Our goal is to expand on the material presented in Math/EEB 581-2 by discussing in particular modeling methods and areas of research that were not included in that sequence but which are currently being actively pursued. The emphasis is on developing participants’ appreciation for additional central questions in mathematical and theoretical ecology that were not addressed in the mostly deterministic dynamical systems coverage of 581-2. The focus of that course sequence is on population and some aspects of community ecology. We will expand on this by including some of the variety of methods used to account for individual behavior as they impact population and community processes. In particular, agent-based modeling methods have become tremendously influential for investigating both foundational and applied research questions across the range of biological scales. Similarly, hybrid modeling methods that mix and link different mathematical approaches have provided new insight for problems that involve interactions at multiple spatial and temporal scales. While the examples we will discuss are mostly derived from ecological systems, the same underlying modeling methods are being applied in essentially every level of biology as well as to human social systems.
We will be basing part of the course on the material in two books about agent-based approaches: Individual-based modeling and ecology by Volker Grimm and Steven Railsback, Princeton University Press (2005) and Modeling populations of adaptive individuals by Steven Railsback and Bret Harvey, Princeton University Press (2020). Both of these are ebooks available through the UTK library. For the hybrid modeling portion of the course, we’ll start with the review Stephanou, V. V. (2016) Hybrid Modelling in Biology: a Classification Review. Math. Model. Nat. Phenom. 11: 37-48 and read through a variety of papers. .
The course presumes mathematical maturity at the level of advanced calculus with prior exposure to basic differential equations, linear algebra, and basic probability. We will not assume that you have previously had the 581-2 sequence or 681 but will de-emphasize the overlap in material associated with those courses. Regarding participant expectations – registered students will be expected, in addition to actively participating in class discussions, to choose an individual project related to the topics that preferably would be connected to their research or to expand their modeling background. This project could involve using software packages to construct and analyze an ABM. A written report on this individual project as well as an oral presentation to the class is expected of all registered participants. Each participant will be expected to make an appointment with the instructor in approximately the middle of the semester to discuss their individual project and draft a short summary of the objectives of the project.
This course is offered in-person and the course meeting time is 4:30-5:45PM on Tuesdays and Thursdays in Ayres 112, starting January 25.
The topic coverage of the course includes an overview of modeling approaches, objectives of agent-based models, connections to to individual-based ecology, pattern-oriented modeling, constructing ABMs, the ODD protocol for describing ABMs, analyzing ABMs, evaluating ABMS, incorporating adaptive and goal-seeking behavior, state and predictions-based theory, enhancing model credibility, software for ABMs, classifying hybrid models, building hybrid models, multimodels, and multi-scale modeling.
Railsback, Steve F. and Volker Grimm. 2012. Agent-based and Individual-Based Modeling: A Practical Introduction. Princeton University Press.
Clark, Colin and Marc Mangel. 2000. Dynamic State Variable Miocels in Ecology. Oxford University Press