Spatial statistics in ecological analysis: from indices to functions

Abstract

• Spatial statistics provides a quantitative description of natural variables distributed in space and time.• The objectives of spatial analysis are to detect spatial patterns and to confirm if a pattern found is significant. • Spatially explicit indices and functions may be applied depending on the information collected from the field. • Development of the specific software supports spatial analyses. AbstractThis paper presents a review of the most common methods in ecological studies aimed at spatial analysis of population structures (horizontal and vertical), based on point process statistics. Methods based on simple spatially explicit indices as well as more sophisticated methods relying on functions are described in a comprehensible manner. Simple indices revealing the information on spatial structure at the scale of the nearest neighbor can be easily implemented in practical forestry. On the other hand, spatial functions, based on much more detailed data, describe the spatial structure in terms of the spatial relationships between the natural processes and population structures and because of this complexity they are rarely used in forest practice. Including both methods in a single paper is also valuable from the potential reader's point of view saving their time for searching and choosing the appropriate method to make their spatial analysis. This paper can also serve as an initial guide for young researchers or those who are going to start their studies on spatial aspects of bio-systems. Avoiding the statistical and mathematical details makes this paper understandable for readers who are not statisticians or mathematicians. Readers will find many references related to each method described here, allowing them to find solutions to different problems observed in practice. This paper ends with a list of the most common specific software packages available to support spatial analysis.

Spatial diversity of forest regeneration after catastrophic wind in northeastern Poland

“…In contrast to distance methods such as the Clark-Evans index, angles do not have to be measured exactly; rather, it is sufficient to classify the angles (Pommerening 2002, Pukkala & Gadow 2012, Szmyt 2014). This index can take four values in the case of 3 neighbors taken into account: 0; 0.33; 0.66 and 1.0.…”

“…This index can take four values in the case of 3 neighbors taken into account: 0; 0.33; 0.66 and 1.0. Values of W≤0.5 indicate a regular distribution of specimens, 0.5<W≤0.6 indicate a random distribution, while W>0.6 indicate a clumped arrangement of trees (Pommerening 2002, Szmyt 2014.…”

Comparison ofT-Square, Point Centered Quarter, andN-Tree Sampling Methods inPittosporum undulatumInvaded Woodlands

“…All these methods are essentially based on the distance measures from event to event or from point to event [1,25].…”

“…Some of the distance methods can be used to determine the general spatial pattern or distribution of a population [13,28] and are useful to determine inter-and intraspecific relationships in plant communities [29]. Advantages arise from ease of use calculation and interpretation by foresters [25]. Their great disadvantage is connected with the loss of detailed information about spatial patterns at different spatial scales [30], describing the spatial structure only at the fine scale of nearest neighbors [25].…”

“…Advantages arise from ease of use calculation and interpretation by foresters [25]. Their great disadvantage is connected with the loss of detailed information about spatial patterns at different spatial scales [30], describing the spatial structure only at the fine scale of nearest neighbors [25].…”