NSF Award
0314512
Henson, Hayward<br/> Understanding and predicting fluctuations in numbers of<br/>organisms in time and space is a fundamental issue in ecology.<br/>The ability to accurately forecast the state of ecosystems with<br/>mathematical models would enable, for example, rigorous<br/>hypothesis testing, prediction of threshold phenomena, and<br/>investigation of system response to disturbance. As in physics,<br/>the primary challenges include the identification of scales at<br/>which asynchronous individual-level activities form patterns,<br/>mechanisms behind pattern formation, and appropriate methods of<br/>data collection. During the last few decades, enormous progress<br/>has been made in ecology through the integration of mathematics,<br/>statistics, and laboratory experiments. The hypothesis that<br/>fluctuations in animal abundance are explainable largely by<br/>simple rules has been rigorously and successfully tested in<br/>controlled laboratory studies. Robust qualitative and<br/>quantitative prediction has become possible for several<br/>laboratory systems, but this success has not been duplicated in<br/>the field. The investigators wish to extend this success to the<br/>field. The existence of a predictive mathematical model for a<br/>field system, and a successful test of nonlinear dynamics theory<br/>in the field, would constitute a major advance in ecology. In<br/>preliminary work the investigators used the techniques of<br/>dynamical systems theory to explain and predict the dynamics of<br/>patch occupancy by seabirds at three temporal scales. Based on<br/>this success, they now 1) develop an accurate mathematical<br/>predictive model of the spatial distribution dynamics of seabirds<br/>in a heterogeneous system of habitat patches, 2) rigorously test<br/>nonlinear dynamics theory in the field, and 3) reduce the schism<br/>between mathematics and biology by developing a paradigm of tight<br/>interdisciplinary vertical integration. Integration of activities<br/>is three-tiered, including interdisciplinary research,<br/>substantial undergraduate participation, and development of a<br/>quantitative literacy program for undergraduates. Collaboration<br/>of undergraduates in a research team with the investigators is<br/>expected to lead to publication and presentations by the<br/>students. Courses in both mathematics and biology train students<br/>in basic mathematical techniques applicable to biology.<br/> The ability to predict how many plants or animals will<br/>occupy a certain habitat at a given time could help solve many<br/>pressing world problems related to the spread of disease, food<br/>production, biological control, environmental protection, species<br/>conservation, interference between national defense activities<br/>and wildlife, and human population growth. Mathematical equations<br/>have been used to accurately predict numbers of organisms in the<br/>laboratory, but such successes have not been extended to<br/>populations outside the laboratory. In preliminary work, the<br/>researchers devised a mathematical equation that accurately<br/>predicts fluctuations in the number of seabirds occupying a<br/>specific habitat on Protection Island National Wildlife Refuge,<br/>Washington. Given the day of the year, the height of the tide,<br/>and the solar elevation for some specific time in the future, the<br/>equation predicts the number of seabirds that will occupy the<br/>habitat at that time. The ability of the equation to predict<br/>several months into the future was tested and validated. The<br/>researchers expand this technique to predict fluctuations within<br/>an entire network of connected habitats. The birds are not<br/>disturbed in any way; they are counted through a scope from a<br/>33-m-high observation point on a bluff more than 100 m west of<br/>the seabird colony. The research involves 1) collaboration<br/>between mathematicians and biologists, 2) extensive research<br/>participation by undergraduate students, and 3) development of a<br/>biomathematics literacy program for both mathematics and biology<br/>undergraduate students.
