Computational Models in the Sciences: Bio/Geo/CS 250: Theodore Wong, Assistant Professor of Biology
Computational Models in the Sciences is not only a new course but also a new kind of course. A multidisciplinary overview of computational methods in the natural and social sciences, it uses the Internet to enhance classroom discussions and allows students a say in what they study. Cross-listed as biology, geology and computer science, the course allows students to model everything from tumor growth to monetary policy.
In the lab-seminar-neither seminar nor lab, but a conversation whose content and trajectory is determined each session by the students and Wong-students help to choose the readings and present modeling projects to the class for criticism and mutual education.
"The successful student may leave the class with little more factual knowledge than she had when she first started it," Wong says, "but she'll have all the right philosophical frameworks and conceptual tools (and some technical skills) to turn any scientific question or puzzle into an interesting and useful computational model-or she'll be able to explain why modeling wouldn't work." The course is not intended to be an exhaustive or complete explication of computational methods in the sciences, Wong says, but an opportunity for students to become efficient and confident in the self-education tasks that occupy the bulk of most scientific modelers' time.
Wong says the class discussions in the spring 2003 semester centered on the usefulness of simple models. "No matter how much time you spend building a model, someone else can always say to you, 'But you didn't include such-and-such!'," he says. "Does the impossibility of including every conceivable detail in a model make modeling a useless activity? And why do so many scientists value very simple-you often hear the word elegant-models? When do scientists value elegance, and when do they value precise realism? Why is there a tradeoff between the two, and is it at all avoidable?"
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All web pages for the course are Wiki pages: collaborative hypertext environments with an emphasis on easy access to, and modification of, information. Students are encouraged to modify the pages by posting questions, links, musings or reading suggestions.
"The Wiki is a new way to use the web, and a new way to structure pedagogical interactions," Wong says. "It takes a lot of getting used to. Students aren't used to being asked to add to or change what other people have written, especially what the professor has written. Even halfway through the semester they don't do it very much, but I'm hoping that as they move into their collaborative projects, they'll see how useful it is to be able to write and overwrite a single group document.
"What's been really useful about the Wiki is that it makes it easy to put together class documents. All the lab activities and take-home assignments are written out as Wiki pages, and after most of the seminar discussions I've had a student write a summary to the Wiki. Because everything is on the web, students can refer to any page from anyplace. The Wiki also tracks changes made to the pages, so students can see when and where I've made changes or corrections to the assignment descriptions.
"The Wiki is going to be an ongoing experiment for me. I'm committed to making my pedagogy very informal and collaborative-especially in a class like the modeling class, where it's really almost impossible to teach in a traditional lecture format. Because the Wiki is by its nature informal and collaborative-and because it's constantly sending an implicit message that knowledge is dynamic-it's going to continue to be a big part of my teaching."
Students complete 10 individual micromodeling projects. These are software routines, each implementing at least one common computational modeling task. Wong presents the microprojects as problems that students solve using strategies discussed in class.
In a micromodeling project for cellular automaton models, for example, students predict patterns of forest fires and seashell pigmentation. In another microproject, students build a set of simulations to explore how a diffusion process is affected by spatial heterogeneity: A population of raccoons might grow in its spatial extent by a process accurately modeled as diffusion with exponential growth, but what if the space through which the population is growing consists of patches that differ in hospitality to raccoons? Does a raccoon population spread as quickly or evenly through a checkerboard region of good and bad habitat as it does through a region that is uniformly intermediate in habitat quality? And what effect do barriers have? And corridors through poor habitat? These sorts of questions can be addressed through diffusion simulations.
A third microproject deals with coalescence, the opposite of branching. Rivers, raindrop trails on windowpanes, and cracks in solid materials exhibit coalescence, and some branching processes-notably the evolutionary diversification of populations-are analyzed in reverse by modeling them as backward coalescent projects. For example, the geographic origin of the "mitochondrial Eve" was estimated using a coalescent model to analyze genetic differences among populations of modern humans. Students build a simple abstract model of the coalescence of random numbers. The objective is to see the relationship, if any, between the lengths of the sequences of numbers and their times to coalescence.
Students use any software package or language from an approved list of nine, three of which Wong teaches in detail: STELLA, NetLogo and Python.
STELLA, Wong explains, is a system-dynamics simulation tool with an intuitive graphical interface. NetLogo is free and for cellular automata and agent-based models. With both STELLA and NetLogo, students start programming in 15 minutes and within a few days can build remarkably sophisticated and scientifically interesting simulations, but only certain kinds. Python is a full-blown, multi-purpose programming language: harder to learn but more versatile. "It takes students longer to learn Python, but it's good to know at least one real language," Wong says. "Knowing an actual programming language will let them do any kind of modeling they might have to do in their later academic lives."
In addition, each student must partake in one group miniproject. These are complete models of scientific phenomena, chosen by each student and her collaborators and approved by Wong through a formal proposal. At the end of the semester, each group's model and results are presented in a public poster session. In the spring 2003 semester, the miniprojects ranged from an HIV epidemiology model to a model on the behavior of ants in colonies.
In the fall 2003 semester, Wong will teach a botany course "much more mathematical than the typical botany course," he says. In spring 2005 he will teach a course in which he and students build a quantitative simulation of Philadelphia's ecosystem and land-use dynamics, which students will add to and refine over the years.
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