This research was funded by the Fundamental Research Funds for the Central Universities, grant number 2019GJZL04. We thank Professor Weisheng Zeng at the Academy of Forest Inventory and Planning, National Forestry and Grassland Administration, China for providing access to data.

1. Data preparation
<ol>
	<li>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 systematically arranged over a grid of 4 km x 8 km. 
	NOTE: Data for modeling (basal area) increment requires at least one growth period (i.e., two observations).</li>
	<li>Randomly divide the data into two datasets, with 80% of the data from the sample plots used for model fitting (model development dataset), which consists of 17,145 observations from 623 sample plots and 20% for model validation (model validation dataset) which consists of 4,753 observations from 156 sample plots. Descriptive statistics for the key variables used are provided in Table 1. 
	NOTE: This step of the modeling procedure can be omitted, and all data is used for model development.</li>
</ol>
<table border="1" fo:keep-together.within-page="1">
	<tbody>
		<tr>
			<td rowspan="2">Variables</td>
			<td colspan="4">Fitting data</td>
			<td></td>
			<td colspan="4">Validation data</td>
		</tr>
		<tr>
			<td>Min</td>
			<td>Max</td>
			<td>Mean</td>
			<td>S.D.</td>
			<td></td>
			<td>Min</td>
			<td>Max</td>
			<td>Mean</td>
			<td>S.D.</td>
		</tr>
		<tr>
			<td>DBH1 (cm)</td>
			<td>5</td>
			<td>124.8</td>
			<td>19.9</td>
			<td>13.2</td>
			<td></td>
			<td>5</td>
			<td>101.5</td>
			<td>19.5</td>
			<td>13.4</td>
		</tr>
		<tr>
			<td>QMD (cm)</td>
			<td>6.7</td>
			<td>82.3</td>
			<td>22.5</td>
			<td>8.5</td>
			<td></td>
			<td>9.2</td>
			<td>73.3</td>
			<td>21.8</td>
			<td>9.2</td>
		</tr>
		<tr>
			<td>ID (cm)</td>
			<td>0.1</td>
			<td>14.4</td>
			<td>1.1</td>
			<td>1</td>
			<td></td>
			<td>0.1</td>
			<td>16.9</td>
			<td>1</td>
			<td>1.1</td>
		</tr>
		<tr>
			<td>BAL (m3)</td>
			<td>0</td>
			<td>5.2</td>
			<td>1.7</td>
			<td>0.9</td>
			<td></td>
			<td>0</td>
			<td>5.4</td>
			<td>1.7</td>
			<td>1</td>
		</tr>
		<tr>
			<td>NT (trees/ha)</td>
			<td>14.9</td>
			<td>3642</td>
			<td>1072</td>
			<td>673.7</td>
			<td></td>
			<td>14.9</td>
			<td>3418</td>
			<td>1205</td>
			<td>829.3</td>
		</tr>
		<tr>
			<td>BA (m2/ha)</td>
			<td>0.1</td>
			<td>77.5</td>
			<td>34.2</td>
			<td>13.9</td>
			<td></td>
			<td>0.1</td>
			<td>80.6</td>
			<td>34.5</td>
			<td>15.3</td>
		</tr>
		<tr>
			<td>EL (m)</td>
			<td>2</td>
			<td>3302</td>
			<td>2189</td>
			<td>340.3</td>
			<td></td>
			<td>1441</td>
			<td>3380</td>
			<td>2256</td>
			<td>308.3</td>
		</tr>
	</tbody>
</table>
Table 1. Summary statistics for fitting and validation data. DBH1: initial diameter at breast height at 1.3 m (DBH), DBH2: DBH measured after 5 years of growth, QMD: quadratic mean diameter, ID: diameter increment for 5 years (DBH2 &#8211; DBH1), BAL: the basal area of trees larger than the subject tree (the subject tree: the tree which was calculated the competition indices), NT: the number of trees per hectare, BA: basal area per hectare, EL: elevation, S.D.: standard deviation.
2. Basic model development
<ol>
	<li>Consult references to identify variables that affect individual-tree basal area increments.</li>
	<li>Select and compute variables based on the data. Generally, the individual-tree basal area increment is affected by three groups of variables: tree size, competition, and site condition27,28,29,30.
	<ol>
		<li>Consider tree-size effects such as DBH1, square of DBH1 (<img alt="Equation 11" src="/files/ftp_upload/60827/60827eq11.jpg" />), the inverse transformation of DBH1 (1/DBH1), and the common logarithm of DBH1 (logDBH1) or combinations of them.</li>
		<li>Consider competitive effects such as both one- and two-sided indices of competition to more comprehensively quantify the level of competition experienced by a tree, as well as its social position within the stand. One-sided competition include BAL and the relative density index (RD=DBH1/QMD); two-sided competition include NT, and BA. 
		NOTE: The distance dependent competition indices should be considered if data is available.</li>
		<li>Consider site effects such as aspect (ASP), slope (SL), and EL. SL and ASP should be included using Stage&#8217;s transformation31.</li>
	</ol>
	</li>
	<li>Select log( <img alt="Equation 12" src="/files/ftp_upload/60827/60827eq12.jpg" /> - <img alt="Equation 11" src="/files/ftp_upload/60827/60827eq11.jpg" /> +1) ( <img alt="Equation 12" src="/files/ftp_upload/60827/60827eq12.jpg" /> denotes square of DBH2) as the dependent variable.</li>
	<li>Develop the basic model using the stepwise regression method. Ensure that the model is biologically reasonable and exhibits significant differences between independent variables. Utilize the variance inflation factor (VIF) to check for multicollinearity.</li>
	<li>Leave the independent variables with p &#60; 0.05 and VIF &#60; 5 in the basic model.</li>
	<li>Output the basic model results and the residual plot. The basic model produced here serves as a foundation for the further development of a mixed-effects model.</li>
</ol>
3. Linear mixed-effects model development with the package &#8220;nlme&#8221; in R software
<ol>
	<li>Read the model development dataset and load the Package &#8220;nlme&#8221;. 
	&#62;model.development.dataset=read.csv(&#34;E:/DATA/JoVE/modelingdata.csv&#34;,&#160; 
	header=TRUE) 
	&#62;library(nlme)</li>
	<li>Select sample plots as random effects to develop the mixed-effects model.</li>
	<li>Fit all possible combinations of random effects with the maximum likelihood (ML) method and output the results. 
	&#62;Model&#60;-lme(Y~1/DBH1+BAL+NT+EL,data=model.development.dataset,&#160; 
	method=&#34;ML&#34;, random =~1|PLOT) 
	&#62;summary(Model) 
	<ol>
		<li>Set random =~1 is the intercept to random parameters. Change the random statements until all combinations are fitted. For example, to set 1/DBH1 and BAL as random parameters, the code is as follows: random =~1/DBH1+BAL-1. In addition, in the process of fitting, the codes may report errors due to the nonconvergence of the fitted model.</li>
	</ol>
	</li>
	<li>Select the best model by Akaike&#8217;s information criterion (AIC), the Bayesian information criterion (BIC), the logarithm likelihood (Loglik), and likelihood ratio test (LRT). 
	&#62;anova(Model.1, Model.6) 
	&#62;anova(Model.6, Model.23) 
	&#62;anova(Model.23, Model.30)</li>
	<li>Determine the structure of Ri. Address the heteroscedasticity and autocorrelation of Ri32. The Ri is written as follows: 
	<img alt="Equation 1" src="/files/ftp_upload/60827/60827eq1.jpg" />&#160; &#160;(1) 
	where &#963;2 is an unknown scaling factor that is equal to the model residual variance, Gi is a diagonal matrix describing heteroscedasticity, and &#915;i is a matrix describing autocorrelation.
	<ol>
		<li>Observe whether the residuals have heteroscedasticity from the residual plot. If there is heteroscedasticity (the residuals have a clear pattern or trend), introduce three frequently used variance functions&#8212;the constant plus power function, the power function, and the exponential function&#8212;to model the errors variance structure. 
		&#62;Model.30.1&#60;-lme(Y~1/DBH1+BAL+NT+EL,data=model.development.dataset, method=&#34;ML&#34;,random=~1/DBH1+BAL+NT|PLOT, 
		weights=varConstPower(form=~ fitted(.))) 
		&#62;summary(Model.30.1) 
		&#62;Model.30.2&#60;-lme(Y~1/DBH1+BAL+NT+EL,data=model.development.dataset, method=&#34;ML&#34;,random=~1/DBH1+BAL+NT|PLOT, 
		weights=varPower(form=~ fitted(.))) 
		&#62;summary(Model.30.2) 
		&#62;Model.30.3&#60;-lme(Y~1/DBH1+BAL+NT+EL,data=model.development.dataset, method=&#34;ML&#34;,random=~1/DBH1+BAL+NT|PLOT, 
		weights=varExp(form=~ fitted(.))) 
		&#62;summary(Model.30.3)</li>
		<li>Determine the best variance function for the model according to the AIC, BIC, Loglik, and LRT. 
		&#62;anova(Model.30, Model.30.1) 
		&#62;anova(Model.30, Model.30.2) 
		&#62;anova(Model.30, Model.30.3)</li>
		<li>Introduce three commonly used autocorrelation structures&#8212;the compound symmetry structure (CS), first-order autoregressive structure [AR(1)], and a combination of first-order autoregressive and moving average structures [ARMA(1,1)]&#8212;to account for autocorrelation. 
		&#62;Model.30.3.1&#60;-lme(Y~1/DBH1+BAL+NT+EL,data=model.development.dataset, method=&#34;ML&#34;, 
		random=~1/DBH1+BAL+NT|PLOT, weights=varExp(form=~fitted(.)), corr= corCompSymm()) 
		&#62;summary(Model.30.3.1) 
		&#62;Model.30.3.2&#60;-lme(Y~1/DBH1+BAL+NT+EL,data=model.development.dataset,&#160; method=&#34;ML&#34;, 
		random=~1/DBH1+BAL+NT|PLOT,weights=varExp(form=~ fitted(.)), corr=corAR1()) 
		&#62;summary(Model.30.3.2) 
		&#62;Model.30.3.3&#60;-lme(Y~1/DBH1+BAL+NT+EL,data=model.development.dataset, method=&#34;ML&#34;, 
		random=~1/DBH1+BAL+NT|PLOT,weights=varExp(form=~ fitted(.)), corr=corARMA(q=1,p=1)) 
		&#62;summary(Model.30.3.3)</li>
		<li>Determine the best autocorrelation structure according to the AIC, BIC, Loglik, and LRT. 
		&#62;anova(Model.30.3, Model.30.3.2) 
		NOTE: The Gi and &#915;i cannot be defined if there is no heteroscedasticity and autocorrelation.</li>
		<li>Output the final results of the mixed-effects model using the restricted maximum likelihood (REML) method. 
		&#62;Mixed.model&#60;-lme(Y~1/DBH1+BAL+NT+EL,data=model.development.dataset, method=&#34;REML&#34;,random=~1/DBH1+BAL+NT|PLOT, 
		weights=varExp(form=~ fitted(.)), corr=corAR1()) 
		&#62;summary(Mixed.model)</li>
	</ol>
	</li>
</ol>
4. Bias correction
<ol>
	<li>Transform the predicted values of basal area increment using the final model on a logarithmic scale to the original scale. However, such a linear back transformation of predicted value from a log-transformed model produces an associated log-transformation bias. To deal with the log-bias, a correction factor was derived and integrated into the prediction equation, which estimates actual predicted basal area increment for a given tree [Equation (2)]: 
	<img alt="Equation 2" src="/files/ftp_upload/60827/60827eq2.jpg" />&#160; &#160;(2) 
	where <img alt="Equation 13" src="/files/ftp_upload/60827/60827eq13.jpg" /> is predicted logarithmic value of basal area increment from the model, while <img alt="Equation 14" src="/files/ftp_upload/60827/60827eq14.jpg" /> is the predicted back transformed value of basal area increment for 5 years after correcting for log-transformation bias. <img alt="Equation 15" src="/files/ftp_upload/60827/60827eq15.jpg" /> is variance from random effects at plot and &#963;2 is residual variance.</li>
	<li>Convert basal area increment ( <img alt="Equation 14" src="/files/ftp_upload/60827/60827eq14.jpg" /> ) to the diameter increment.</li>
</ol>
5. Model prediction and evaluation
<ol>
	<li>Prepare the model validation dataset produced in section 1.2 for prediction.</li>
	<li>Use the linear mixed-effects model to predict individual-tree basal area increment. The random components were calculated using the following best linear unbiased predictor: 
	<img alt="Equation 3" src="/files/ftp_upload/60827/60827eq3.jpg" />&#160; &#160;(3) 
	where <img alt="Equation 16" src="/files/ftp_upload/60827/60827eq16.jpg" /> is a vector for the random components; <img alt="Equation 17" src="/files/ftp_upload/60827/60827eq17.jpg" /> is the variance-covariance matrix for between-plots variability; <img alt="Equation 18" src="/files/ftp_upload/60827/60827eq18.jpg" /> is the design matrix for the random components acting at the complementary observations; <img alt="Equation 19" src="/files/ftp_upload/60827/60827eq19.jpg" /> is the residual vector whose components are given by the difference between the basal area increments and the predicted increments using the fixed-effects model.</li>
	<li>Evaluate and compare the predictive ability of the basic model and the linear mixed-effects model using the following three statistical indicators23,33. 
	<img alt="Equation 4" src="/files/ftp_upload/60827/60827eq4.jpg" />&#160; &#160;(4) 
	<img alt="Equation 5" src="/files/ftp_upload/60827/60827eq5.jpg" />&#160; &#160;(5) 
	<img alt="Equation 6" src="/files/ftp_upload/60827/60827eq6.jpg" />&#160; &#160;(6) 
	where obji is the basal area increments, esti is the predicted basal area increments, <img alt="Equation 20" src="/files/ftp_upload/60827/60827eq20.jpg" /> is the mean of observations, and N is the number of observations.</li>
</ol>

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E. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Comparing+methods+to+estimate+Reineke's+Maximum+Size-Density+Relationship+species+boundary+line+slope.">Comparing methods to estimate Reineke's Maximum Size-Density Relationship species boundary line slope.</a> Forest Science. 53 (3), 435-442 (2007).</li><li>Zhang, L., Bi, H., Gove, J. H., Heath, L. S. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=A+comparison+of+alternative+methods+for+estimating+the+self-thinning+boundary+line.">A comparison of alternative methods for estimating the self-thinning boundary line.</a> Canadian Journal of Forest Research. 35 (6), 1507-1514 (2005).</li><li>Hart, D. R., Chute, A. S. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Estimating+von+Bertalanffy+growth+parameters+from+growth+increment+data+using+a+linear+mixed-effects+model,+with+an+application+to+the+sea+scallop+Placopecten+magellanicus.">Estimating von Bertalanffy growth parameters from growth increment data using a linear mixed-effects model, with an application to the sea scallop Placopecten magellanicus.</a> Ices Journal of Marine Science. 66 (9), 2165-2175 (2009).</li><li>Uzoh, F. C. C., Oliver, W. W. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Individual+tree+diameter+increment+model+for+managed+even-aged+stands+of+ponderosa+pine+throughout+the+western+United+States+using+a+multilevel+linear+mixed+effects+model.">Individual tree diameter increment model for managed even-aged stands of ponderosa pine throughout the western United States using a multilevel linear mixed effects model.</a> Forest Ecology &amp; Management. 256 (3), 438-445 (2008).</li><li>Cond&#233;s, S., Sterba, H. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Comparing+an+individual+tree+growth+model+for+Pinus+halepensis+Mill.+in+the+Spanish+region+of+Murcia+with+yield+tables+gained+from+the+same+area.">Comparing an individual tree growth model for Pinus halepensis Mill. in the Spanish region of Murcia with yield tables gained from the same area.</a> European Journal of Forest Research. 127 (3), 253-261 (2008).</li><li>Pokharel, B., Dech, J. P. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Mixed-effects+basal+area+increment+models+for+tree+species+in+the+boreal+forest+of+Ontario,+Canada+using+an+ecological+land+classification+approach+to+incorporate+site+effects.">Mixed-effects basal area increment models for tree species in the boreal forest of Ontario, Canada using an ecological land classification approach to incorporate site effects.</a> Forestry. 85 (2), 255-270 (2012).</li><li>Wykoff, W. R. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=A+basal+area+increment+model+for+individual+conifers+in+the+northern+Rocky+Mountains.">A basal area increment model for individual conifers in the northern Rocky Mountains.</a> Forest Science. 36 (4), 1077-1104 (1990).</li><li>Stage, A. R. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Notes:+An+Expression+for+the+Effect+of+Aspect,+Slope,+and+Habitat+Type+on+Tree+Growth.">Notes: An Expression for the Effect of Aspect, Slope, and Habitat Type on Tree Growth.</a> Forest Science. 22 (4), 457-460 (1976).</li><li>Gregorie, T. G. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Generalized+Error+Structure+for+Forestry+Yield+Models.">Generalized Error Structure for Forestry Yield Models.</a> Forest Science. 33 (2), 423-444 (1987).</li><li>Zhao, L., Li, C., Tang, S. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Individual-tree+diameter+growth+model+for+fir+plantations+based+on+multi-level+linear+mixed+effects+models+across+southeast+China.">Individual-tree diameter growth model for fir plantations based on multi-level linear mixed effects models across southeast China.</a> Journal of Forest Research. 18 (4), 305-315 (2013).</li><li>Hall, D. B., Bailey, R. L. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Modeling+and+Prediction+of+Forest+Growth+Variables+Based+on+Multilevel+Nonlinear+Mixed+Models.">Modeling and Prediction of Forest Growth Variables Based on Multilevel Nonlinear Mixed Models.</a> Forest Science. 47 (3), 311-321 (2001).</li><li>Yang, Y., Huang, S., Meng, S. X., Trincado, G., Vanderschaaf, C. L. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=A+multilevel+individual+tree+basal+area+increment+model+for+aspen+in+boreal+mixedwood+stands+:+Journal+canadien+de+la+recherche+forestie&#768;re.">A multilevel individual tree basal area increment model for aspen in boreal mixedwood stands : Journal canadien de la recherche forestie&#768;re.</a> Revue Canadienne De Recherche Foresti&#232;re. 39 (39), 2203-2214 (2009).</li><li>Pinheiro, J. C., Bates, D. M. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Mixed-effects+models+in+S+and+S-Plus.">Mixed-effects models in S and S-Plus.</a> Publications of the American Statistical Association. 96 (455), 1135-1136 (2000).</li></ol>

The authors have nothing to disclose.

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 effects34,35. 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...

Compared with even-aged monoculture, uneven-aged mixed-species forest management with multiple objectives has received increased attention recently1,2,3. 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 schemes5,6,7. Forest growth and yield models are classified into individual-tree models, size-class models, and whole-stand growth models6,7,8. Unfortunately, size-class models and whole-stand models are not appropriate for uneven-aged mixed-species forests, which require a more detailed description to support the forest management decision-making process. For this reason, individual-tree growth and yield models have received increased attention throughout the last few decades because of their ability to make predictions for forest stands with a variety of species compositions, structures, and management strategies9,10,11.
Ordinary least squares (OLS) regression is the most commonly used method for the development of individual-tree growth models12,13,14,15. The datasets for individual-tree growth models collected repeatedly over a fixed length of time on the same sampling unit (i.e., sample plot or tree) have a hierarchical stochastic structure, with a lack of independence and high spatial and temporal correlation among observations10,16. The hierarchical stochastic structure violates the fundamental assumptions of OLS regression: namely independent residuals and normally distributed data with equal variances. Therefore, the use of OLS regression inevitably produces biased estimates of the standard error of parameter estimates for these data13,14.
Mixed-effects models provide a powerful tool for analyzing data with complex structures, such as repeated measures data, longitudinal data, and multi-level data. Mixed-effects models consist of both fixed components, common to the complete population, and random components, which is specific to each sampling level. In addition, mixed-effects models take into account heteroscedasticity and autocorrelation in space and time by defining non-diagonal variance-covariance structure matrices17,18,19. For this reason, mixed-effects models have been extensively used in forestry, such as in diameter-height models20,21, crown models22,23, self-thinning models24,25, and growth models26,27.
Here, the main objective was to develop an individual-tree basal area increment model using a linear mixed-effects approach. We hope that the mixed-effects approach could be broadly applied.

<table><tbody><tr><td>Computer</td><td>acer</td><td></td><td></td></tr><tr><td>Microsoft Office 2013</td><td></td><td></td><td></td></tr><tr><td>R x64 3.5.1</td><td></td><td></td><td></td></tr></tbody></table>

development of an individual-tree basal area increment model using a linear mixed-effects approach

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&#8217;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.

The basic basal area increment model for P. asperata was expressed as Equation (7). The parameter estimates, their corresponding standard errors, and the lack-of-fit statistics are shown in Table 2. The residual plot is shown in Figure 1. Pronounced heteroscedasticity of the residuals was observed. 
<img alt="Equation 7" src="/files/ftp_upload/60827/60827eq7.jpg" />&#160; &#160;(7)
<table border="1" fo:keep-together.within-page="1">
	<tbody>
		<tr>
			<td></td>
			<td><...

Watch this Scientific Journal Video about Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach at JoVE.com

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

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.

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 ...

development-an-individual-tree-basal-area-increment-model-using

Research

JoVE Journal

Biology

3.3K Views.  Beijing Forestry University. Modellen met gemengde effecten zijn flexibele en nuttige instrumenten voor het analyseren van gegevens met een hiërarchische stochastische structuur in de bosbouw en kunnen ook worden gebruikt om de prestaties van bosgroeimodellen aanzienlijk te verbeteren. Hier wordt een protocol gepresenteerd dat informatie synthetiseert met betrekking tot lineaire mixed-effects modellen.

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

Protocol for Assessing the Relative Effects of Environment and Genetics on Antler and Body Growth for a Long-lived Cervid

Cervid phenotype can be placed into one of two categories: efficiency, which promotes survival over extravagant morphometric growth, and luxury, which promotes growth of large weaponry and body size. Populations of the same species display each phenotype depending on environmental conditions. Although antler and body size of male white-tailed deer (Odocoileus virginianus) varies by physiographic region in Mississippi, USA and is strongly correlated with regional variation in nutritional quality, the effects of population-level genetics from native stocks and previous re-stocking efforts cannot be disregarded. This protocol describes how we designed a controlled study, where other factors that influence phenotype, such as age and nutrition, are controlled. We brought wild-caught pregnant females and six-month-old fawns from three distinct physiographic regions in Mississippi, USA to the Mississippi State University Rusty Dawkins Memorial Deer Unit. Deer from the same region were bred to produce a second generation of offspring, allowing us to assess generational responses and maternal effects. All deer ate the same high-quality (20% crude protein deer pellet) diet ad libitum. We uniquely marked each neonate and recorded body mass, hind foot, and total body length. Each subsequent fall, we sedated individuals via remote injection and sampled the same morphometrics plus antlers of adults. We found that all morphometrics increased in size from first to second generation, with full compensation of antler size (regional variation no longer present) and partial compensation of body mass (some evidence of regional variation) evident in the second generation. Second generation males that originated from our poorest quality soil region displayed about a 40% increase in antler size and about a 25% increase in body mass when compared to their wild harvested counterparts. Our results suggest phenotypic variation of wild male white-tailed deer in Mississippi are more related to differences in nutritional quality than population-level genetics.

Phenotypic differences among cervid populations may be related to population-level genetics or nutrition; discerning which is difficult in the wild. This protocol describes how we designed a controlled study where nutritional variation was eliminated. We found that phenotypic variation of male white-tailed deer was more limited by nutrition than genetics.

Cervid phenotype can be placed into one of two categories: efficiency, which promotes survival over extravagant morphometric growth, and luxury, which ...

Environment

A Simple Planting Technique for Re-establishing Trees Where Frequent Inundation Occurs

Many of the Everglades tree islands have lost elevation over the past century and most of their trees have died such that they are now covered with herbaceous plants. This protocol describes a simple, cost-effective tree planting technique needed for restoring degraded Everglade tree islands. The design is patterned after a natural Everglades process that creates floating peat islands, which allows tree survival and growth in flooded conditions and often leads to the development of tree islands. Commercially available peat bags were used as the medium for the growth and establishment of potted native tree saplings. The pop-up configuration floated initially and provided additional elevation to minimize inundation, with a single native tree species sapling and a single tree fertilizer spike. During a 3 year study involving 105 pop-ups, most plants survived (80%) and many thrived. Determining whether this technique can establish trees on a degraded tree island will require longer studies and extensive field tests.

This protocol describes a simple, cost-effective tree planting technique for restoring degraded Everglades tree islands that experience inundation. The design creates an island (pop-up) which floats initially and adds elevation to promote tree survival and growth under flooded conditions.

Many of the Everglades tree islands have lost elevation over the past century and most of their trees have died such that they are now covered with ...

Leaf Area Index Estimation Using Three Distinct Methods in Pure Deciduous Stands

Accurate estimations of leaf area index (LAI), defined as half of the total leaf surface area per unit of horizontal ground surface area, are crucial for describing the vegetation structure in the fields of ecology, forestry, and agriculture. Therefore, procedures of three commercially used methods (litter traps, needle technique, and a plant canopy analyzer) for performing LAI estimation were presented step-by-step. Specific methodological approaches were compared, and their current advantages, controversies, challenges, and future perspectives were discussed in this protocol. Litter traps are usually deemed as the reference level. Both the needle technique and the plant canopy analyzer (e.g., LAI-2000) frequently underestimate LAI values in comparison with the reference. The needle technique is easy to use in deciduous stands where the litter completely decomposes each year (e.g., oak and beech stands). However, calibration based on litter traps or direct destructive methods is necessary. The plant canopy analyzer is a commonly used device for performing LAI estimation in ecology, forestry, and agriculture, but is subject to potential error due to foliage clumping and the contribution of woody elements in the field of view (FOV) of the sensor. Eliminating these potential error sources was discussed. The plant canopy analyzer is a very suitable device for performing LAI estimations at the high spatial level, observing a seasonal LAI dynamic, and for long-term monitoring of LAI.

An accurate estimation of leaf area index (LAI) is crucial for many models of material and energy fluxes within plant ecosystems and between an ecosystem and the atmospheric boundary layer. Therefore, three methods (litter traps, needle technique, and PCA) for taking precise LAI measurements were in the presented protocol.

Accurate estimations of leaf area index (LAI), defined as half of the total leaf surface area per unit of horizontal ground surface area, are crucial for ...

A Method for Quantifying Foliage-Dwelling Arthropods

Terrestrial arthropods play an important role in our environment. Quantifying arthropods in a way that allows for a precise index or estimates of density requires a method with high detection probability and a known sampling area. While most described methods provide a qualitative or semi-quantitative estimate adequate for describing species presence, richness, and diversity, few provide an adequately consistent detection probability and known or consistent sampling areas to provide an index or estimate with adequate precision to detect differences in abundance across environmental, spatial, or temporal variables. We describe how to quantify leaf-dwelling arthropods by sealing the leaves and end of branches in a bag, clipping and freezing the bagged material, and rinsing the previously frozen material in water to separate arthropods from the substrate and quantify them. As we demonstrate, this method can be used at a landscape scale to quantify leaf-dwelling arthropods with adequate precision to test for and describe how spatial, temporal, environmental, and ecological variables influence arthropod richness and abundance. This method allowed us to detect differences in density, richness, and diversity of leaf-dwelling arthropods among 5 genera of trees commonly found in southeastern deciduous forests.

We describe how to quantify leaf dwelling arthropods by sealing the leaves and end of branches in a bag, clipping and freezing the bagged material, and rinsing the previously frozen material in water to separate arthropods from the substrate for quantification.

Terrestrial arthropods play an important role in our environment. Quantifying arthropods in a way that allows for a precise index or estimates of density ...

Quantifying Corticolous Arthropods Using Sticky Traps

Terrestrial arthropods play an important role in our environment. Quantifying arthropods in a way that allows for a precise index or estimate of density requires a method with high detection probability and a consistent sampling area. We used manufactured sticky traps to compare abundance, total length (a surrogate for biomass), richness, and Shannon diversity of corticolous arthropods among the boles of 5 tree species. Efficacy of this method was adequate to detect variation in corticolous arthropods among tree species and provide a standard error of the mean that was &#60;20% of the mean for all estimates with sample sizes from 7 to 15 individual trees of each species. Our results indicate, even with these moderate sample sizes, the level of precision of arthropod community metrics produced with this approach is adequate to address most ecological questions regarding temporal and spatial variation in corticolous arthropods. Results from this method differ from other quantitative approaches such as chemical knockdown, visual inspection, and funnel traps in that they provide an indication of corticolous arthropod activity over a relatively long-term, better including temporary bole residents, flying arthropods that temporarily land on the tree bole and crawling arthropods that use the tree bole as a travel route from the ground to higher forest foliage. Furthermore, we believe that commercially manufactured sticky traps provide more precise estimates and are logistically simpler than the previously described method of directly applying a sticky material to tree bark or applying a sticky material to tape or other type of backing and applying that to the tree bark.

We describe a semi-quantitative approach of measuring characteristics of corticolous (bark-dwelling) arthropod communities. We placed commercially manufactured sticky traps on tree boles to estimate abundance, total length (a surrogate to biomass), richness, and Shannon diversity for comparison among tree species.

Terrestrial arthropods play an important role in our environment. Quantifying arthropods in a way that allows for a precise index or estimate of density ...

Field Measurement of Effective Leaf Area Index using Optical Device in Vegetation Canopy

Leaf area index (LAI) is an essential canopy variable describing the amount of foliage in an ecosystem. The parameter serves as the interface between green components of plants and the atmosphere, and many physiological processes occur there, primarily photosynthetic uptake, respiration, and transpiration. LAI is also an input parameter for many models involving carbon, water, and the energy cycle. Moreover, ground-based in situ measurements serve as the calibration method for LAI obtained from remote sensing products. Therefore, straightforward indirect optical methods are necessary for making precise and rapid LAI estimates. The methodological approach, advantages, controversies, and future perspectives of the newly developed LP 110 optical device based on the relation between radiation transmitted through the vegetation canopy and canopy gaps were discussed in the protocol. Furthermore, the instrument was compared to the world standard LAI-2200 Plant Canopy Analyzer. The LP 110 enables more rapid and more straightforward processing of data acquired in the field, and it is more affordable than the Plant Canopy Analyzer. The new instrument is characterized by its ease of use for both above- and below-canopy readings due to its greater sensor sensitivity, in-built digital inclinometer, and automatic logging of readings at the correct position. Therefore, the hand-held LP 110 device is a suitable gadget for performing LAI estimation in forestry, ecology, horticulture, and agriculture based on the representative results. Moreover, the same device also enables the user to take accurate measurements of incident photosynthetically active radiation (PAR) intensity.

Fast and precise leaf area index (LAI) estimation in terrestrial ecosystems is crucial for a wide range of ecological studies and calibrating remote sensing products. Presented here is the protocol for using the new LP 110 optical device for taking ground-based in situ LAI measurements.

Leaf area index (LAI) is an essential canopy variable describing the amount of foliage in an ecosystem. The parameter serves as the interface between ...

How to Extract Climate Variability from Tree-Rings

Tree rings have been used to reconstruct climatological variables in many locations around the world. Moreover, tree-rings can provide valuable insights into climatic variability of the last few centuries and, in some areas, several millennia. Despite the important development, that dendrochronology has had in recent decades to study the dendroclimatic potential of a large number of species present in different ecosystems, much remains to be done and explored. In addition to this, in the last few years more people (students, teachers and researchers) around the world are interested in implementing this science to extend the timeline of climate information backwards and understand how climate has changed on scales of decades, centuries or millennia. Therefore, the objective of this work is to describe the general aspects and basic steps needed to conduct a tree-ring climate reconstruction, from site selection and field sampling to laboratory methods and data analysis. In this method's video and manuscript, the general basis in tree-ring climatic reconstructions is explained so newcomers and students can use it as an available guide into this field of research.

Tree-ring climate reconstructions can be helpful to better understand past climate variability beyond instrumental records. This protocol shows how to reconstruct past climate using tree rings and meteorological instrumental records.

Tree rings have been used to reconstruct climatological variables in many locations around the world. Moreover, tree-rings can provide valuable insights ...

Advanced Workflow for Taking High-Quality Increment Cores - New Techniques and Devices

In dendroecological research, precise dating of each single growth ring is a basic requirement for all studies, focusing on ring-width variations only, chemical or isotope analyses, or wood anatomical studies. Independent of the sampling strategy for a certain study (e.g., climatology, geomorphology), the way samples are taken is crucial for their successful preparation and analyses.
Until recently, it was sufficient to use a (more or less) sharp increment corer to obtain core samples that could be sanded for further analyses. Since wood anatomical characteristics can be applied to long time series, the need to obtain high-quality increment cores has taken on a new meaning. Essentially, the corer needs to be sharp(ened) when used. When coring a tree by hand, there are some problems in handling the corer, resulting in the hidden occurrence of micro cracks along the entire core: When starting to drill by hand, the drill bit is strongly pressed against the bark and the outermost ring until the thread has fully entered the trunk. At the same time, the drill bit is moved up and down as well as sideward. Then, the corer is drilled all the way into the trunk; however, it is necessary to stop after each turn, change the grip, and turn again. All these movements, as well as the start/stop-coring, puts mechanical stress on the core. The resulting micro cracks make it impossible to create continuous micro sections, as they fall apart along all these cracks.
We present a protocol to overcome these obstacles by applying a new technique using a cordless drill to minimize these problems when coring a tree, as well as its effect on the preparation of long micro sections. This protocol includes the preparation of long micro sections, as well as a procedure to sharpen corers in the field.

Here, we present a protocol on how to avoid micro cracks in increment cores by applying a cordless drill with a torque multiplier to minimize problems when coring trees, as well as its effect on preparing long micro sections. This protocol also includes a procedure to sharpen corers in the field.

In dendroecological research, precise dating of each single growth ring is a basic requirement for all studies, focusing on ring-width variations only, ...

High-Throughput Tree Ring Analysis and Density Estimation

Tree Core Analysis with X-ray Computed Tomography

An X-ray computed tomography (CT) toolchain is presented to obtain tree-ring width (TRW), maximum latewood density (MXD), other density parameters, and quantitative wood anatomy (QWA) data without the need for labor-intensive surface treatment or any physical sample preparation. The focus here is on increment cores and scanning procedures at resolutions ranging from 60 &#181;m down to 4 &#181;m. Three scales are defined at which wood should be looked at: (i) inter-ring scale, (ii) ring scale, i.e., tree-ring analysis and densitometry scale, as well as (iii) anatomical scale, the latter approaching the conventional thin-section quality. Custom-designed sample holders for each of these scales enable high-throughput scanning of multiple increment cores. A series of software routines were specifically developed to efficiently treat three-dimensional X-ray CT images of the tree cores for TRW and densitometry. This work briefly explains the basic principles of CT, which are needed for a proper understanding of the protocol. The protocol is presented for some known species that are commonly used in dendrochronology. The combination of rough density estimates, TRW and MXD data, as well as quantitative anatomy data, allows us to broaden and deepen current analyses for climate reconstructions or tree response, as well as further develop the field of dendroecology/climatology and archeology.

Author Spotlight: Advancements in X-ray CT Tool Chain for Tree Core Analysis

Here we show how to process tree cores with an X-ray computed tomography toolchain. Except for chemical extraction for some purposes, no further physical lab treatment is needed. The toolchain can be used for biomass estimations, for obtaining MXD/tree-ring width data as well as for obtaining quantitative wood anatomy data.

An X-ray computed tomography (CT) toolchain is presented to obtain tree-ring width (TRW), maximum latewood density (MXD), other density parameters, and ...

Using Cholesky Decomposition to Explore Individual Differences in Longitudinal Relations between Reading Skills

The Cholesky decomposition method is the gold standard used in the field of behavioral genetics. The method is popular because it is easy to program and solve. Using this method, researchers can explore individual differences in longitudinal relations of different variables across multiple time points. The method allows investigators to decompose variance into (1) unique&#160;genetic, shared and non-shared environmental effects that arise at specific time points as well as (2) overlapping genetic, shared and non-shared environmental effects that carry over from one time point to another. However, the method does not identify the mechanisms or origins underlying these effects. The current report focuses on application of the Cholesky decomposition method in the field of educational psychology. Specifically, it discusses individual differences in longitudinal relations between kindergarten letter knowledge, kindergarten phonological awareness, first grade word-level reading skills, and seventh grade reading comprehension.

This paper demonstrates use of the gold standard method in behavioral genetics, the Cholesky decomposition method, to estimate unique, overlapping genetic and environmental influences on different variables to answer longitudinally motivated research questions.

The Cholesky decomposition method is the gold standard used in the field of behavioral genetics. The method is popular because it is easy to program and ...

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

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