Performance of 45 NonLinear Models for Determining Critical Period of Weed Control and Acceptable Yield Loss in Soybean Agroforestry Systems
Abstract
:1. Introduction
2. Materials and Methods
2.1. Study Site
2.2. Experimental Design and Crop Management
2.3. Data Collection
2.4. Statistical Analysis
2.4.1. Selection of Candidate Models
2.4.2. Measures for GoodnessofFit
2.4.3. Evaluation of Model Assumptions
2.4.4. Model Calibration
2.4.5. Data Analysis
3. Results
3.1. Choose Candidate Models for Determining CPWC
3.2. Evaluation of Model Assumptions
3.3. Model Calibration
3.4. Predicted AYL Based on the Best Fitted Model
4. Discussion
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Duration of Weedy and WeedFree Periods ^{1}  Remarks 

W—0 DAE  Weedy until 70 days after emergence (DAE) 
W—7 DAE  Weedy after 7 until 70 DAE 
W—14 DAE  Weedy after 14 until 70 DAE 
W—21 DAE  Weedy after 21 until 70 DAE 
W—28 DAE  Weedy after 28 until 70 DAE 
W—35 DAE  Weedy after 35 until 70 DAE 
W—42 DAE  Weedy after 42 until 70 DAE 
W—49 DAE  Weedy after 49 until 70 DAE 
W—56 DAE  Weedy after 56 until 70 DAE 
W—63 DAE  Weedy after 63 until 70 DAE 
WF—7 DAE  WeedFree after 7 until 70 DAE 
WF—14 DAE  WeedFree after 14 until 70 DAE 
WF—21 DAE  WeedFree after 21 until 70 DAE 
WF—28 DAE  WeedFree after 28 until 70 DAE 
WF—35 DAE  WeedFree after 35 until 70 DAE 
WF—42 DAE  WeedFree after 42 until 70 DAE 
WF—49 DAE  WeedFree after 49 until 70 DAE 
WF—56 DAE  WeedFree after 56 until 70 DAE 
WF—63 DAE  WeedFree after 63 until 70 DAE 
WF—0 DAE  WeedFree until 70 DAE 
Decline  Distribution  Dose–Response  Exponential  Growth  Miscellaneous  Power Law Family  Sigmoidal  YieldSpacing Models 


































 




 


 

 

No.  Model  Family  Equation  References 

1.  Bleasdale  YieldSpacing Models  $\mathrm{y}={\left(\mathrm{a}+\mathrm{bx}\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{1ex}{$\mathrm{c}$}\right.}$  [24] 
2.  Exponential  Exponential Models  ${\mathrm{y}=\mathrm{ae}}^{\mathrm{bx}}$  [24] 
3.  Exponential Association 2  Growth Models  $\mathrm{y}=\mathrm{a}\left(1{\mathrm{e}}^{\mathrm{bx}}\right)$  [24] 
4.  Exponential Association 3  Growth Models  $\mathrm{y}=\mathrm{a}\left(\mathrm{b}{\mathrm{e}}^{\mathrm{cx}}\right)$  [24] 
5.  Exponential Decline  Decline Models  ${\mathrm{y}=\mathrm{q}}_{0}{\mathrm{e}}^{\raisebox{1ex}{$\mathrm{x}$}\!\left/ \!\raisebox{1ex}{$\mathrm{a}$}\right.}$  [25] 
6.  Farazdaghi–Harris  YieldSpacing Models  $\mathrm{y}=1/\left({\mathrm{a}+\mathrm{bx}}^{\mathrm{c}}\right)$  [26] 
7.  DRGamma  Dose–Response Models  [26]  
8.  DRHill  Dose–Response Models  $\mathrm{y}=\mathsf{\alpha}+\frac{{\mathsf{\theta}\mathrm{x}}^{\mathsf{\eta}}}{{\mathsf{\kappa}}^{\mathsf{\eta}}{+\mathrm{x}}^{\mathsf{\eta}}}$  [26] 
9.  DRLogistic  Dose–Response Models  $\mathrm{y}=\mathsf{\gamma}+\frac{1\mathsf{\gamma}}{{1+\mathrm{e}}^{\mathsf{\alpha}\mathsf{\beta}\mathrm{x}}}$  [26] 
10.  DRProbit  Dose–Response Models  $\mathrm{y}=\mathsf{\gamma}+\frac{1\mathsf{\gamma}}{2}\left[1+\mathrm{erf}\left(\frac{\mathsf{\alpha}+\mathsf{\beta}\mathrm{x}}{\sqrt{2}}\right)\right]$  [26] 
11.  DRWeibull  Dose–Response Models  $\mathrm{y}=\mathsf{\gamma}+\left(1\mathsf{\gamma}\right)\left({1\mathrm{e}}^{{\mathsf{\beta}\mathrm{x}}^{\mathsf{\alpha}}}\right)$  [26] 
12.  Gaussian Model  Miscellaneous  ${\mathrm{y}=\mathrm{ae}}^{\frac{{\left(\mathrm{x}\mathrm{b}\right)}^{2}}{{2\mathrm{c}}^{2}}}$  [24] 
13.  Geometric  Power Law Family  ${\mathrm{y}=\mathrm{ax}}^{\mathrm{bx}}$  [24] 
14.  Gompertz Relation  Sigmoidal Models  ${\mathrm{y}=\mathrm{ae}}^{{\mathrm{e}}^{\mathrm{b}\mathrm{cx}}}$  [24] 
15.  Harmonic Decline  Decline Models  ${\mathrm{y}=\mathrm{q}}_{0}/\left(1+\mathrm{x}/\mathrm{a}\right)$  [24] 
16.  Hyperbolic Decline  Decline Models  ${\mathrm{y}=\mathrm{q}}_{0}{\left(1+\mathrm{bx}/\mathrm{a}\right)}^{\left(1/\mathrm{b}\right)}$  [24] 
17.  Heat Capacity  Miscellaneous  $\mathrm{y}=\mathrm{a}+\mathrm{bx}+\mathrm{c}/{\mathrm{x}}^{2}$  [24] 
18.  Hoerl  Power Law Family  ${\mathrm{y}=\mathrm{ab}}^{\mathrm{x}}{\mathrm{x}}^{\mathrm{c}}$  [27] 
19.  Logistic  Sigmoidal Models  $\mathrm{y}=\mathrm{a}/\left({1+\mathrm{be}}^{\mathrm{cx}}\right)$  [24] 
20.  Logistic Power  Sigmoidal Models  $\mathrm{y}=\mathrm{a}/\left(1+{\left(\mathrm{x}/\mathrm{b}\right)}^{\mathrm{c}}\right)$  [27] 
21.  Log Normal CDF  Distribution Models  $\mathrm{y}=\frac{1}{2}\mathrm{erfc}\left(\frac{\mathrm{ln}\left(\mathrm{x}\right)\mathsf{\mu}}{\mathsf{\sigma}\sqrt{2}}\right)$  [27] 
22.  Log Normal PDF  Distribution Models  $\mathrm{y}=\frac{1}{\mathrm{x}\mathsf{\sigma}\sqrt{2\mathsf{\pi}}}{\mathrm{e}}^{\frac{1}{2}{\left(\frac{\mathrm{ln}\left(\mathrm{x}\right)\mathsf{\mu}}{\mathsf{\sigma}}\right)}^{2}}$  [27] 
23.  Modified Exponential  Exponential Models  ${\mathrm{y}=\mathrm{ae}}^{\mathrm{b}/\mathrm{x}}$  [24] 
24.  Modified Geometric  Power Law Family  ${\mathrm{y}=\mathrm{ax}}^{\mathrm{b}/\mathrm{x}}$  [24] 
25.  Modified Hoerl  Power Law Family  ${\mathrm{y}=\mathrm{ab}}^{1/{\mathrm{x}}_{{\mathrm{x}}^{\mathrm{c}}}}$  [24] 
26.  Modified Power  Power Law Family  ${\mathrm{y}=\mathrm{ab}}^{\mathrm{x}}$  [24] 
27.  Morgan–Mercer–Flodin (MMF)  Sigmoidal Models  $\mathrm{y}=\frac{{\mathrm{ab}+\mathrm{cx}}^{\mathrm{d}}}{{\mathrm{b}+\mathrm{x}}^{\mathrm{d}}}$  [28] 
28.  Natural Logarithm  Exponential Models  $\mathrm{y}=\mathrm{a}+\mathrm{bln}\left(\mathrm{x}\right)$  [27] 
29.  Normal (Gaussian) CDF  Distribution Models  $\mathrm{y}=\frac{1}{2}\left[1+\mathrm{erf}\left(\frac{\mathrm{x}\mathsf{\pi}}{\mathsf{\sigma}\sqrt{2}}\right)\right]$  [27] 
30.  Normal (Gaussian) PDF  Distribution Models  $\mathrm{y}=\frac{1}{\mathsf{\sigma}\sqrt{2\mathsf{\pi}}}{\mathrm{e}}^{\frac{1}{2}{\left(\frac{\mathrm{x}\mathsf{\mu}}{\mathsf{\sigma}}\right)}^{2}}$  [27] 
31.  Power  Power Law Family  ${\mathrm{y}=\mathrm{ax}}^{\mathrm{b}}$  [24] 
32.  Rational Model  Miscellaneous  $\mathrm{y}=\frac{\mathrm{a}+\mathrm{bx}}{{1+\mathrm{cx}+\mathrm{dx}}^{2}}$  [24] 
33.  Ratkowsky  Sigmoidal Models  $\mathrm{y}=\mathrm{a}/\left({1+\mathrm{e}}^{\mathrm{b}\mathrm{cx}}\right)$  [28] 
34.  Reciprocal  YieldSpacing Models  $\mathrm{y}=1/\left(\mathrm{a}+\mathrm{bx}\right)$  [24] 
35.  Reciprocal Logarithm  Exponential Models  $\mathrm{y}=\frac{1}{\mathrm{a}+\mathrm{bln}\left(\mathrm{x}\right)}$  [27] 
36.  Reciprocal Quadratic  YieldSpacing Models  $\mathrm{y}=1/\left({\mathrm{a}+\mathrm{bx}+\mathrm{cx}}^{2}\right)$  [24] 
37.  Richards  Sigmoidal Models  $\mathrm{y}=\frac{\mathrm{a}}{{\left({1+\mathrm{e}}^{\mathrm{b}\mathrm{cx}}\right)}^{1/\mathrm{d}}}$  [29] 
38.  Root  Power Law Family  ${\mathrm{y}=\mathrm{ab}}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{1ex}{$\mathrm{x}$}\right.}$  [24] 
39.  Saturation Growth Rate  Growth Models  $\mathrm{y}=\mathrm{ax}/\left(\mathrm{b}+\mathrm{x}\right)$  [24] 
40.  Shifted Power  Power Law Family  $\mathrm{y}=\mathrm{a}{\left(\mathrm{x}\mathrm{b}\right)}^{\mathrm{c}}$  [24] 
41.  Sinusoidal  Miscellaneous  $\mathrm{y}=\mathrm{a}+\mathrm{bcos}\left(\mathrm{cx}+\mathrm{d}\right)$  [24] 
42.  Steinhart–Hart Equation  Miscellaneous  $\mathrm{y}=\frac{1}{\mathrm{a}+\mathrm{bln}\left(\mathrm{x}\right)+\mathrm{c}(\mathrm{ln}\left(\mathrm{x}\right){)}^{3}}$  [24] 
43.  Truncated Fourier Series  Miscellaneous  $\mathrm{y}=\mathsf{\alpha}\mathrm{cos}\left(\mathrm{x}+\mathrm{d}\right)+\mathrm{bcos}(2\mathrm{x}+\mathrm{d})+\mathrm{cos}(3\mathrm{x}+\mathrm{d})$  [27] 
44.  Vapour Pressure Model  Exponential Models  ${\mathrm{y}=\mathrm{e}}^{\mathrm{a}+\mathrm{b}/\mathrm{x}+\mathrm{cln}\left(\mathrm{x}\right)}$  [24] 
45.  Weibull  Sigmoidal Models  $\mathrm{y}=\mathrm{a}{\mathrm{be}}^{{\mathrm{cx}}^{\mathrm{d}}}$  [30] 
No.  Models  Periods ^{1}  GoodnessofFit  

${\mathbf{R}}_{\mathbf{adj}}^{2}$  RMSE  AICc  BIC  
1.  Bleasdale  W  0.946  8.143  44.091  52.018 
WF  0.952  7.348  42.035  49.529  
2.  Exponential  W  0.933  7.607  40.851  48.092 
WF  0.952  6.873  38.819  45.628  
3.  Exponential Association 2  W  0.000  32.789  70.070  83.550 
WF  0.966  5.796  35.411  41.523  
4.  Exponential Association 3  W  0.956  7.340  42.015  49.500 
WF  0.974  5.397  35.863  42.065  
5.  Exponential Decline  W  0.946  7.617  40.876  48.122 
WF  0.952  6.873  38.819  45.628  
6.  Farazdaghi–Harris  W  0.991  3.246  25.697  30.163 
WF  0.957  6.951  40.925  48.180  
7.  DRGamma  W  0.986  4.099  30.361  35.585 
WF  0.000  33.528  72.395  86.167  
8.  DRHill  W  0.000  37.861  77.570  92.334 
WF  0.991  3.490  29.890  34.974  
9.  DRLogistic  W  0.000  73.558  88.109  104.131 
WF  0.000  77.572  89.172  105.216  
10.  DRProbit  W  0.000  73.558  88.109  104.131 
WF  0.000  77.572  89.172  105.216  
11.  DRWeibull  W  0.000  73.558  88.109  104.131 
WF  0.000  77.572  89.172  105.216  
12.  Gaussian  W  0.983  4.125  30.487  35.733 
WF  0.987  3.813  28.913  33.832  
13.  Geometric  W  0.967  5.973  36.015  42.280 
WF  0.936  7.949  41.731  49.159  
14.  Gompertz Relation  W  0.000  31.328  71.038  84.698 
WF  0.983  4.427  31.902  37.343  
15.  Harmonic Decline  W  0.859  12.326  50.503  59.836 
WF  0.872  11.199  48.585  57.518  
16.  Hyperbolic Decline  W  0.969  6.192  38.613  45.394 
WF  0.978  4.925  34.032  39.874  
17.  Heat Capacity  W  0.957  7.270  41.822  49.266 
WF  0.984  4.334  31.477  36.841  
18.  Hoerl  W  0.990  3.101  24.783  29.113 
WF  0.973  5.483  36.181  42.447  
19.  Logistic  W  0.843  12.427  52.545  62.331 
WF  0.987  3.829  28.999  33.932  
20.  Logistic Power  W  0.992  2.710  22.085  26.039 
WF  0.968  5.973  37.890  44.505  
21.  Log Normal CDF  W  0.000  68.807  84.895  100.613 
WF  0.000  72.642  85.979  101.690  
22.  Log Normal PDF  W  0.000  64.208  83.573  99.144 
WF  0.000  66.136  84.103  99.595  
23.  Modified Exponential  W  0.512  22.901  62.891  74.936 
WF  0.888  10.521  47.336  55.992  
24.  Modified Geometric  W  0.640  19.688  59.869  71.269 
WF  0.931  8.268  42.515  50.113  
25.  Modified Hoerl  W  0.972  5.903  37.657  44.246 
WF  0.982  4.560  32.493  38.043  
26.  Modified Power  W  0.946  7.617  40.876  48.122 
WF  0.952  6.873  38.819  45.628  
27.  MMF  W  0.996  2.097  19.414  23.035 
WF  0.980  4.721  33.189  38.870  
28.  Natural Logarithm  W  0.863  10.852  47.956  56.725 
WF  0.832  12.840  51.320  60.857  
29.  Normal (Gaussian) CDF  W  0.000  68.807  84.895  100.613 
WF  0.000  72.701  85.996  101.709  
30.  Normal (Gaussian) PDF  W  0.000  61.212  82.556  98.006 
WF  0.000  65.515  83.914  99.383  
31.  Power  W  0.731  15.178  54.666  64.924 
WF  0.968  5.586  34.675  40.642  
32.  Rational Model  W  0.996  2.323  21.748  25.658 
WF  0.995  2.608  24.065  28.268  
33.  Ratkowsky  W  0.982  4.223  30.962  36.291 
WF  0.987  3.829  28.999  33.932  
34.  Reciprocal  W  0.859  50.503  50.503  59.836 
WF  0.873  11.199  48.586  57.519  
35.  Reciprocal Logarithm  W  0.641  19.634  59.814  71.202 
WF  0.958  6.449  37.547  44.092  
36.  Reciprocal Quadratic  W  0.996  2.311  18.904  22.466 
WF  0.995  2.435  21.532  25.443  
37.  Richards  W  0.995  2.379  22.222  26.194 
WF  0.996  2.298  19.944  23.708  
38.  Root  W  0.512  22.901  62.892  74.937 
WF  0.888  10.521  47.336  55.992  
39.  Saturation Growth Rate  W  0.438  24.580  64.308  76.648 
WF  0.966  5.794  35.405  41.516  
40.  Shifted Power  W  0.918  10.010  48.219  57.046 
WF  0.978  4.925  34.032  39.874  
41.  Sinusoidal  W  0.994  2.694  24.711  29.031 
WF  0.992  3.191  28.099  32.885  
42.  Steinhart–Hart Equation  W  0.957  7.236  41.729  49.154 
WF  0.980  4.721  33.189  38.870  
43.  Truncated Fourier Series  W  0.000  73.623  90.870  107.092 
WF  0.000  79.345  92.368  108.695  
44.  Vapour Pressure Model  W  0.954  6.726  40.266  47.386 
WF  0.981  4.560  32.493  38.043  
45.  Weibull  W  0.997  1.732  15.883  19.128 
WF  0.993  3.113  27.601  32.308 
No.  Models  Periods ^{1}  GoodnessofFit  

${\mathbf{R}}_{\mathbf{adj}}^{2}$  RMSE  AICc  BIC  
1.  Bleasdale  W  0.931  8.188  44.200  52.151 
WF  0.961  6.741  40.311  47.435  
2.  Exponential  W  0.947  7.533  40.653  47.853 
WF  0.961  6.305  37.095  43.547  
3.  Exponential Association 2  W  0.000  29.249  67.786  80.828 
WF  0.966  5.858  35.625  41.780  
4.  Exponential Association 3  W  0.961  6.183  38.585  45.361 
WF  0.969  5.970  37.882  44.496  
5.  Exponential Decline  W  0.931  7.659  40.985  48.254 
WF  0.961  6.305  37.095  43.547  
6.  Farazdaghi–Harris  W  0.992  2.861  23.171  27.272 
WF  0.960  6.796  40.475  47.634  
7.  DRGamma  W  0.987  3.526  27.351  32.074 
WF  0.000  34.020  72.687  86.509  
8.  DRHill  W  0.997  1.822  16.893  20.238 
WF  0.993  3.115  27.618  32.328  
9.  DRLogistic  W  0.000  69.330  86.925  102.844 
WF  0.000  75.296  88.576  104.562  
10.  DRProbit  W  0.000  69.330  86.925  102.844 
WF  0.000  75.296  88.576  104.562  
11.  DRWeibull  W  0.000  69.330  86.925  102.844 
WF  0.000  75.296  88.576  104.562  
12.  Gaussian  W  0.981  4.790  33.478  39.261 
WF  0.987  29.496  29.496  34.513  
13.  Geometric  W  0.956  6.119  36.498  42.858 
WF  0.947  7.319  40.079  47.154  
14.  Gompertz Relation  W  0.000  35.125  73.326  87.396 
WF  0.983  4.423  31.885  37.323  
15.  Harmonic Decline  W  0.842  11.615  49.314  58.383 
WF  0.883  10.894  48.033  56.844  
16.  Hyperbolic Decline  W  0.965  5.845  37.458  44.007 
WF  0.980  4.810  33.563  39.315  
17.  Heat Capacity  W  0.965  5.861  37.515  44.076 
WF  0.983  4.384  31.705  37.110  
18.  Hoerl  W  0.992  3.116  24.877  29.221 
WF  0.975  5.403  35.888  42.095  
19.  Logistic  W  0.859  13.186  53.731  63.781 
WF  0.961  6.740  40.309  47.433  
20.  Logistic Power  W  0.992  3.037  24.363  28.632 
WF  0.966  6.242  38.772  45.571  
21.  Log Normal CDF  W  0.000  64.852  83.711  99.298 
WF  0.000  70.469  85.372  101.014  
22.  Log Normal PDF  W  0.000  58.588  81.680  97.021 
WF  0.000  63.230  83.204  98.586  
23.  Modified Exponential  W  0.884  10.860  47.971  56.744 
WF  0.888  10.661  47.600  56.315  
24.  Modified Geometric  W  0.608  18.314  58.421  69.506 
WF  0.927  8.618  43.346  51.125  
25.  Modified Hoerl  W  0.952  6.845  40.618  47.811 
WF  0.983  4.379  31.684  37.085  
26.  Modified Power  W  0.931  7.659  40.985  48.254 
WF  0.961  6.305  37.095  43.547  
27.  MMF  W  0.996  2.296  21.519  25.399 
WF  0.978  5.410  38.656  45.431  
28.  Natural Logarithm  W  0.892  10.797  47.854  56.601 
WF  0.808  13.928  52.947  62.841  
29.  Normal (Gaussian) CDF  W  0.000  64.852  83.711  99.298 
WF  0.000  70.567  85.400  101.045  
30.  Normal (Gaussian) PDF  W  0.000  58.407  81.617  96.950 
WF  0.000  65.701  83.971  99.447  
31.  Power  W  0.760  16.086  55.827  66.342 
WF  0.966  5.838  35.558  41.699  
32.  Rational Model  W  0.996  2.453  22.839  26.894 
WF  0.996  2.323  21.748  25.681  
33.  Ratkowsky  W  0.982  4.725  33.205  38.938 
WF  0.987  3.824  28.973  33.902  
34.  Reciprocal  W  0.842  11.615  49.314  58.383 
WF  0.883  10.894  48.033  56.844  
35.  Reciprocal Logarithm  W  0.620  18.032  58.112  69.129 
WF  0.961  6.304  37.091  43.542  
36.  Reciprocal Quadratic  W  0.993  2.573  21.051  24.871 
WF  0.996  2.194  20.608  24.430  
37.  Richards  W  0.997  2.125  19.971  23.658 
WF  0.996  2.194  17.464  21.061  
38.  Root  W  0.481  21.063  61.219  72.909 
WF  0.888  10.661  47.600  56.315  
39.  Saturation Growth Rate  W  0.413  22.400  62.450  74.402 
WF  0.966  5.847  35.597  41.746  
40.  Shifted Power  W  0.901  9.842  47.882  56.635 
WF  0.980  4.810  33.563  39.315  
41.  Sinusoidal  W  0.989  3.960  32.415  38.003 
WF  0.993  3.0819  27.403  32.080  
42.  Steinhart–Hart Equation  W  0.939  7.744  43.087  50.799 
WF  0.980  4.774  33.411  39.134  
43.  Truncated Fourier Series  W  0.000  69.928  89.841  105.995 
WF  0.000  76.577  91.658  107.926  
44.  Vapour Pressure Model  W  0.970  6.056  38.169  44.861 
WF  0.983  4.379  31.682  37.083  
45.  Weibull  W  0.998  1.839  17.073  20.436 
WF  0.994  0.9972  25.140  29.485 
AYL (%)  Dry Season  Wet Season  

Beginning  End  Beginning  End  
5  20  56  20  59 
10  22  54  23  53 
15  24  52  26  49 
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Alam, T.; Suryanto, P.; Susyanto, N.; Kurniasih, B.; Basunanda, P.; Putra, E.T.S.; Kastono, D.; Respatie, D.W.; Widyawan, M.H.; Nurmansyah; et al. Performance of 45 NonLinear Models for Determining Critical Period of Weed Control and Acceptable Yield Loss in Soybean Agroforestry Systems. Sustainability 2022, 14, 7636. https://doi.org/10.3390/su14137636
Alam T, Suryanto P, Susyanto N, Kurniasih B, Basunanda P, Putra ETS, Kastono D, Respatie DW, Widyawan MH, Nurmansyah, et al. Performance of 45 NonLinear Models for Determining Critical Period of Weed Control and Acceptable Yield Loss in Soybean Agroforestry Systems. Sustainability. 2022; 14(13):7636. https://doi.org/10.3390/su14137636
Chicago/Turabian StyleAlam, Taufan, Priyono Suryanto, Nanang Susyanto, Budiastuti Kurniasih, Panjisakti Basunanda, Eka Tarwaca Susila Putra, Dody Kastono, Dyah Weny Respatie, Muhammad Habib Widyawan, Nurmansyah, and et al. 2022. "Performance of 45 NonLinear Models for Determining Critical Period of Weed Control and Acceptable Yield Loss in Soybean Agroforestry Systems" Sustainability 14, no. 13: 7636. https://doi.org/10.3390/su14137636