predatoryand herbivorous mites. The project is stimulated by Huffaker'sclassic experiment, which provided the first demonstration of themediating role of spatial processes in certain ecologicalinteractions. Huffaker noted that synchronies in the phases ofpopulation cycles of localized aggregates within host plants ofherbivorous mites and of the mites that preyed upon themoccasionally spread over an entire area, but that the synchronycan be broken by demographic and environmental stochasticity. Heconjectured that the complementary regularizing mechanisms thatgenerate synchrony, and the complementary stochastic mechanismsthat generate asynchrony, together generate the complex waves andpatterns seen in these predator-prey interactions in nature.Existing stochastic patch models have been formulated thatsuccessfully simulate complex, and evidently chaotic,spatio-temporal patterns that have typically accompaniedpersistent dynamics. Accordingly, such models have difficulty inproviding reliable predictions of behavior due to the largevariance seen in replicate data sets. This substantially limitstheir practical application to the biological control of croppests. In previous work, the investigator formulated a family ofdeterministic models, including an idealized paradigm defining aclass of reaction-diffusion systems. He studies two generalissues relating to the analysis and practical applications of thereaction-diffusion system and related models. First, heinvestigates the presence of several distinct families of stablewaves and spatial patterns of these equations, theirinstabilities and bifurcations, and the presence of exoticwave-like patterns. By combined analytical and approximatemethods, he describes theoretical mechanisms by which suchunstable waves can form the organizing center of spatio-temporalchaos, while in other regimes, complex but non-chaotic, stablespatio-temporal patterns appear spontaneously. A second topicconcerns the derivation of the model, which is based onexperiment. This addresses the manner in which thereaction-diffusion model simulates stochasticity throughpostulated low-density thresholds in the growth rates. Theinvestigator studies hybrid numerical procedures addressing thecrucial issue of parameter estimation, which can be problematicboth for stochastic patch models and for the reaction-diffusionmodel, but at opposite spatio-temporal scales. For example, thelow-density thresholds involve the micro-local dynamics of asmall number of individuals, whereas large-scale emigration overlarge regions is difficult to measure in a laboratory. However,simple stable waves may suggest one instance in which this may bepossible. The investigator examines this in numericalsimulations with patch models, which may form the basis for newand simpler experimental designs that can detect such behavior.Together, these two approaches present a unified picture of how"dynamic stochasticity" driven by the presence of certainunstable waves and spatio-temporal patterns is theoreticallylinked to parameters of population change governing behavior atthe smallest micro-local scales, and thus the generation ofasynchrony through demographic and environmental stochasticity. Plant-eating mites, and the mites that eat them in turn,often show cycles of growth and decline in numbers that areclosely related. Sometimes the populations decline rapidly tonear-extinction levels. But in a classic experiment Huffaker andcolleagues showed that these strongly coupled cycles can bemoderated by small changes in demographic or geographic factors,leading to a long-term survival of both species that shows itselfin patterns, in time and space, of the numbers of predator andprey mites. Of course, when the prey mite is eating a valuablecrop, one wants both mite populations to go extinct. So issues ofhow mite populations vary together are of considerable practicalimportance in the biological control of crop pests. The economicimpact of phytophageous species is considerable, and although theuse of predatory mites as a biological control is widespread incertain local agricultures, many agricultural enterprises rely onchemical pest controls. Chemical controls provide a short-termsolution, but have many damaging long-term effects. However, therisks and uncertainties of biological pest control are difficultto quantify due to their complex and unpredictable patterns ofbehavior. The investigator's numerical simulations indicate thepresence of many different kinds of chaos, some of which achievebetter levels of suppression of both herbivore populations andcrop damage. The project explores new theoretical andcomputational tools that may find practical application in thebiological control of crop pests and, in other contexts, ininoculative control of certain exotic species.