Modeling—A Primer Version 2.0 A BioQUEST Collection Text Module by William C. Wimsatt University of Chicago Jeffrey C. Schank University of Chicago User's Manual A BioQUEST Library VII Online module published by the BioQUEST Curriculum Consortium The BioQUEST Curriculum Consortium (1986) actively supports educators interested in the reform of undergraduate biology and engages in the collaborative development of curricula. We encourage the use of simulations, databases, and tools to construct learning environments where students are able to engage in activities like those of practicing scientists. Email: [email protected] Website: http://bioquest.org Editorial Staff Editor: John R. Jungck Beloit College Managing Editor: Ethel D. Stanley Beloit College, BioQUEST Curriculum Consortium Associate Editors: Sam Donovan University of Pittsburgh Stephen Everse University of Vermont Marion Fass Beloit College Margaret Waterman Southeast Missouri State University Ethel D. Stanley Beloit College, BioQUEST Curriculum Consortium Online Editor: Amanda Everse Beloit College, BioQUEST Curriculum Consortium Editorial Assistant: Sue Risseeuw Beloit College, BioQUEST Curriculum Consortium Editorial Board Ken Brown University of Technology, Sydney, AU Peter Lockhart Massey University, NZ Joyce Cadwallader St Mary of the Woods College Ed Louis The University of Nottingham, UK Eloise Carter Oxford College Claudia Neuhauser University of Minnesota Angelo Collins Knowles Science Teaching Foundation Patti Soderberg Conserve School Terry L. Derting Murray State University Daniel Udovic University of Oregon Roscoe Giles Boston University Rama Viswanathan Beloit College Louis Gross University of Tennessee-Knoxville Linda Weinland Edison College Yaffa Grossman Beloit College Anton Weisstein Truman University Raquel Holmes Boston University Richard Wilson (Emeritus) Rockhurst College Stacey Kiser Lane Community College William Wimsatt University of Chicago Copyright © 1993 -2006 by John N. Calley and John R. Jungck All rights reserved. Copyright, Trademark, and License Acknowledgments Portions of the BioQUEST Library are copyrighted by Annenberg/CPB, Apple Computer Inc., Beloit College, Claris Corporation, Microsoft Corporation, and the authors of individually titled modules. All rights reserved. System 6, System 7, System 8, Mac OS 8, Finder, and SimpleText are trademarks of Apple Computer, Incorporated. 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Some modules' software use the BioQUEST Toolkit licensed from Project BioQUEST. Introductory Note: Welcome to the Unfinished Land of Model-Building! The software with this manual is quite stable, and contains mostly errors of omission rather than of commission. The manual itself is another matter. It has continued to grow like topsy, and will ultimately evolve into a book on strategies of model-building, criticism, and evaluation, using the software as a means of delivery, with exercises using it keyed to all of these activities. To our knowledge, there is as yet no text like this at any level, much less at a level which renders it approachable to students without far more math and/or programming experience than are the norm for non-hard-science majors. Although designed originally for a biology course, they have also been used to good advantage in two philosophy of science courses, and are now being tried out as part of the methodological part of the course in an upper division/graduate course on computer modeling in the biological sciences. Those who can should perhaps better write the programs to do these things themselves, my physicist friends tell me, but we don't want to disenfranchise those who can't. Perhaps we can motivate some of them to become those who can. As it is, there are many things to explore in there pages and programs, but the exercises could be better arranged, and there is no indication of relative difficulty (or even of relative length) of the exercises. We have focused on getting in the relevant materials, rather than on their optimal arrangement, or even presentation. These two simulations presented here evolved from two different exercises used in one form or another for the last 16 years in Wimsatt's Biology Common Core course, BioSci 147: “Genetics in an Evolutionary Perspective,” and they have not yet been sufficiently integrated. The index needs a lot of further work--and does not at present include references to many of the appendices. In the meantime, we welcome suggestions for what you found difficult, what you would like to see included, any additional exercises you have added, and the like. The course in which these were used was a non-majors course which tended to attract a fair number of math, physics, chemistry, and economics majors because it used computer simulations, and a fair number of humanities majors because it had a lot of history. Needless to say, the distribution of interests and special talents was distinctly bimodal! Thus, there are exercises for students who have never had calculus (and didn’t like what algebra they did have), and for students who have gone far beyond it. I hope that you have as much fun with this as we have. We owe an enormous debt of thanks to the students over the years in Wimsatt’s BioSci 147 for acting as guinea pigs for and contributors to many of the ideas found in this module--first implemented on HP-25 programmable calculators in 1976, and on Apple Macintoshes since 1985. Special thanks are due to Apple for their conception of a people-friendly machine which solved the problems of bimodal distribution mentioned above, for their friendly support (including a “Paris” prototype, when nothing else was fast enough), and to the 1990 BioSci 147 class, who used something approximating the versions of the programs and labs you see here, but without much of the multiple windows, text processing, and recording support of this version, and who put up with twice-weekly version updates near the end. The 1992 class had to live through the vi Model Building comparable uncertainty (including suggestions that they not do certain labs until the following week so we had time to implement new things for them to try). Extra special thanks are due to Scott Franklin, whose bifurcation/accumulation program provided the idea testing and inspiration for the N vs r plot mode, to Michael Post, whose elegant “TwigMaker” program deserves to make it into the next version of the Model-Building exercises, and to Matt Ryan and other members of the BioSci 267 class, whose ß-testing enthusiasm verged on the diabolical. Note: the manual is written in Palatino, Times, Geneva, and sometimes Chicago fonts. Make sure that these screen fonts are on your computer if you wish to preserve formatting for reading or printing the manual. If you should decide to print out the manual, or lots of graphics, see the note in the "how to" section on the much greater speed of "Quickdraw" printers as compared to Postscript printers for "Quickdraw" graphics. (The difference in printing time can easily be a factor of 20, and some of the graphics in this manual may take as much as 15-20 minutes to print out on a slow Postscript printer.) Editor's note: This document is also available in PDF format. In most cases you will probably find it quicker and easier to use the PDF format if you are reading the manual on a computer screen or if you want to print it. VGV 8/13/00 William C. Wimsatt Jeffrey C. Schank The University of Chicago June 12, 1992 Table of Contents What You Need To Know and General Overview..............................................................1 Introduction To Using Models in Biology .............................................................................3 Model-Building and Exploration with the Minimum-Density Limited Logistic Growth Equation.......................................................................................................................13 Why Study "Simple" Growth Equations? ..................................................................13 A Basic Strategy of Model-Building and Analysis: .......................................17 Start with Simple Models .................................................................................17 Complexity.........................................................................................................18 Human Limitations on Representing Complex Systems................18 The Evolution of Models......................................................................20 Pedagogy................................................................................................20 Major