Lattice geometry, gap formation and scale invariance in forests

Pagnutti, Christopher; Anand, Madhur; Azzouz, Mohamed

doi:10.1016/j.jtbi.2005.02.018

Cited by 9 publications

(4 citation statements)

References 29 publications

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“…The system thus spontaneously self-organizes by driving itself to the edge of the chaotic phase until P(t) stabilizes at a critical level P c , which corresponds to the percolation threshold. As in the sandpile case, Pagnutti et al [153] revealed that the system then displays two scaleinvariant properties: the distribution of gap sizes between trees and the distribution of fire lifetimes. Turcotte [154] and Boer et al [155] have verified the power laws of both properties in numerical simulations and using real data from North American and Australian forest fires.…”

Section: Self-organized Criticalitymentioning

confidence: 99%

Scale invariance in natural and artificial collective systems: a review

Khaluf

Ferrante

Simoens

et al. 2017

J. R. Soc. Interface.

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Self-organized collective coordinated behaviour is an impressive phenomenon, observed in a variety of natural and artificial systems, in which coherent global structures or dynamics emerge from local interactions between individual parts. If the degree of collective integration of a system does not depend on size, its level of robustness and adaptivity is typically increased and we refer to it as scale-invariant. In this review, we first identify three main types of self-organized scale-invariant systems: scale-invariant spatial structures, scale-invariant topologies and scale-invariant dynamics. We then provide examples of scale invariance from different domains in science, describe their origins and main features and discuss potential challenges and approaches for designing and engineering artificial systems with scale-invariant properties.

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Section: Self-organized Criticalitymentioning

confidence: 99%

Scale invariance in natural and artificial collective systems: a review

Khaluf

Ferrante

Simoens

et al. 2017

J. R. Soc. Interface.

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“…Manrubia and Solé (1997) and Pagnutti et al (2005) dealt with lattice models of forest dynamics with a richer vertical layering; Solé et al (2005) addressed the interaction between dispersal strategies and vertical forest stratification. These authors used simulations of cellular automata.…”

mentioning

confidence: 99%

A Pair-Approximation Model for Spatial Patterns in Tree Populations with Asymmetrical Resource Competition

Garcia-Domingo

Saldaña

2013

Mathematical Population Studies

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A pair-approximation model for the spatial dynamics of a height-structured tree population 10 is defined on a regular lattice where each site can be in one of three states: empty (gap site), occupied by an immature tree, and occupied by a mature tree. The nonlinearities are associated with resource competition effects of mature trees on immature ones (asymmetric competition) affecting the mortality of the latter but not their growth. The survival-extinction transition of the forest is expressed; the early dynamics of colonization are described in terms 15 of local densities. Predictions of the pair approximation model are compared with results from numerical simulations of cellular automata.

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“…From the viewpoint of spatial organization this means that the plant community of a given spatial area exhibits properties which go beyond the features of an ensemble of independent small‐scale subunits. In the simplest case, emergent phenomena may be a result of simple, local interactions between the subunits, in some cases accompanied with the phenomena of scale‐invariance (Pagnutti et al 2005). Nevertheless, both empirical and theoretical studies indicate that they often originate from diverse processes, acting on different spatial and temporal scales (O'Neill et al 1986, Levin 1992, Perry 1995, Peterson et al 1998), Therefore, the state of each site is influenced by both its immediate as well as its broader neighbourhood.…”

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confidence: 99%

Multi‐scale regulated plant community dynamics: mechanisms and implications

Szabó¹,

Meszéna²

2007

Oikos

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Plant competition is not a direct interaction, but operates via environmental feedback loops, which interconnect population densities and environmental regulating variables. It is suggested that due to scale dependent elements of these feedback loops, competition may occur eventually on very different scales, necessitating a cross-scale extension of plant competition theory. After introducing the concept of cross-scale competition, we incorporate its elements into a metacommunity model and study its implications on community organization. It is found that both the equilibrium community composition, regarding coexisting functional types, and its stability depend on scale dependent attributes of environmental feedback loops and disturbance regimes. We argue that plant communities are likely to exhibit properties, which are in line with the hierarchical ecosystem concept. Environmental feedback loops on different scales act as distinct organizational levels, what can be affected by disturbances of corresponding spatial extent.

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Lattice geometry, gap formation and scale invariance in forests

Cited by 9 publications

References 29 publications

Scale invariance in natural and artificial collective systems: a review

Scale invariance in natural and artificial collective systems: a review

A Pair-Approximation Model for Spatial Patterns in Tree Populations with Asymmetrical Resource Competition

Multi‐scale regulated plant community dynamics: mechanisms and implications

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