Aggregation dynamics explain vegetation patch-size distributions

• Published in: Theoretical population biology 2016-04, Vol.108, p.70-74
• Main Authors: Irvine, M.A., Bull, J.C., Keeling, M.J.
• Format: Article
• Language: English
• Subjects: Aggregation; Ecosystem; Models, Biological; Patch-size distribution; Pattern formation; Population Dynamics; Spatial ecology
• ISSN: 0040-5809; 1096-0325
• DOI: 10.1016/j.tpb.2015.12.001

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.