Design-based estimation of mark variograms in forest ecosystem surveys

Mark variograms are widely adopted in forest ecosystem studies for analyzing spatial interaction among trees. Inference on mark variograms can be performed under a model-dependent perspective (ergodic variograms) or under a deterministic perspective (non-ergodic variograms). A simple and workable definition of non-ergodic mark variogram is introduced based on distances between pairs of trees distinguished by distance classes. Design-based estimators of mark variogram values are proposed as the ratio of two Horvitz-Thompson estimators using replicated plots randomly located on the study area and making use of the inclusion probabilities of the pairs of trees. Jackknife estimators of their variances are considered. A simulation study is performed on a real forest stand to check the statistical performance of the proposed strategy. (c) 2019 Elsevier B.V. All rights reserved.