Population Dynamics in Spatial Habitats

Tilman, David; Lehman, Clarence; Kareiva, Peter

doi:10.2307/j.ctv36zpzm.6

Cited by 102 publications

(131 citation statements)

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“…Individual plants typically interact more with nearby than with distant individuals (Rees et al, 1996;Tilman et al, 1997). Consequently, an introduction's success or failure can depend on effects regulated by neighborhood, rather than global, densities (Higgins et al, 1996;Wilson, 1998).…”

Section: Spatial Model For Invader -Resident Competitionmentioning

confidence: 99%

Spatial dynamics of invasion: the geometry of introduced species

Korniss

Caraco

2005

Journal of Theoretical Biology

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Many exotic species combine low probability of establishment at each introduction with rapid population growth once introduction does succeed. To analyze this phenomenon, we note that invaders often cluster spatially when rare, and consequently an introduced exotic's population dynamics should depend on locally structured interactions. Ecological theory for spatially structured invasion relies on deterministic approximations, and determinism does not address the observed uncertainty of the exotic-introduction process. We take a new approach to the population dynamics of invasion and, by extension, to the general question of invasibility in any spatial ecology. We apply the physical theory for nucleation of spatial systems to a lattice-based model of competition between plant species, a resident and an invader, and the analysis reaches conclusions that differ qualitatively from the standard ecological theories. Nucleation theory distinguishes between dynamics of single-cluster and multi-cluster invasion. Low introduction rates and small system size produce single-cluster dynamics, where success or failure of introduction is inherently stochastic. Single-cluster invasion occurs only if the cluster reaches a critical size, typically preceded by a number of failed attempts. For this case, we identify the functional form of the probability distribution of time elapsing until invasion succeeds. Although multi-cluster invasion for sufficiently large systems exhibits spatial averaging and almostdeterministic dynamics of the global densities, an analytical approximation from nucleation theory, known as Avrami's law, describes our simulation results far better than standard ecological approximations.

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Section: Spatial Model For Invader -Resident Competitionmentioning

confidence: 99%

Spatial dynamics of invasion: the geometry of introduced species

Korniss

Caraco

2005

Journal of Theoretical Biology

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“…The metapopulation modeling approach is an essential theoretical framework used in population ecology, genetics and adaptive evolution to describe population dynamics whenever the spatial structure of populations is known to play a key role in the system's evolution (Hanski & Gilpin, 1997;Hanski & Gaggiotti, 2004;Tilman & Kareiva, 1997;Bascompte & Solé, 1998). Metapopulation models rely on the basic assumption that the system under study is characterized by a highly fragmented environment in which the population is structured and localized in relatively isolated discrete patches or subpopulations connected by some degree of migration.…”

Section: Introductionmentioning

confidence: 99%

Epidemic modeling in metapopulation systems with heterogeneous coupling pattern: Theory and simulations

Colizza

Vespignani

2008

Journal of Theoretical Biology

443

490

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The spatial structure of populations is a key element in the understanding of the large scale spreading of epidemics. Motivated by the recent empirical evidence on the heterogeneous properties of transportation and commuting patterns among urban areas, we present a thorough analysis of the behavior of infectious diseases in metapopulation models characterized by heterogeneous connectivity and mobility patterns. We derive the basic reaction-diffusion equation describing the metapopulation system at the mechanistic level and derive an early stage dynamics approximation for the subpopulation invasion dynamics. The analytical description uses degree block variables that allows us to take into account arbitrary degree distribution of the metapopulation network. We show that along with the usual single population epidemic threshold the metapopulation network exhibits a global threshold for the subpopulation invasion. We find an explicit analytic expression for the invasion threshold that determines the minimum number of individuals traveling among subpopulations in order to have the infection of a macroscopic number of subpopulations. The invasion threshold is a function of factors such as the basic reproductive number, the infectious period and the mobility process and it is found to decrease for increasing network heterogeneity. We provide extensive mechanistic numerical Monte Carlo simulations that recover the analytical finding in a wide range of metapopulation network connectivity patterns. The results can be useful in the understanding of recent data driven computational approaches to disease spreading in large transportation networks and the effect of containment measures such as travel restrictions.

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“…The numerical simulations were performed with a two-dimensional analytic model of this flow (19,21). It is a specific model in the broad class of spatially extended systems (24,25), but here the motion of individuals is determined by well-known physical (hydrodynamical) laws. Technically, we do not study a partial differential equation or cellular automaton governing the dynamics of populations as in most available approaches (24,25) but follow the interaction of individuals whose motion is driven by the advection of the hydrodynamical flow (26).…”

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confidence: 99%

Chaotic flow: The physics of species coexistence

Károlyi

Péntek

Scheuring

et al. 2000

Proc. Natl. Acad. Sci. U.S.A.

126

101

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Hydrodynamical phenomena play a keystone role in the population dynamics of passively advected species such as phytoplankton and replicating macromolecules. Recent developments in the field of chaotic advection in hydrodynamical flows encourage us to revisit the population dynamics of species competing for the same resource in an open aquatic system. If this aquatic environment is homogeneous and well-mixed then classical studies predict competitive exclusion of all but the most perfectly adapted species. In fact, this homogeneity is very rare, and the species of the community (at least on an ecological observation time scale) are in nonequilibrium coexistence. We argue that a peculiar small-scale, spatial heterogeneity generated by chaotic advection can lead to coexistence. In open flows this imperfect mixing lets the populations accumulate along fractal filaments, where competition is governed by an ''advantage of rarity'' principle. The possibility of this generic coexistence sheds light on the enrichment of phytoplankton and the information integration in early macromolecule evolution.

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Population Dynamics in Spatial Habitats

Cited by 102 publications

References 0 publications

Spatial dynamics of invasion: the geometry of introduced species

Spatial dynamics of invasion: the geometry of introduced species

Epidemic modeling in metapopulation systems with heterogeneous coupling pattern: Theory and simulations

Chaotic flow: The physics of species coexistence

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