Mathematical Modeling in Biology: A Research Methods Approach is a textbook written primarily for advanced mathematics and science undergraduate students and graduate-level biology students. Although the applications center on ecology, the expertise of the authors, the methodology can be imported to any other science, including social science and economics. The aim of the book, beyond being a useful aid to teaching and learning the core modelling skills needed for mathematical biology, is to encourage students to think deeply and clearly about the meaning of mathematics in science and to learn significant research methods. Most importantly, it is hoped that students will experience some of the excitement of doing research.
I. Introduction to Modeling
1. Mathematical Modeling
2. Avian Bone Growth: A Case Study
II. Discrete-Time Models
3. Discrete-Time Maps
4. Chaos: Simple Rules Can Generate Complex Results
5. Higher Dimensional Discrete-time Models
6. Flour Beetle Dynamics: A Case Study
III. Continuous-time Models
7. Introduction to Differential Equations
8. Scalar Differential Equations
9. Systems of Differential Equations
10. Seabird Behavior: A Case Study
IV. Regression Models
11. Regression Models
12. Climate Change and Seabird Cannibalism: A Case Study
A.Linear Algebra Basics
B. MATLAB: The Basics
C. Connecting Models to Data: A Brief Summary with Sample Codes
Shandelle M. Henson is a Professor of Mathematics and Professor of Ecology at Andrews University, Michigan, USA. She uses dynamical systems theory and bifurcation theory to study nonlinear population dynamics and the effects of climate change on marine organisms. Shandelle earned a PhD in mathematics at the University of Tennessee, Knoxville and did several years of postdoctoral work at the University of Arizona. She serves as editor-in-chief of the journal Natural Resource Modeling and is a co-author of the book Chaos in Ecology: Experimental Nonlinear Dynamics (Academic Press 2003) which documented chaotic dynamics in laboratory populations of insects.
James L. Hayward is a Professor Emeritus of Biology at Andrews University, Michigan, USA. He earned a PhD in zoology from Washington State University, and he has studied the behaviours and population dynamics of marine birds and mammals in the Pacific Northwest of North America since he began graduate studies in 1972. In addition, Jim has studied the behaviour of marine iguanas and flightless cormorants on the remote and uninhabited island of Fernandina, the westernmost island in the Galapagos. He also is a recognized expert in the fossilization of eggshells in birds and dinosaurs.
Shandelle and Jim, a wife-husband research team, are widely published in both the technical and popular literature, and both have won awards for their teaching. They have applied mathematical methods to the behavioural dynamics of seabirds at Protection Island National Wildlife Refuge in the Strait of Juan de Fuca, Washington, USA since 2002. They reside in Niles, Michigan, USA and they have a daughter, son-in-law, and four grandsons. They enjoy hiking, geology, art, music, and literature.