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>

<ol>
	<li>Meng, J., Lu, Y., Ji, Z. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Transformation+of+a+Degraded+Pinus+massoniana+Plantation+into+a+Mixed-Species+Irregular+Forest:+Impacts+on+Stand+Structure+and+Growth+in+Southern+China.">Transformation of a Degraded Pinus massoniana Plantation into a Mixed-Species Irregular Forest: Impacts on Stand Structure and Growth in Southern China.</a> Forests. 5 (12), 3199-3221 (2014).</li><li>Sharma, A., Bohn, K., Jose, S., Cropper, W. P. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Converting+even-aged+plantations+to+uneven-aged+stand+conditions:+A+simulation+analysis+of+silvicultural+regimes+with+slash+pine+(Pinus+elliottii+Engelm).">Converting even-aged plantations to uneven-aged stand conditions: A simulation analysis of silvicultural regimes with slash pine (Pinus elliottii Engelm).</a> Forest Science. 60 (5), 893-906 (2014).</li><li>Zhu, J., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Feasibility+of+implementing+thinning+in+even-aged+Larix+olgensis+plantations+to+develop+uneven-aged+larch&#8211;broadleaved+mixed+forests.">Feasibility of implementing thinning in even-aged Larix olgensis plantations to develop uneven-aged larch&#8211;broadleaved mixed forests.</a> Journal of Forest Research. 15 (1), 71-80 (2010).</li><li>Leites, L. P., Robinson, A. P., Crookston, N. L. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Accuracy+and+equivalence+testing+of+crown+ratio+models+and+assessment+of+their+impact+on+diameter+growth+and+basal+area+increment+predictions+of+two+variants+of+the+Forest+Vegetation+Simulator.">Accuracy and equivalence testing of crown ratio models and assessment of their impact on diameter growth and basal area increment predictions of two variants of the Forest Vegetation Simulator.</a> Canadian Journal of Forest Research. 39 (3), 655-665 (2009).</li><li>Pretzsch, H. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=.">.</a> Forest Dynamics, Growth and Yield. , (2009).</li><li>Weiskittel, A. R., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Forest+growth+and+yield+modeling.">Forest growth and yield modeling.</a> Forest Growth &amp; Yield Modeling. 7 (2), 223-233 (2002).</li><li>Burkhart, H. E., Tom&#233;, M. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=.">.</a> Modeling Forest Trees and Stands. , (2012).</li><li>Zhang, X. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Chinese+Academy+Of+Forestry.+A+linkage+among+whole-stand+model,+individual-tree+model+and+diameter-distribution+model.">Chinese Academy Of Forestry. A linkage among whole-stand model, individual-tree model and diameter-distribution model.</a> Journal of Forest Science. 56 (56), 600-608 (2010).</li><li>Peng, C. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Growth+and+yield+models+for+uneven-aged+stands:+past,+present+and+future.">Growth and yield models for uneven-aged stands: past, present and future.</a> Forest Ecology &amp; Management. 132 (2), 259-279 (2000).</li><li>Lhotka, J. M., Loewenstein, E. F. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=An+individual-tree+diameter+growth+model+for+managed+uneven-aged+oak-shortleaf+pine+stands+in+the+Ozark+Highlands+of+Missouri,+USA.">An individual-tree diameter growth model for managed uneven-aged oak-shortleaf pine stands in the Ozark Highlands of Missouri, USA.</a> Forest Ecology &amp; Management. 261 (3), 770-778 (2011).</li><li>Port&#233;, A., Bartelink, H. H. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Modelling+mixed+forest+growth:+a+review+of+models+for+forest+management.">Modelling mixed forest growth: a review of models for forest management.</a> Ecological Modelling. 150 (1), 141-188 (2002).</li><li>Moses, L. E., Gale, L. C., Altmann, J. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Methods+for+analysis+of+unbalanced,+longitudinal,+growth+data.">Methods for analysis of unbalanced, longitudinal, growth data.</a> American Journal of Primatology. 28 (1), 49-59 (2010).</li><li>Biging, G. S. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Improved+Estimates+of+Site+Index+Curves+Using+a+Varying-Parameter+Model.">Improved Estimates of Site Index Curves Using a Varying-Parameter Model.</a> Forest Science. 31 (31), 248-259 (1985).</li><li>Kowalchuk, R. K., Keselman, H. J. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Mixed-model+pairwise+multiple+comparisons+of+repeated+measures+means.">Mixed-model pairwise multiple comparisons of repeated measures means.</a> Psychological Methods. 6 (3), 282-296 (2001).</li><li>Hayes, A. F., Cai, L. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Using+heteroskedasticity-consistent+standard+error+estimators+in+OLS+regression:+An+introduction+and+software+implementation.">Using heteroskedasticity-consistent standard error estimators in OLS regression: An introduction and software implementation.</a> Behavior Research Methods. 39 (4), 709-722 (2007).</li><li>Gutzwiller, K. J., Riffell, S. K. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=.">.</a> Using Statistical Models to Study Temporal Dynamics of Animal-Landscape Relations. , (2007).</li><li>Calama, R., Montero, G. <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 linear mixed model for tree diameter increment in stone pine (Pinus pinea): a calibrating approach. 39, (2005).</li><li>Vonesh, E. F., Chinchilli, V. M. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Linear+and+nonlinear+models+for+the+analysis+of+repeated+measurements.">Linear and nonlinear models for the analysis of repeated measurements.</a> Journal of Biopharmaceutical Statistics. 18 (4), 595-610 (1996).</li><li>Zobel, J. M., Ek, A. R., Burk, T. E. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Comparison+of+Forest+Inventory+and+Analysis+surveys,+basal+area+models,+and+fitting+methods+for+the+aspen+forest+type+in+Minnesota.">Comparison of Forest Inventory and Analysis surveys, basal area models, and fitting methods for the aspen forest type in Minnesota.</a> Forest Ecology &amp; Management. 262 (2), 188-194 (2011).</li><li>Sharma, M., Parton, J. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Height-diameter+equations+for+boreal+tree+species+in+Ontario+using+a+mixed-effects+modeling+approach.">Height-diameter equations for boreal tree species in Ontario using a mixed-effects modeling approach.</a> Forest Ecology &amp; Management. 249 (3), 187-198 (2007).</li><li>Crecente-Campo, F., Tom&#233;, M., Soares, P., Di&#233;guez-Aranda, U. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=A+generalized+nonlinear+mixed-effects+height&#8211;diameter+model+for+Eucalyptus+globulus+L.+in+northwestern+Spain.">A generalized nonlinear mixed-effects height&#8211;diameter model for Eucalyptus globulus L. in northwestern Spain.</a> Forest Ecology &amp; Management. 259 (5), 943-952 (2010).</li><li>Fu, L., Sharma, R. P., Hao, K., 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=A+generalized+interregional+nonlinear+mixed-effects+crown+width+model+for+Prince+Rupprecht+larch+in+northern+China.">A generalized interregional nonlinear mixed-effects crown width model for Prince Rupprecht larch in northern China.</a> Forest Ecology &amp; Management. 389 (2017), 364-373 (2017).</li><li>Hao, X., Yujun, S., Xinjie, W., Jin, W., Yao, F. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Linear+mixed-effects+models+to+describe+individual+tree+crown+width+for+China-fir+in+Fujian+Province,+southeast+China.">Linear mixed-effects models to describe individual tree crown width for China-fir in Fujian Province, southeast China.</a> Plos One. 10 (4), 0122257 (2015).</li><li>Vanderschaaf, C. L., Burkhart, H. 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 models for every sample plot with OLS regression. Parameters that have high variability and less overlap in confidence intervals across the sample plots among these models can be regarded as random ones17.
To account for heteroscedasticity and autocorrelation, three variance functions and three autocorrelation structures were introduced. Consistent with the results of Calama and Montero17 and Uzoh and Oliver27, the exponential function and AR(1) were determined to be the optimal variance function and autocorrelation structure, respectively.
There are two most commonly used methods in statistical software programs to estimate mixed-effects models: ML and REML17. ML is more flexible because models that differ in either their fixed effects or their random effects can be directly compared. However, the estimator for the variance obtained by ML is biased because ML does not account for the fact that the intercept and slope are estimated as well (as opposed to being known for certain). REML can provide superior ML estimates. Therefore, when the model comparisons were completed, the REML method was used for final model fitting17,18,36.
In this study, we found that the individual-tree basal area increment model for P. asperata using a linear mixed-effects approach represented a significant improvement over the basic model using OLS regression. Mixed-effects models provide an efficient tool for modeling data with hierarchical stochastic structure, making it widely applicable in fields such as agriculture, biology, economics, manufacturing, and geophysics.

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.

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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>Estimate</td>
			<td>Standard error</td>
			<td>t-test</td>
			<td>P-value</td>
			<td>VIF</td>
		</tr>
		<tr>
			<td>int</td>
			<td>2.41</td>
			<td>2.26E-02</td>
			<td>106.78</td>
			<td>&#60;2e-16</td>
			<td>-</td>
		</tr>
		<tr>
			<td>1/DBH1</td>
			<td>-5.84</td>
			<td>7.57E-02</td>
			<td>-77.19</td>
			<td>&#60;2e-16</td>
			<td>1.12</td>
		</tr>
		<tr>
			<td>BAL</td>
			<td>-0.0954</td>
			<td>3.34E-03</td>
			<td>-28.54</td>
			<td>&#60;2e-16</td>
			<td>1.08</td>
		</tr>
		<tr>
			<td>NT</td>
			<td>-0.000158</td>
			<td>4.74E-06</td>
			<td>-33.31</td>
			<td>&#60;2e-16</td>
			<td>1.12</td>
		</tr>
		<tr>
			<td>EL</td>
			<td>-0.00011</td>
			<td>9.07E-06</td>
			<td>-12.13</td>
			<td>&#60;2e-16</td>
			<td>1.05</td>
		</tr>
		<tr>
			<td colspan="6">AIC = 16789</td>
		</tr>
		<tr>
			<td colspan="6">BIC = 16836</td>
		</tr>
		<tr>
			<td colspan="6">Loglik = -8389</td>
		</tr>
	</tbody>
</table>
Table 2. Basic model results. The estimated parameters, their corresponding standard errors, and the lack-of-fit statistics derived from Equation (7). VIF: variance inflation factor, AIC: Akaike&#8217;s information criterion, BIC: Bayesian information criterion, and Loglik: logarithm likelihood.
<img alt="Figure 1" class="xfigimg" src="/files/ftp_upload/60827/60827fig1.jpg" /> 
Figure 1. Residual plot derived from Equation (7). The residuals have a clear trend, i.e., pronounced heteroscedasticity of the residuals was observed. <a href="https://www-jove-com.remotexs.ntu.edu.sg/files/ftp_upload/60827/60827fig1large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
There were 31 possible combinations of random-effects parameters for Equation (7). After fitting, 30 combinations reached convergence (Table 3). Among these 30 combinations, Model 30 of Equation (8) was selected since it yielded the lowest AIC (9083), the lowest BIC (9207), the largest LogLik (-4525), and the LRT was significantly different when compared with the other models. 
<img alt="Equation 8" src="/files/ftp_upload/60827/60827eq8.jpg" />&#160; &#160;(8) 
where &#946;1 &#8211; &#946;5 are the fixed effects parameters and b1 &#8211; b4 are the random-effects parameters.
<table border="1" fo:keep-together.within-page="1">
	<tbody>
		<tr>
			<td rowspan="2">Model</td>
			<td colspan="5">Random parameters</td>
			<td rowspan="2">AIC</td>
			<td rowspan="2">BIC</td>
			<td rowspan="2">LogLik</td>
			<td rowspan="2">LRT</td>
			<td rowspan="2">P-value</td>
		</tr>
		<tr>
			<td>int</td>
			<td>1/DBH1</td>
			<td>BAL</td>
			<td>NT</td>
			<td>EL</td>
		</tr>
		<tr>
			<td>1</td>
			<td>&#9650;</td>
			<td></td>
			<td></td>
			<td></td>
			<td></td>
			<td>10175</td>
			<td>10230</td>
			<td>-5081</td>
			<td></td>
			<td></td>
		</tr>
		<tr>
			<td>2</td>
			<td></td>
			<td>&#9650;</td>
			<td></td>
			<td></td>
			<td></td>
			<td>11630</td>
			<td>11684</td>
			<td>-5808</td>
			<td></td>
			<td></td>
		</tr>
		<tr>
			<td>3</td>
			<td></td>
			<td></td>
			<td>&#9650;</td>
			<td></td>
			<td></td>
			<td>11772</td>
			<td>11826</td>
			<td>-5879</td>
			<td></td>
			<td></td>
		</tr>
		<tr>
			<td>4</td>
			<td></td>
			<td></td>
			<td></td>
			<td>&#9650;</td>
			<td></td>
			<td>10556</td>
			<td>10611</td>
			<td>-5271</td>
			<td></td>
			<td></td>
		</tr>
		<tr>
			<td>5</td>
			<td></td>
			<td></td>
			<td></td>
			<td></td>
			<td>&#9650;</td>
			<td>10259</td>
			<td>10313</td>
			<td>-5123</td>
			<td></td>
			<td></td>
		</tr>
		<tr>
			<td rowspan="2">6</td>
			<td rowspan="2">&#9650;</td>
			<td rowspan="2">&#9650;</td>
			<td rowspan="2"></td>
			<td rowspan="2"></td>
			<td rowspan="2"></td>
			<td rowspan="2">9268</td>
			<td rowspan="2">9338</td>
			<td rowspan="2">-4625</td>
			<td>911.1</td>
			<td rowspan="2">&#60;.0001</td>
		</tr>
		<tr>
			<td>(1 vs 6)</td>
		</tr>
		<tr>
			<td>7</td>
			<td>&#9650;</td>
			<td></td>
			<td>&#9650;</td>
			<td></td>
			<td></td>
			<td>9411</td>
			<td>9481</td>
			<td>-4697</td>
			<td></td>
			<td></td>
		</tr>
		<tr>
			<td>8</td>
			<td>&#9650;</td>
			<td></td>
			<td></td>
			<td>&#9650;</td>
			<td></td>
			<td>10179</td>
			<td>10249</td>
			<td>-5081</td>
			<td></td>
			<td></td>
		</tr>
		<tr>
			<td>9</td>
			<td>&#9650;</td>
			<td></td>
			<td></td>
			<td></td>
			<td>&#9650;</td>
			<td>10179</td>
			<td>10249</td>
			<td>-5080</td>
			<td></td>
			<td></td>
		</tr>
		<tr>
			<td>10</td>
			<td></td>
			<td>&#9650;</td>
			<td>&#9650;</td>
			<td></td>
			<td></td>
			<td>10829</td>
			<td>10899</td>
			<td>-5406</td>
			<td></td>
			<td></td>
		</tr>
		<tr>
			<td>11</td>
			<td></td>
			<td>&#9650;</td>
			<td></td>
			<td>&#9650;</td>
			<td></td>
			<td>9532</td>
			<td>9601</td>
			<td>-4757</td>
			<td></td>
			<td></td>
		</tr>
		<tr>
			<td>12</td>
			<td></td>
			<td>&#9650;</td>
			<td></td>
			<td></td>
			<td>&#9650;</td>
			<td>9335</td>
			<td>9405</td>
			<td>-4659</td>
			<td></td>
			<td></td>
		</tr>
		<tr>
			<td>13</td>
			<td></td>
			<td></td>
			<td>&#9650;</td>
			<td>&#9650;</td>
			<td></td>
			<td>9803</td>
			<td>9873</td>
			<td>-4892</td>
			<td></td>
			<td></td>
		</tr>
		<tr>
			<td>14</td>
			<td></td>
			<td></td>
			<td>&#9650;</td>
			<td></td>
			<td>&#9650;</td>
			<td>9465</td>
			<td>9535</td>
			<td>-4723</td>
			<td></td>
			<td></td>
		</tr>
		<tr>
			<td>15</td>
			<td></td>
			<td></td>
			<td></td>
			<td>&#9650;</td>
			<td>&#9650;</td>
			<td>10200</td>
			<td>10270</td>
			<td>-5091</td>
			<td></td>
			<td></td>
		</tr>
		<tr>
			<td>16</td>
			<td>&#9650;</td>
			<td>&#9650;</td>
			<td>&#9650;</td>
			<td></td>
			<td></td>
			<td colspan="3">Nonconvergence</td>
			<td></td>
			<td></td>
		</tr>
		<tr>
			<td>17</td>
			<td>&#9650;</td>
			<td>&#9650;</td>
			<td></td>
			<td>&#9650;</td>
			<td></td>
			<td>9271</td>
			<td>9364</td>
			<td>-4624</td>
			<td></td>
			<td></td>
		</tr>
		<tr>
			<td>18</td>
			<td>&#9650;</td>
			<td>&#9650;</td>
			<td></td>
			<td></td>
			<td>&#9650;</td>
			<td>9274</td>
			<td>9367</td>
			<td>-4625</td>
			<td></td>
			<td></td>
		</tr>
		<tr>
			<td>19</td>
			<td>&#9650;</td>
			<td></td>
			<td>&#9650;</td>
			<td>&#9650;</td>
			<td></td>
			<td>9417</td>
			<td>9510</td>
			<td>-4696</td>
			<td></td>
			<td></td>
		</tr>
		<tr>
			<td>20</td>
			<td>&#9650;</td>
			<td></td>
			<td>&#9650;</td>
			<td></td>
			<td>&#9650;</td>
			<td>9417</td>
			<td>9510</td>
			<td>-4697</td>
			<td></td>
			<td></td>
		</tr>
		<tr>
			<td>21</td>
			<td>&#9650;</td>
			<td></td>
			<td></td>
			<td>&#9650;</td>
			<td>&#9650;</td>
			<td>10184</td>
			<td>10277</td>
			<td>-5080</td>
			<td></td>
			<td></td>
		</tr>
		<tr>
			<td>22</td>
			<td></td>
			<td>&#9650;</td>
			<td>&#9650;</td>
			<td>&#9650;</td>
			<td></td>
			<td>9332</td>
			<td>9425</td>
			<td>-4654</td>
			<td></td>
			<td></td>
		</tr>
		<tr>
			<td rowspan="2">23</td>
			<td rowspan="2"></td>
			<td rowspan="2">&#9650;</td>
			<td rowspan="2">&#9650;</td>
			<td rowspan="2"></td>
			<td rowspan="2">&#9650;</td>
			<td rowspan="2">9132</td>
			<td rowspan="2">9225</td>
			<td rowspan="2">-4554</td>
			<td>142.7</td>
			<td rowspan="2">&#60;.0001</td>
		</tr>
		<tr>
			<td>(23 vs 6)</td>
		</tr>
		<tr>
			<td>24</td>
			<td></td>
			<td>&#9650;</td>
			<td></td>
			<td>&#9650;</td>
			<td>&#9650;</td>
			<td>9293</td>
			<td>9386</td>
			<td>-4634</td>
			<td></td>
			<td></td>
		</tr>
		<tr>
			<td>25</td>
			<td></td>
			<td></td>
			<td>&#9650;</td>
			<td>&#9650;</td>
			<td>&#9650;</td>
			<td>9443</td>
			<td>9536</td>
			<td>-4709</td>
			<td></td>
			<td></td>
		</tr>
		<tr>
			<td>26</td>
			<td>&#9650;</td>
			<td>&#9650;</td>
			<td>&#9650;</td>
			<td>&#9650;</td>
			<td></td>
			<td>9083</td>
			<td>9207</td>
			<td>-4525</td>
			<td></td>
			<td></td>
		</tr>
		<tr>
			<td>27</td>
			<td>&#9650;</td>
			<td>&#9650;</td>
			<td>&#9650;</td>
			<td></td>
			<td>&#9650;</td>
			<td>9086</td>
			<td>9210</td>
			<td>-4527</td>
			<td></td>
			<td></td>
		</tr>
		<tr>
			<td>28</td>
			<td>&#9650;</td>
			<td>&#9650;</td>
			<td></td>
			<td>&#9650;</td>
			<td>&#9650;</td>
			<td>9280</td>
			<td>9404</td>
			<td>-4624</td>
			<td></td>
			<td></td>
		</tr>
		<tr>
			<td>29</td>
			<td>&#9650;</td>
			<td></td>
			<td>&#9650;</td>
			<td>&#9650;</td>
			<td>&#9650;</td>
			<td>9425</td>
			<td>9549</td>
			<td>-4696</td>
			<td></td>
			<td></td>
		</tr>
		<tr>
			<td rowspan="2">30</td>
			<td rowspan="2"></td>
			<td rowspan="2">&#9650;</td>
			<td rowspan="2">&#9650;</td>
			<td rowspan="2">&#9650;</td>
			<td rowspan="2">&#9650;</td>
			<td rowspan="2">9083</td>
			<td rowspan="2">9207</td>
			<td rowspan="2">-4525</td>
			<td>56.8</td>
			<td rowspan="2">&#60;.0001</td>
		</tr>
		<tr>
			<td>(30 vs 23)</td>
		</tr>
		<tr>
			<td>31</td>
			<td>&#9650;</td>
			<td>&#9650;</td>
			<td>&#9650;</td>
			<td>&#9650;</td>
			<td>&#9650;</td>
			<td>9091</td>
			<td>9254</td>
			<td>-4525</td>
			<td></td>
			<td></td>
		</tr>
	</tbody>
</table>
Table 3. Evaluation indices of each linear mixed-effects model. &#9650;: random-effects parameter was selected for fitting; LRT: likelihood ratio test.
The linear mixed-effects models with variance functions and correlation structures are shown in Table 4. According to the AIC, BIC, Loglik, and LRT, the exponential function and AR(1) were selected as the best variance function and autocorrelation structure, respectively.
<table border="1" fo:keep-together.within-page="1">
	<tbody>
		<tr>
			<td>Model</td>
			<td>Variance function</td>
			<td>Correlation structure</td>
			<td>AIC</td>
			<td>BIC</td>
			<td>LogLik</td>
			<td>LRT</td>
			<td>P-value</td>
		</tr>
		<tr>
			<td>30</td>
			<td>No</td>
			<td>Independent</td>
			<td>9083</td>
			<td>9207</td>
			<td>-4525</td>
			<td></td>
			<td></td>
		</tr>
		<tr>
			<td>30.1</td>
			<td>ConstPower</td>
			<td>Independent</td>
			<td>9075</td>
			<td>9215</td>
			<td>-4520</td>
			<td>11.8a</td>
			<td>0.0028</td>
		</tr>
		<tr>
			<td>30.2</td>
			<td>Power</td>
			<td>Independent</td>
			<td>9073</td>
			<td>9205</td>
			<td>-4520</td>
			<td>11.7a</td>
			<td>6.00E-04</td>
		</tr>
		<tr>
			<td>30.3</td>
			<td>Exponent</td>
			<td>Independent</td>
			<td>9073</td>
			<td>9204</td>
			<td>-4519</td>
			<td>12.3a</td>
			<td>5.00E-04</td>
		</tr>
		<tr>
			<td>30.3.1</td>
			<td>Exponent</td>
			<td>CS</td>
			<td colspan="5">Nonconvergence</td>
		</tr>
		<tr>
			<td>30.3.2</td>
			<td>Exponent</td>
			<td>AR(1)</td>
			<td>9050</td>
			<td>9189</td>
			<td>-4507</td>
			<td>24.9b</td>
			<td>&#60;.0001</td>
		</tr>
		<tr>
			<td>30.3.3</td>
			<td>Exponent</td>
			<td>ARMA(1,1)</td>
			<td colspan="5">Nonconvergence</td>
		</tr>
	</tbody>
</table>
Table 4. Comparisons of the linear mixed-effects individual-tree basal area increment models performance with different variance functions and different correlation structures. CS: compound symmetry structure, AR(1): a first-order autoregressive structure, ARMA(1,1): a combination of first-order autoregressive and moving average structures; a Likelihood ratio was calculated for Model 30; b Likelihood ratio was calculated for Model 30.3.
The final linear mixed-effects individual-tree basal area increment model was proposed using the REML method [Equation (9)]. The estimated fixed parameters, their corresponding standard errors, and the lack-of-fit statistics are shown in Table 5. The residual plot of the final model is shown in Figure 2. A significant improvement was observed in the residuals. 
<img alt="Equation 9" src="/files/ftp_upload/60827/60827eq9.jpg" />&#160; &#160;(9) 
where 
<img alt="Equation 10" src="/files/ftp_upload/60827/60827eq10.jpg" />&#160; &#160;(10)
<table border="1" fo:keep-together.within-page="1">
	<tbody>
		<tr>
			<td></td>
			<td>Estimate</td>
			<td>Standard error</td>
			<td>t-Test</td>
			<td>P-value</td>
		</tr>
		<tr>
			<td>int</td>
			<td>2.8086</td>
			<td>7.99E-02</td>
			<td>35.14</td>
			<td>&#60;0.01</td>
		</tr>
		<tr>
			<td>1/DBH1</td>
			<td>-6.2402</td>
			<td>1.56E-01</td>
			<td>-40.01</td>
			<td>&#60;0.01</td>
		</tr>
		<tr>
			<td>BAL</td>
			<td>-0.1324</td>
			<td>8.07E-03</td>
			<td>-16.41</td>
			<td>&#60;0.01</td>
		</tr>
		<tr>
			<td>NT</td>
			<td>-0.0001</td>
			<td>2.26E-05</td>
			<td>-4.921</td>
			<td>&#60;0.01</td>
		</tr>
		<tr>
			<td>EL</td>
			<td>-0.0003</td>
			<td>3.32E-05</td>
			<td>-7.86</td>
			<td>&#60;0.01</td>
		</tr>
		<tr>
			<td colspan="5">AIC = 9105</td>
		</tr>
		<tr>
			<td colspan="5">BIC = 9244</td>
		</tr>
		<tr>
			<td colspan="5">Loglik = -4535</td>
		</tr>
	</tbody>
</table>
Table 5. Mixed-effects model results. The estimated fixed parameters, their corresponding standard errors, and the lack-of-fit statistics derived from Equation (9).
<img alt="Figure 2" class="xfigimg" src="/files/ftp_upload/60827/60827fig2.jpg" /> 
Figure 2. Residual plot derived from Equation (9). Compared with Figure 1, a significant improvement was observed in the residuals. <a href="https://www-jove-com.remotexs.ntu.edu.sg/files/ftp_upload/60827/60827fig2large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
Table 6 listed the three prediction statistics of Equation (7) and Equation (9). Compared with the basic model, the performance of the linear mixed-effects model was significantly improved.
<table border="1" fo:keep-together.within-page="1">
	<tbody>
		<tr>
			<td>Model</td>
			<td>Bias</td>
			<td>RMSE</td>
			<td>R2</td>
		</tr>
		<tr>
			<td>Basic model</td>
			<td>0.297</td>
			<td>0.377</td>
			<td>0.479</td>
		</tr>
		<tr>
			<td>Mixed-effects model</td>
			<td>0.221</td>
			<td>0.286</td>
			<td>0.699</td>
		</tr>
	</tbody>
</table>
Table 6. Evaluation indices of the basic model and the linear mixed-effects model. A significant improvement was observed from the three prediction statistics.

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

Nanyang Technological University

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JoVE Journal

Biology

3.3K Views.  Beijing Forestry University. 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.

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

Microfabricated Post-Array-Detectors (mPADs): an Approach to Isolate Mechanical Forces

In this video, we will present our approach to measure cellular traction forces using a microfabricated array of posts.  Traction forces are generated through myosin-actin interactions and play an important role in our physiology.  During development, they enable cells to move from one location to the next in order to form the early structures of tissue.  Traction forces help in the healing processes.  They are necessary for the proper closure of wounds or the migration and crawling of leukocytes through our body.  These same forces can be detrimental to our health in the case of cancer metastasis or vascular growth towards a tumor.  The most common method by which to study cells in vitro has been to use a glass or polystyrene dish.  However, the rigidity of the substrates makes it impossible to physically measure cell traction forces, and there are relatively few methods to study traction forces.  Our lab has developed a technique to overcome these limitations.  The method is based on a vertical array of flexible cantilevers, the stiffness and size scale of which are such that individual cells spread across many cantilevers and deflect them in the process.  The pillars we use are 3 &mu;m in diameter, 10 &mu;m tall, and are configured in a regular array with 9 &mu;m center-to-center spacing.  But these physical dimensions can be readily varied to accommodate a variety of studies.  We start with a silicon master, but the final posts are made out of silicone rubber called poly (dimethyl siloxane), or PDMS.  We can measure the deflections under a microscope and calculate the magnitude and direction of traction forces required to produce the observed deflections.  We call these substrates microfabricated post-array-detectors, or mPADs.  Here, we will show you how we fabricate and use the mPADs to assess modulations of cellular contractility.

Microfabricated Post-Array-Detectors mPADs: an Approach to Isolate Mechanical Forces

In this video, we demonstrate how to fabricate and utilize microfabricated post array detectors (mPADs) to assess modulations of cellular contractility.

In this video, we will present our approach to measure cellular traction forces using a microfabricated array of posts.  Traction forces are generated ...

Development of New Therapeutic Applications Using Microfluidics

Spatial Multiobjective Optimization of Agricultural Conservation Practices using a SWAT Model and an Evolutionary Algorithm

Finding the cost-efficient (i.e., lowest-cost) ways of targeting conservation practice investments for the achievement of specific water quality goals across the landscape is of primary importance in watershed management. Traditional economics methods of finding the lowest-cost solution in the watershed context (e.g.,5,12,20) assume that off-site impacts can be accurately described as a proportion of on-site pollution generated. Such approaches are unlikely to be representative of the actual pollution process in a watershed, where the impacts of polluting sources are often determined by complex biophysical processes. The use of modern physically-based, spatially distributed hydrologic simulation models allows for a greater degree of realism in terms of process representation but requires a development of a simulation-optimization framework where the model becomes an integral part of optimization.
Evolutionary algorithms appear to be a particularly useful optimization tool, able to deal with the combinatorial nature of a watershed simulation-optimization problem and allowing the use of the full water quality model. Evolutionary algorithms treat a particular spatial allocation of conservation practices in a watershed as a candidate solution and utilize sets (populations) of candidate solutions iteratively applying stochastic operators of selection, recombination, and mutation to find improvements with respect to the optimization objectives. The optimization objectives in this case are to minimize nonpoint-source pollution in the watershed, simultaneously minimizing the cost of conservation practices. A recent and expanding set of research is attempting to use similar methods and integrates water quality models with broadly defined evolutionary optimization methods3,4,9,10,13-15,17-19,22,23,25. In this application, we demonstrate a program which follows Rabotyagov et al.'s approach and integrates a modern and commonly used SWAT water quality model7 with a multiobjective evolutionary algorithm SPEA226, and user-specified set of conservation practices and their costs to search for the complete tradeoff frontiers between costs of conservation practices and user-specified water quality objectives. The frontiers quantify the tradeoffs faced by the watershed managers by presenting the full range of costs associated with various water quality improvement goals. The program allows for a selection of watershed configurations achieving specified water quality improvement goals and a production of maps of optimized placement of conservation practices.

This work demonstrates an integration of a water quality model with an optimization component utilizing evolutionary algorithms to solve for optimal (lowest-cost) placement of agricultural conservation practices for a specified set of water quality improvement objectives. The solutions are generated using a multi-objective approach, allowing for explicit quantification of tradeoffs.

Finding the cost-efficient (i.e., lowest-cost) ways of targeting conservation practice investments for the achievement of specific water quality goals ...

A Semi-quantitative Approach to Assess Biofilm Formation Using Wrinkled Colony Development

Biofilms, or surface-attached communities of cells encapsulated in an extracellular matrix, represent a common lifestyle for many bacteria. Within a biofilm, bacterial cells often exhibit altered physiology, including enhanced resistance to antibiotics and other environmental stresses 1. Additionally, biofilms can play important roles in host-microbe interactions. Biofilms develop when bacteria transition from individual, planktonic cells to form complex, multi-cellular communities 2. In the laboratory, biofilms are studied by assessing the development of specific biofilm phenotypes. A common biofilm phenotype involves the formation of wrinkled or rugose bacterial colonies on solid agar media 3. Wrinkled colony formation provides a particularly simple and useful means to identify and characterize bacterial strains exhibiting altered biofilm phenotypes, and to investigate environmental conditions that impact biofilm formation. Wrinkled colony formation serves as an indicator of biofilm formation in a variety of bacteria, including both Gram-positive bacteria, such as Bacillus subtilis 4, and Gram-negative bacteria, such as Vibrio cholerae 5, Vibrio parahaemolyticus 6, Pseudomonas aeruginosa 7, and Vibrio fischeri 8.
The marine bacterium V. fischeri has become a model for biofilm formation due to the critical role of biofilms during host colonization: biofilms produced by V. fischeri promote its colonization of the Hawaiian bobtail squid Euprymna scolopes 8-10. Importantly, biofilm phenotypes observed in vitro correlate with the ability of V. fischeri cells to effectively colonize host animals: strains impaired for biofilm formation in vitro possess a colonization defect 9,11, while strains exhibiting increased biofilm phenotypes are enhanced for colonization 8,12. V. fischeri therefore provides a simple model system to assess the mechanisms by which bacteria regulate biofilm formation and how biofilms impact host colonization.
In this report, we describe a semi-quantitative method to assess biofilm formation using V. fischeri as a model system. This method involves the careful spotting of bacterial cultures at defined concentrations and volumes onto solid agar media; a spotted culture is synonymous to a single bacterial colony. This 'spotted culture' technique can be utilized to compare gross biofilm phenotypes at single, specified time-points (end-point assays), or to identify and characterize subtle biofilm phenotypes through time-course assays of biofilm development and measurements of the colony diameter, which is influenced by biofilm formation. Thus, this technique provides a semi-quantitative analysis of biofilm formation, permitting evaluation of the timing and patterning of wrinkled colony development and the relative size of the developing structure, characteristics that extend beyond the simple overall morphology.

We provide a simple, semi-quantitative method to investigate biofilm formation in vitro. This method takes advantage of the Zeiss stemi 2000-C Dissecting Microscope (with camera attachment) to monitor both the timing and pattern of biofilm formation, as assessed by the development of wrinkled colonies.

Biofilms, or surface-attached communities of cells encapsulated in an extracellular matrix, represent a common lifestyle for many bacteria. Within a ...

Conversion of a Capture ELISA to a Luminex xMAP Assay using a Multiplex Antibody Screening Method

The enzyme-linked immunosorbent assay (ELISA) has long been the primary tool for detection of analytes of interest in biological samples for both life science research and clinical diagnostics. However, ELISA has limitations. It is typically performed in a 96-well microplate, and the wells are coated with capture antibody, requiring a relatively large amount of sample to capture an antigen of interest . The large surface area of the wells and the hydrophobic binding of capture antibody can also lead to non-specific binding and increased background. Additionally, most ELISAs rely upon enzyme-mediated amplification of signal in order to achieve reasonable sensitivity. Such amplification is not always linear and can thus skew results.
In the past 15 years, a new technology has emerged that offers the benefits of the ELISA, but also enables higher throughput, increased flexibility, reduced sample volume, and lower cost, with a similar workflow 1, 2. Luminex xMAP Technology is a microsphere (bead) array platform enabling both monoplex and multiplex assays that can be applied to both protein and nucleic acid applications 3-5. The beads have the capture antibody covalently immobilized on a smaller surface area, requiring less capture antibody and smaller sample volumes, compared to ELISA, and non-specific binding is significantly reduced. Smaller sample volumes are important when working with limiting samples such as cerebrospinal fluid, synovial fluid, etc. 6. Multiplexing the assay further reduces sample volume requirements, enabling multiple results from a single sample.
Recent improvements by Luminex include: the new MAGPIX system, a smaller, less expensive, easier-to-use analyzer; Low-Concentration Magnetic MagPlex Microspheres which eliminate the need for expensive filter plates and come in a working concentration better suited for assay development and low-throughput applications; and the xMAP Antibody Coupling (AbC) Kit, which includes a protocol, reagents, and consumables necessary for coupling beads to the capture antibody of interest. (See Materials section for a detailed list of kit contents.)
In this experiment, we convert a pre-optimized ELISA assay for TNF-alpha cytokine to the xMAP platform and compare the performance of the two methods 7-11. TNF-alpha is a biomarker used in the measurement of inflammatory responses in patients with autoimmune disorders.
We begin by coupling four candidate capture antibodies to four different microsphere sets or regions. When mixed together, these four sets allow for the simultaneous testing of all four candidates with four separate detection antibodies to determine the best antibody pair, saving reagents, sample and time. Two xMAP assays are then constructed with the two most optimal antibody pairs and their performance is compared to that of the original ELISA assay in regards to signal strength, dynamic range, and sensitivity.

An ELISA can be easily converted to a Luminex xMAP assay and, through the benefits of multiplexing, several antibodies can be screened simultaneously to identify an optimum antibody pair, resulting in increased sensitivity and dynamic range, while reducing assay cost.

The enzyme-linked immunosorbent assay (ELISA) has long been the primary tool for detection of analytes of interest in biological samples for both life ...

Cell Tracking Using Photoconvertible Proteins During Zebrafish Development

Embryogenesis is a dynamic process that is best studied by using techniques that allow the documentation of developmental changes in vivo. The use of genetically-encoded fluorescent proteins has proven a valuable strategy for elucidating dynamic morphogenetic processes as they occur in the intact organism. During the past decade, the development of photoactivatable and photoconvertible fluorescent proteins has opened the possibility to investigate the fate of discrete subpopulations of tagged proteins1. Unlike photoactivatable proteins, photoconvertible fluorescent proteins (PCFPs) are readily tracked and imaged in their native emission state prior to photoconversion, making it easier to identify and select regions by optical inspection. PCFPs, such as Kaede2, KikGR3, Dendra4 and EosFP5, can be shifted from green to red upon exposure to UV or blue light due to a His-Tyr-Gly tripeptide sequence which forms a green chromophore that can be photoconverted to a red one by a light-catalyzed &beta;-elimination and subsequent extension of a &pi;-conjugated system3. PCFPs and their monomeric variants are useful tools for tracking cells6-10 and studying protein dynamics11-14, respectively. During recent years, PCFPs have been expressed in different animal model, such as zebrafish6, chicken7,8 and mouse9,10 for cell fate tracking. Here we report a protocol for cell-specific photoconversion of PCFPs in the living zebrafish embryo and further tracking of photoconverted proteins at later developmental stages. This methodology allows studying, in a tissue-specific manner, cell biological events underlying morphogenesis in the zebrafish animal model.

Here, we present a method for the photoactivated switch of photoconvertible fluorescent proteins (PCFPs) in the living zebrafish embryo and further tracking of photoconverted protein at specific time points during development. This methodology allows monitoring of cell biological events underlying different developmental processes in a live vertebrate organism.

Embryogenesis is a dynamic process that is best studied by using techniques that allow the documentation of developmental changes in vivo. The use of ...

Assessing Species-specific Contributions To Craniofacial Development Using Quail-duck Chimeras

The generation of chimeric embryos is a widespread and powerful approach to study cell fates, tissue interactions, and species-specific contributions to the histological and morphological development of vertebrate embryos. In particular, the use of chimeric embryos has established the importance of neural crest in directing the species-specific morphology of the craniofacial complex. The method described herein utilizes two avian species, duck and quail, with remarkably different craniofacial morphology. This method greatly facilitates the investigation of molecular and cellular regulation of species-specific pattern in the craniofacial complex.&#160;Experiments in quail and duck chimeric embryos have already revealed neural crest-mediated tissue interactions and cell-autonomous behaviors that regulate species-specific pattern in the craniofacial skeleton, musculature, and integument. The great diversity of neural crest derivatives suggests significant potential for future applications of the quail-duck chimeric system to understanding vertebrate development, disease, and evolution.

This article describes a method to generate chimeric embryos that are&#160;designed to test the species-specific contributions of neural crest and/or other tissues to craniofacial development.

The generation of chimeric embryos is a widespread and powerful approach to study cell fates, tissue interactions, and species-specific contributions to ...

Development of a Quantitative Recombinase Polymerase Amplification Assay with an Internal Positive Control

It was recently demonstrated that recombinase polymerase amplification (RPA), an isothermal amplification platform for pathogen detection, may be used to quantify DNA sample concentration using a standard curve. In this manuscript, a detailed protocol for developing and implementing a real-time quantitative recombinase polymerase amplification assay (qRPA assay) is provided. Using HIV-1 DNA quantification as an example, the assembly of real-time RPA reactions, the design of an internal positive control (IPC) sequence, and co-amplification of the IPC and target of interest are all described. Instructions and data processing scripts for the construction of a standard curve using data from multiple experiments are provided, which may be used to predict the concentration of unknown samples or assess the performance of the assay. Finally, an alternative method for collecting real-time fluorescence data with a microscope and a stage heater as a step towards developing a point-of-care qRPA assay is described. The protocol and scripts provided may be used for the development of a qRPA assay for any DNA target of interest.

Provided is a protocol for developing a real-time recombinase polymerase amplification assay to quantify initial concentration of DNA samples using either a thermal cycler or a microscope and stage heater. Also described is the development of an internal positive control. Scripts are provided for processing raw real-time fluorescence data.

It was recently demonstrated that recombinase polymerase amplification (RPA), an isothermal amplification platform for pathogen detection, may be used to ...

Using a Whole-mount Immunohistochemical Method to Study the Innervation of the Biliary Tract in Suncus murinus

This work describes the whole-mount immunohistochemistry staining method in detail, using neurofilament protein antibody to label the innervation of the biliary tract in Suncus murinus (S. murinus&#160;). First, the specimen was dissected from S. murinus and fixed in 4% paraformaldehyde (PFA). Second, an enzymatic treatment and potential endogenous peroxidase inactivation were performed. The specimen was then exposed to the primary antibody, anti-neurofilament protein antibody, for 3-6 days. It was then incubated with the secondary antibody conjugated with horseradish peroxidase. The color reaction was revealed by reacting the specimen with a 3,3&#39;-diaminobenzidine (DAB) substrate. This method can be applied to analyze the innervation of all visceral organs. Furthermore, this protocol can also be adapted to test other neuronal antibodies, but optimization of the antibodies should be done first. This method was originally introduced by Kuratani and Tanaka1,2,3.

Using a Whole-mount Immunohistochemical Method to Study the Innervation of the Biliary Tract in Suncus murinus

A whole-mount immunohistochemical approach, to visualize neurofilament protein expression in the extrahepatic biliary tract in Suncus murinus. is presented here. This protocol can be used to analyze the innervation of all visceral organs in S. murinus or other species.

This work describes the whole-mount immunohistochemistry staining method in detail, using neurofilament protein antibody to label the innervation of the ...

Mass Spectrometry Analysis to Identify Ubiquitylation of EYFP-tagged CENP-A (EYFP-CENP-A)

Studying the structure and the dynamics of kinetochores and centromeres is important in understanding chromosomal instability (CIN) and cancer progression. How the chromosomal location and function of a centromere (i.e., centromere identity) are determined and participate in accurate chromosome segregation is a fundamental question. CENP-A is proposed to be the non-DNA indicator (epigenetic mark) of centromere identity, and CENP-A ubiquitylation is required for CENP-A deposition at the centromere, inherited through dimerization between cell division, and indispensable to cell viability.
Here we describe mass spectrometry analysis to identify ubiquitylation of EYFP-CENP-A K124R mutant suggesting that ubiquitylation at a different lysine is induced because of the EYFP tagging in the CENP-A K124R mutant protein. Lysine 306 (K306) ubiquitylation in EYFP-CENP-A K124R was successfully identified, which corresponds to lysine 56 (K56) in CENP-A through mass spectrometry analysis. A caveat is discussed in the use of GFP/EYFP or the tagging of high molecular weight protein as a tool to analyze the function of a protein. Current technical limit is also discussed for the detection of ubiquitylated bands, identification of site-specific ubiquitylation(s), and visualization of ubiquitylation in living cells or a specific single cell during the whole cell cycle.
The method of mass spectrometry analysis presented here can be applied to human CENP-A protein with different tags and other centromere-kinetochore proteins. These combinatory methods consisting of several assays/analyses could be recommended for researchers who are interested in identifying functional roles of ubiquitylation.

Mass Spectrometry Analysis to Identify Ubiquitylation of EYFP-tagged CENP-A EYFP-CENP-A

CENP-A ubiquitylation is an important requirement for CENP-A deposition at the centromere, inherited through dimerization between cell division, and indispensable to cell viability. Here we describe mass spectrometry analysis to identify ubiquitylation of EYFP-tagged CENP-A (EYFP-CENP-A) protein.

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Using a Whole-mount Immunohistochemical Method to Study the Innervation of the Biliary Tract in Suncus murinus

Mass Spectrometry Analysis to Identify Ubiquitylation of EYFP-tagged CENP-A (EYFP-CENP-A)