Predicting crown width and length using nonlinear mixed-effects models: a test of competition measures using Chinese fir (Cunninghamia lanceolata (Lamb.) Hook.)

Abstract

Key message Including individual-tree competition indices as predictor variables could significantly improve the performance of crown width and length models for Chinese fir (Cunninghamia lanceolata (Lamb.) Hook.). Moreover, distance-dependent competition indices are superior to distance-independent ones when modeling crown width and length. Compared with crown width and length basic models with optimum competition indices, the performance of the two-level nonlinear mixed-effects models improved. Context Crown width (CW) and crown length (CL) are two important variables widely included as the predictors in growth and yield models that contribute to forest management strategies. Aims Individual-tree crown width and length models were developed with data from 1498 Chinese fir (Cunninghamia lanceolata (Lamb.) Hook.) trees in 16 sample plots located at Jiangle County, Fujian Province, southeastern China. Two hypotheses were proposed: (1) including individual-tree competition indices as predictor variables could significantly improve performance of both the CW-DBH and CL-DBH models; and (2) the distance-dependent competition indices would perform better than distance-independent ones. Methods The models were fitted using generalized linear least squares or generalized nonlinear least squares methods. In addition, to prevent correlations between observations from the same sampling unit, we introduced age classes and sample plots as random effects to develop the two-level nonlinear mixed-effects models. ResultsWe found introduction of competition indices could significantly improve the performance of the CW-DBH and CL-DBH models. The distance-dependent competition index (i.e., competitor to subject tree distance) performed best in modeling the crown width and length models. Compared with crown width and length basic models with optimum competition indices, the performance of the two-level nonlinear mixed-effects models was significantly better. Conclusion The two hypotheses were accepted. We hope these models will contribute to scientific management of Chinese fir plantations.

Predicting crown width using nonlinear mixed-effects models accounting for competition in multi-species secondary forests

“…Twelve candidate nonlinear CW-D functions (see Table 1 ) were selected from previous studies based on the suitability of their mathematical features, the possible biological interpretation of model parameters, and satisfactory predictions of the CW-D relationship in the literature ( Fu et al, 2013 ; Raptis et al, 2018 ; Wang et al, 2021 ), and the best fitting performance model was named as the basic CW model for studied secondary forest.…”

“…For distance-dependent indices, identifying competitor trees are of great importance to derive competition indices. Generally, studies either identify four neighboring trees (four neighboring trees as competitors in four different directions around the subject tree) or use fixed radii (competitors are identified as all neighboring trees around the subject tree within a search radius of 3.5 times the mean crown radius of canopy trees) ( Wang et al, 2021 ); in our study, the relevant radius is 5 m. We applied these two methods to calculate the Hegyi indices SHGR and SHGN, respectively ( Table 2 ). The crown width for stand-growth trees is significantly influenced by competition among individual trees, the Hegyi index is based on the principle that larger and closer competitor would have higher competition impact on a subject tree ( Sharma, Vacek & Vacek, 2016 ), has been being developed since the 1970s to quantify individual-tree-level competition ( Hegyi, 1974 ) and frequently used to develop various spatially explicit forest models including crown models ( Pommerening, 2008 ; Sharma, Vacek & Vacek, 2016 ).…”

“…To eliminate edge effects and improve the accuracy of the distance-dependent indices, we made 8 copies of the sample plot, and then moved one of each copy from its original position into up, down, left, right, upper left, lower left, lower right, and upper right directions, respectively. Thus a new, larger sample plot consisting of 9 copies is created; this edge correction can individually evaluate each tree to determine whether all nearest neighbors are truly located within the plot ( Wang et al, 2021 ). For summary statistics of studied variables, see Tables 3 and 4 .…”

Two new methods applied to crown width additive models: a case study for three tree species in Northeastern China

“…Each pre-selected combination of variables was tested for multicollinearity based on a variance inflation factor (VIF), and covariates were removed using a VIF = 5 decision threshold. The maximum number of covariates for each CR equation was set to 2 to avoid problems such as over-parameterization, poor convergence, and slow computational speed of parameter estimation (Wang et al 2021).…”

Deep learning for crown profile modelling of Pinus yunnanensis secondary forests in Southwest China

“…Crown profile models are key components of growth and yield models in the evaluation of competition among trees, forest microclimate, and biodiversity (Dong et al, 2016;Sun et al, 2022). Accurate information concerning crown profile is critical in analyzing biological processes (e.g., photosynthesis, stand growth, survival, and competition) (Rautiainen et al, 2008;Dong et al, 2016;Wang et al, 2021), whilst providing a more accurate estimate of carbon balance (Plesoianu et al, 2020;Yang et al, 2022). In mixed species ecosystems, modeling individual specie crown profile models is necessary if seeking to analyse species-specific phenological trends, plasticity, and responses to extreme events (Fawcett et al, 2021).…”