Modeling Biological Systems: Principles and ApplicationsJames W. Haefner This book is intended as a text for a first course on creating and analyzing computer simulation models of biological systems. The expected audience for this book are students wishing to use dynamic models to interpret real data mueh as they would use standard statistical techniques. It is meant to provide both the essential principles as well as the details and equa tions applicable to a few particular systems and subdisciplines. Biological systems, however, encompass a vast, diverse array of topics and problems. This book discusses only a select number of these that I have found to be useful and interesting to biologists just beginning their appreciation of computer simulation. The examples chosen span classical mathematical models of well-studied systems to state-of-the-art topics such as cellular automata and artificial life. I have stressed the relationship between the models and the biology over mathematical analysis in order to give the reader a sense that mathematical models really are useful to biologists. In this light, I have sought examples that address fundamental and, I think, interesting biological questions. Almost all of the models are directly COIIl pared to quantitative data to provide at least a partial demonstration that some biological models can accurately predict. |
Contents
III | 3 |
IV | 5 |
V | 6 |
VI | 9 |
VII | 10 |
VIII | 11 |
IX | 12 |
XI | 15 |
CXXV | 225 |
CXXVI | 226 |
CXXVII | 227 |
CXXVIII | 228 |
CXXIX | 231 |
CXXX | 233 |
CXXXI | 234 |
CXXXII | 235 |
XII | 16 |
XIII | 17 |
XV | 21 |
XVI | 22 |
XVII | 24 |
XVIII | 28 |
XIX | 30 |
XX | 31 |
XXI | 32 |
XXII | 35 |
XXIV | 36 |
XXV | 38 |
XXVI | 39 |
XXVII | 41 |
XXVIII | 43 |
XXIX | 44 |
XXX | 45 |
XXXI | 47 |
XXXII | 50 |
XXXIV | 52 |
XXXV | 53 |
XXXVI | 55 |
XXXVII | 57 |
XXXVIII | 58 |
XXXIX | 59 |
XL | 63 |
XLI | 64 |
XLII | 65 |
XLIII | 66 |
XLIV | 73 |
XLV | 74 |
XLVI | 80 |
XLVII | 85 |
XLVIII | 86 |
XLIX | 87 |
LII | 88 |
LIV | 89 |
LV | 95 |
LVI | 96 |
LIX | 97 |
LX | 99 |
LXI | 101 |
LXII | 104 |
LXIII | 106 |
LXV | 107 |
LXVI | 108 |
LXVII | 111 |
LXVIII | 113 |
LXIX | 114 |
LXX | 117 |
LXXI | 118 |
LXXII | 120 |
LXXIII | 121 |
LXXV | 122 |
LXXVI | 123 |
LXXVII | 125 |
LXXVIII | 127 |
LXXIX | 129 |
LXXXI | 130 |
LXXXII | 132 |
LXXXIII | 133 |
LXXXIV | 135 |
LXXXVII | 136 |
LXXXVIII | 137 |
LXXXIX | 138 |
XCI | 139 |
XCII | 140 |
XCIII | 141 |
XCIV | 142 |
XCV | 145 |
XCVI | 147 |
XCVIII | 148 |
XCIX | 149 |
C | 151 |
CI | 153 |
CII | 154 |
CIII | 155 |
CIV | 157 |
CV | 169 |
CVI | 176 |
CVII | 177 |
CVIII | 178 |
CIX | 179 |
CX | 180 |
CXI | 186 |
CXII | 192 |
CXIII | 194 |
CXV | 197 |
CXVI | 210 |
CXVII | 212 |
CXVIII | 214 |
CXIX | 215 |
CXX | 217 |
CXXII | 220 |
CXXIV | 221 |
CXXXIII | 239 |
CXXXV | 241 |
CXXXVI | 247 |
CXXXVIII | 250 |
CXXXIX | 252 |
CXL | 256 |
CXLII | 257 |
CXLIII | 260 |
CXLIV | 261 |
CXLV | 262 |
CXLVI | 263 |
CXLVII | 264 |
CXLVIII | 265 |
CL | 266 |
CLI | 269 |
CLII | 270 |
CLIV | 272 |
CLV | 273 |
CLVI | 279 |
CLVII | 281 |
CLVIII | 286 |
CLIX | 290 |
CLX | 293 |
CLXII | 294 |
CLXIII | 295 |
CLXIV | 296 |
CLXV | 297 |
CLXVI | 300 |
CLXVII | 304 |
CLXVIII | 306 |
CLXIX | 307 |
CLXXI | 309 |
CLXXII | 315 |
CLXXIII | 316 |
CLXXIV | 317 |
CLXXV | 318 |
CLXXVI | 322 |
CLXXVII | 324 |
CLXXVIII | 325 |
CLXXIX | 326 |
CLXXXI | 328 |
CLXXXII | 329 |
CLXXXIII | 331 |
CLXXXIV | 334 |
CLXXXV | 339 |
CLXXXVI | 340 |
CLXXXVII | 341 |
CLXXXVIII | 343 |
CLXXXIX | 346 |
CXC | 348 |
CXCI | 352 |
CXCII | 354 |
CXCIII | 356 |
CXCIV | 357 |
CXCVI | 358 |
CXCVIII | 361 |
CXCIX | 363 |
CC | 364 |
CCI | 366 |
CCII | 367 |
CCIII | 368 |
CCIV | 370 |
CCV | 373 |
CCVI | 376 |
CCVII | 377 |
CCVIII | 378 |
CCIX | 379 |
CCX | 382 |
CCXII | 383 |
CCXIII | 392 |
CCXVI | 394 |
CCXVII | 399 |
CCXVIII | 400 |
CCXIX | 401 |
CCXX | 402 |
CCXXI | 403 |
CCXXIII | 406 |
CCXXIV | 407 |
CCXXV | 408 |
CCXXVII | 411 |
CCXXVIII | 413 |
CCXXIX | 414 |
CCXXX | 417 |
CCXXXI | 419 |
CCXXXII | 421 |
CCXXXIII | 422 |
CCXXXIV | 424 |
CCXXXV | 425 |
CCXXXVII | 429 |
CCXXXVIII | 433 |
CCXXXIX | 435 |
CCXL | 439 |
463 | |
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Common terms and phrases
algorithm Allee effect analysis aphid applied approach attractor auxiliary variable basic behavior calculate capita cell chaos Chapter chemostat compartment complex components constant curve decreases density density-dependent depends derivative describe deviation difference equations differential equations distribution driving variables dynamics ecological effects equilibrium error estimate example feedback Figure finite difference flow Forrester diagram frequency function glucagon glucose growth rate hypotheses increase individual initial conditions input insulin integration interactions iterations K₁ leaf levels limit cycle linear linear regression logistic map Lyapunov exponents mathematical matrix maximum method model output N₁ nonlinear nullcline nutrient objects observations parameter values perturbations phase space photosynthesis plant plot Poincaré section population potential predator predictions prey probability probability distribution problem processes produce quantity random regression relative represent robot scale shown in Fig simple simulation slope solution solve space spatial species stable statistical step stochastic structure temperature tion validation walleye