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. |
Contents
III | 5 |
V | 5 |
VI | 7 |
VII | 9 |
VIII | 11 |
IX | 15 |
X | 16 |
XI | 17 |
CXX | 197 |
CXXI | 199 |
CXXIII | 201 |
CXXIV | 203 |
CXXV | 205 |
CXXVII | 208 |
CXXVIII | 209 |
CXXIX | 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 |
XLIX | 71 |
L | 73 |
LI | 74 |
LII | 75 |
LIII | 78 |
LIV | 79 |
LV | 81 |
LVIII | 82 |
LIX | 83 |
LX | 84 |
LXI | 87 |
LXII | 88 |
LXIII | 90 |
LXV | 92 |
LXVI | 94 |
LXVII | 96 |
LXVIII | 97 |
LXIX | 100 |
LXXI | 105 |
LXXII | 107 |
LXXIII | 110 |
LXXIV | 113 |
LXXV | 114 |
LXXVI | 116 |
LXXVII | 117 |
LXXVIII | 118 |
LXXIX | 119 |
LXXX | 122 |
LXXXI | 125 |
LXXXII | 128 |
LXXXIII | 129 |
LXXXIV | 131 |
LXXXVI | 135 |
LXXXVII | 137 |
LXXXVIII | 139 |
LXXXIX | 140 |
XC | 143 |
XCI | 146 |
XCIII | 148 |
XCIV | 149 |
XCV | 154 |
XCVI | 156 |
XCVIII | 160 |
XCIX | 161 |
C | 166 |
CI | 167 |
CII | 169 |
CIII | 171 |
CIV | 173 |
CV | 175 |
CVI | 176 |
CVIII | 177 |
CIX | 178 |
CX | 180 |
CXI | 182 |
CXII | 185 |
CXIV | 189 |
CXV | 190 |
CXVI | 191 |
CXVIII | 192 |
CXIX | 194 |
CXXX | 213 |
CXXXI | 214 |
CXXXIII | 215 |
CXXXIV | 216 |
CXXXV | 220 |
CXXXVI | 223 |
CXXXVIII | 225 |
CXXXIX | 227 |
CXL | 228 |
CXLI | 231 |
CXLII | 233 |
CXLIII | 236 |
CXLV | 238 |
CXLVI | 240 |
CXLVII | 241 |
CXLVIII | 242 |
CXLIX | 245 |
CL | 248 |
CLI | 250 |
CLII | 252 |
CLIII | 253 |
CLIV | 258 |
CLV | 259 |
CLVI | 260 |
CLVII | 261 |
CLIX | 263 |
CLX | 264 |
CLXI | 266 |
CLXII | 267 |
CLXIII | 268 |
CLXIV | 272 |
CLXV | 273 |
CLXVI | 275 |
CLXVIII | 277 |
CLXIX | 278 |
CLXX | 279 |
CLXXI | 281 |
CLXXIII | 284 |
CLXXIV | 285 |
CLXXV | 287 |
CLXXVII | 288 |
CLXXVIII | 289 |
CLXXIX | 290 |
CLXXX | 291 |
CLXXXI | 293 |
CLXXXII | 295 |
CLXXXIV | 297 |
CLXXXV | 298 |
CLXXXVI | 299 |
CLXXXVII | 300 |
CLXXXVIII | 304 |
CLXXXIX | 310 |
CXC | 312 |
CXCI | 314 |
CXCIII | 317 |
CXCIV | 319 |
CXCV | 324 |
CXCVI | 325 |
CXCVII | 326 |
CXCVIII | 328 |
CXCIX | 330 |
CCI | 331 |
CCII | 332 |
CCIII | 333 |
CCIV | 336 |
CCV | 338 |
CCVI | 341 |
CCVII | 343 |
CCVIII | 344 |
CCIX | 345 |
CCX | 348 |
CCXI | 350 |
CCXII | 351 |
CCXIII | 353 |
CCXIV | 357 |
CCXV | 360 |
CCXVI | 362 |
CCXVIII | 363 |
CCXIX | 364 |
CCXX | 366 |
CCXXI | 368 |
CCXXII | 369 |
CCXXIV | 372 |
CCXXV | 373 |
CCXXVI | 375 |
CCXXVII | 377 |
CCXXVIII | 379 |
CCXXIX | 380 |
385 | |
394 | |
397 | |
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Common terms and phrases
a₁ a₂ amplitude analysis approach approximation autocorrelations b₁ b₂ behaviour biological birth and death birth process birth-death process branching carrying capacity cells clearly colony competition computed constant corresponding cos(wt curve damping death rate denote density deterministic deterministic model diffusion distribution dN₁/dt effect environment epidemic equations equilibrium point estimates example exponential Figure fluctuations give rise increases individual infectives initial population limit cycle linear logistic logistic curve logistic growth Lotka-Volterra Lotka-Volterra model mathematical mean migration rates MINITAB N₁ N₁(t N₂ non-spatial Note occur oscillations parameter values peak period PN(t Po(t predator-prey predators prey and predators probability provides quasi-equilibrium r₁ r₂ random variable random walk realizations Renshaw root systems shows simulation run Sitka spruce solution spatial species stable equilibrium stepping-stone structure susceptibles theoretical time-delay trajectories ultimate extinction v₁ v₂ variance variation Volterra wavefront whence whilst X₁ yields zero