Preface
Population biology is a quantitative science dealing with changes in the size and composition of populations, and population biologists often use mathematical models to infer population dynamics. These models use information about the properties of individuals and basic assumptions about their interactions to predict population size, gene frequency, and optimal behavioral strategies of individuals, forming an important conceptual framework for courses in ecology, evolution, and behavior.
Students bring a range of quantitative backgrounds to the study of population biology. Although the models taught in introductory courses are not difficult, math anxieties and the abstract nature of the equations impede many students. The Populus software addresses this problem. Computer simulations provide a visual demonstration of model dynamics, helping students develop an intuitive connection between the form of the equations, their quantitative parameter values, and the resulting model behavior.
The first rudiments of Populus were produced in collaboration with my Minnesota colleagues Peter Abrams, Jim Curtsinger, and Dave Tilman, with 1986 funding from IBM, and integrated into a functional package by a superb student programmer, Chris Bratteli. We used the program at the University of Minnesota, shared it with a few friends elsewhere, and gradually improved it, supported by the National Science Foundation. In 1991, with 30 Populus models spanning introductory courses in ecology and evolution, I began to distribute the software and to encourage gratis duplication. Chris and I continued to develop Populus with a second programmer, Elizabeth Goehring, until 1995, when my attention turned to other interests.
The penultimate DOS version of Populus (3.4) became widely used, and pressure to revise it escalated as microprocessors with clock speeds beyond the capacity of Borland Turbo Pascal began to cause runtime errors. Together with a third programmer, Lars Roe, I began to rebuild Populus for Java virtual machines in summer 1998. We also patched version 3.4 to fix the Borland runtime error, producing version 3.42 for DOS windows in Win95, Win98, and WinNT. Populus 3.42 is available for download from http://ecology.umn.edu/populus.The Web site also provides full instructions.
The new Java Populus, version 5.x, is available from the same Web site, http://ecology.umn.edu/populus. This program runs as a local application (not an applet) on any platform that supports a Java Virtual Machine, including both Windows and Macintosh computers. Linked sets of input and output windows in the new interface allow toggled parameter increments to show up instantly on the appropriate graphs, so the effect of changing parameter values is immediate and clear. The current Java Populus version supports all of the basic ecological models described in this book and several basic evolutionary models. We will update this posting as the new package grows to full equivalence with DOS Populus 3.42 and beyond.
Minnesota ecology classes invest about a third of their lab meetings in model simulation. The remaining two thirds are devoted to experiments, foraging games, data manipulation, and role-playing discussion. Students first encounter a mathematical model in lecture after a series of empirical examples that motivate its central issues. I derive the equations and explain their significant properties before students come to the computer lab, then use simulation exercises to reinforce this initial exposure. We have found this sequence essential; students who attempt simulations without the conceptual preparation provided by a lecture or reading assignment take less away from the experience. This book should foster that conceptual preparation. It will supplement any of the mayor texts, guiding lab experience with the mathematical models of an introductory ecology course.
Sessions in the computer lab are structured around a series of questions designed to exercise pedagogically important features of the model. Problems and exercises in this book exemplify the conceptual focus that provides a good skeleton. We often begin and end the computer lab with a brief summary and questions, but students should have a great deal of freedom to experiment with parameter values and running conditions. Populus works best as a teaching tool when students are able to use it almost like a video game, testing ''what if' scenarios.
Here are a few additional suggestions based on our Minnesota teaching experience with Populus simulations:
- It is helpful to have students work in pairs in a facility where they can discuss what they are seeing on the screen.
- Teaching assistants and faculty play an important role by looking over shoulders and engaging the students in discussion about the dynamics they are observing. The layout of the room must allow this circulation.
- When staff members see an instructive simulation, it is useful to have the whole class run that case and to give a brief explanation.
- Students need space to lay out their notebooks and papers around the computer.
- It is valuable to have the computer lab available for student use outside of the formal lab session and to make sure that each student with a computer has a personal copy of Populus.
- Resist the temptation to squeeze consideration of three or four mathematical models into one long lab session.
- Two dozen students, a dozen computers, one teaching assistant, one professor and a well-ventilated room make a good computer-lab combination. Brain function is inversely proportional to the number of hot computers and hot bodies crowded into a small space!
Simulation models in the Populus software cover subject matter from several course venues, including introductory ecology, introductory evolution, theoretical ecology, and population genetics. We decided early that proper documentation would require separate books for the ecological and evolutionary models. Reviewers subsequently convinced us to subdivide still further, producing a small, inexpensive treatment of the models used in elementary courses, followed by a more comprehensive book for the sophisticated clientele. Accordingly, we defer interesting ecological models of demographic stochasticity, resource competition, discrete predator-prey systems, diffusion, metapopulations, and macroparasites to that larger book.
Many people have played a role in bringing the Populus software to its present state. First among them is Chris Bratteli, who worked with me throughout his baccalaureate career at Minnesota; his skill with Pascal brought the first three generations of the program into being and provided a superb foundation for subsequent development. Liz Goehring carried on ably with the final DOS versions. Lars Roe has created the new interface of the Java Populus and is translating our proven Pascal algorithms for this new programming environment.
Special thanks to population biologists Peter Abrams, John Addicott, Sonia Altizer, Dave Andow, Janis Antonovics, Graham Bell, Doug Boucher, Andy Clark, Rob Colwell, Hugh Comins, James Crow, Jim Curtsinger, Andy Dobson, John Endler, Mike Gilpin, Lou Gross, Mike Hassell, Bob Holt, Yoh Iwasa, Mark Kirkpatrick, Rich Lenski, Bruce Levin, Simon Levin, Robert May, Martin Novak, Mike Rosenzweig, Jon Seger, Ruth Shaw, Frank Shaw, Frank Stewart, and Dave Tilman. Each of these colleagues has taken time to help us with the implementation of particular models.
This book owes its existence to two editors at Prentice Hall. The persistence and vision of Executive Life Sciences Editor Teresa Ryu persuaded me to write it at a time when many other interests competed for my attention. It was easier to write the book than to dissuade Teresa! Production Editor Kim Dellas has ably seen the manuscript into print. Working with both of them has been a pleasure.
It has been my privilege to have many superb teaching assistants from the Ecology, Evolution and Behavior Graduate Program at the University of Minnesota, and many of the exercises and problems in this book trace their lineage to those collaborations. It is an honor to acknowledge Sonia Altizer, Paul Cabe, Alison Chubb, Julie Etterson, Sarah Hotchkiss, Kevin Johnson, Sue Lewis, Elena Litchman, David Lytle, Mike Sorensen, Stuart Wagenius, Sarah Webb, and Bethany Woodworth. They are gifted teachers.
My first and best reviewer is always my wife, Karen Oberhausen She is joined by Soma M. Altizer, Emory University; Kemuel Badger, Ball State University; Joel S. Brown, University of Illinois at Chicago; R Stephen Dobson, Auburn University; John Endler, University of California-Santa Barbara; Aaron M. Ellison, Mount Holyoke College; T. Luke George, Humboldt State University; Douglas E. Gill, University of Maryland; Richard Halliburton, Western Connecticut State University; David Hogg, University of Wisconsin; Robert D. Holt, University of Kansas; Brian Inouye, University of CaliforniaDavis; Stephen H. Jenkins, University of Nevada, Reno; Mark McKone, Carleton College; Mark McPeek, Dartmouth College; Manuel A. Morales, University of Maryland; William Morris, Duke University; Larry Rockwood, George Mason University; Wendy E. Sera, Baylor University; Daniel Simberloff, University of Tennessee; Donald M. Waller, University of Wisconsin-Madison; and Henry M. Wilbur, University of Virginia. I thank each of these reviewers for helping me to improve the focus and clarity of the manuscript.
Don Alstad
University of Minnesota
