Seabird Habitat Patch Dynamics: Connecting Mathematical Models and Data

Henson，Hayward理解和预测组织数量在时间和空间上的波动是生态学中的一个基本问题。用数学模型准确地预测生态系统状态的能力将使精确的假设测试、阈值现象的预测和系统对干扰的响应的研究成为可能。就像在物理学中一样，主要的挑战包括确定异步的个人层面活动形成模式的规模、模式形成背后的机制以及适当的数据收集方法。在过去的几十年里，通过数学、统计学和实验室实验的结合，生态学取得了巨大的进步。动物数量的波动在很大程度上可以用简单的规则来解释，这一假设已经在对照的实验室研究中得到了严格和成功的检验。稳健的定性和定量预测已成为几个实验室系统的可能，但这一成功并未在该领域复制。调查人员希望将这一成功推广到该领域。田野系统预测数学模型的存在，以及非线性动力学理论在田野中的成功检验，将构成生态学的一大进步。在前期工作中，研究人员使用动力系统理论的技术来解释和预测海鸟在三个时间尺度上占据斑块的动态。基于这一成功，他们现在1)开发了一个准确的海鸟在不同生境斑块系统中空间分布动态的数学预测模型，2)在实地严格测试了非线性动力学理论，3)通过发展一种紧密的跨学科垂直整合范例来减少数学和生物学之间的鸿沟。活动的整合分为三个层次，包括跨学科研究，大量的本科生参与，以及为本科生制定量化识字计划。本科生与研究人员在一个研究团队中的合作预计将导致学生发表论文和发表演讲。数学和生物课程都训练学生掌握适用于生物的基本数学技巧。预测在特定时间内有多少植物或动物在某一特定栖息地死亡，这可能有助于解决与疾病传播、粮食生产、生物防治、环境保护、物种保护、国防活动与野生动物之间的干扰以及人类人口增长有关的许多紧迫的世界问题。数学方程已经被用来准确地预测实验室中的生物体数量，但这样的成功还没有推广到实验室以外的种群。在前期工作中，研究人员设计了一个数学方程，准确地预测了占据华盛顿州保护区国家野生动物保护区特定栖息地的海鸟数量的波动。给定一年中的某一天，潮汐的高度，以及未来某一特定时间的太阳高度，该方程预测了届时占据栖息地的海鸟的数量。对该方程预测未来几个月的能力进行了测试和验证。研究人员扩展了这项技术，以预测整个相互连接的栖息地网络中的波动。这些鸟没有受到任何干扰；它们是从海鸟聚居地以西100米多的悬崖上33米高的观测点上通过望远镜计数的。这项研究涉及1)数学家和生物学家之间的合作，2)本科生广泛的研究参与，3)为数学和生物本科生制定非数学素养计划。

Henson, Hayward Understanding and predicting fluctuations in numbers oforganisms in time and space is a fundamental issue in ecology.The ability to accurately forecast the state of ecosystems withmathematical models would enable, for example, rigoroushypothesis testing, prediction of threshold phenomena, andinvestigation of system response to disturbance. As in physics,the primary challenges include the identification of scales atwhich asynchronous individual-level activities form patterns,mechanisms behind pattern formation, and appropriate methods ofdata collection. During the last few decades, enormous progresshas been made in ecology through the integration of mathematics,statistics, and laboratory experiments. The hypothesis thatfluctuations in animal abundance are explainable largely bysimple rules has been rigorously and successfully tested incontrolled laboratory studies. Robust qualitative andquantitative prediction has become possible for severallaboratory systems, but this success has not been duplicated inthe field. The investigators wish to extend this success to thefield. The existence of a predictive mathematical model for afield system, and a successful test of nonlinear dynamics theoryin the field, would constitute a major advance in ecology. Inpreliminary work the investigators used the techniques ofdynamical systems theory to explain and predict the dynamics ofpatch occupancy by seabirds at three temporal scales. Based onthis success, they now 1) develop an accurate mathematicalpredictive model of the spatial distribution dynamics of seabirdsin a heterogeneous system of habitat patches, 2) rigorously testnonlinear dynamics theory in the field, and 3) reduce the schismbetween mathematics and biology by developing a paradigm of tightinterdisciplinary vertical integration. Integration of activitiesis three-tiered, including interdisciplinary research,substantial undergraduate participation, and development of aquantitative literacy program for undergraduates. Collaborationof undergraduates in a research team with the investigators isexpected to lead to publication and presentations by thestudents. Courses in both mathematics and biology train studentsin basic mathematical techniques applicable to biology. The ability to predict how many plants or animals willoccupy a certain habitat at a given time could help solve manypressing world problems related to the spread of disease, foodproduction, biological control, environmental protection, speciesconservation, interference between national defense activitiesand wildlife, and human population growth. Mathematical equationshave been used to accurately predict numbers of organisms in thelaboratory, but such successes have not been extended topopulations outside the laboratory. In preliminary work, theresearchers devised a mathematical equation that accuratelypredicts fluctuations in the number of seabirds occupying aspecific habitat on Protection Island National Wildlife Refuge,Washington. Given the day of the year, the height of the tide,and the solar elevation for some specific time in the future, theequation predicts the number of seabirds that will occupy thehabitat at that time. The ability of the equation to predictseveral months into the future was tested and validated. Theresearchers expand this technique to predict fluctuations withinan entire network of connected habitats. The birds are notdisturbed in any way; they are counted through a scope from a33-m-high observation point on a bluff more than 100 m west ofthe seabird colony. The research involves 1) collaborationbetween mathematicians and biologists, 2) extensive researchparticipation by undergraduate students, and 3) development of abiomathematics literacy program for both mathematics and biologyundergraduate students.