Using Linear Mixed-Effects Models with Quantile Regression to Simulate the Crown Profile of Planted Pinus sylvestris var. Mongolica Trees

Abstract

Abstract:Crown profile is mostly related to the competition of individual trees in the stands, light interception, growth, and yield of trees. A total of 76 sample trees with a total number of 889 whorls and 3658 live branches were used to develop the outer crown profile model of the planted Pinus sylvestris var. mongolica trees in Heilongjiang Province, China. The power-exponential equation, modified Kozak equation, and simple polynomial equation were used and the model which showed the best performance was used as the basic model. The dummy variable approach was used to analyze the effect of stand age and stand density on the crown profile. Quantile regression for linear mixed-effects model, where the correlations between the series measurements on the same subject were considered, was used to model the outer crown profile. The results indicated that the power-exponential equation had the smallest error and was used as the basic model. Based on the dummy variable approach, stand age and stand density showed significant effects on the crown profile on the whole. Thus, they were directly included into the linear form of the power-exponential equation by a natural logarithm transformation to develop the quantile regression for the linear mixed-effects model. The 0.95th quantile regression model performed best in modeling the outer crown profile when compared to other quantiles. The prediction accuracy of the 0.95th quantile regression model by adding the random effects increased when compared to the quantile regression without random effect. The quantile regression for the linear mixed-effects model also showed an excellent performance in the largest crown radius prediction when compared to the quantile regression model. From suppressed trees to dominant trees, the crown radius increased, with tree size increasing for the same stand age and stand density increases. The crown radius of the suppressed trees from 21 to 40 year stands was the largest and the smallest was from older (>40 years) stands. The crown radius for both the intermediate and dominant trees from 21 to 40 year stands were similar and were larger than the younger (10-20 years) stands. The crown radius increased with tree size when the stand variables were constant. Furthermore, the crown radius increased with the increase of stand age, decreased with increasing stand density, and decreased with increased ratio of tree height to diameter at the breast height (HD) for trees with the same tree variables. Stand density had a weaker effect on the crown profile when compared to the HD. The growth rate of the crown radius of planted Pinus sylvestris var. mongolica trees increased with increasing stand age, and decreased with decreasing stand density. The growth rate of the crown radius decreased with increasing HD.

The Feasibility of Modelling the Crown Profile of Larix olgensis Using Unmanned Aerial Vehicle Laser Scanning Data

“…Among trees of the same age, trees with a large DBH are more dominant, more competitive, and intercept more light, and they therefore grow better. It is clear from these results that the effect of tree growth on crown shape is consistent with the results of the study by Sun et al [ 8 ].…”

“…The parabola equation is the equation most widely used to describe the outer crown profile due to its flexibility [ 5 , 8 , 49 ], and its reparameterized form is shown below as Equation (1). where OR is the outer crown radius; RDINC is the relative depth into the crown; LCR is the largest crown radius; and , , and are parameters to be estimated.…”

“…The shape and size of the crown affect tree physiological processes, such as photosynthesis, respiration and transpiration, due to the utilization of light and precipitation [ 2 , 3 ]. Additionally, the crown profile reflects a tree’s characteristics and growth (such as its species, age, and size) [ 1 , 4 , 5 , 6 ] and the tree’s response to the surrounding environment, such as competition and site conditions [ 5 , 7 ], and is thus closely related to species diversity and ecosystem stability [ 8 ].…”

A Crown Width-Diameter Model for Natural Even-Aged Black Pine Forest Management

“…For this reason, a number of covariates at tree and at stand level were added to increase the percentage of crown variation that could be explained by the model. Basal area, as a measure of stand density, is expected to affect crown width [59], while the canopy base height has been mentioned as a valid predictor of crown width by a number of relevant studies [31][32][33][34]. Tree height has also been used as a valid regressor of crown width allometry at tree level [31,32], while both the RSI and the fraction between diameter and quadratic mean diameter have been found to affect crown width variation according to Ducey [29].…”

Tree-Ring Analysis Reveals Density-Dependent Vulnerability to Drought in Planted Mongolian Pines

“…A previous study reported that the crown diameter of Mongolian pine increased with both age and stand density [65]. As crowns may overlap, competition is a crucial factor that affects Mongolian pine growth [66]; thus, trees growing in a dense forest may undergo decline more readily.…”