Mathematical Models in Biology
Serving as a basic introduction to concepts in deterministic biological modeling, this text shows how relatively simple mathematics can be applied to a variety of models to draw interesting conclusions.
TABLE OF CONTENTS Mathematical Models in Biology
List of Figures
Chapter 1: The Theory of Linear Difference Equations Applied to Population Growth
- Figure 1.1: The golden mean ? appears in a variety of geometric forms that include: (a) Polyhedra such as the icosahedron, a Platonic solid with 20 equilateral triangle faces ( ?=ratio of sides of an inscribed golden rectangle; three golden rectangles are shown here). (b) The golden rectangle and every rectangle formed by removing a square from it. Note that corners of successive squares can be connected by a logarithmic spiral). (c) A regular pentagon ( ?=the ratio of lengths of the diagonal and a side). (d) The approximate proportions of the Parthenon (dotted line indicates a golden rectangle). (e) Geometric designs such as spirals that result from the arrangement of leaves, scales, or florets on plants (shown here on the head of a sunflower). The number of spirals running in opposite directions quite often bears one of the numerical ratios 2/3, 3/5, 5/8, 8/13, 13/21, 21/34, 34/5, . . . [see R.V. Jean (1984, 86)]; note that these are the ratios of successive Fibonacci numbers. (f) Logarithmic spirals (such as those obtained in (b) are common in shells such as the abalone Haliotis, where each increment in size is similar to the preceding one. See D.W. Thompson (1974) for an excellent summary. [(a and b) from M. Gardner (1961), The Second Scientific American Book of Mathematical Puzzles and Diversions, pp. 92 93. Copyright 1961 by Martin Gardner. Reprinted by permission of Simon & Schuster, Inc.,...
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