Modeling Coupled Natural-Human Systems

Semester Taught - Spring

Catalog Description

Credits: 3

In this course, we will explore some approaches to modeling coupled natural-human systems (CNHs).  By definition, modeling such systems requires concepts drawn from both natural and social sciences, a selected few of which will be studied in this course.
In particular, concepts of stability and regime shift will be studied from the point of view of dynamical systems modeling.  Basic concepts from game theory, e.g., pure-strategy and mixed-strategy Nash equilibriums, will be demonstrated in such classic games as prisoner’s dilemma, hawk-dove, coordination, etc.  The evolutionary dynamics of these games will be explored through the replicator equations.  These concepts will then be put together to develop a few models that mathematically operationalize a conceptual framework of CNHs.  Properties and implications of these models will be derived and discussed.
Some more sophisticated problems will be explored through numerical simulation in MATLAB; codes for selected problems will be provided.  Potential topics include the effects of stochastic noise and complex adaptive system approaches to selected problems.
Note for graduate students: Graduate students will be required to do extra problems that involve deeper levels of knowledge and mathematical skills in selected assignments and midterm exams.


Basic calculus and college-level probability courses

Course Objectives

Upon completion of this course, students will be able to:

    • Understand the covered concepts, their mathematical basis, and their connections.
    • Evaluate the applicability and limitations of mathematical models
    • Formulate problems and develop simple models to study them, using the tools learned in this course.  This is what you’re expected to do in your final project.


Dr. Rachata Muneepeerakul
Office: Room 227 Rogers Hall
Phone: 392-1864 x227
Email: muneepe@ufl.edu

Material/Supply Fees


Class Materials Required

No textbooks are required.  The materials for this course will be drawn from several sources. Below are some examples (we may not cover all of them):
Gintis, H. (2000). Game theory evolving: A problem-centered introduction to modeling strategic behavior. Princeton University Press.
Nowak, M. A. (2006). Evolutionary dynamics: Exploring the equations of life. Harvard University Press.
Hardin, G. (1968). The tragedy of the commons. Science, 162(3859), 1243-1248.
Ostrom, E., Burger, J., Field, C. B., Norgaard, R. B., & Policansky, D. (1999). Revisiting the commons: local lessons, global challenges. Science, 284(5412), 278-282.
Nowak, M. A. (2006). Five rules for the evolution of cooperation. Science, 314(5805), 1560-1563.
Scheffer, M., et al. (2009). Early-warning signals for critical transitions. Nature, 461(7260), 53-59.
Scheffer, M., et al. (2012). Anticipating critical transitions. Science, 338(6105), 344-348.
Yu, D. J., M. R. Qubbaj, R. Muneepeerakul, J. M. Anderies, and R. Aggarwal (published online), The effect of infrastructure design on commons dilemmas in social-ecological system dynamics, Proceedings of the National Academy of Sciences, doi:10.1073/pnas.0709640104.
Anderies, J. M., M. A. Janssen, and E. Ostrom (2004), A framework to analyze the robustness of social-ecological systems from an institutional perspective, Ecology and Society, 9(1), 18.
Anderies, J. M., A. A. Rodriguez, M. A. Janssen, and O. Cifdaloz (2007), Panaceas, uncertainty, and the robust control framework in sustainability science, Proceedings of the National Academy of Sciences, 104(39), 15,194–15,199, doi:10.1073/pnas.0702655104.



Assignments 35%
Midterm Exam 20%
Midterm Exam II 20%
Final Exam 25%

Final grade will be rounded to the nearest integer; for example, 85.5 will be rounded to 86.
86-100 = A | 76-85 = B | 66-75 = C | 56-65 = D | 0-55 = E

Tentative Schedule




Overview; Basic game theory: classic 2x2 games, Nash equilibrium


Mixed-strategy Nash equilibrium in symmetric and asymmetric 2x2 games


3x3 games; Basic evolutionary game theory: replicator equations


Analysis of 1-D replicator equations; 1-D stability analysis


Regime shifts; Examples of models with regime shifts


MIDTERM 1; Analysis of replicator equations for games with more strategies


2-D stability analysis


2-D stability analysis; MATLAB introductory session


2-D stability analysis


MIDTERM 2; Putting them together to develop CNH models


Analysis of selected CNH models


Analysis of selected CNH models; PROJECT PROGRESS REPORTS


MATLAB sessions on selected complex adaptive systems.


MATLAB workshops for final projects



* The schedule is tentative.  Actual schedule would depend on progress and interest in class.
There will be 5-8 assignments throughout the semester, depending on progress and interest in class.  The assignments are usually due within 1-1.5 weeks after the date they are assigned.

Academic Honesty

All students admitted to the University of Florida have signed a statement of academic honesty committing themselves to be honest in all academic work and understanding that failure to comply with this commitment will result in disciplinary action. This statement is a reminder to uphold your obligation as a UF student and to be honest in all work submitted and exams taken in this course and all others.

Accommodation for Students with Disabilities

Students requesting classroom accommodation must first register with the Dean of Students Office. That office will provide the student with documentation that he/she must provide to the course instructor when requesting accommodation.

Use of Library, Personal References, PC Programs and Electronic Databases

These items are university property and should be utilized with other users in mind. Never remove, mark, modify nor deface resources that do not belong to you. If you're in the habit of underlining text, do it only on your personal copy. It is inconsiderate, costly to others, and dishonest to use common references otherwise.

Software Use

All faculty, staff and students of the University are required and expected to obey the laws and legal agreements governing software use. Failure to do so can lead to monetary damages and/or criminal penalties for the individual violator. Because such violations are also against University policies and rules, disciplinary action will be taken as appropriate. We, the members of the University of Florida community, pledge to hold ourselves and our peers to the highest standards of honesty and integrity.

UF Counseling and Career Services

Resources are available on-campus for students having personal problems or lacking clear career and academic goals which interfere with their academic performance. These resources include:

  1. University Counseling and Wellness Center, 3190 Radio Road, Gainesville, FL 32611
  2. Career Connections Center, Reitz Union, 392-1601, career development assistance and counseling.