RUI: The Dynamics of Biological Invasions

Schreiber0077986研究员开发了差分式和微分式模型的数学方法，以更好地预测生物入侵在什么条件下成功，以及成功入侵对生态群落结构的影响。重点介绍了避免种群方程结构扰动的方法，以及适用于具有非线性动力学(如周期性、准周期性和混沌)的系统的方法。这些方法涉及平滑遍历理论的技术的使用和发展，并将这些方法应用于寄主-寄生蜂相互作用和三营养食物网的模型。研究了寄主-寄生蜂相互作用的两个方面。首先，由于寄生蜂在寄主密度高度可变的系统中释放时会有卵限制(外来昆虫达到害虫状态时的典型情况)，因此考虑了一个包含这种卵限制的寄主-寄生蜂相互作用模型。由于成功的生物防治只有在寄生蜂种群建立后才能发生，因此对该模型的拟议分析旨在确定寄主种群动态的变异性如何影响寄生蜂种群的侵袭率。其次，将前人关于寄主-寄生蜂系统中斑块选择策略的协同进化的工作扩展到包括两个重要的生物学因素，即寄生蜂的性别分配策略和植物动态。关键问题是，操纵作物异质性是否能导致行为性状的共同进化，同时稳定系统并增加农田。第三，为了更好地了解入侵导致的生态群落如何聚集，这一建议进行了三营养化系统的研究，每个营养层都有一个以上的物种。在这些系统中，三种生态力量(明显的竞争、资源竞争和行会内的捕食)发挥着重要作用，并可能导致演替的不传递性(例如，一系列入侵将群落A带到群落B，把B带到C，把C带回A)。重点放在栖息地生产力和入侵时机对群落组装过程的影响。此外，该项目还包括一个旨在刺激本科生研究的项目。入侵美国的非本土物种每年给美国农业、林业和其他几个经济领域造成约1380亿美元的经济损失。据估计，仅外来昆虫物种每年就造成130亿美元的农作物损失，其中约42%的濒危物种名单上的物种正处于危险之中，主要是因为非本地物种。由于生物入侵通常涉及几个物种之间的非线性相互作用，数学模型作为简单的漫画，允许人们以低廉的成本回答这样的问题：什么特征使一个物种成为成功的入侵者？哪些生态群落在入侵后最容易受到巨大的长期变化的影响？如何才能操纵作物异质性，将非本地害虫的经济影响降至最低？该项目建议开发分析方法，并将这些方法应用到模型中，以解决这些和其他当前对群落生态学、恢复生态学、生物防治和进化生物学感兴趣的问题。

Schreiber0077986 The investigator develops mathematical methods fordifference and differential equation models to better predictunder what conditions biological invasions succeed and theimplications of successful invasions on the structure ofecological communities. An emphasis is placed on methods that arerobust to structural perturbations of the population equationsand that apply to systems with nonlinear dynamics (e.g.,periodicity, quasiperiodicity, and chaos). The methods involvethe use and development of techniques from smooth ergodic theory.Application of these methods to models of host-parasitoidinteractions and tritrophic food webs is pursued. Two aspects ofhost-parasitoid interactions are examined. First, becauseparasitoids experience egg limitation when released in systemswith highly variable host densities (the typical situation whenan exotic insect has reached pest status), a model ofhost-parasitoid interactions that incorporates thisegg-limitation is considered. As successful biological controlonly occurs after a parasitoid population has established itself,the proposed analysis of the model intends to determine howvariability in the dynamics of the host population influences theinvasion rate of the parasitoid population. Second, previous workon the coevolution of patch selection strategies inhost-parasitoid systems is extended to include two importantbiological factors, the sex-allocation strategies of parasitoidsand plant dynamics. The key issue is whether the manipulation ofcrop heterogeneity can lead to the coevolution of behavioraltraits that simultaneously stabilize the system and increase cropyields. Third, to better understand how ecological communitiesassemble due to invasions, this proposal undertakes the study oftritrophic systems with more than one species at each trophiclevel. In these systems, three ecological forces (apparentcompetition, resource competition and intraguild predation) playan important role and can lead to successional intransitivites(e.g., a sequence of invasions that takes community A tocommunity B, B to C and C back to A). Emphasis is placed on theinfluence of habitat productivity and the timing of invasions onthe community assembly process. In addition, the project includesa program designed to stimulate undergraduate research. Invading non-native species in the United States causeestimated economic losses of 138 billion dollars annually inagriculture, forestry and several other segments of the U.S.economy. Exotic insect species alone are estimated to cause 13billion dollars in crop losses annually and approximately 42% ofthe species on the threatened or endangered species lists are atrisk primarily because of nonnative species. As biologicalinvasions often involve nonlinear interactions between severalspecies, mathematical models, as simple caricatures, allow one toinexpensively answer questions such as: What characteristics makea species a successful invader? Which ecological communities aremost susceptible to large long-term changes following aninvasion? How can crop heterogeneity be manipulated to minimizethe economic impact of non-native pests? The project proposes todevelop analytical methods, and to apply these methods to modelsthat address these and other questions of current interest tocommunity ecology, restoration ecology, biological control, andevolutionary biology.