Modelling Biological Populations in Space and TimeThis volume develops a unifying approach to population studies that emphasizes the interplay between modeling and experimentation and that will provide mathematicians and biologists with a framework within which population dynamics can be fully explored and understood. A unique feature of the book is that deterministic and stochastic models are considered together; spatial effects are investigated by developing models that highlight the consequences that geographical restriction and species mobility may have on population development. Model-based simulations of processes are used to explore hitherto unforeseen features and thereby suggest further profitable lines of both experimentation and theoretical study. Most aspects of population dynamics are covered, including birth-death and logistic processes, competition and predator-prey relationships, chaos, reaction time delays, fluctuating environments, spatial systems, velocities of spread, epidemics, and spatial branching structures. |
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Contents
III | 1 |
V | 5 |
VI | 7 |
VII | 9 |
VIII | 11 |
IX | 15 |
X | 16 |
XI | 17 |
CXIX | 197 |
CXX | 199 |
CXXII | 201 |
CXXIII | 203 |
CXXIV | 205 |
CXXVI | 208 |
CXXVII | 209 |
CXXVIII | 210 |
XIII | 20 |
XIV | 24 |
XV | 27 |
XVI | 28 |
XVIII | 30 |
XIX | 31 |
XX | 33 |
XXII | 34 |
XXIII | 36 |
XXIV | 38 |
XXV | 39 |
XXVI | 41 |
XXVIII | 42 |
XXIX | 44 |
XXX | 46 |
XXXII | 47 |
XXXIII | 48 |
XXXIV | 50 |
XXXV | 51 |
XXXVI | 53 |
XXXVII | 55 |
XXXVIII | 58 |
XXXIX | 59 |
XL | 60 |
XLI | 63 |
XLII | 64 |
XLIII | 65 |
XLIV | 66 |
XLV | 68 |
XLVI | 69 |
XLVII | 70 |
XLVIII | 71 |
XLIX | 73 |
L | 74 |
LI | 75 |
LII | 78 |
LIII | 79 |
LIV | 81 |
LVII | 82 |
LVIII | 83 |
LIX | 84 |
LX | 87 |
LXI | 88 |
LXII | 90 |
LXIV | 92 |
LXV | 94 |
LXVI | 96 |
LXVII | 97 |
LXVIII | 100 |
LXX | 105 |
LXXI | 107 |
LXXII | 110 |
LXXIII | 113 |
LXXIV | 114 |
LXXV | 116 |
LXXVI | 117 |
LXXVII | 118 |
LXXVIII | 119 |
LXXIX | 122 |
LXXX | 125 |
LXXXI | 128 |
LXXXII | 129 |
LXXXIII | 131 |
LXXXV | 135 |
LXXXVI | 137 |
LXXXVII | 139 |
LXXXVIII | 140 |
LXXXIX | 143 |
XC | 146 |
XCII | 148 |
XCIII | 149 |
XCIV | 154 |
XCV | 156 |
XCVII | 160 |
XCVIII | 161 |
XCIX | 166 |
C | 167 |
CI | 169 |
CII | 171 |
CIII | 173 |
CIV | 175 |
CV | 176 |
CVII | 177 |
CVIII | 178 |
CIX | 180 |
CX | 182 |
CXI | 185 |
CXIII | 189 |
CXIV | 190 |
CXV | 191 |
CXVII | 192 |
CXVIII | 194 |
CXXIX | 213 |
CXXX | 214 |
CXXXII | 215 |
CXXXIII | 216 |
CXXXIV | 220 |
CXXXV | 223 |
CXXXVII | 225 |
CXXXVIII | 227 |
CXXXIX | 228 |
CXL | 231 |
CXLI | 233 |
CXLII | 236 |
CXLIV | 238 |
CXLV | 240 |
CXLVI | 241 |
CXLVII | 242 |
CXLVIII | 245 |
CXLIX | 248 |
CL | 250 |
CLI | 252 |
CLII | 253 |
CLIII | 258 |
CLIV | 259 |
CLV | 260 |
CLVI | 261 |
CLVIII | 263 |
CLIX | 264 |
CLX | 266 |
CLXI | 267 |
CLXII | 268 |
CLXIII | 272 |
CLXIV | 273 |
CLXV | 275 |
CLXVII | 277 |
CLXVIII | 278 |
CLXIX | 279 |
CLXX | 281 |
CLXXII | 284 |
CLXXIII | 285 |
CLXXIV | 287 |
CLXXVI | 288 |
CLXXVII | 289 |
CLXXVIII | 290 |
CLXXIX | 291 |
CLXXX | 293 |
CLXXXI | 295 |
CLXXXIII | 297 |
CLXXXIV | 298 |
CLXXXV | 299 |
CLXXXVI | 300 |
CLXXXVII | 304 |
CLXXXVIII | 310 |
CLXXXIX | 312 |
CXC | 314 |
CXCII | 317 |
CXCIII | 319 |
CXCIV | 324 |
CXCV | 325 |
CXCVI | 326 |
CXCVII | 328 |
CXCVIII | 330 |
CC | 331 |
CCI | 332 |
CCII | 333 |
CCIII | 336 |
CCIV | 338 |
CCV | 341 |
CCVI | 343 |
CCVII | 344 |
CCVIII | 345 |
CCIX | 348 |
CCX | 350 |
CCXI | 351 |
CCXII | 353 |
CCXIII | 357 |
CCXIV | 360 |
CCXV | 362 |
CCXVII | 363 |
CCXVIII | 364 |
CCXIX | 366 |
CCXX | 368 |
CCXXI | 369 |
CCXXIII | 372 |
CCXXIV | 373 |
CCXXV | 375 |
CCXXVI | 377 |
CCXXVII | 379 |
CCXXVIII | 380 |
385 | |
394 | |
397 | |
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Common terms and phrases
amplitude analysis approach approximation assumption autocorrelations become extinct behaviour binomial biological birth and death birth process birth-death process branching carrying capacity cells clearly colony competition computed constant corresponding damping death rate denote density determined deterministic deterministic model diffusion distribution effect environment epidemic equilibrium point equilibrium values estimates event example exponential Figure fluctuations give rise increases individual infectives initial population limit cycle linear logistic curve logistic equation logistic growth Lotka Lotka-Volterra model mathematical maximum mean migration rates MINITAB non-spatial Normal Note obtained occur oscillations Paramecium parameter values pattern peak period pN(t population growth population sizes predator-prey predators predicted prey and predators probability provides quasi-equilibrium random variable random walk realizations Renshaw root systems Section shows simulation run Sitka spruce situations solution spatial species stable equilibrium structure susceptibles theoretical time-delay trajectories ultimate extinction variance variation velocity Volterra wavefront whence whilst yields zero