Seabird Habitat Patch Dynamics: Connecting Mathematical Models and Data

海沃德？亨森 理解和预测生物体数量在时间和空间上的波动是生态学的一个基本问题。用数学模型准确预测生态系统状态的能力将使例如严格假设检验、阈值现象预测和系统对干扰的反应研究成为可能。 在物理学中，主要的挑战包括识别异步个人水平活动形成模式的尺度，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，这一假设已经在受控的实验室研究中得到了严格和成功的检验。 强有力的定性和定量预测已经成为可能的几个实验室系统，但这一成功还没有复制在外地。 研究人员希望将这一成功推广到野外。 野外系统的预测数学模型的存在，以及非线性动力学理论在野外的成功试验，将构成生态学的一个重大进步。 在初步工作中，调查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的斑块占据动态。 基于这一成功，他们现在1）在栖息地斑块的异质系统中开发一个精确的海鸟空间分布动态的预测模型，2）在该领域严格测试非线性动力学理论，3）通过开发一个紧密的跨学科垂直整合的范式来减少数学和生物学之间的分裂。 活动的整合有三个层次，包括跨学科研究，大量的本科生参与，以及为本科生制定定量扫盲计划。 研究团队中的本科生与研究人员的合作有望导致学生的出版和演讲。 数学和生物学课程都训练学生应用于生物学的基本数学技巧。 预测在特定时间有多少动植物会占据某一栖息地的能力，可以帮助解决许多紧迫的世界问题，这些问题与疾病传播、粮食生产、生物控制、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口增长有关。 数学方程已经被用来准确地预测实验室中的生物数量，但这种成功还没有扩展到实验室外的种群。 在初步工作中，研究人员设计了一个数学方程，可以准确地预测在华盛顿保护岛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，以及未来某个特定时间的太阳高度，这个方程就可以预测出在那个时候占据栖息地的海鸟数量。 该方程预测未来几个月的能力进行了测试和验证。 研究人员将这种技术扩展到预测整个栖息地网络的波动。 这些鸟没有受到任何干扰;它们是在海鸟群以西100多米处的海崖上，从一个33米高的观察点通过瞄准镜计数的。 研究涉及1）数学家和生物学家之间的合作，2）本科生的广泛研究参与，3）数学和生物本科生的非生物数学素养计划的发展。

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.