title: Aggregation dynamics explain vegetation patch-size distributions.
abstract: Vegetation patch-size distributions have been an intense area of study for theoreticians and applied ecologists alike in recent years. Of particular interest is the seemingly ubiquitous nature of power-law patch-size distributions emerging in a number of diverse ecosystems. The leading explanation of the emergence of these power-laws is due to local facilitative mechanisms. There is also a common transition from power law to exponential distribution when a system is under global pressure, such as grazing or lack of rainfall. These phenomena require a simple mechanistic explanation. Here, we study vegetation patches from a spatially implicit, patch dynamic viewpoint. We show that under minimal assumptions a power-law patch-size distribution appears as a natural consequence of aggregation. A linear death term also leads to an exponential term in the distribution for any non-zero death rate. This work shows the origin of the breakdown of the power-law under increasing pressure and shows that in general, we expect to observe a power law with an exponential cutoff (rather than pure power laws). The estimated parameters of this distribution also provide insight into the underlying ecological mechanisms of aggregation and death.
authors.affiliation: Centre for Complexity Science, University of Warwick, Coventry, CV4 7AL, UK. Electronic address: m.irvine.1@warwick.ac.uk.
authors.forename: M A
authors.initials: MA
authors.lastname: Irvine
authors.affiliation: Department of Biosciences, Wallace Building, Swansea University, Swansea, SA2 8PP, UK.
authors.forename: J C
authors.initials: JC
authors.lastname: Bull
authors.affiliation: Centre for Complexity Science, University of Warwick, Coventry, CV4 7AL, UK.
authors.forename: M J
authors.initials: MJ
authors.lastname: Keeling
mesh_terms: D017753:Ecosystem; D008954:Models, Biological; D011157:Population Dynamics
keywords: Aggregation; Patch-size distribution; Pattern formation; Spatial ecology