China has a long tradition of managing planted forests. Different species of Populus, Eucalyptus, Larix, Cunninghamia and Pinus are planted to satisfy the local demand for wood products and provide ecological services at the same time. Evidence of the greater resilience of natural forests provides the motivation to develop asymmetric planting patterns, which is the focus of this study. We present a new method for designing plantation patterns that follow those observed in natural ecosystems and to maintain some regularity for operational convenience. Based on the uniform angle index, we analyzed the spatial structure of six natural forests in different regions of China. The uniform angle index describes the degree of spatial uniformity of the n nearest neighbors of a given reference tree. Accordingly, we identified all possible patterns of a neighborhood group within a regular planting pattern and developed a method to optimize planting point arrangements that contain some randomness as well as a minimum degree of regularity. (1) There are 13 types of structural units in a regular planting, including seven random units, five even units and one cluster unit; (2) Five near-natural arrangements are presented with a minimum proportion of 50% of random units. These five arrangements represent a combination of regularity for operational convenience and asymmetry. The new planting patterns developed in this study are expected to increase the asymmetric competition and resilience of these important ecosystems. Some experimental plantings, based on our findings, have already been established, e.g., in Pinus tabulaeformis plantations in Tianshui, Gansu Province, and in a Populus deltoides plantation in Fangshan near Beijing.

Forest structure is largely determined by nearest neighbor interactions, and reveals detailed interpretations of the current situation and development potential of the stand. A structure-based method is needed to analyze the relationship of nearest neighbor tree groups and therefore to characterize the forest spatial heterogeneity in a comprehensively and systematically way. A natural mixed forest of Quercus aliena var. acutiserrata and Pinus tabulaeformis in the Xiaolong Mountains, China was taken as an example to demonstrate the telescope method (i.e. N-variate distributions). Each tree with DBH ≥ 5 cm was investigated and located, and the frequencies of N-variate distributions flexibly combined with four structure parameters, uniform angle index, mingling, dominance and crowding were calculated using Excel pivot tables and the Winkelmass software. The telescope method could systematically interpret the forest structural characteristics at different resolutions. Especially, the quadrivariate distribution provides the most detailed and comprehensive spatial structure information. Based on the vertical projection dimension reduction and marginal probability distribution function, the continuous recursive process well revealed the inherently quantitative relationships among different distributions. This could be conducive to flexibly optimizing and reconstructing forest structure, and effectively selecting the trees to be removed.

Comprehensive evaluation of forest state is the precondition and critical step for forest management. To solve the problem that the radar plot and unit circle only focus on the value of each the evaluation index, this paper proposes a novel method for comprehensively and simultaneously evaluating the functionality and inhomogeneity of forest state based on the modified unit circle method. We evaluated the forest state of the Quercus aliena BL. var. acuteserrata Maxim. ex Wenz. broad-leaved mixed forest in the Xiaolong Mountains Forest Area of Gansu Province and the Pinus koraiensis Sieb. et Zucc. broad-leaved mixed forest in Jilin Province in China. According to the principle of comprehensive, scientific and operability, 10 evaluation indices on forest structure and vitality were selected to construct the evaluation indicator system. Each index was normalized based on the assignment method and ensured to be strictly positive based on reciprocal transformation method. The areas and arc length of the closed graph, formed by connecting every two adjacent indicators, in the radar plot and unit circle were extracted. Based on the isoperimetric theorem (isoperimetric inequality), a comprehensive evaluation model was constructed. Compared with radar chart and unit circle method, each index in the newly proposed unit circle method is represented by an independent sector region, reflecting the contribution of the index to the overall evaluation result. Each index has the same relative importance weight, contributing to the estimation the relative sizes of each aspect of forest state. The unique area and arc length of the closed graph help summarize the overall performance with a global score. The expression effect of improved unit circle has been enhanced, and as an English proverb put it, “A picture is worth a thousand words.” The new proposed method simultaneously evaluates the functionality and inhomogeneity of the forest state and it is a powerful tool for the diagnosis of forest state problems and the decision-making of forest management.