Modeling - A Primer
In this module and its associated programs, Logistic Growth and Blending Inheritance (found in the Collection Candidates section), you will explore how to use, analyze, and criticize some important and historically influential models in biology. We will focus on simple models in ecology and population genetics, since these disciplines have a long-standing tradition of model-building, and have explored its powers and limitations with the greatest sophistication. This module will allow you to explore mathematically simple models using a variety of modes of visualization provided by the programs Logistic Growth and Blending Inheritance.
We will show you, with the help of the accompanying programs, that models are very powerful and interesting tools in science, which not only can generate predictions (a commonly emphasized function of modeling) but also (and more importantly) can guide explanation, interpretation, understanding, and discovery in science. When models are used in combination with computers, we can use our most powerful strategy for analyzing the behavior of models—visualization. The use and understanding of techniques of visualization are a major focus of this module. We will see that data generated by a model (or biologically real system) can be visualized in multiple ways, and that visualizing data in multiple ways allows us to detect novel patterns in data which may be missed by applying only one or two strategies of analysis. We come to understand the modes of transformation better, and to recognize characteristic “signatures,” “footprints,” or diagnostic patterns whose presence in one mode of visualization indicate what is going on in another. By viewing data in multiple ways we can also detect patterns in the data which are robust; that is, by detecting something in a variety of ways we are in a much better position to say that it is a real feature of the model or biological system we are studying and not an artifact of our analysis or strategy for manipulating that system.
In the Introduction we discuss a philosophy or methodology of using models in science. We point out not only some of the important uses, functions, and benefits ofusing models in science, but also biases, errors, and, in general, things to keep cautiously in mind when using models. We also point out that the kinds of models used in science extend beyond mathematical and computer models to experiments as models of natural systems. Thus, the points we make about the uses and abuses of models in science are applicable more broadly to the practice of science in general.
There are two main sections to this module which, when used together with the programs Logistic Growth and Blending Inheritance, illustrate a number of important uses and functions of models in science. The first section, Model Building and Exploration with the Minimum-Density Limited Logistic Growth Equation, explores with a variety of graphical modes the behavior of several simple and closely related models of population growth. Among other things, you will be introduced to the concept of chaos and how to use the computer to visually analyze the behavior of chaotic systems.
The second section, Understanding the Role of Mendelian Inheritance in Evolution by Simulating Blending Inheritance, explores the consequences of a false but very influential model of inheritance proposed by Charles Darwin and widely accepted in the 19th century. A central point of this section is to show that even literally false models can be very useful for understanding and interpreting models such as those of Mendelian genetics which we take to be correct.
We have also included several appendices which should provide material for further thought and analysis both of the equations themselves, and of how accurately they may apply to different real situations. It is hoped that a close analysis of these cases will prime your consideration of the other models you will encounter elsewhere in science.
This document is available in Portable Document Format (PDF), Microsoft Word for Macintosh version 5.1 format, and Microsoft Word for Windows version 6.0. To access the PDF file you must install the Acrobat™ Reader (versions for Macintosh and Windows are included on the CD).
Note: The two computer programs that accompany this module, Logistic Growth and Blending Inheritance, can be found in the Modeling Tools Folder in the Collection Candidates area on The BioQUEST Library CD.