Environmental and Ecological Statistics

, Volume 23, Issue 2, pp 279–299 | Cite as

Two neighborhood-free plot designs for adaptive sampling of forests

  • Haijun Yang
  • Steen Magnussen
  • Lutz Fehrmann
  • Philip Mundhenk
  • Christoph Kleinn


Adaptive cluster sampling (ACS) has the potential of being superior for sampling rare and geographically clustered populations. However, setting up an efficient ACS design is challenging. In this study, two adaptive plot designs are proposed as alternatives: one for fixed-area plot sampling and the other for relascope sampling (also known as variable radius plot sampling). Neither includes a neighborhood search which makes them much easier to execute. They do, however, include a conditional plot expansion: at a sample point where a predefined condition is satisfied, sampling is extended to a predefined larger cluster-plot or a larger relascope plot. Design-unbiased estimators of population total and its variance are derived for each proposed design, and they are applied to ten artificial and one real tree position maps to estimate density (number of trees per ha) and basal area (the cross-sectional area of a tree stem at breast height) per hectare. The performances—in terms of relative standard error (SE%)—of the proposed designs and their non-adaptive alternatives are compared. The adaptive plot designs were superior for the clustered populations in all cases of equal sample sizes and in some cases of equal area of sample plots. However, the improvement depends on: (1) the plot size factor; (2) the critical value (the minimum number of trees triggering an expansion); (3) the subplot distance for the adapted cluster-plots, and (4) the spatial arrangement of the sampled population. For some spatial arrangements, the improvement is relatively small. The adaptive designs may be particularly attractive for sampling in rare and compactly clustered populations with critical value of 1, subplot distance equal to the diameter of initial circular plots, or plot size factor of 2.5 for an initial basal area factor of 2.


Adaptive sampling Conditional plot expansion Forest inventory Inclusion zones Neighborhood-free plot design 



First of all, we would like to gratefully acknowledge the financial support of DFG (German Research Foundation) for the research project KL 894/10-1. The results presented in this paper are part of that project. Our sincere thanks go to Prof. Dr. Shouzheng Tang, Prof. Dr. Yuancai Lei and Dr. Guangyu Zhu for their kind support during the field work of mapping our real population. Finally, we are grateful to the anonymous reviewers for a very careful and thorough reviewing of this manuscript with valuable comments and suggestions that prompted a number of improvements.

Compliance with ethical standards

Conflict of interest

We hereby declare that we have no conflict of interest.


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Haijun Yang
    • 1
  • Steen Magnussen
    • 2
  • Lutz Fehrmann
    • 1
  • Philip Mundhenk
    • 1
  • Christoph Kleinn
    • 1
  1. 1.Forest Inventory and Remote SensingGeorg-August-Universität GöttingenGöttingenGermany
  2. 2.Natural Resources Canada, Canadian Forest ServicePacific Forestry CentreVictoriaCanada

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