Seabird Habitat Patch Dynamics: Connecting Mathematical Models and Data

理解和预测生物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，严格的假设检验，阈值现象的预测，以及系统对干扰的响应的调查成为可能。正如在物理学中一样，主要的挑战包括确定异步个人层面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验证。可靠的定性和定量预测已经成为几个实验室系统的可能，但这一成功尚未在该领域复制。研究人员希望将这一成功推广到现场。野外系统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验证，将构成生态学的重大进步。在前期工作中，研究者运用动力系统理论的方法，在三个时间尺度上对海鸟占用斑块的动态进行了解释和预测。基于这一成功，他们现在1)建立了海鸟在栖息地斑块异质系统中的空间分布动态的精确数学预测模型，2)严格测试了该领域的非线性动力学理论，3)通过建立紧密跨学科垂直整合的范式来减少数学与生物学之间的分裂。整合活动的三个层次，包括跨学科的研究，大量的本科生参与，并为本科生制定定量的扫盲计划。研究小组的本科生与研究人员的合作有望导致学生发表论文和演讲。数学和生物学课程培养学生应用于生物学的基本数学技术。预测在特定时间有多少植物或动物将占据某一栖息地的能力将有助于解决许多紧迫的世界性问题，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里的生物数量，但这样的成功还没有推广到实验室外的种群。在初步工作中，研究人员设计了一个数学方程，可以准确预测占据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。给定一年中的哪一天，潮水的高度，以及未来某个特定时间的太阳高度，这个方程就能预测到那个时间占据栖息地的海鸟的数量。该方程预测未来几个月的能力得到了测试和验证。研究人员将这项技术扩展到预测整个连接栖息地网络内的波动。鸟儿没有受到任何干扰；在海鸟聚居地以西100多米的悬崖上，有一个33米高的观测点，通过一个瞄准镜对它们进行计数。该研究涉及1)数学家和生物学家之间的合作，2)本科生广泛参与研究，3)为数学和生物学本科生制定生物数学素养计划。

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.