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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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.

<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>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.bdigitaluss.remotexs.co/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.bdigitaluss.remotexs.co/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

Universidad San Sebastian

Research

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

Experimental Protocol for Manipulating Plant-induced Soil Heterogeneity

Coexistence theory has often treated environmental heterogeneity as being independent of the community composition; however biotic feedbacks such as plant-soil feedbacks (PSF) have large effects on plant performance, and create environmental heterogeneity that depends on the community composition. Understanding the importance of PSF for plant community assembly necessitates understanding of the role of heterogeneity in PSF, in addition to mean PSF effects. Here, we describe a protocol for manipulating plant-induced soil heterogeneity. Two example experiments are presented: (1) a field experiment with a 6-patch grid of soils to measure plant population responses and (2) a greenhouse experiment with 2-patch soils to measure individual plant responses. Soils can be collected from the zone of root influence (soils from the rhizosphere and directly adjacent to the rhizosphere) of plants in the field from conspecific and heterospecific plant species. Replicate collections are used to avoid pseudoreplicating soil samples. These soils are then placed into separate patches for heterogeneous treatments or mixed for a homogenized treatment. Care should be taken to ensure that heterogeneous and homogenized treatments experience the same degree of soil disturbance. Plants can then be placed in these soil treatments to determine the effect of plant-induced soil heterogeneity on plant performance. We demonstrate that plant-induced heterogeneity results in different outcomes than predicted by traditional coexistence models, perhaps because of the dynamic nature of these feedbacks. Theory that incorporates environmental heterogeneity influenced by the assembling community and additional empirical work is needed to determine when heterogeneity intrinsic to the assembling community will result in different assembly outcomes compared with heterogeneity extrinsic to the community composition.

Understanding the role of environmental heterogeneity in species coexistence has typically focused on types of heterogeneity that are extrinsic to the community&#8217;s species composition. We provide novel detailed methods for creating soil heterogeneity treatments using soils subject to plant-soil feedback conditioning, or heterogeneity intrinsic to the community composition.

Coexistence theory has often treated environmental heterogeneity as being independent of the community composition; however biotic feedbacks such as ...

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 ...

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 ...

JenaTron - An Experimental Approach to Study the Effects of Plant History and Soil History on Grassland Ecosystem Functioning

The global loss of biodiversity has motivated many studies that experimentally vary plant species richness and examine the consequences for ecosystem functioning. Such experiments generally show a positive relationship between above- and below-ground biodiversity and the functioning of terrestrial ecosystems. Moreover, this relationship tends to strengthen over time, seen as enhanced functioning of diverse plant communities and reduced functioning of low-diversity plant communities. Differences in multitrophic community assembly and biotic interactions in high- versus low-diversity plant communities are hypothesized to affect plant performance by altering consumer community structure and function and driving plastic or micro-evolutionary responses of plant species in the plant communities. To resolve this complex interplay of community history, we separated these effects into plant and soil history. Plant history refers to all plant-level responses to past abiotic and biotic selection pressures experienced in their communities, while soil history relates to all abiotic and biotic soil properties developed as a legacy of plant-soil interactions under variable plant diversity. We set up a biodiversity experiment in an Ecotron, a terrestrial mesocosm facility that allows controlling environmental conditions above- and below-ground, to test whether the strengthening biodiversity-ecosystem functioning relationship is due to soil history, plant history, or a combination of both. We established a plant diversity gradient consisting of 1, 2, 3, and 6 grassland plant species and factorially nested with soil history and plant history treatments for each level of plant species richness. Representative results demonstrate the successful establishment of target treatments in the Ecotron experiment, observing the effects of plant and soil history on initial plant development and final plant growth. Additionally, we provide a case study for data analysis of individual response variables. We outline research objectives and methods to comprehensively assess the multifunctional responses to the experimental treatments necessary to ultimately address the overarching hypothesis.

Here we present a study established in the iDiv Ecotron, terrestrial mesocosm chambers with controlled environmental conditions above- and below-ground, to study the independent and interactive effects of plant history and soil history on ecosystem functioning of grassland communities along a plant diversity gradient.

The global loss of biodiversity has motivated many studies that experimentally vary plant species richness and examine the consequences for ecosystem ...

Invasive Plant Biomass Assessment by Unmanned Aerial Vehicle Remote Sensing Data

Computer Vision-Based Biomass Estimation for Invasive Plants

We report on the detailed steps of a method to estimate the biomass of invasive plants based on UAV remote sensing and computer vision. To collect samples from the study area, we prepared a sample square assembly to randomize the sampling points. An unmanned aerial camera system was constructed using a drone and camera to acquire continuous RGB images of the study area through automated navigation. After completing the shooting, the aboveground biomass in the sample frame was collected, and all correspondences were labeled and packaged. The sample data was processed, and the aerial images were segmented into small images of 280 x 280 pixels to create an image dataset. A deep convolutional neural network was used to map the distribution of Mikania micrantha in the study area, and its vegetation index was obtained. The organisms collected were dried, and the dry weight was recorded as the ground truth biomass. The invasive plant biomass regression model was constructed using the K-nearest neighbor regression (KNNR)&#160;by extracting the vegetation index from the sample images as an independent variable and integrating it with the ground truth biomass as a dependent variable. The results showed that it was possible to predict the biomass of invasive plants accurately. An accurate spatial distribution map of invasive plant biomass was generated by image traversal, allowing precise identification of high-risk areas affected by invasive plants. In summary, this study demonstrates the potential of combining unmanned aerial vehicle remote sensing with&#160;machine learning techniques to estimate invasive plant biomass. It contributes significantly to the research of new technologies and methods for real-time monitoring of invasive plants and provides technical support for intelligent monitoring and hazard assessment at the regional scale.

Author Spotlight: UAV Remote Sensing for Efficient Invasive Plant Biomass Estimation

We report detailed procedures for an invasive plant biomass estimation method that utilizes data obtained from unmanned aerial vehicle (UAV) remote sensing to assess biomass and capture the spatial distribution of invasive species. This approach proves highly beneficial for conducting hazard assessment and early warning of invasive plants.

We report on the detailed steps of a method to estimate the biomass of invasive plants based on UAV remote sensing and computer vision. To collect samples ...

Engineering

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data

This report describes a novel Stata-based application of trigonometric regression modelling to 55 years of multiple sclerosis relapse data from 46 clinical centers across 20 countries located in both hemispheres. Central to the success of this method was the strategic use of plot analysis to guide and corroborate the statistical regression modelling. Initial plot analysis was necessary for establishing realistic hypotheses regarding the presence and structural form of seasonal and latitudinal influences on relapse probability and then testing the performance of the resultant models. Trigonometric regression was then necessary to quantify these relationships, adjust for important confounders and provide a measure of certainty as to how plausible these associations were. Synchronization of graphing techniques with regression modelling permitted a systematic refinement of models until best-fit convergence was achieved, enabling novel inferences to be made regarding the independent influence of both season and latitude in predicting relapse onset timing in MS. These methods have the potential for application across other complex disease and epidemiological phenomena suspected or known to vary systematically with season and/or geographic location.

Combining plot analysis with trigonometric regression is a robust method for exploring complex, cyclical phenomena such as relapse onset timing in multiple sclerosis (MS). This method enabled unbiased characterisation of seasonal trends in relapse onset permitting novel inferences around the influence of seasonal variation, ultraviolet radiation (UVR) and latitude.

This report describes a novel Stata-based application of trigonometric regression modelling to  55 years of multiple sclerosis relapse data from 46 ...