Arne Pommerening's Forest Biometrics & Quantitative Ecology Lab

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Tree location map of Clocaenog plot 6. Orange: Japanese larch (Larix kaempferi (Lamb.) Carr.), Olive: Sitka spruce (Picea sitchensis (Bong.) Carr.), Maroon: Rowan (Sorbus aucuparia L.), White: other species (including Scots pine, lodgepole pine, Norway spruce, sessile oak, ash, birch, willow and holly). The size of the circles are scaled by stem diameter at 1.3 m above ground level. The map was prepared with the R script TreeDiversityIndices.R‎ in conjunction with the spatstat package.
Philodendron International


This website and all associated computer code are part of a research area, which is dedicated to systems analysis of forest ecosystems, an important branch of ecological statistics integrating research on forest structure, tree growth analysis, monitoring and modelling. All data, that are collected in forest ecosystems, have not only a temporal but also a spatial dimension. The properties of the whole system “forest”, e.g. forest growth and interactions between trees, to a large degree depend on the structure of this system. This has been known in forest science for a long time and has given rise to traditional terms such as “growing space” and “initial spacing”. In the last decades, new methods were developed in the statistical fields of point process statistics, geostatistics and random set statistics. These allow better and more detailed research of the interplay between spatial patterns and ecological processes. Apart from statistics and mathematics also other research fields such as physics and materials science have contributed to structural research. The latter subject area has coined the term of structure-property relationships. According to this term ecological processes not only leave traces as spatial patterns, but the spatial structure of materials or of a forest also determines to a large degree the properties of the system under study. This suggests that the results of forest management, e.g. forest products, but also natural regeneration responding to silvicultural systems, are examples of such system properties, which are largely determined by its structure. Structure-property relationships also apply to ecosystem services such as growth and yield and the provision of habitats and recreation. Competition and survival of trees are such properties as well as the sampling error of forest resource inventories, which is strongly correlated with spatial forest structure. Spatial statistics and inventory research are therefore closely related. Also any impact on forests - whether natural or human-induced - is primarily a change of forest structure. It is crucial for my research vision that the quantification, the understanding and the modelling of (spatial) woodland structure and its temporal evolution play a decisive role for the development of sampling and monitoring designs as well as for forest modelling. Spatial statistics and sampling theory share many overlaps which can be used as synergies. And there is certainly no sustainable silviculture and forest management without a proper understanding of woodland structure as every forest practioner can tell you. The publications below, particularly those relating to reconstruction (Pommerening, 2006; Pommerening and Stoyan, 2008) prove and illustrate this research vision.


A group photo of my research team at Umeå: Arne Pommerening, Anton Grafström, Xin Zhao, Anders Muszta, Kenneth Nyström and Jaime Uría Díez (from left to right).

I work as a Professor in Mathematical Statistics Applied to Forest Sciences at the Swedish University of Agricultural Sciences in Umeå and my research areas include woodland structure analysis and modelling, spatio-temporal dynamics of plant point patterns, individual-based modelling with a focus on plant interactions, plant growth analysis, methods of quantifying and monitoring biodiversity and the analysis of human behaviour of selecting trees. Much of my research is computer-based using simulation experiments and my research is strongly interdisciplinary and international.

My Chair is described in greater detail here. Recently I have started a webblog on current issues in Forest Biometrics and you are welcome to follow the discussions on this address. I am also the director of the Centre for Statistics (Statistics@SLU), a centre for statistical consultation and education at the Swedish University of Agricultural Sciences. In addition I direct the graduate Research School in Applied Statistics and Scientific Computing.

On this websites you find information on some of my research and teaching work. As a service to the international research community I provide computer programs and code that I prepared for teaching and research so that you can explore, test and better understand the methods described in my work.

CRANCOD - A Program for the Analysis and Reconstruction of Spatial Forest Structure

In the last few decades an impressive number of structural indices (also referred to as nearest neigbour summary statistics [NNSS]) have been developed to quantify spatial forest structure. Of particular interest in this regard is the development of a family of individual tree neighbourhood-based indices, which are measures of small-scale variations in tree locations, species and dimensions, developed by Gadow and colleagues at Göttingen University (Germany). Especially when expressed as frequency distributions these indices offer valuable information on spatial woodland structure. Forest structure is closely correlated to and an expression of biodiversity at forest stand level (α diversity). Therefore the structural quantities used in CRANCOD play an important role as surrogate measures of biodiversity (Pommerening, 2002).

The CRANCOD program is a virtual laboratory for analysing and experimenting with nearest neighbour summary statistics and second-order characteristics. CRANCOD has been designed for use with large research plots including full enumerations of trees and in addition offers the opportunity to analyse forest inventory data consisting of multiple sample plots of circular or rectangular shape and varying plot size based on a systematic grid. The program has inbuilt flexibility with the user able to select the number of neighbour trees and to choose between six different methods of edge correction. CRANCOD can, of course, also be used to analyse research and sample plots without spatial information (stand analysis).

The integrated sampling simulator ISIS allows the simulation of sampling with systematic selection of sample plots of varying plot geometry.

Saving individual-tree results in addition to the summary files provides the opportunity to carry out individual-tree based follow-up research. A special visualisation tool allows the user to visually explore nearest neighbour summary statistics. Tree species codings and colours can be flexibly edited externally. A number of language options allow optimal adaptation of the program in different countries.

Mean directional index in Clocaenog plot 6. The arithmetic mean, the bar plots and the density distributions indicate slight regularity of tree locations. The mean directional index was calculated with the R script TreeDiversityIndices.R‎.

Author, copyrights and contact: Prof. Arne Pommerening ( or

Software version: 1.4

Licenses: The core version of CRANCOD is a public domain software. However, the program is protected by intellectual property rights and users are expected to acknowledge CRANCOD and its developer when publishing results.

You can find more about the philosophy and objectives of the program along with other details including a downloadable version here.

Selected R scripts and C++ files

Some of the functionality of CRANCOD and additional methods have also been implemented in the R language and in C++. (Computation time can be significantly reduced when combining the advantages of both languages.) When using R scripts/C++ files from the list below for research purposes please acknowledge the author. Instructions on how to integrate R and C++ code are provided here.

Non-spatial analysis

  • Download the script StandAnalysis.R to calculate basal area, trees per hectare, mean diameters, height diameter regression, top height/diameter, diameter distribution and Shannon index along with the Clocaenog 6 sample data. Last updated on 06.07.2012.

Tree growth and modelling

  • Download the script BEM.R and the necessary C++ file BEM.cpp to use the stand development model by Prof. Günter Wenk and colleagues. The model is based on relative growth rates (see my publications). A short model guide will help to get used to the model. Also read Wenk (1994). The file BEMreport.Rnw will allow you to produce Latex/pdf reports of the model outputs. Find an example output here. Last updated on 25.07.2014.
  • Download the R package WenkRegression to model volume, height and diameter development of single stem analysis trees for identifying unusual growth patterns along with sample data from a Sitka spruce tree in Gwydyr forest (North Wales). Unpack the zip file and load the package in R using the package installer. A help file (invoked in R by the command help(WenkRegression)) contains all necessary details. For the modelling theory refer to Wenk (1994) and to my publications in this field. To get started use this example R file. Last updated on 02.12.2015.
  • Download the script AllometricCoefficient.R to calculate the allometric coefficient m quantifying the relationship between diameter and height growth of trees along with sample data from a Sitka spruce tree in Gwydyr forest (North Wales). There is a brief interpretation guide for your convenience. This methodology can also be applied to time series data from forest monitoring with arbitrary survey cycles. Last updated on 20.05.2013.

Diversity indices

Second-order characteristics


  • Download the script Construction.R to simulate a point pattern with a user-defined value of the aggregation index by Clark and Evans (1954) along with a short documentation. Last updated on 18.01.2013.
  • Download a faster version of the script Construction.R along with the necessary C++ code. Last updated on 18.01.2013.
Mark variogram (with bandwidth h = 4.0 m, red line) based on breast-height diameter of Clocaenog plot 6 indicating that trees at close proximity tend to be similar in size (positive autocorrelation). This has been caused by cohorts of regeneration trees. The shaded area is the acceptance region for the random labelling hypothesis. The lower and upper envelopes give the 2.5% and 97.5% quantiles. The random labelling hypothesis clearly needs to be rejected for distances up to 15 m. The dashed line indicates the mark variance. The mark variogram was estimated with the R script MarkVariogramC.R‎.

A selection of publications

Pommerening, A., 2002. Approaches to quantifying forest structures. Forestry 75, 305-324. [PdF file]
Pommerening, A. and Murphy, S. T., 2004. A review of the history, definitions and methods of continuous cover forestry with special attention to afforestation and restocking. Forestry. 77, 27–44. [PdF file]
Pommerening, A., 2006. Evaluating structural indices by reversing forest structural analysis. For. Ecol. Manage. 224, 266–277. [PdF file]
Pommerening, A. and Stoyan, D., 2006. Edge-correction needs in estimating indices of spatial forest structure. Can. J. For. Res. 36, 1723–1739. [PdF file]
Mason, W. L., Connolly, T., Pommerening, A. and Edwards, C., 2007. Spatial structure of semi-natural and plantation stands of Scots pine (Pinus sylvestris L.) in northern Scotland. Forestry 80, 567-586. [PdF file]
Pommerening, A. and Stoyan, D., 2008. Reconstructing spatial tree point patterns from nearest neighbour summary statistics measured in small subwindows. Can. J. For. Res. 38, 1110–1122. [PdF file]
Pommerening, A., 2008. Analysing & modelling spatial woodland structure. Habilitation thesis BOKU University Vienna. Bangor, 145p. [PdF file]
Davies, O. and Pommerening, A., 2008. The contribution of structural indices to the modelling of Sitka spruce (Picea sitchensis) and birch (Betula spp.) crowns. For. Ecol. Manage. 256, 68–77. [PdF file]
Crecente-Campo, F., Pommerening, A. and Rodríguez-Soalleiro, R., 2009. Impacts of thinning on structure, growth and risk of crown fire in a Pinus sylvestris L. plantation in northern Spain. For. Ecol. Manage. 257, 1945-1954. [PdF file]
LeMay, V., Pommerening, A. and Marshall, P., 2009. Spatio-temporal structure of multi-storied, multi-aged interior Douglas fir (Pseudotsuga menziesii var glauca) stands. J. Ecol. 97, 1062-1074. [PdF file]
Motz, K., Sterba, H. and Pommerening, A., 2010. Sampling measures of tree diversity. For. Ecol. Manage. 260, 1985–1996. [PdF file]
Murphy, S. T. and Pommerening, A., 2010. Modelling the growth of sitka spruce (Picea sitchensis (BONG.) CARR.) in Wales using Wenk's model approach. Allg. Forst- u. J.-Ztg. 181, 35-43. [PdF file]
Pommerening, A., LeMay, V. and Stoyan, D., 2011. Model-based analysis of the influence of ecological processes on forest point pattern formation - A case study. Ecol. Model. 222, 666-678. [PdF file]
Pommerening, A., Gonçalves, A. C. and Rodríguez-Soalleiro, R., 2011. Species mingling and diameter differentiation as second-order characteristics. Allg. Forst- u. J.-Ztg. 182, 115-129. [PdF file]
Gonçalves, A. C. and Pommerening, A., 2011. Spatial dynamics of cone production in Mediterranean climates: A case study of Pinus pinea L. in Portugal. For. Ecol. Manage. 266, 83–93. [PdF file]
Gadow, K. v., Zhang, C. Y., Wehenkel, C., Pommerening, A., Corral-Rivas, J., Korol, M., Myklush, S., Hui, G. Y., Kiviste, A. and Zhao, X. H., 2012. Forest structure and diversity, 29 - 83. In: Pukkala, T. and Gadow, K. v. (Eds.), 2012: Continuous cover forestry. 2nd edition. Managing Forest Ecosystems 23. Springer. Dordrecht, 296p. [PdF file]
Pommerening, A. and Särkkä, A., 2013. What mark variograms tell about spatial plant interactions. Ecol. Model. 251, 64-72. [PdF file]
Schütz, J.P. and Pommerening, A., 2013. Can Douglas fir (Pseudotsuga menziesii (Mirb.) Franco) sustainably grow in complex forest structures? For. Ecol. Manage. 303, 175-183. [PdF file]
Lilleleht, A., Sims, A. and Pommerening, A., 2014. Spatial forest structure reconstruction as a strategy for mitigating edge-bias in circular monitoring plots. For. Ecol. Manage. 316, 47-53. [PdF file]
Hui, G. and Pommerening, A., 2014. Analysing tree species and size diversity patterns in multi-species uneven-aged forests of Northern China. For. Ecol. Manage. 316, 125-138. [PdF file]
Pommerening, A. and Maleki, K., 2014. Differences between competition kernels and traditional size-ratio based competition indices used in forest ecology. For. Ecol. Manage. 331, 135-143. [PdF file]
Pommerening, A. and Muszta, A., 2015. Methods of modelling relative growth rate. Forest Ecosystems. 2, 5. [PdF file]
Abellanas, B., Abellanas, M., Pommerening, A., Lodares, D., Cuadros, S., 2016. A forest simulation approach using weighted Voronoi diagrams. An application to Mediterranean fir Abies pinsapo Boiss stands. Forest Systems. 25, e062. [PdF file]
Brzeziecki, B., Pommerening, A., Miścicki, S., Drozdowski, S. and Żybura, H., 2016. A common lack of demographic equilibrium among tree species in Białowieża National Park (NE Poland): evidence from long-term plots. Journal of Vegetation Science 27, 460-469. Doi: 10.1111/jvs.12369. [Link]
Pommerening, A., Brzeziecki, B. and Binkley, D., 2016. Are long-term changes in plant species composition related to asymmetric growth dominance in the pristine Białowieża Forest? Basic and Applied Ecology 17, 408-417. Doi: 10.1016/j.baae.2016.02.002. [Link]
Pommerening, A. and Muszta, A., 2016. Relative plant growth revisited: towards a mathematical standardisation of separate approaches. Ecological Modelling 320, 383-392. [Link]
Vítková, L., Ní Dhubháin, Á and Pommerening, A., 2016. Agreement in tree marking: What is the uncertainty of human tree selection in selective forest management? Forest Science 62, 288-296. Doi: 10.5849/forsci.15-133. [Link]
Uria-Diez, J. and Pommerening, A., 2017. Crown plasticity in Scots pine (Pinus sylvestris L.) as a strategy of adaptation to competition and environmental factors. Ecological Modelling 356, 117-126. [Link]

Mingling distribution of beech (Fagus sylvatica L., red) and ash (Fraxinus excelsior L., green) in the mixed species woodland Södderich 55B (near Göttingen, Germany). A common situation in woodlands managed for valuable hardwoods: Whilst dominant ash trees mostly have neighbours of different species, the dominated beech trees are arranged in conspecific clusters. The mingling index was calculated with the R script TreeDiversityIndices.R‎.
Modelling the growth of stem-analysis tree 486 (Sitka spruce) in Gwydyr Forest (North Wales) using the Wenk approach based on the Gompertz function and on relative increment. Black: observed data, red line: Wenk model. The growth parameter c1 = 0.268, the parameter c2 = 1.218 and the allometric coefficients m1 = 2.742 and m2 = 1.032 were determined through simultaneous regression. This was accomplished with the R package WenkRegression.

Additional text resources

Visitors of this website who are unfamiliar with the topic of forest structure research and forestry summary characteristics may want to read the following documents:

Feedback and cooperation

The developer of the CRANCOD software and the R scripts is particularly interested in feedback concerning any aspect of the program and of the provided listings to improve their functionality and usefulness in future versions. Please report your feedback to or The author is very open to any kind of cooperation, particularly in terms of joint publications. It would also be possible to maintain CRANCOD and the associated R/C++ files with an international project team in the future.

Recent external workshops, research visits and (summer) schools

  • Lectures on forest growth and yield at Göttingen University, Germany, 23 - 27 July 2012.
  • "Analysing & Modelling Forest Structure – an Introduction" at Tartu University of Life Sciences, Estonia, 8 - 12 October 2012.
  • Lectures at Warsaw University of Life Sciences in November, December 2013 and January 2014.
  • "Analysis of human tree selection behaviour". Lectures at Göttingen University, Germany, 19 - 21 June 2014 and 7 - 9 April 2015.
  • Programme and schedule of the Research School in Applied Forest Statistics and Scientific Programming (SLU, Umeå) for 2017.
  • R code relating to the NOVA course "Introduction to Scientific Programming and Simulation" at Umeå on 16.06.2017 (Introduction to simulations).

For internal courses please visit the SLU website. Do not hesitate to contact Arne Pommerening on or if you are interested in any kind research cooperation or if you simply have a question.


The CRANCOD software, all its libraries and algorithms, the R scripts and C++ files have been prepared with great care. However, the developer can not be made liable in the unlikely case of damage caused to your computer while using CRANCOD, the R scripts/packages and C++ files or of incorrect outputs.