Development of a Local Size Hierarchy Causes Regular Spacing of Trees in an Even-aged Abies Forest: Analyses Using Spatial Autocorrelation and the Mark Correlation Function

Abstract

This is the first study to detect local size hierarchies as a prelude to regular spacing using the mark correlation function. The results confirm that use of the mark correlation function together with the spatial autocorrelation function is an effective tool to analyse the development of a local size hierarchy of trees in a forest.

Spatial autocorrelation of tree attributes in naturally regenerated managed beech (Fagus sylvatica) forests in the Beskid Niski Mountains, southern Poland

“…In other ecological situations also positive correlation of tree heights is possible, for example in forests with trees of different age, where young trees appear in clusters. An interesting example is discussed in Suzuki et al (2008). In an even-aged Abies forests in Japan they observed that the correlation of tree heights changed from positive to "no correlation" during the early stage of stand development, whereas in the older stages of forest development it was changed again from "no correlation" to negative one.…”

“…Applications of marked point process statistics in forest sciences can be found in Penttinen et al (1992), Wälder and Stoyan (1996), Degenhardt (1999), Stoyan and Penttinen (2000), Gavrikov and Stoyan (1995), Pommerening (2002), Kint et al (2003), Wälder and Wälder (2008), Suzuki et al (2008), Law et al (2009, Ledo et al (2011), Pommerening andSärkkä (2013).…”

“…Mark correlation function or mark variograms describe a multitude of scales of inter-tree distances (Penttinen et al 1992;Gavrikov and Stoyan 1995;Penttinen 2006;Pommerening 2002;Kint et al 2003;Suzuki et al 2008;Comas et al 2011;Ledo et al 2011;Pommerening and Särkkä 2013). Studies on spatial correlations of quantitative marks can answer questions on differences between marks in dependence on the distances of the corresponding trees (Illian et al 2008).…”

Spatial statistics in ecological analysis: from indices to functions

“…plants, trees) and environmental factors on their sizes. It characterizes squared differences between marks (m) of pairs of points within the distance of r under the condition that there are points at locations x and x + r (Stoyan and Penttinen 2000;Stoyan and Wälder 2000;Suzuki et al 2008;Gonçalves et al 2011;Pommerening and Särkkä 2013):…”

“…Examples of applications of different functions mentioned above can be found in Kuuluvainen et al (1996), Kenkel (1997), Rozas (2003), Getzin et al (2006), Wiegand et al (2007), Illian et al (2008), Suzuki et al (2008), Wälder and Wälder (2008), Gray and He (2009), Nuske et al (2009), Picard et al (2009, Rozas et al (2009), Zhang et al (2010, Ledo et al (2011);Nanami et al (2011), Iszkuło et al (2012 and Pommerening et al (2013). …”