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C. Palaghianu 2010. The use of Voronoi tessellation to characterize sapling populations
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The use of Voronoi tessellation to characterize sapling populations
Ciprian Palaghianu *
Forestry Faculty, “Stefan cel Mare” University of Suceava, Romania
Abstract
The area potentially available to an individual plant represents a concept extensively used in
population ecology but it has fewer implementations in forest research. In this paper I use a
Voronoi tessellation in order to determine area potentially available to a sapling. The Voronoi
polygons were used to characterize spatial pattern of sapling distribution as well as the
competition relations between the individuals. Mathematically, the Voronoi tessellation
represents one of the best solutions to determine neighbouring competitors of a tree. The area of
Voronoi cells is frequently connected to biometrical attributes and the growth of the saplings.
Furthermore, analyzing the Voronoi tessellation of a sapling population can indicate the spatial
pattern of the saplings. It is considered that weighted Voronoi polygons may be more fitted for
assessing sapling relationships but it is more difficult to implement such specific algorithms.
Keywords: Voronoi tessellation, area potentially available, spatial pattern, sapling populations
1. Introduction
Researches used many times mathematical and especially geometrical techniques in their effort
to explain individual competition.
The area potentially available (APA) concept represents an uncommon, but rather promising
approach, introduced in plant ecology by Brown (1965). The same concept was independently
developed by Mead (1966), but early investigations in the field of plants growing space were
conducted also by Konig, mentioned in his book „Die Forst-Mathematik” (1835).
From the biological point of view, APA generally defines the area used by an individual to
access vital resources, the available area for a plant to satisfy its needs in water, nutrients and
light. So APA is very appealing to researchers interested in growth modelling, in their effort to
solve an everlasting problem: “Do trees grow faster because they are larger Or they are larger
because they have been growing faster” (Wichmann, 2002; Garcia, 2008).
Considering the difficulty of the analysis there are few researches using this approach (Mark,
Esler, 1970; Moore et al., 1973; Mercier, Baujard, 1997). Smith (1987) considers that this
approach is ignored or even avoided due to misapprehend of APA geometrical foundation and
computing difficulties. The late period is well-known for its computer development and also
numerous and various algorithms were produced. So, the APA re-enters in researcher’s
attention as a promising investigation tool.
The APA was used to solve not only competition issues but also mortality and dynamics of
seedlings (Owens, Norton, 1989) or spatial pattern (Mercier, Baujard, 1997). Regarding spatial
pattern, Garcia (2008) considers the interaction between neighbouring growing areas as a result
of autocorrelation. Two neighbours which are closer than average, will both have APA
undersized values and vice versa. Winsauer and Mattson (1992) have mentioned some
advantages to make use of APA in forest researches – potentially available areas are not
intersecting each other, there are sensitive to population dynamics and they are correlated with
* Ciprian Palaghianu. Tel.:+40745614487
Email address: cpalaghianu@usv.ro
Forest Landscapes and Global Change-New Frontiers in Management, Conservation and Restoration. Proceedings of the IUFRO Landscape Ecology
Working Group International Conference, September 21-27, 2010, Bragança, Portugal. J.C. Azevedo, M. Feliciano, J. Castro & M.A. Pinto (eds.)
2010, Instituto Politécnico de Bragança, Bragança, Portugal.