Spatiotemporal Models of Population and Community DynamicsThis book presents a comprehensive typology and a comprehensible description of spatiotemporal models used in population dynamics. The main types included are: reaction-diffusion systems, patch models, matapopulation approaches, host parasitoid models, cellular automata (interacting particle systems), tessellations and distance models. The models are introduced through examples and with informative verbal explanations to help understanding. Some of the cellular automation examples are models not yet published elsewhere. Possible extensions of certain model types are suggested. |
Contents
1 Introduction | 1 |
12 SPATIAL EXTENSIONS OF THE CLASSICAL APPROACH | 4 |
NEIGHBOURHOOD MODELLING | 5 |
14 THE ROLE OF SPATIOTEMPORAL MODELS IN ECOLOGY | 10 |
2 Reactiondiffusion models of population growth and dispersion | 13 |
22 RANDOM WALK APPROXIMATIONS TO DIFFUSION | 15 |
222 Random walk in continuous time and space | 17 |
23 THE DIFFUSION EQUATION | 22 |
423 Metapopulations with synchronous local dynamics | 117 |
424 Rescue effect due to spatial heterogeneity | 120 |
phenomenological model | 122 |
mechanistic model | 124 |
427 Multistate metapopulation models | 125 |
the structure of metacommunity models | 130 |
continuous time models | 131 |
4210 Discrete time metacommunity models | 134 |
231 The flow balance approximation to diffusion | 24 |
232 Density flow | 26 |
233 Diffusion in 2D and 3D spaces | 27 |
initial and boundary conditions solutions stability analyses and numerical approximations of PDE models | 29 |
235 Solutions of the diffusion equation | 34 |
236 Densitydependent diffusion with biased random walk | 37 |
24 ADVECTION | 38 |
241 Constant rate advection with step probability adjustment | 39 |
242 Constant rate advection with step length adjustment | 40 |
243 Advection induced by a milieu gradient | 41 |
POPULATION GROWTH IN DIFFUSIVE SYSTEMS | 42 |
251 Constant rate growth and dispersion | 43 |
252 The critical habitat size problem | 45 |
253 Densitydependent growth and dispersion | 46 |
SPECIES INTERACTIONS IN DIFFUSIVE SYSTEMS | 49 |
262 Diffusive instability in models of interacting species | 52 |
263 Competitive coexistence through habitatpartitioning | 55 |
27 SUMMARY | 57 |
3 Population dynamics in patchy environments | 59 |
32 THE PATCHABUNDANCE APPROACH | 61 |
322 The general model | 62 |
323 The problem of state variable choice | 63 |
331 The multispecies multipatch LotkaVolterra model | 68 |
332 Persistence and coexistence conditions | 69 |
sourcesink dynamics | 73 |
335 Spatial pattern and competitive coexistence | 74 |
336 Single species resilience and risk spreading | 76 |
34 PREDATION IN PATCHY HABITATS | 78 |
341 Diffusive coupling of identical predatorprey patches | 82 |
342 Dispersal asymmetry and stability in a twopatch LotkaVolterra model | 86 |
343 Aggregation and stability in a twopatch environment | 88 |
344 The effects of predator mobility and delayed functional response | 94 |
35 CHAOTIC DYNAMICS OF SINGLESPECIES SYSTEMS IN PATCHY ENVIRONMENTS | 95 |
dispersion and stability in coupled maps | 96 |
the multipatch extension of the coupled logistic model | 99 |
353 Selforganized criticality defeats chaos in a coupled map lattice | 104 |
36 SUMMARY | 109 |
metapopulations and aggregated interactions | 111 |
42 METAPOPULATIONS AND METACOMMUNITIES | 112 |
421 Colonizationextinction equilibrium in the basic model | 113 |
the asynchronous agestructured model | 114 |
4211 Comparing patchabundance and patchoccupancy models | 136 |
incidence function models | 137 |
43 AGGREGATION MODELS OF SPECIES INTERACTIONS | 140 |
the NicholsonBailey model | 141 |
aggregation of encounters in a patchy host distribution | 144 |
433 Spatially undetermined aggregation of interactions | 149 |
44 SUMMARY | 151 |
5 Sitebased neighbourhood models | 155 |
52 INTERACTING PARTICLE SYSTEMS AND CELLULAR AUTOMATA | 156 |
522 Meanfield and configurationfield approximations to interacting particle systems | 159 |
523 Aspects of complexity in interacting particle systems | 163 |
53 INTERACTING PARTICLE SYSTEMS AND CELLULAR AUTOMATA IN ECOLOGY | 164 |
531 Discrete individuality and dynamical coexistence | 165 |
532 Interacting particle system models of competing metapopulations with temporary and permanent habitat destruction | 172 |
533 The temporal refuge effect in onesided competition an example for a configurationfield approximation | 174 |
534 The role of mesoscale patterns in the dynamics of predator prey cellular automata | 182 |
535 Plant competition along an environmental gradient | 185 |
536 Plant competition in a fractal environment | 188 |
537 The effect of clonal integration on plant competition for mosaic habitat space | 195 |
538 Percolation models of spreading populations epidemics and forest fires | 198 |
54 SUMMARY | 199 |
6 Individualbased neighbourhood models | 202 |
62 TESSELLATION MODELS | 203 |
the Voronoi assignment model | 206 |
622 An interpretation of the selfthinning rule on the individual level | 207 |
623 Tessellation models of territory establishment | 210 |
linking tessellations to demography | 212 |
weighted tessellations | 213 |
63 DISTANCE MODELS | 218 |
631 Fixed radius neighbourhood models | 220 |
632 Zone of influence models | 231 |
633 Ecological field models | 239 |
64 SUMMARY | 242 |
7 Epilogue | 244 |
The Taylor expansion of univariate and bivariate functions | 246 |
Stability analysis with the local linearization method | 248 |
The definition of leading principal minors | 250 |
| 251 | |
| 270 | |
Common terms and phrases
abundance actual advection aggregation analytical applied approach assumed assumption asynchrony behaviour Biol biological boundary cellular automata clonal coexistence colonization competition configuration-field constant coupled map lattices Czárán density dependence diffusion equation diffusion models discrete dispersal distribution Ecol ecological effect environment environmental equilibrium example extinction rate fecundity Figure focal fractal Fractal dimension function grid growth rate habitat patches Hanski heterogeneity host i-state initial interacting particle systems interior fixed point IPS model IPSS lattice Levin linear Lotka-Volterra model matrix mechanism metapopulation models multispecies neighbourhood models neighbours occupied Oecologia Pacala parasitoid particle systems patch model patch occupancy patch-abundance models persistence perturbations plant polygon population density population dynamics population growth positive possible predator predator-prey predictor prey probability propagules ramets random walk reaction-diffusion rules seedling simulation single-species spatial pattern spatiotemporal species stability stochastic structure subpopulation synchronous temporal tessellation tessellation models theoretical tion unstable values Voronoi Voronoi diagram Voronoi polygon