Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Summary

Mixed-effects models are flexible and useful tools for analyzing data with a hierarchical stochastic structure in forestry and could also be used to significantly improve the performance of forest growth models. Here, a protocol is presented that synthesizes information relating to linear mixed-effects models.

Abstract

Here, we developed an individual-tree model of 5-year basal area increments based on a dataset including 21898 Picea asperata trees from 779 sample plots located in Xinjiang Province, northwest China. To prevent high correlations among observations from the same sampling unit, we developed the model using a linear mixed-effects approach with random plot effect to account for stochastic variability. Various tree- and stand-level variables, such as indices for tree size, competition, and site condition, were included as fixed effects to explain the residual variability. In addition, heteroscedasticity and autocorrelation were described by introducing variance functions and autocorrelation structures. The optimal linear mixed-effects model was determined by several fit statistics: Akaike’s information criterion, Bayesian information criterion, logarithm likelihood, and a likelihood ratio test. The results indicated that significant variables of individual-tree basal area increment were the inverse transformation of diameter at breast height, the basal area of trees larger than the subject tree, the number of trees per hectare, and elevation. Furthermore, errors in variance structure were most successfully modeled by the exponential function, and the autocorrelation was significantly corrected by first-order autoregressive structure (AR(1)). The performance of the linear mixed-effects model was significantly improved relative to the model using ordinary least squares regression.

Introduction

Compared with even-aged monoculture, uneven-aged mixed-species forest management with multiple objectives has received increased attention recently^1,2,3. Prediction of different management alternatives is necessary for formulating robust forest management strategies, especially for complex uneven-aged mixed-species forest⁴. Forest growth and yield models have been used extensively to forecast tree or stand development and harvest under various management schemes^5,6,....

Protocol

1. Data preparation

1. Prepare modeling data, which includes individual-tree information (species and diameter at breast height at 1.3 m) and plot information (slope, aspect, and elevation). In this study, the data were obtained from the 8th (2009) and 9th (2014) Chinese National Forest Inventory in Xinjiang Province, northwest China, which includes 21,898 observations of 779 sample plots. These sample plots are square-shaped with a size of 1 Mu (Chinese unit of area equivalent to 0.067 ha) and are systematicall.......

Discussion

A crucial issue for the development of mixed-effects models is to determine which parameters can be treated as random effects and which should be considered fixed effects^34,35. Two methods have been proposed. The most common approach is to treat all parameters as random effects and then have the best model selected by AIC, BIC, Loglik, and LRT. This was the method employed by our study³⁵. An alternative is to fit basal area increment model.......

Materials

Name	Company	Catalog Number	Comments
Computer	acer
Microsoft Office 2013
R x64 3.5.1