Evolutionary responses to limiting factors in heterogeneous environments

所有生物都有潜力产生后代，其数量呈指数增长，但最终由于限制繁殖成功的各种因素的作用而无法实现。 生态学领域主要致力于研究这些限制因素。 关于特定微生物、植物和动物分类群的不同潜在限制因素的相对重要性的争论弥漫在进化生态学文献中;突出的例子包括死亡率的外在与内在来源，生物体生长所需的不同宏量和微量营养素，生物体不同关键结构特征的物理磨损或破坏，种群调节中的资源与捕食者，植物的花粉与资源限制，昆虫的卵与宿主限制。虽然已经取得了重要的进展，发展理论，以解决这些争论在特定的背景下，这些理论的治疗已经发展孤立于彼此。然而，这些争论中的许多都有一个共同的逻辑结构：焦点生物生活在异质环境中，具有有限的代谢资源池来改善多种限制因素，并且不能立即调整代谢分配以完美地匹配环境。 本计画将发展一个具有此逻辑结构的演化问题分析的一般数学架构，并将此架构应用于演化生态学中几个主要限制因子的争论，并将模型预测与经验数据对抗。数学框架将提供广泛适用的方法在随机过程和动力系统的接口。这些方法将被用来了解（i）昆虫是否受到有限的卵供应或短寿命的限制，以定位主机和（ii）植物是否受到其吸引传粉者的能力或繁殖的其他方面的限制。为了建立理论与自然界之间的对话，将收集和分析有关卵限制和花粉限制的数据，以评估理论。保护和恢复生态学家感兴趣的是预测动物和植物对环境变化的反应，并能够操纵这些反应以达到有益的目的。该项目将通过提供对生物体如何响应可能限制繁殖成功的不同因素而进化的更深入理解来促进这些目标。一个适应性始终受到某一特定因素限制的生物种群，将对该因素的扰动作出可预见的反应。另一方面，适应性在不同时间或地点受到不同因素限制的生物种群对扰动的反应较难预测。该项目的一个关键主题是花粉限制，这与有记录的全球授粉昆虫（如蜜蜂）数量的下降有直接关系。 这些种群数量的下降威胁着世界范围内的植物群落和作物产量。该项目的成果将被纳入一门关于授粉生态学的新课程，纳入两本关于微积分和建模应用于生命科学的教科书，并纳入生物学学生的入门课程。此外，本科生，研究生和博士后助理将以垂直整合的方式进行培训。

All organisms have the potential to produce descendants whose numbers grow exponentially, but are eventually prevented from doing so by the action of various factors that limit reproductive success. The field of ecology is largely devoted to the study of these limiting factors. Debates concerning the relative importance of different potentially limiting factors for particular microbe, plant, and animal taxa pervade the evolutionary ecology literature; prominent examples include extrinsic versus intrinsic sources of mortality, different macro- and micronutrients required for organismal growth, physical wear or breakage of different key structural features of an organism, resources versus predators in population regulation, pollen versus resource limitation in plants, and egg versus host limitation in insects. While important progress has been made developing theory to resolve these debates in particular contexts, these theoretical treatments have been developed in isolation from one another. Many of these debates, however, share a common logical structure: the focal organism lives in a heterogeneous environment, has a finite pool of metabolic resources to ameliorate multiple limiting factors, and can not instantaneously adjust metabolic allocations to perfectly match the environment. This project will develop a general mathematical framework for analyzing evolutionary problems with this logical structure, apply this framework to several major limiting factor debates in evolutionary ecology, and confront the modeling predictions with empirical data. The mathematical framework will provide broadly applicable methods at the interface of stochastic processes and dynamical systems. These methods will be used to understand (i) whether insects are limited by a finite supply of eggs or a short lifespan to locate hosts and (ii) whether plants are limited by their ability to attract pollinators or by other aspects of reproduction. To establish a dialogue between the theory and the natural world, data on egg limitation and pollen limitation will be collected and analyzed to evaluate the theory. Conservation and restoration ecologists are interested in anticipating the responses of animals and plants to changing environments and in being able to manipulate those responses to beneficial ends. This project will contribute to these goals by providing a deeper understanding of how organisms evolve in response to different factors that may limit reproductive success. A population of organisms whose fitness is consistently limited by one particular factor will respond predictably to perturbations of that factor. On the other hand, a population of organisms whose fitness is limited by different factors at different times or places will respond to perturbations less predictably. A key topic of this project, pollen limitation, has direct bearing on documented global declines in the populations of pollinating insects such as bees. These population declines threaten plant communities and crop productivity world wide. Results from this project will be incorporated into a new course on pollination ecology, into two textbooks dealing with calculus and modeling as applied to the life sciences, and into entry-level courses for biology students. Moreover, undergraduates, graduate students, and post-doctoral associates will be trained in a vertically integrated manner.