Seabird Habitat Patch Dynamics: Connecting Mathematical Models and Data

Andrews University, Berrien Springs MI

Investigators

Abstract

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