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Article

Modelling the Effect of Weed Competition on Long-Term Volume Yield of Eucalyptus globulus Labill. Plantations across an Environmental Gradient

by
Felipe Vargas
1,2,*,
Carlos A. Gonzalez-Benecke
3,
Rafael Rubilar
4 and
Manuel Sanchez-Olate
2
1
Bioforest S.A., Concepción 83422, Chile
2
Departamento de Silvicultura, Facultad de Ciencias Forestales, Universidad de Concepción, Concepción 83422, Chile
3
Department of Forest Engineering, Resources and Management, Oregon State University, Corvallis, OR 97331, USA
4
Cooperativa de Productividad Forestal, Departamento de Silvicultura, Facultad de Ciencias Forestales, Universidad de Concepción, Concepción 83422, Chile
*
Author to whom correspondence should be addressed.
Forests 2018, 9(8), 480; https://doi.org/10.3390/f9080480
Submission received: 10 July 2018 / Revised: 24 July 2018 / Accepted: 30 July 2018 / Published: 8 August 2018
(This article belongs to the Section Forest Ecology and Management)
Browse Figures
Versions Notes

Abstract

:
Several studies have quantified the responses of Eucalyptus globulus Labill. plantations to weed control on its early development (2–3 years after establishment). However, long-term results of competing vegetation effects have not been included into growth and yield models that incorporate treatments of competing vegetation control, and its interaction with site resource availability. In this article, we compared several models predicting stand volume yield of E. globulus plantations established across an environmental gradient, growing under different intensity levels of competing vegetation control. Four sites were selected encompassing a gradient in rainfall and amount of competing vegetation. Treatments were applied at stand establishment and were monitored periodically until age 9 years. Competing vegetation control intensity levels considered 0, 5, 20, 44, and 100% weed-free cover around individual E. globulus cuttings. Maximum competing vegetation biomass production during the first growing season were 2.9, 6.5, 2.2, and 12.9 Mg ha−1, for sites ranging from low to high annual rainfall. As expected, reductions in volume yield at age 9 years were observed as competing vegetation control intensity decreased during the first growing season. A strong relationship was established between stem volume yield loss and the intensity of competing vegetation control, the amount of competing vegetation biomass produced during the first growing season and mean annual rainfall. The slope of the relationship was different among sites and was related mainly to water and light limitations. Our results suggest that the biomass of competing vegetation (intensity of competition), affecting site resource availability, contribute to observed long-term effects on E. globulus plantations productivity. The site with the lowest mean annual rainfall showed the highest volume yield loss at age 9 years. Sites with highest rainfall showed contrasting results related to the amount of competing vegetation biomass.

1. Introduction

Expansion of Eucalyptus plantations in the world has been very successful because of their high-volume production and adaptability to a wide range of sites. The Eucalyptus plantations exceed 20 million hectares worldwide [1], including more than 110 species of Eucalyptus introduced in more than 90 countries [2]. In Chile, Eucalyptus plantations exceed 850,000 hectares, of which 68% corresponds to E. globulus [3].
The application of competing vegetation control treatments requires a good understanding of tree growth and how competing vegetation affect site resource availability over time and which key resources affect stand growth [4,5]. It is well known that reducing weeds biomass during early stand establishment can increase light, water and nutrient and site resource availability [6,7,8] allowing better survival and tree growth [9,10,11,12].
Previous studies about managing of the intensity of competing vegetation or weed control (defined as the size of area free of competing vegetation around each tree) have shown an increase in stem volume—as the intensity of control increases in fast growing species such as Pinus taeda L. [13], Pinus radiata D.Don [14,15], Pseudotsuga menziesii (Mirb.) Franco [10], and Eucalyptus spp. [16]. The optimal intensity of weed control required to reach the maximum stand volume yield depends on the species planted, amount of competing vegetation and site resource availability and at each site [14,16]. Even though there are numerous studies that quantify growth responses associated with control of competing vegetation in Eucalyptus plantations [8,16,17,18], these results have not been included into growth models that incorporate different treatments of intensity of weed control on Eucalyptus plantations. The stem volume yield loss (or stand yield loss) due to weed competition is affected by several factors including: The abundance of weed biomass, spatial proximity to the plantation trees, soil water holding capacity, rainfall and temperature during the growing season [19]. A model can predict the yield loss associated with different intensities of competing vegetation control [20]. Modelling plantation-weed interactions can help also to improve understanding of ecophysiological processes involved. Empirical approaches have been used to model the response to competing vegetation control on the juvenile growth for Pinus radiata [21,22,23], Pinus taeda [24] and Pseudotsuga menziesii [25]. A negative hyperbolic curve showed a good correlation between the amount of weed biomass, the survival and the volume yield of the Pinus ponderosa Douglas ex C. Lawson seedlings [26].
The development of a stand growth response model would improve our ability to predict long-term effect of competing vegetation on E. globulus plantations productivity across sites. From a modelling perspective, there is a strong need to understand how competing vegetation affect site resource availability over time and how resources affect stand growth in order to make more sustainable management decisions. The purpose of this study was to model the effect of area free of competing vegetation on stem volume response of E. globulus plantations. We hypothesize that: (i) The relationship between stand yield loss and intensity of competing vegetation control is not linear. (There is an optimal intensity of competing vegetation control to reach the maximum stand volume yield). (ii) Sites with high water availability require smaller area free of competition at establishment than sites with low water availability to reach the maximum growth potential at 9 years of age in E. globulus plantations.

2. Materials and Methods

2.1. Site Characteristics

The experiment was established in four sites selected in south-central zone of Chile, consisting of an environmental gradient (Table 1), where other work has been completed [18]. Climate at the study sites showed a dry summer and rainfall mainly during winter (June-September). The study sites were characterized according to their annual mean rainfall (low rainfall (LR), medium rainfall (MR), or high rainfall (HR)) (Table 1) and by the amount of weed biomass produced (Mg ha−1) during the first growing season. Thus, site LR2.9 had a low rainfall, and produced 2.9 Mg ha−1 of weed biomass; site MR6.5 had a medium rainfall, and produced 6.5 Mg ha−1 of weed biomass; site HR2.2 had a high rainfall, and produced 2.2 Mg ha−1 of weed biomass; and site HR12.9 had a high rainfall and produced 12.9 Mg ha−1 of weed biomass (Figure 1).
At the LR2.9 site, dominant herbaceous weed was Arrhenaterum elatius L. and dominant woody shrub was Acacia dealbata Link. At the MR6.5 site, dominant herbaceous weed was Senecio vulgaris L., and dominant woody shrub was Ulex europaeus L. At the HR2.2 site, dominant herbaceous weed was Digitalis purpurea L., Taraxacum officinale F.H. Wigg and Holcus lanatus L., and dominant woody shrub was Aristotelia chilensis (Molina) Stuntz. At the HR12.9 site, dominant herbaceous weed was Lolium multiflorum Lam., and dominant woody shrub was Rubus constrictus P. J. Müll. & Lefevre.
The LR2.9 site came from a reforestation, harvest slash was burnt, follow by a soil preparation (80 cm deep). This site was planted in July 2004 with a planting shovel. The MR6.5 site was reforestation, harvest slash was shredded and planted in July 2004 with a planting shovel. The HR2.2 site was reforestation, harvest slash was mechanically arranged in strips (windrows) and planted in August 2003 with a planting shovel. The HR12.9 site was a forestation plantation on a former pasture land and was planted in September 2004 with a planting shovel. All sites were planted with a mix of the top 5% half-sib families produced from cuttings and ranked by genetic performance.

2.2. Experimental Design and Treatments

The effect of weed control intensity was evaluated through a randomized complete block design (five replicates). Treatments included five levels of intensity of competing vegetation control around individual E. globulus cuttings: 0 (I0), 5 (I5), 20 (I20), 44 (I44), and 100% (I100) weed-free cover. At each experimental plot 90 cuttings were planted (9 rows × 10 plants), with a measurement plot of 30 cuttings (5 rows × 6 plants) and a buffer of two tree rows implemented around each measurement plot. All the sites were planted at a density of 1736 trees ha−1 (spacing of 2.4 × 2.4 m), except for site LR2.9, with a density of 1666 trees ha−1 (spacing of 3.0 × 2.0 m), because it was subsoiled before planting.
At each site, an herbicide application was made prior to planting (3.0 kg ha−1 simazine + 2.5 kg ha−1 glyphosate + 1 mL L−1 Silwet surfactant) using backpack sprayers. Herbicides and surfactant were applied when wind speeds did not exceed 2 km h−1 using a volume rate of 120 litres ha−1. The simazine was Simazina 90 WG (Water dispersible granules) (Formulation of 90% simazine), glyphosate used was Roundup Max (Formulation of 48% glyphosate), and Silwet surfactant. A second herbicide application was made between February and March of the subsequent year at each site, using the same prescription (application method, chemicals and rates) as in the herbicide application prior to planting. A third herbicide application was made between September and October of the subsequent year at each site, using the same prescription (application method, chemicals and rates) as the previous application, except at HR2.2 due to the low level of competing vegetation present. The planted E. globulus cuttings were sheltered from the spray.
At site LR2.9 and MR6.5 a fertilizer application was made 30 days after planting. Fertilizer was applied manually a blend of 180 g plant−1 of diammonium phosphate and 30 g plant−1 of boronatrocalcite (commercial fertilizers), equivalent a 32.4, 36.2 and 3.0 g plant−1 of elemental nitrogen, phosphorus, and boron, respectively.

2.3. Competing Vegetation Biomass Measurements

At each site, the amount of weed biomass was quantified through an additional plot (90 plants in total) with no competing vegetation control. During the first growing seasons, the amount of weed was monthly evaluated from two subplots of 2 × 2 m randomly selected within the additional biomass plot installed at each block. The detailed explanation of how samples of competing vegetation were taken from each subplot to determine their dry mass was reported by Vargas et al. (2018) [18].

2.4. Volume Yield

From planting up 9 years, stem diameter at 1.3 m height (cm) and total tree height (m) were measured every year between May and June. Individual commercial stem volume was determined using the Kozak’s taper function [27] and considering a top diameter limit (TDL) of 6 cm for each tree (Table 2).

2.5. Data Analysis

Statistical analysis was performed using the statistical software program R-Project (version 3.3, www.r-project.org). We compared several Non-linear models predicting the effect of different intensity levels of competing vegetation control on long-term volume yield loss. CurveExpert Básico version 2.1.0 (www.curveexpert.net) (Hyams Development) was used for exploratory curve analysis. The statistical software program R-Project (version 3.3) was used to create all figures.

2.5.1. Modelling Approach

We used a non-linear model fitting approach to analyze stand yield loss as a function of site variables (mean annual rainfall, mean annual maximum temperature, mean annual minimum temperature) and competition variables (intensity of weed control and amount of weed biomass during the first and second growing seasons). Equations used to represent stand yield loss are hyperbolic family curves [26,28]. We used Akaike’s information criteria (AIC) to evaluate goodness-of-fit for nonlinear regression models. AIC is an estimator of the relative quality of the statistical models for a given dataset. This estimator was calculated and ranked accordingly by minimum AIC [29]. Table 3 presents a list of equations used to stand yield loss modeling.
After testing several models, a negative hyperbolic model was selected with the form:
Yij = a + (b − a) Exp[−Exp(c)Xj] + εij
where Yij is the percentage response in volume relative to the non-treated control at age 9 years and Xj is intensity of competing vegetation control (ranging from 0 to 100%) during the first and second growing seasons for the ith site and jth treatment. Exp is base of natural logarithm; εij is the error of the model with ε ~ N(0, σ2); i is to denote 1–5 treatments; j is to denote 1–4 sites; a, b and c are curve fit parameters. Parameter a is the asymptote as Xj → ∞, b represents the stand yield loss when no competing vegetation control, and c is the logarithm of the rate constant.

2.5.2. Estimating the Parameter b

The parameter b of model (1) represents the value of Yij when Xj is equal to zero, so this parameter may be related with site and competition variables. Thus, the parameter b of the model (1) was reparametrized through a linear model to account for the influence of the amount of competing vegetation biomass and mean annual rainfall on stand yield loss.
Yijk = a + ((b1 + b2 Vijk + b3 Ri + b4 Vijk × Ri) − a) Exp[(−Exp(c) Xj)] + εijk
where, Yijk is stand yield loss (%), Vijk is maximum production of competing vegetation biomass (Mg ha−1) during the first growing season of the kth block at the ijth site-treatment combination, Ri is average annual rainfall at the ith site and Xj is intensity of competing vegetation control of the jth treatment. εijk is the error of the model with ε ~ N(0, σ2); i = 1–5 treatments, j = 1–4 sites, k = 1–5 blocks; a, b1, b2, b3, b4, and c are curve fit parameters. Normality (Kolmogorov–Smirnov’s test) and homogeneity test of variance (Levene’s test) were checked. The significance level used to evaluate all statistical analysis was p < 0.05.

2.5.3. Model Validation

In this study, the yield loss model was fitted to the entire data set. The predictive ability of the final fitted model was assessed by using the leave one out cross validation (LOOCV) technique [31,32]. In this method we pick only one plot as the test set. Then we build a model with all the plots remaining (training plots) and evaluate its error with the test plot. If a single observation is used to calculate the error test, it varies greatly depending on which observation has been selected. To avoid this, the process is repeated as many times as available observations, excluding in each iteration a different observation, adjusting the model with the rest and calculating the error with that observation. Finally, the error estimate by LOOCV is obtained by repeating this procedure for each of the training plots available, averaging the results [32]. Two measures of accuracy were used to evaluate the goodness-of-fit between predicted and observed values for stand yield loss: Coefficient of determination (R2) and root mean square error (RMSE). For the variable stand yield loss, a F-tests was used to determine if the relationship between observed and predicted values had an intercept and slope different than zero and one, respectively.

3. Results

3.1. Modelling the Effects of Weed Competition on Volume Yield

After applying the step-wise method and evaluating AIC, a negative hyperbolic curve with upward concavity (Equation (1)) was the selected model to predict the relationship between stand yield loss of E. globulus and area free of competing vegetation at establishment (Table 4).
The b parameter of Equation (1), that represents stand yield loss with no competing vegetation control was reparametrized to account for the influence of mean annual rainfall and the amount of competing vegetation on stand yield loss. Equation (2), was used to model yield losses of E. globulus and area free of competing vegetation, amount of competing biomass controlled during the first growing season and mean annual rainfall also showed a strong relationship (R2: 0.79; p < 0.001). A summary of parameters estimated for Equation (2) is shown in Table 5.
When intensity of weed control, amount of weed biomass controlled during the first growing season and mean annual rainfall were combined, the model explained 79% of the variation in stand yield loss (Equation (2)). The reparametrized model showed a significant improvement over the univariate model (Equation (2)). Mean annual minimum temperature and mean annual maximum temperature did not improve the reparametrized model.
All sites showed a general trend of stand yield loss as intensity of weed control decreased. However, sites under study showed high variability in plantation yield loss among sites (Figure 2).
Comparing all sites, maximum stand yield loss occurred when area free of competing vegetation was equal to zero. In average, at the age of nine years, stand yield loss ranged from 35 to 91% when no competing vegetation control was applied at establishment. Interestingly, maximum stand yield loss was observed at sites with the highest and lowest mean annual rainfall (LR2.9 and HR12.9).

3.2. Model Validation

A strong correlation was observed between predicted and observed values (p < 0.001; R2 = 0.76; RMSE = 16.6), without clear tendencies to over-estimate for the tested variable. However, there was a tendency to under-estimate when the stand yield loss was higher 70%. Across all sites, the relationship between observed and predicted values were not statistically different from one to the slope (estimated value: 0.77; p < 0.001) and zero to the intercept (estimated value: 7.63; p < 0.001), respectively (Figure 3).

4. Discussion

The first hypothesis was accepted because the relationship between stand yield loss and intensity of weed control was not linear. Therefore, there is an optimal intensity of competing vegetation control to reach the maximum stand volume yield (Figure 2). We reject our second hypothesis because sites with high water availability (HR2.2 and HR12.9) do not require necessarily smaller area free of competition at establishment than sites with low water availability (LR2.9) to reach the maximum potential growth at age 9 years in E. globulus plantations.
The model described in this study, was developed by incorporating sites with contrasting environmental conditions, successfully account for stand yield losses attributable to weed competition. This study represents, the first reported model to predict the effect of weed competition on long-term volume yield of E. globulus. It was observed a tendency of decreasing stand yield loss as the intensity of weed control increased across sites. Similar responses have been reported in previous studies that included different intensities of competing vegetation in E. globulus [16,17] and Pseudotsuga menziesii [10]. In addition, a strong relationship was found between stand yield loss and intensity of competing vegetation, amount of weed biomass during the first growing season and mean annual rainfall (Equation (2), R2 = 0.79). Little and Schumann (1996) [33], reported similar results in E. globulus plantations, where stand yield loss was correlated to the amount of weed biomass observed. Similar results of stand yield loss as the intensity of competing vegetation control increased were observed in P. radiata by Mason and Kirongo (1999) [34]. The above approach was observed in the treatment I5 (5% of the total treated area), where there was a significant decrease in the stand yield loss compared to the treatment I0 (without weed control) at sites with a high amount of weed biomass (MR6.5 and HR12.9). Similar response was observed by Wagner (2000) [35], who observed that even a small area free of weed might substantially decrease for cutting survival and growth.
In our study, the slope of the yield loss curve for each site increased considerably when intensity of weed control was less than 20% (Figure 2), suggesting that E. globulus has a low tolerance to competition by weed during the stand establishment [17,36]. Changes in the slope of the relationship between stand yield loss and area free of competing vegetation were related to differences in the availability and the efficient use of site resources by the weed. Our results suggest that stand yield loss related the effect of weed competition may be associated with a decline in soil water availability [37,38,39]. Seasonal water deficit becomes smaller in sites with higher rainfall. However, trees growing at sites with moderate to high rainfall may have some degree of water limitations, even more if rainfall is irregular and soil water storage is low [40]. Additionally, at sites with high amount of weed (LR12.9), light availability may be critical for shadowing effect of the weed on E. globulus cuttings at stand establishment. At sites with high abundance of graminoids, low soil nitrogen availability may be critical in sites with low fertility [41].
The model was validate using data from plots with contrasting productivity. The slope of the relationship between observed and predicted stand yield loss was near one (Estimated value: 0.77; p < 0.001), supporting the strength of the model and its ability for assessing long-term effect of competing vegetation on E. globulus plantations productivity considering a sites gradient. Although the fitted model performed well for the data used for validation, the prediction of the model outside the geographical range of the sites under study (Fitted data) is uncertain. Therefore, we recommend using this model exclusively within the area geographical of the sites under study (see Table 1).
On sites with contrasting annual rainfall (LR2.9 and HR12.9), the high stand yield loss observed on I0 treatment (93% and 91%, respectively), has different causes that explain the yield loss. At site LR2.9 had the lowest annual rainfall of all the study sites, suggesting lower soil water availability during the growing season, increasing severely stand yield loss. Similar findings have been reported by Richardson et al. (1993) [42], on dryland sites, suggesting that growth reductions related to weed competition may be associated primarily with competition for water. On the other hand, the site HR12.9 had the highest annual rainfall and the highest amount of weed biomass across all sites, suggesting that a high competition for light may had increased the E. globulus cuttings yield loss. These responses were consistent with the results observed by Balandier et al. (2006) [7] and Garau et al. (2009) [17], where E. globulus yield loss due to weed competition was related to decreases in available light and soil water. The contrasting stand yield loss levels observed on non-treated control plots (35% at HR2.2 and 91% at HR12.9) between the two southern sites that had higher rainfall (HR2.2, 2055 mm; HR12.9, 2103 mm), suggest that the high amount of weed biomass reduced light availability, decreasing survival and tree growth. Similar results have been reported for E. globulus by Garau et al. (2009) [17], where weed biomass accounted for 98% of the variation in stem volume. Similar relationships were observed for other forest planted in different environments [26,36,43,44].

5. Conclusions

A strong relationship was established between stand yield loss and the intensity of competing vegetation control, the amount of competing vegetation biomass produced during the first growing season and mean annual rainfall. The relationship between stand yield loss and intensity of competing vegetation control was not linear. Therefore, there is an optimal intensity of competing vegetation control to reach the maximum stand volume yield.
The site LR2.9 with the lowest mean annual rainfall and the site HR12.9 with the highest weed biomass, showed the highest volume yield loss at the age of nine years, when no weed control was applied. Sites with highest mean annual rainfall showed contrasting results of volume yield loss related to the amount of competing vegetation biomass.
Modelling plantation-weed interactions can help also to improve understanding of ecophysiological processes involved and how competing vegetation affect site resource availability over time and which key resources affect stand growth. One of the most important contributions of the response model developed in this study, is improve our ability to predict the effect of weed control on long-term volume yield loss of E. globulus across sites.

Author Contributions

F.V. analyzed the data and wrote the paper; C.A.G.-B. and R.R. conducted the statistical analysis, contributed to the writing of the paper and data interpretation. M.S.-O. contributed to the writing of the paper.

Funding

This research was supported by Bioforest S.A. and Forestal Arauco S.A.

Acknowledgments

We thanks to Forestal Arauco S.A. and Bioforest S.A. for financial and technical support. We thank P. Aracena and J. Zapata-Valenzuela for their useful comments prior to publication. We thank field staff from Bioforest S.A. and Forestal Arauco S.A. who provided fieldwork and site management assistance.

Conflicts of Interest

The authors declare no conflict of interest.

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Forests 09 00480 g001 550
Figure 1. Location of sites used in this study for E. globulus in Chile.
Figure 1. Location of sites used in this study for E. globulus in Chile.
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Figure 2. Proportion of stand yield loss under different vegetation control intensity across a rainfall and the amount of competing vegetation biomass gradient. The study sites were characterized according to their annual mean rainfall (LR, MR or HR) and by the amount of weed biomass produced (Mg ha−1) during the first growing season.
Figure 2. Proportion of stand yield loss under different vegetation control intensity across a rainfall and the amount of competing vegetation biomass gradient. The study sites were characterized according to their annual mean rainfall (LR, MR or HR) and by the amount of weed biomass produced (Mg ha−1) during the first growing season.
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Forests 09 00480 g003 550
Figure 3. Model validation for four tested sites (100 plots total). Observed versus predicted values of proportion of stand yield loss. The dotted line represents to the 1 to 1 relationship.
Figure 3. Model validation for four tested sites (100 plots total). Observed versus predicted values of proportion of stand yield loss. The dotted line represents to the 1 to 1 relationship.
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Table
Table 1. Mean annual rainfall (Rain), mean annual maximum temperature (Tmax), mean annual minimum temperature (Tmin), clay content (Clay), and organic matter (OM), in the first 20 cm of soil depth for each site.
Table 1. Mean annual rainfall (Rain), mean annual maximum temperature (Tmax), mean annual minimum temperature (Tmin), clay content (Clay), and organic matter (OM), in the first 20 cm of soil depth for each site.
Sites CharacteristicsSites
LR2.9MR6.5HR2.2HR12.9
Latitude/Longitude72°3′/36°42′73°29′/37°40′72°52′/39°13′72°56′/39°28′
Altitude (m)8211233573
Rain (mm y−1)1198145420552103
Tmax (°C)19.817.416.717.1
Tmin (°C)6.37.56.06.7
Clay (%)43.040.118.333.2
OM (%)5.09.216.513.0
Soil orderUltisolAlfisolUltisolAndisol
Table
Table 2. Average stand volume (m3 ha−1) at age 9 for Eucalyptus globulus stands that received different treatments of vegetation control intensity. The study sites were characterized according to their annual mean rainfall (low rainfall (LR), medium rainfall (MR), or high rainfall (HR)) and by the amount of weed biomass produced (Mg ha−1) during the first growing season. Adapted from Vargas et al. 2018 [18].
Table 2. Average stand volume (m3 ha−1) at age 9 for Eucalyptus globulus stands that received different treatments of vegetation control intensity. The study sites were characterized according to their annual mean rainfall (low rainfall (LR), medium rainfall (MR), or high rainfall (HR)) and by the amount of weed biomass produced (Mg ha−1) during the first growing season. Adapted from Vargas et al. 2018 [18].
TreatmentLR2.9MR6.5HR2.2HR12.9
I09.5159.0164.926.8
I525.4222.0184.6101.5
I2061.9276.6195.3155.4
I4471.3324.5222.9233.6
I100127.2343.4251.9288.9
Table
Table 3. Equations used for stand yield loss modeling to different treatments of intensity of competing vegetation control of planted E. globulus.
Table 3. Equations used for stand yield loss modeling to different treatments of intensity of competing vegetation control of planted E. globulus.
ModelsReferences
(1) Yij = a + (b − a) Exp[−Exp(c)Xj] + εij Pinheiro and Bates 2000 [29]
(2) Yijk = a × Exp[−Exp(b)Xj] + c × Exp[−Exp(d)Zk] + εijkPinheiro and Bates 2000 [29]
(3) Yij = Exp(−a × Xj) + εij Ratkowsky 1990 [30]
(4) Yij = a/((b × Xj) + Exp(c × Xj)) + εij Ratkowsky 1990 [30]
Table
Table 4. Fit statistics for the tested yield loss models, using Akaike’s information criteria (AIC), Coefficient of determination (R2) and root mean square error (RMSE).
Table 4. Fit statistics for the tested yield loss models, using Akaike’s information criteria (AIC), Coefficient of determination (R2) and root mean square error (RMSE).
ModelsAICR2RMSE
(1) Yij = a + (b − a) Exp[−Exp(c)Xj] + εij7810.5919.66
(2) Yijk = a × Exp[−Exp(b)Xj] + c × Exp[−Exp(d)Zk] + εijk8610.5126.35
(3) Yij = Exp(−a × Xj) + εij9940.4344.72
(4) Yij = a/((b × Xj) + Exp(c × Xj)) + εij8470.5621.99
Table
Table 5. Parameter asymptotic estimates and their standard error and P for the stand yield loss equation based on competing vegetation biomass (V), average annual rainfall (R) and intensity of competing vegetation control (X).
Table 5. Parameter asymptotic estimates and their standard error and P for the stand yield loss equation based on competing vegetation biomass (V), average annual rainfall (R) and intensity of competing vegetation control (X).
ParameterAsymptotic EstimateStandard Errorp
a−2.44794.48380.586
b1194.352919.6128<0.001
b2−19.04213.7018<0.001
b3−0.08200.0106<0.001
b40.01130.0018<0.001
c−3.59710.1821<0.001

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Vargas, F.; Gonzalez-Benecke, C.A.; Rubilar, R.; Sanchez-Olate, M. Modelling the Effect of Weed Competition on Long-Term Volume Yield of Eucalyptus globulus Labill. Plantations across an Environmental Gradient. Forests 2018, 9, 480. https://doi.org/10.3390/f9080480

AMA Style

Vargas F, Gonzalez-Benecke CA, Rubilar R, Sanchez-Olate M. Modelling the Effect of Weed Competition on Long-Term Volume Yield of Eucalyptus globulus Labill. Plantations across an Environmental Gradient. Forests. 2018; 9(8):480. https://doi.org/10.3390/f9080480

Chicago/Turabian Style

Vargas, Felipe, Carlos A. Gonzalez-Benecke, Rafael Rubilar, and Manuel Sanchez-Olate. 2018. "Modelling the Effect of Weed Competition on Long-Term Volume Yield of Eucalyptus globulus Labill. Plantations across an Environmental Gradient" Forests 9, no. 8: 480. https://doi.org/10.3390/f9080480

APA Style

Vargas, F., Gonzalez-Benecke, C. A., Rubilar, R., & Sanchez-Olate, M. (2018). Modelling the Effect of Weed Competition on Long-Term Volume Yield of Eucalyptus globulus Labill. Plantations across an Environmental Gradient. Forests, 9(8), 480. https://doi.org/10.3390/f9080480

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