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Full Description
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 modeling 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.
Features
Minimal pre-requisites beyond a solid background in calculus, such as a calculus I course.
Suitable for upper division mathematics and sciences students and graduate-level biology students.
Provides sample MATLAB codes and instruction in Appendices along with datasets available on https://bit.ly/3fcLF3D
Contents
I. Introduction to Modeling 1. Mathematical Modeling. 1.1. What You Should Know About This Chapter. 1.2 The modeling cycle. 1.3. Biology. 1.4. Mathematics. 1.5. Statistics. 1.6. Epistemology: How We Know. 1.7. Exercises. 2. Avian Bone Growth: A Case Study. 2.1. What you should know about this chapter. 2.2. Scientific Problem. 2.3. Translation into Mathematics. 2.4. Model Parametrization. 2.5. Model Selection. 2.6. Model Validation. 2.7. Exercises. II. Discrete-Time Models. 3. Discrete-Time Maps. 3.1. What you should know about this chapter. 3.2. Compartmental Model. 3.3. Linear Maps. 3.4. Nonlinear Maps. 3.5. Linearization. 3.6. The Ricker Nonlinearity. 3.7. Exercises. 4. Chaos: Simple Rules Can Generate Complex Results. 4.1. What you should know about this chapter. 4.2. Ricker Model Revisited. 4.3. New Paradigms Associated from Chaos. 4.4. May's Hypothesis. 4.5. Exercises. 5. Higher Dimensional Discrete-time Models. 5.1. What you should know about this chapter. 5.2. Intraspecific Interactions. 5.3. Interspecific Interactions. 5.4. Example of an Age-structured Single-Species Model. 5.5. Example of a Two-Species Model. 5.6. n-dimensional Linear Difference Equations. 5.7. Solving Linear Systems of Difference Equations. 5.8. Nonlinear Systems. 5.9. Exercises. 6. Flour Beetle Dynamics: A Case Study. 6.1. What you should know about this chapter. 6.2. Flour Beetles. 6.3. Data. 6.4. Assumptions. 6.5. Alternative Deterministic Models. 6.6. Stochastic Models. 6.7. Model Parametrization. 6.8. Model Selection. 6.9. Model Validation. 6.10. The "Hunt for Chaos" Experiments. 6.11. Exercises. III. Continuous-time Models 7. Introduction to Differential Equations. 7.1. What you should know about this chapter. 7.2. Compartmental Models. 7.3. Exercises. 8. Scalar Differential Equations. 8.1. What you should know about this chapter. 8.2. Linear Equations. 8.3. Nonlinear Equations. 8.4. Bifurcations. 8.5. Exercises. 9. Systems of Differential Equations. 9.1. What you should know about this chapter. 9.2. Linear Systems of ODEs and Phase Plane Analysis. 9.3. Nonlinear Systems of ODEs. 9.4. Limit Cycles, Cycle Chains, and Bifurcations. 9.5. Lotka-Volterra Models and Nullcline Analysis. 9.6. Exercises. 10. Seabird Behavior: A Case Study. 10.1. What you should know about this chapter. 10.2. The Scientific Problem. 10.3. Historical Data. 10.4. General Model. 10.5. Alternative Models. 10.6. Model Parametrization. 10.7. Model Selection. 10.8. Model Validation. 10.9. Test of a priori predictions. 10.10. Steady-state model. 10.11. Discussion. Exercises. IV. Regression Models. 11. Regression Models. 11.1. What You Should Know About This Chapter. 11.2. Linear Regression. 11.3. Logistic Regression. 11.4. Generalized Linear Models (GLMs). 11.5. Interaction Terms. 11.6. Exercises. 12. Climate Change and Seabird Cannibalism: A Case Study. 12.1. What You Should Know About This Chapter. 12.2. The Scientific Problem. 12.3. Data. 12.4. Logistic Regression Analysis. 12.5. Model Validation. 12.6. Outcomes. 12.7. Climate Change, Cannibalism, and Reproductive Synchrony. 12.8. Exercises. V. Appendix. A. Linear Algebra Basics. B. MATLAB: The Basics. C. Connecting Models to Data: A Brief Summary with Sample Codes.
