# Modeling Hairy Vetch and Cereal Rye Cover Crop Decomposition and Nitrogen Release

^{1}

^{2}

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## Abstract

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## 1. Introduction

^{−bx}, where y is the mass of substrate at time x, b is the rate constant, and e is the base of the natural logarithms (2.71828)) has been widely used for nutrient mineralization, residue decomposition, and plant population studies [5,7,9,10,11,12]. It was applied for modeling litter decomposition for numerous grasses and legumes [7] and fine litter decomposition of forest soil [12]. Ruffo and Bollero [13] and Sievers and Cook [5] used this model with an asymptote (y = ae

^{−bx}+ yₒ, where yₒ is an asymptote) for cereal rye (Secale cereale L.) and hairy vetch (Vicia villosa Roth) decomposition and nutrient release. Polglase et al. [14] used a single exponential model for P mineralization from soil organic matter in a pine forest, whereas Fernández et al. [15] used it for modeling C mineralization in soils after wildfires in Spain. The strength of this model is that it produces a single rate constant, which can be used directly to compare decay rates from different treatments. However, it does not accurately describe decomposition or mineralization kinetics, where rate constants vary with time due to rapid loss or an extended lag phase in early decomposition [9,12,16]. The CC-derived labile fraction of soil organic matter composed of light (low specific density or mineral-free) and heavy (high specific density or mineral-bound) fractions tends to follow a different kinetic model in describing the decomposition and mineralization [17,18].

^{−bx}+ ce

^{−dx}, where b and d are the rate constants) separates organic matter into a soluble fraction (e.g., sucrose) or fast pool and cell-wall (e.g., detergent fibers) or slow pool [19] fraction. It was reported to have improved goodness of fit of single exponential models for residue decomposition and nutrient release mechanisms [9,18,20]. Berndt [9] suggested this model over the single exponential model when comparing kinetic parameters of decay of C remaining for hybrid bermudagrass (Cynodon dactylon (L.) Pers. × Cynodon transvaalensis Burtt-Davy) thatch. Wang et al. [20] predicted temperature- and moisture-dependent rate constants for soil N mineralization with a modified double exponential model under standard temperature (35 °C) and moisture conditions (55% water holding capacity). Dhakal et al. [11] reported that the double exponential model described alfalfa (Medicago sativa L.) population decline in a semiarid environment, which resulted in the highest adjusted R

^{2}(0.94 to 0.97) and the lowest standard error of estimate (SEE) for the upright-type alfalfa cultivars. Fernandez et al. [15] and Camargo et al. [21] reported this model as fitting mineralization data better than a single exponential model. Although all models generated an R

^{2}greater than 0.98 for in vitro mineralization of C, the double exponential model could not fit some of the samples, whereas exponential with a linear combination (y = ae

^{−bx}+ cx + yₒ, where c is the slope of the linear function) yielded superior results to the double exponential, exponential plus an asymptote, and hyperbolic model [y = ab/(b + x)] [17]. Dendooven et al. [22] reported poor fit of the double exponential function in fitting N mineralization data to characterize active and recalcitrant organic N pools derived from sugar-beet (Beta vulgaris L.) and bean (Phaseolus vulgaris L.) residue.

^{2}and lowest residual sum of squares and Akaike information criterion (AIC; [24]) may be considered best for decomposition studies.

## 2. Materials and Methods

#### 2.1. Experiment Locations

^{3}m

^{−3}for Exp. 1, whereas the top 5-cm soil profile ranged from 0.15 to 0.42 m

^{3}m

^{−3}and 0.07 to 0.37 m

^{3}m

^{−3}for Exp. 2 in 2017 and 2018, respectively.

#### 2.2. Sampling and Data Collection

^{−1}. Aboveground biomass was clipped 3 to 4 d after burndown and air-dried for 1 wk to be used as a residue in the litterbags, whereas samples clipped before herbicide application were oven-dried to determine in situ CC production and C to N ratio. Belowground biomass was collected by taking intact root cores of 5 cm in diameter and 15 cm in length. Ten grams of air-dried aboveground CC biomass was placed into traditionally made 20 × 20 cm nylon mesh bags, with 5 mm mesh on the upper side and 2 mm mesh on the bottom. The aboveground biomass used was equivalent to 1277 and 2203 kg ha

^{−1}dry mass and 14.7 and 92.3 kg N ha

^{−1}with a C to N ratio of 34.7 and 9.5 for cereal rye and hairy vetch, respectively, which was much greater than the actual in situ productivity, i.e., 578 and 791 kg ha

^{−1}dry mass and 13.5 and 21.4 kg N ha

^{−1}for cereal rye and hairy vetch, respectively [5]. A total of 14 litterbags were installed in each no-till sub-plot under soybean [Glycine max (L.) Merr.] and corn (Zea mays L.) main plot, which were rotated every year in four replicates, giving a total number of 112 litterbags (56 cereal rye + 56 hairy vetch). Litterbags were placed on the ground on 5 May 2015, and biomass samples were collected on the same day for ‘week 0′ sampling. After that, two litterbags per plot were collected at 2, 4, 6, 8, 12, and 16 wk after litterbag installation. Corn and soybean were planted on the 4th and 12th of June 2015, respectively, and the growth stage of the crops was noted at the time of litterbag collection. The intact root cores remained in plastic liners, wrapped with 16 mesh size at open ends were used for belowground study. The same number of cores as the litterbags were inserted 5 cm below the soil surface and collected on the same day as mentioned for the litterbags. Collected soil cores were washed to retrieve belowground biomass then oven-dried and ground to analyze for its constituents. Corn was fertilized with N at the late vegetative stage [5]. Aboveground biomass and collected residue samples for each CC were dried, ground to pass through a 1-mm screen, and analyzed for lignin, acid detergent fiber, neutral detergent fiber, and C and N concentration. The complete field events were described by Sievers and Cook [5] in greater detail.

^{−1}, 2,4-D (Dichlorophenoxyacetic acid) at 0.80 kg ae ha

^{–1}, and ammonium sulfate (2.5% v/v) on 13 and 28 April in 2017 and 2018, respectively. Aboveground CC biomass was collected 2 to 3 d after spraying, washed, and air-dried for 1 to 3 d. Fifty grams of air-dried samples were packed into the litterbags of the mesh size described above for Exp. 1. The packed CC biomass was equivalent to 2206 to 2743 kg ha

^{−1}for cereal rye and 1198 to 1624 kg ha

^{−1}for hairy vetch dry biomass. A total of 132 litterbags were used in each year. At “wk 0” all litterbags were placed on the ground to simulate installation and returned to the lab for further analysis. Six days after “wk 0” in 2017 and 8 d after “wk 0” in 2018, tillage operation was performed at reduced treatment plots to plant the main season crop. After that, litterbags in tillage treatment were placed in a vertical opening down to 15 cm into the soil. The no-till treatment had litterbags on the soil surface throughout the study in both years. In 2017, litterbags were installed on 19 April (week 0) and then one litterbag per plot was collected weekly for 10 wks, whereas in 2018, they were placed on 2 May and collected at 1, 2, 3, 4, 5, 6, 8, 10, 12, and 14 wks after installation. Sample preparation, grinding, and lab analysis was similar to the method described above.

_{t}/X

_{o}) × 100

_{o}was the initial CC mass or N mass at week 0. To standardize time after litterbag installation based on daily air temperature and DDD, it was calculated as follows [26]:

_{Max}+ T

_{Min})/2] − T

_{Base}

_{Max}and T

_{Min}are the daily maximum and minimum air temperature, respectively, T

_{Base}is the base temperature for the CC decomposition, which was considered 0 °C [26]. When T

_{Max}or T

_{Min}were less than T

_{Base}, the T

_{Max}and T

_{Min}computed were equal to T

_{Base}. For the days when T

_{Max}was greater than 30 °C, the T

_{Max}was changed to 30 °C.

#### 2.3. Comparison of Empirical Models

^{−bx}

^{−bx}+ yₒ

^{b}

^{/(c + x)}

^{−bx}+ ce

^{−dx}

^{−bx}+ ce

^{−dx}+ yₒ

^{−bx}+ cx + yₒ

^{2}, standard error of estimate (SEE), residual mean squares (RMS), predicted residual error sum of squares (PRESS), and Akaike information criterion was also used for model comparison. Model fitting excluded influential outliers using Leverage and Cook’s D.

^{2}, and the lowest SEE, RMS, PRESS, and AIC values were considered the best fit for hairy vetch and cereal rye CC decomposition and nutrient mineralization. Model parameters were estimated for each species, year, and study. Regression plots were obtained from SigmaPlot 14.0 [31].

## 3. Results

#### 3.1. Modeling Percent Mass Remaining

^{2}value of 0.97 except for the two-parameter single exponential decay model (0.91) (Table 1). The modified three-parameter single exponential function had the lowest RMS, SEE, PRESS, and AIC values. Although five-parameter double exponential and hyperbolic decay models had SEE comparable to the modified single exponential model, these models failed the tests for normality and independence of residuals (Durbin-Watson), whereas the modified single exponential model passed those tests, including the constant variance of errors. The four-parameter double exponential model produced greater R

^{2}and lower SEE and PRESS statistics, while the four-parameter single exponential with linear combination resulted in a comparable R

^{2}and SEE to the double exponential model, and lower RMS and AIC for cereal rye aboveground biomass (Table 1). However, the latter failed the normality test and the test for independence of residuals. The double exponential model passed all those test criteria and appeared to be a promising model for aboveground cereal rye residue decomposition. The five-parameter double exponential model with an asymptote had non-significant rate constants, especially for the resistant fraction of the cereal rye residue.

^{2}and the lowest AIC and PRESS statistic (Table 2). The model also satisfied the assumption of normally distributed population, constant variance, and independence of residuals. Double exponential models had at least one of the parameters as non-significant in predicting the hairy vetch and cereal rye mass decomposition.

^{2}value (0.90) except for a simple single exponential function (0.86) for hairy vetch (Table 3). None of the models passed all tests for normality, constant variance, and independence of residuals for cereal rye percent mass remaining. The five-parameter double exponential model passed the tests for normality and constant variance at α = 0.05 but produced non-significant estimates of parameters. The single exponential with an asymptote yielded the lowest PRESS and AIC and passed tests for normality and independence of residuals at α = 0.05 with significant model parameters. This single exponential model was found to be best for cereal rye in Exp. 2.

^{2}and low SEE values except a two-parameter single exponential model for both CC residues. None of the models passed all three statistical tests viz. test for normality, constant variance, and independence of residuals for both hairy vetch and cereal rye. Results showed better fit with five-parameter double exponential plus an asymptote than the single exponential and hyperbolic models for hairy vetch CC decomposition. However, the two-parameter hyperbolic model also produced standard errors and AIC values close to the five-parameter double exponential model in minimizing RMS, SEE, and AIC. Despite that, the choice between the five-parameter double exponential and two-parameter hyperbolic model would suggest the former model as the best fit with significant heteroskedasticity (Table 4). In contrast to the exponential models, the two-parameter hyperbolic model seemed to have the best fit for the cereal rye percent mass remaining data, as the SEE, RMS, PRESS, and AIC appeared lower than or equal to exponential and three-parameter hyperbolic models. This model also passed the test for the constant variance of the errors. Overall, the five-parameter double exponential model with an asymptote appeared suitable for hairy vetch decomposition modeling, whereas cereal rye had inconsistent results for individual small datasets and the two-parameter hyperbolic model for the combined data.

#### 3.2. Modeling Percent Nitrogen Remaining

^{2}of the models was near perfect (>0.96) while for cereal rye it ranged from 0.67 to 0.70 when fit to percent N remaining data (Table 5). All models passed the constant variance of residuals test for both CCs except for the three-parameter single exponential model with an asymptote. The modified three-parameter single exponential model appeared to have the best fit for the hairy vetch percent N remaining, which minimized RMS and SEE and lowered the PRESS and AIC statistics, relative to other decay models. For the aboveground cereal rye percent N remaining, the four-parameter single exponential model with the linear combination had the highest adjusted R

^{2}(0.70) and the lowest RMS, SEE, PRESS, and AIC values in relation to other exponential and hyperbolic models (Table 5), but the rate constant was not significant. This means the model cannot explain the N release rates. Thus, the three-parameter single exponential model was chosen based on relatively smaller SEE, RMS, and AIC and greater adjusted R

^{2}. This model also passed assumptions for the normal population, constant variance, and independence of residuals.

^{2}and minimized RMS, SEE, PRESS, and AIC for hairy-vetch N remaining data when compared to exponential and three-parameter hyperbolic decay models. For cereal rye N remaining, three-parameter hyperbolic decay function with an asymptote fitted best in minimizing RMS, SEE, and AIC, while the model also passed the assumption of normality, constant variance, and independence of residuals.

^{2}value and significant rate constants. The model also passed a test for constant variance and independence of residuals. The model that best minimized the RMS and SEE for the percent N remaining of cereal rye was the modified three-parameter single exponential. The model produced the greatest R

^{2}and had the lowest AIC value. However, the tests for normality, variance, and residuals were not satisfied by any of the models for cereal rye.

^{2}(0.94) and the lowest SEE, RMS, PRESS, and AIC values for hairy vetch N remaining (Table 8). All models failed the test for normality for both CCs. The five-parameter double exponential function passed a test for constant variance and independence of residuals. For cereal rye percent N remaining, the three-parameter hyperbolic model with an asymptotic best minimized the RMS and SEE and had the lowest PRESS and AIC values (Table 8). None of the models could satisfy the assumption of normality, constant variance, and independence of residuals. The double exponential model also produced high adjusted R

^{2}and minimized the RMS and SEE, but had non-significant rate constants for percent N remaining of cereal rye residue. The modified three-parameter single exponential model was equally as good as the hyperbolic decay model.

## 4. Discussion

^{2}, Table 1, Table 2, Table 3, Table 4, Table 5, Table 6, Table 7 and Table 8) of hairy vetch CC residue and cumulative DDD than that of cereal rye residue (Figure 1 and Figure 2). The decomposition rate constants and asymptotes were dissimilar for these two CCs (Table 1, Table 2, Table 3, Table 4, Table 5, Table 6, Table 7 and Table 8). Although Exp. 2 had two tillage systems (reduced vs. no-tillage), there was no effect on decomposition rate constant and N release in 2017 and 2018 [25], indicating that the management factor had lesser impact than the substrate quality factor. The inherent plant chemical constituents determine the rate of decomposition and N mineralization into the soil [4]. In both CC decomposition experiments, the CN ratio was greater for cereal rye (35:1 and 24:1 for Exp. 1 and 2, respectively) than hairy vetch (10:1, 9:1 for Exp. 1 and 2, respectively) [5,25]. Greater N concentration and less fiber content in hairy vetch may have accelerated the decomposition and N release in the early days or with less accumulated DDD, a relationship reported by Ruffo and Bollero [13] and Otte et al. [39]. Nitrogen and soluble carbohydrate fraction of the plant residue enhanced the microbial growth efficiency and improved the bermudagrass residue decomposition in FL, USA [9]. In both experiments, the residuals were higher for the cereal rye mass remaining and N release data than for hairy vetch. The lack of fit was due to large variability in initial mass and N content of cereal rye and immobilization of the N in the first 4 wks [5]. Rufo and Bollero [13] also reported the lack of fit for cereal rye when compared to hairy vetch. The presence of high neutral detergent fiber and lignin concentration [5] likely influenced the tensile strength of leaves and decomposability of cereal rye, which provide mechanical and chemical defense against microbial and chemical degradation [40]. Cornelissen et al. [41] reported that leaf tensile strength was related to litter decomposition for C3 grasses and also suggested that the complex leaf base content of the grass species can result in high variation in mass and N loss.

^{2}values and lower standard errors with the double exponential model with two rate constants when compared to a single exponential with or without an asymptote, especially for hairy vetch CC residue, indicated two residue pools, i.e., fast and slow decomposing fractions. This could be due to the presence of labile versus and recalcitrant fractions of the plant materials. However, in some cases, the addition of asymptotic or linear or another exponential component to the simple single exponential model resulted in non-finite residuals and failed to cross-validate the model, mainly for cereal rye for individual datasets from Exp. 1 and 2. In such cases, the slopes (or rate constants) for the double exponential model or exponential model with the linear combination had poor predictability at α ≤ 0.01. This indicates that the sample size was too small to have a sufficient sampling frame for the model, which gave undue weight to the initial data points for the short study period. We noticed that the issue of non-finite residuals was eliminated with combined data from Exp. 1 and 2, which extended the x-axis from 14 wk (cumulative DDD = 2382) to 16 wk (cumulative DDD = 2633) and increased the number of XY pairs. That was the reason Otte et al. [39] suggested using the simple asymptotic model rather than a double exponential model for cereal rye biomass decomposition. However, an asymptotic model may not always give the best results when compared to non-asymptotic models. The plant chemical constituents and environmental conditions may also affect the model performances [40,42]. Both of our experiments received more than half of the total cumulative rain in the first few weeks and the volumetric soil water content was near the field capacity, which might help accelerate the residue degradation as most of the soil microbes are highly active and thrive under moist warm conditions [42]. Hairy vetch aboveground biomass was well represented by a double exponential model with an asymptote with high R

^{2}and minimal residual errors and AIC with shorter fast-pool turnover time (~25% of the total accumulated DDD), compared to that of cereal rye (~40% of the total accumulated DDD). Juma et al. [16] suggested that a model of N cycling in soil should have at least three to four compartments to account for different sources of N.

_{0}or NR

_{0}) of the mineralizable pool [27], which might be affected by environmental and management factors and generate more variance. In our study, the belowground initial mineralizable pool was considerably smaller than the aboveground pool, and a significant portion of root mass remained undecomposed after 550 DDD [5]; thus, exponential models produced an ambiguous estimate of parameters. The evidence of a wide range of parameter estimates of the first-order equation was also reported by Nicolardot et al. [46] and Talpaz et al. [47].

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Exponential and hyperbolic decay models explaining percent mass remaining of hairy vetch and cereal rye cover crop aboveground residue against cumulative decomposition degree days at 0 °C base temperature. (

**i**) Two-parameter single exponential, (

**ii**) three-parameter single exponential, (

**iii**) modified three-parameter single exponential, (

**iv**) four-parameter double exponential, (

**v**) five-parameter double exponential, (

**vi**) four-parameter single exponent with linear combination, (

**vii**) two-parameter hyperbolic, and (

**viii**) three-parameter hyperbolic. The upper equation represents hairy vetch and the lower cereal rye. Data were pooled from Exp. 1 and 2. All models were significant at P < 0.0001.

**Figure 2.**Exponential and hyperbolic decay models explaining percent nitrogen remaining of hairy vetch and cereal rye cover crop aboveground residue against cumulative decomposition degree days at 0 °C base temperature. (

**i**) Two-parameter single exponential, (

**ii**) three-parameter single exponential, (

**iii**) modified three-parameter single exponential, (

**iv**) four-parameter double exponential, (

**v**) five-parameter double exponential, (

**vi**) four-parameter single exponent with linear combination, (

**vii**) two-parameter hyperbolic, and (

**viii**) three-parameter hyperbolic. The upper equation represents hairy vetch and the lower cereal rye. Data were pooled from Exp. 1 and 2. All models were significant at P < 0.0001.

**Table 1.**Evaluation of models used to describe percent mass remaining of aboveground biomass of hairy vetch and cereal rye cover crops at Exp. 1 in 2015. Data were from no-till plots at Carbondale, IL.

Model ^{1} | Crop | Adj. R^{2} | RMS ^{2} | SEE ^{3} | PRESS ^{4} | AIC ^{5} | Normality ^{6} | Variance ^{7} | D-W Statistic ^{8} | Parameter Estimates | ||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

a | b | c | d | yₒ | ||||||||||

1 | Hairy vetch | 0.91 | 80.2 | 9.0 | 4580.3 | 250.0 | Fail, P = 0.005 | Fail, P = 0.009 | Fail, 0.432 | 100.34 ** | 0.002 ** | - | - | - |

Cereal rye | 0.79 | 161.7 | 12.7 | 9177.5 | 284.1 | Pass, P = 0.259 | Pass, P = 0.079 | Pass, 1.727 | 92.68 ** | 0.0006 ** | - | - | - | |

2 | Hairy vetch | 0.97 | 31.2 | 5.6 | 1815.9 | 198.3 | Fail, P < 0.001 | Pass, P = 0.648 | Fail, 1.102 | 93.85 ** | 0.003 ** | 11.89 | ||

Cereal rye | 0.79 | 158.9 | 12.6 | 9017.1 | 284.5 | Pass, P = 0.285 | Pass, P = 0.309 | Pass, 1.812 | 80.71 ** | 0.0009 ** | - | - | 15.24 | |

3 | Hairy vetch | 0.97 | 26.8 | 5.2 | 1545.9 | 189.3 | Pass, P = 0.065 | Pass, P = 0.300 | Pass, 1.710 | 4.78 ** | 2201.52 ** | 702.96 ** | - | - |

Cereal rye | 0.80 | 155.1 | 12.5 | 8779.9 | 283.1 | Pass, P = 0.292 | Pass, P = 0.481 | Pass, 1.862 | 3.32ns | 11699.76ns | 3457.59ns | - | - | |

4 | Hairy vetch | 0.97 | 28.5 | 5.3 | 1661.6 | 194.6 | Fail, P < 0.001 | Pass, P = 0.285 | Fail, 1.242 | 24.58 ** | 0.0004 * | 82.90 ** | 0.005 ** | - |

Cereal rye | 0.82 | 139.0 | 11.8 | 7785.5 | 278.5 | Pass, P = 0.052 | Pass, P = 0.182 | Pass, 2.103 | 79.82 ** | 0.0005 ** | 27644.80ns | 0.343ns | - | |

5 | Hairy vetch | 0.97 | 27.4 | 5.2 | 1759.5 | 193.8 | Fail, P < 0.001 | Pass, P = 0.468 | Fail, 1.300 | 61.23 * | 0.002 * | 42.62 ** | 0.014ns | 9.63 |

Cereal rye | 0.82 | 139.4 | 11.8 | NAN ^{9} | 280.1 | Fail, P < 0.047 | Pass, P = 0.119 | Fail, 2.128 | 2190.3ns | 0.213ns | 123.42ns | 0.0002ns | −47.87 | |

6 | Hairy vetch | 0.97 | 28.9 | 5.4 | 1660.1 | 195.5 | Fail, P < 0.001 | Pass, P = 0.201 | Fail, 1.218 | 87.29 ** | 0.004 ** | −0.004 * | - | 19.79 |

Cereal rye | 0.82 | 138.2 | 11.8 | 8245.4 | 278.2 | Fail, P = 0.043 | Pass, P = 0.101 | Fail, 2.100 | 37.31 ** | 0.011ns | −0.020ns | - | 70.93 | |

7 | Hairy vetch | 0.97 | 27.1 | 5.2 | 1556.4 | 189.9 | Fail, P = 0.001 | Pass, P = 0.198 | Fail, 1.245 | 110.95 ** | 189.65 ** | - | - | - |

Cereal rye | 0.80 | 150.9 | 12.3 | 8449.8 | 280.3 | Pass, P = 0.203 | Pass, P = 0.650 | Pass, 1.884 | 100.14 ** | 832.76 ** | - | - | - | |

8 | Hairy vetch | 0.97 | 27.2 | 5.2 | 1562.9 | 190.6 | Fail, P < 0.001 | Pass, P = 0.186 | Fail, 1.281 | 110.18 ** | 174.06 ** | - | - | 1.71 |

Cereal rye | 0.80 | 152.8 | 12.4 | 8627.8 | 282.3 | Pass, P < 0.285 | Pass, P = 0.798 | Fail, 1.890 | 106.20 ** | 1017.81 * | - | - | −7.45 |

^{1}Decay models: 1, y = ae

^{−bx}; 2, y = ae

^{−bx}+ yₒ; 3, y = ae

^{b}

^{/(c + x)}; 4, y = ae

^{−bx}+ ce

^{−dx}; 5, y = ae

^{−bx}+ ce

^{−dx}+ yₒ; 6, y = ae

^{−bx}+ cx + yₒ; 7, y = ab/(b + x); 8, y = ab/(b + x) + yₒ.

^{2}Residual mean square of the model.

^{3}Standard error of estimate of the model parameters.

^{4}Predicted residual sum of squares estimate of the model.

^{5}Akaike information criterion value of the model.

^{6}Shapiro-Wilk test for normality of the data where pass and fail assumptions were made at α ≤ 0.05.

^{7}Constant variance test using Spearman rank correlation where pass or fail assumptions were made at α ≤ 0.05.

^{8}Durbin-Watson test of independence of residuals where pass or fail assumptions were made at α ≤ 0.05.

^{9}Not-a-number notation for non-finite residuals. * t-test significant at α ≤ 0.01, ** at α ≤ 0.001, and ns, not significant at the α = 0.01 level.

**Table 2.**Evaluation of models used to describe percent mass remaining of belowground biomass of hairy vetch and cereal rye cover crops at Exp. 1 in 2015. Data were from no-till plots at Carbondale, IL.

Model ^{1} | Crop | Adj. R^{2} | RMS ^{2} | SEE ^{3} | PRESS ^{4} | AIC ^{5} | Normality ^{6} | Variance ^{7} | D-W Statistic ^{8} | Parameter Estimates | ||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

a | b | c | d | yₒ | ||||||||||

1 | Hairy vetch | 0.88 | 126.6 | 11.3 | 7304.6 | 270.7 | Fail, P < 0.001 | Pass, P = 0.267 | Fail, 1.303 | 104.33 ** | 0.003 ** | - | - | - |

Cereal rye | 0.69 | 353.3 | 18.8 | 19,379.1 | 315.4 | Fail, P = 0.001 | Pass, P = 0.121 | Pass, 2.143 | 93.03 ** | 0.0001 ** | - | - | - | |

2 | Hairy vetch | 0.91 | 95.8 | 9.8 | 5546.6 | 256.6 | Fail, P = 0.001 | Pass, P = 0.246 | Fail, 1.628 | 100.37 ** | 0.005 ** | - | - | 8.46 |

Cereal rye | 0.70 | 338.6 | 18.4 | 18,583.3 | 314.5 | Fail, P < 0.001 | Pass, P = 0.854 | Fail, 2.811 | 85.02 ** | 0.002 ** | - | - | 13.04 | |

3 | Hairy vetch | 0.92 | 82.2 | 9.1 | 4752.2 | 248.2 | Fail, P = 0.002 | Pass, P = 0.158 | Pass, 1.798 | 3.71 * | 1623.72 * | 472.32 * | - | - |

Cereal rye | 0.71 | 328.5 | 18.1 | 18,063.2 | 312.8 | Fail, P < 0.001 | Pass, P = 0.281 | Pass, 2.190 | 4.79ns | 4337.90ns | 1418.28ns | - | - | |

4 | Hairy vetch | 0.93 | 76.8 | 8.8 | NAN ^{9} | 245.8 | Fail, P = 0.003 | Pass, P = 0.545 | Pass, 1.849 | 1026.54ns | 0.135ns | 39.78ns | 0.001ns | - |

Cereal rye | 0.71 | 318.1 | 17.8 | 16,835.1 | 311.1 | Fail, P < 0.060 | Pass, P = 0.535 | Pass, 2.292 | 66.64 ** | 0.0007 ** | 9498.81ns | 0.269ns | - | |

5 | Hairy vetch | 0.93 | 77.5 | 8.8 | 4468.6 | 247.8 | Fail, P = 0.003 | Pass, P = 0.388 | Pass, 1.883 | 40.00 ** | 0.001 * | 859.02ns | 0.129ns | 2.85 |

Cereal rye | 0.72 | 317.6 | 17.8 | 17,428.7 | 313.9 | Fail, P = 0.005 | Pass, P = 0.535 | Pass, 2.292 | 66.51 ** | 0.0007ns | 520.95ns | 0.130ns | 0.21 | |

6 | Hairy vetch | 0.92 | 85.0 | 9.2 | 5003.9 | 251.4 | Fail, P = 0.003 | Pass, P = 0.408 | Pass, 1.740 | 92.64 ** | 0.008 ** | −0.007 ** | - | 21.00 |

Cereal rye | 0.71 | 325.6 | 18.0 | 18,431.4 | 313.8 | Fail, P = 0.030 | Pass, P = 0.565 | Pass, 2.147 | 203.75ns | 0.071ns | −0.018 ** | - | 53.99 | |

7 | Hairy vetch | 0.93 | 78.3 | 8.9 | 4458.8 | 244.3 | Pass, P = 0.051 | Pass, P = 0.280 | Pass, 1.841 | 120.03 ** | 103.28 ** | - | - | - |

Cereal rye | 0.72 | 311.1 | 17.6 | 16,264.1 | 309.9 | Pass, P = 0.001 | Pass, P = 0.300 | Pass, 2.201 | 103.57 ** | 393.84 ** | - | - | - | |

8 | Hairy vetch | 0.93 | 79.7 | 8.9 | 4587.3 | 246.5 | Fail, P = 0.002 | Pass, P = 0.322 | Pass, 1.836 | 120.36 ** | 97.08 ** | - | - | 0.85 |

Cereal rye | 0.72 | 324.4 | 18.0 | 17,762.1 | 312.2 | Fail, P < 0.001 | Pass, P = 0.222 | Pass, 2.209 | 104.27 ** | 409.89 * | - | - | −1.04 |

^{1}Decay models: 1, y = ae

^{−bx}; 2, y = ae

^{−bx}+ yₒ; 3, y = ae

^{b}

^{/(c + x)}; 4, y = ae

^{−bx}+ ce

^{−dx}; 5, y = ae

^{−bx}+ ce

^{−dx}+ yₒ; 6, y = ae

^{−bx}+ cx + yₒ; 7, y = ab/(b + x); 8, y = ab/(b + x) + yₒ.

^{2}Residual mean square of the model.

^{3}Standard error of estimate of the model parameters.

^{4}Predicted residual sum of squares estimate of the model.

^{5}Akaike information criterion value of the model.

^{6}Shapiro-Wilk test for normality of the data where pass and fail assumptions were made at α ≤ 0.05.

^{7}Constant variance test using Spearman rank correlation where pass or fail assumptions were made at α ≤ 0.05.

^{8}Durbin-Watson test of independence of residuals where pass or fail assumptions were made at α ≤ 0.05.

^{9}Not-a-number notation for non-finite residuals. * t-test significant at α ≤ 0.01, ** at α ≤ 0.001, and ns, not significant at the α = 0.01 level.

**Table 3.**Evaluation of models used to describe percent mass remaining of aboveground hairy vetch and cereal rye cover crops at Exp. 2 in 2017 and 2018 at Carbondale, IL. Data were pooled across tillage treatments, replicates, and years.

Model ^{1} | Crop | Adj. R^{2} | RMS ^{2} | SEE ^{3} | PRESS ^{4} | AIC ^{5} | Normality ^{6} | Variance ^{7} | D-W Statistic ^{8} | Parameter Estimates | ||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

a | b | c | d | yₒ | ||||||||||

1 | Hairy vetch | 0.86 | 99.2 | 10.0 | 13,317.1 | 611.0 | Fail, P = 0.011 | Fail, P = 0.015 | Fail, 1.401 | 93.75 ** | 0.001 ** | - | - | - |

Cereal rye | 0.80 | 133.2 | 11.5 | 17,764.8 | 649.9 | Pass, P = 0.817 | Fail, P = 0.005 | Fail, 0.728 | 97.49 ** | 0.0008 ** | - | - | - | |

2 | Hairy vetch | 0.90 | 74.1 | 8.6 | 9937.1 | 573.5 | Pass, P = 0.090 | Fail, P < 0.001 | Pass, 1.746 | 86.53 ** | 0.002 ** | - | - | 14.82 |

Cereal rye | 0.84 | 104.7 | 10.2 | 14,028.8 | 619.3 | Pass, P = 0.067 | Fail, P = 0.042 | Pass, 1.603 | 79.92 ** | 0.002 ** | - | - | 25.37 | |

3 | Hairy vetch | 0.90 | 71.2 | 8.4 | 9540.4 | 568.3 | Fail, P = 0.014 | Pass, P = 0.056 | Pass, 1.687 | 4.15 * | 3873.53 ** | 1198.89 ** | - | - |

Cereal rye | 0.83 | 108.7 | 10.4 | 14,558.5 | 624.2 | Pass, P = 0.068 | Fail, P = 0.041 | Fail, 0.880 | 7.71ns | 4729.64ns | 1803.46 ** | - | - | |

4 | Hairy vetch | 0.90 | 72.5 | 8.5 | 9779.1 | 571.8 | Fail, P = 0.025 | Fail, P = 0.049 | Pass, 1.688 | 37.75 ** | 0.0005 ** | 66.37 ** | 0.004 ** | - |

Cereal rye | 0.84 | 105.5 | 10.3 | 14,227.4 | 621.4 | Fail, P = 0.047 | Fail, P = 0.042 | Fail, 0.903 | 79.92 ** | 0.002 * | 25.37ns | 4.12ns | - | |

5 | Hairy vetch | 0.90 | 70.7 | 8.4 | 9417.4 | 566.3 | Pass, P = 0.054 | Pass, P = 0.151 | Pass, 1.651 | 23.14 * | 0.017 * | 75.50 ** | 0.002 ** | 11.98 |

Cereal rye | 0.84 | 103.9 | 10.2 | 14,053.0 | 620.5 | Pass, P = 0.139 | Fail, P = 0.062 | Fail, 0.929 | −788.41 * | 0.003ns | 861.00 * | 0.003ns | 28.86 | |

6 | Hairy vetch | 0.90 | 72.7 | 8.5 | 9790.6 | 572.2 | Fail, P = 0.030 | Fail, P = 0.014 | Pass, 1.698 | 75.84 ** | 0.003 ** | −0.007 * | - | 27.63 |

Cereal rye | 0.84 | 104.3 | 10.2 | 14,087.7 | 619.9 | Pass, P = 0.063 | Fail, P = 0.010 | Fail, 0.930 | 111.11 * | 0.001 * | 0.013ns | - | −6.96 | |

7 | Hairy vetch | 0.90 | 70.8 | 8.4 | 9833.4 | 569.8 | Fail, P < 0.001 | Pass, P = 0.239 | Pass, 1.646 | 107.55 ** | 301.93 ** | - | - | - |

Cereal rye | 0.83 | 109.5 | 10.5 | 14,550.8 | 624.1 | Pass, P = 0.081 | Fail, P = 0.047 | Fail, 0.873 | 106.31 ** | 652.86 ** | - | - | - | |

8 | Hairy vetch | 0.90 | 71.0 | 8.4 | 9494.5 | 567.9 | Fail, P = 0.005 | Pass, P = 0.185 | Pass, 1.656 | 108.67 ** | 325.01 ** | - | - | −2.00 |

Cereal rye | 0.83 | 110.3 | 10.5 | 14,765.7 | 626.1 | Pass, P = 0.079 | Pass, P = 0.058 | Fail, 0.878 | 105.03 ** | 624.55 ** | - | - | 1.64 |

^{1}Decay models: 1, y = ae

^{−bx}; 2, y = ae

^{−bx}+ yₒ; 3, y = ae

^{b}

^{/(c + x)}; 4, y = ae

^{−bx}+ ce

^{−dx}; 5, y = ae

^{−bx}+ ce

^{−dx}+ yₒ; 6, y = ae

^{−bx}+ cx + yₒ; 7, y = ab/(b + x); 8, y = ab/(b + x) + yₒ.

^{2}Residual mean square of the model.

^{3}Standard error of estimate of the model parameters.

^{4}Predicted residual sum of squares estimate of the model.

^{5}Akaike information criterion value of the model.

^{6}Shapiro-Wilk test for normality of the data where pass and fail assumptions were made at α ≤ 0.05.

^{7}Constant variance test using Spearman rank correlation where pass or fail assumptions were made at α ≤ 0.05.

^{8}Durbin-Watson test of independence of residuals where pass or fail assumptions were made at α ≤ 0.05. * t-test significant at α ≤ 0.01, ** at α ≤ 0.001, and ns, not significant at the α = 0.01 level.

**Table 4.**Evaluation of models using combined data from Exp. 1 and 2 for percent mass remaining of aboveground hairy vetch and cereal rye cover crops in Carbondale, IL.

Model ^{1} | Crop | Adj. R^{2} | RMS ^{2} | SEE ^{3} | PRESS ^{4} | AIC ^{5} | Normality ^{6} | Variance ^{7} | D-W Statistic ^{8} |
---|---|---|---|---|---|---|---|---|---|

1 | Hairy vetch | 0.87 | 104.9 | 10.2 | 19,914.9 | 878.9 | Fail, P < 0.001 | Fail, P = 0.020 | Fail, 1.012 |

Cereal rye | 0.79 | 145.6 | 12.1 | 27,436.5 | 935.5 | Pass, P = 0.415 | Pass, P = 0.478 | Fail, 1.053 | |

2 | Hairy vetch | 0.91 | 73.0 | 8.5 | 13,881.3 | 811.8 | Fail, P < 0.001 | Fail, P = 0.007 | Fail, 1.349 |

Cereal rye | 0.82 | 123.2 | 11.1 | 23,233.2 | 905.4 | Fail, P = 0.006 | Fail, P < 0.001 | Fail, 1.224 | |

3 | Hairy vetch | 0.91 | 68.8 | 8.3 | 13,071.3 | 800.6 | Fail, P < 0.001 | Fail, P = 0.562 | Fail, 1.349 |

Cereal rye | 0.82 | 122.8 | 11.1 | 23,145.5 | 904.8 | Fail, P = 0.006 | Fail, P = 0.009 | Fail, 1.231 | |

4 | Hairy vetch | 0.91 | 69.8 | 8.4 | 13,333.5 | 804.6 | Fail, P < 0.001 | Pass, P = 0.746 | Fail, 1.349 |

Cereal rye | 0.82 | 123.2 | 11.1 | 23,335.2 | 906.5 | Fail, P = 0.006 | Fail, P = 0.003 | Fail, 1.231 | |

5 | Hairy vetch | 0.91 | 68.4 | 8.3 | 12,948.6 | 798.5 | Fail, P < 0.001 | Pass, P = 0.557 | Fail, 1.330 |

Cereal rye | 0.82 | 123.8 | 11.1 | 23,550.1 | 908.5 | Fail, P = 0.006 | Fail, P = 0.004 | Fail, 1.231 | |

6 | Hairy vetch | 0.91 | 70.3 | 8.4 | 13,383.3 | 805.7 | Fail, P < 0.001 | Pass, P = 0.307 | Fail, 1.351 |

Cereal rye | 0.82 | 123.1 | 11.1 | 23,307.4 | 906.3 | Fail, P = 0.006 | Fail, P = 0.004 | Fail, 1.231 | |

7 | Hairy vetch | 0.91 | 69.0 | 8.3 | 13,396.9 | 803.3 | Fail, P < 0.001 | Pass, P = 0.548 | Fail, 1.330 |

Cereal rye | 0.82 | 122.5 | 11.1 | 23,007.9 | 903.2 | Fail, P = 0.007 | Pass, P = 0.080 | Fail, 1.230 | |

8 | Hairy vetch | 0.91 | 68.7 | 8.3 | 13,032.0 | 800.3 | Fail, P < 0.001 | Pass, P = 0.672 | Fail, 1.333 |

Cereal rye | 0.82 | 123.1 | 11.1 | 23,194.0 | 905.3 | Fail, P = 0.006 | Fail, P = 0.016 | Fail, 1.232 |

^{1}Decay models: 1, y = ae

^{−bx}; 2, y = ae

^{−bx}+ yₒ; 3, y = ae

^{b}

^{/(c + x)}; 4, y = ae

^{−bx}+ ce

^{−dx}; 5, y = ae

^{−bx}+ ce

^{−dx}+ yₒ; 6, y = ae

^{−bx}+ cx + yₒ; 7, y = ab/(b + x); 8, y = ab/(b + x) + yₒ.

^{2}Residual mean square of the model.

^{3}Standard error of estimate of the model parameters.

^{4}Predicted residual sum of squares estimate of the model.

^{5}Akaike information criterion value of the model.

^{6}Shapiro-Wilk test for normality of the data where pass and fail assumptions were made at α ≤ 0.05.

^{7}Constant variance test using Spearman rank correlation where pass or fail assumptions were made at α ≤ 0.05.

^{8}Durbin-Watson test of independence of residuals where pass or fail assumptions were made at α ≤ 0.05.

**Table 5.**Evaluation of models used to describe percent N remaining of aboveground biomass of hairy vetch and cereal rye cover crops at Exp. 1 in 2015. Data were from no-till plots at Carbondale, IL.

Model ^{1} | Crop | Adj. R^{2} | RMS ^{2} | SEE ^{3} | PRESS ^{4} | AIC ^{5} | Normality ^{6} | Variance ^{7} | D-W Statistic ^{8} | Parameter Estimates | ||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

a | b | c | d | yₒ | ||||||||||

1 | Hairy vetch | 0.96 | 38.4 | 6.2 | 2199.6 | 208.8 | Fail, P = 0.008 | Pass, P = 0.104 | Fail, 0.429 | 106.34 ** | 0.004 ** | - | - | - |

Cereal rye | 0.67 | 276.4 | 16.6 | 15,599.4 | 313.6 | Fail, P = 0.004 | Pass, P = 0.299 | Pass, 1.854 | 94.65 ** | 0.0005 ** | - | - | - | |

2 | Hairy vetch | 0.98 | 16.1 | 4.0 | 938.4 | 161.4 | Fail, P < 0.001 | Fail, P = 0.028 | Fail, 1.028 | 102.38 ** | 0.005 ** | - | - | 6.84 |

Cereal rye | 0.67 | 280.7 | 16.8 | 15,891.1 | 315.8 | Pass, P = 0.173 | Pass, P = 0.155 | Pass, 1.848 | 108.15 * | 0.0004 * | - | - | −14.74 | |

3 | Hairy vetch | 0.99 | 10.6 | 3.3 | 613.6 | 136.8 | Fail, P < 0.001 | Pass, P = 0.559 | Fail, 1.470 | 2.17 ** | 2361.90 ** | 595.70** | - | - |

Cereal rye | 0.67 | 281.1 | 16.8 | 15,926.2 | 315.8 | Pass, P = 0.167 | Pass, P = 0.130 | Pass, 1.847 | 880723.4ns | 174597.8ns | −19078.5ns | - | - | |

4 | Hairy vetch | 0.99 | 11.2 | 3.3 | 674.3 | 142.1 | Fail, P < 0.001 | Pass, P = 0.161 | Fail, 1.459 | 22.13 ** | 0.0008 ** | 89.84 ** | 0.007 ** | - |

Cereal rye | 0.68 | 272.7 | 16.5 | 15,296.2 | 315.5 | Fail, P = 0.002 | Pass, P = 0.289 | Fail, 1.987 | 86.57 ** | 0.0005 ** | 1200.31ns | 0.212ns | - | |

5 | Hairy vetch | 0.99 | 10.9 | 3.3 | 691.7 | 142.2 | Fail, P < 0.001 | Pass, P = 0.343 | Fail, 1.499 | 75.72 ** | 0.009 * | 34.52 * | 0.002 * | 3.66 |

Cereal rye | 0.69 | 263.3 | 16.2 | NAN ^{9} | 315.0 | Fail, P = 0.004 | Pass, P = 0.260 | Pass, 2.076 | 100.71ns | 0.076ns | 8662.20ns | 2.64ns | −8582.2 | |

6 | Hairy vetch | 0.99 | 12.0 | 3.5 | 703.4 | 146.1 | Fail, P < 0.001 | Pass, P = 0.182 | Fail, 1.380 | 96.77 ** | 0.006 ** | −0.004 ** | - | 14.15 |

Cereal rye | 0.70 | 258.1 | 16.1 | 14,270.3 | 312.5 | Pass, P = 0.100 | Pass, P = 0.258 | Pass, 2.076 | 258.83ns | 0.121ns | −0.023 ** | - | 79.95 | |

7 | Hairy vetch | 0.99 | 10.8 | 3.3 | 629.6 | 138.9 | Fail, P < 0.001 | Pass, P = 0.152 | Fail, 1.456 | 122.35 ** | 93.96 ** | - | - | - |

Cereal rye | 0.66 | 289.7 | 17.0 | 16,230.0 | 316.2 | Fail, P = 0.006 | Pass, P = 0.372 | Pass, 1.808 | 99.65 ** | 1102.91 ** | - | - | - | |

8 | Hairy vetch | 0.99 | 10.6 | 3.3 | 616.1 | 138.0 | Fail, P < 0.001 | Pass, P = 0.337 | Fail, 1.479 | 121.99 ** | 100.75 ** | - | - | −0.98 |

Cereal rye | 0.67 | 279.8 | 16.7 | 15,816.8 | 315.6 | Pass, P = 0.138 | Pass, P = 0.180 | Pass, 1.860 | 162.87ns | 3260.55ns | - | - | −68.64 |

^{1}Decay models: 1, y = ae

^{−bx}; 2, y = ae

^{−bx}+ yₒ; 3, y = ae

^{b}

^{/(c + x)}; 4, y = ae

^{−bx}+ ce

^{−dx}; 5, y = ae

^{−bx}+ ce

^{−dx}+ yₒ; 6, y = ae

^{−bx}+ cx + yₒ; 7, y = ab/(b + x); 8, y = ab/(b + x) + yₒ.

^{2}Residual mean square of the model.

^{3}Standard error of estimate of the model parameters.

^{4}Predicted residual sum of squares estimate of the model,

^{5}Akaike information criterion value of the model.

^{6}Shapiro-Wilk test for normality of the data where pass and fail assumptions were made at α ≤ 0.05.

^{7}Constant variance test using Spearman rank correlation where pass or fail assumptions were made at α ≤ 0.05.

^{8}Durbin-Watson test of independence of residuals where pass or fail assumptions were made at α ≤ 0.05.

^{9}Not-a-number notation for non-finite residuals. * t-test significant at α ≤ 0.01, ** at α ≤ 0.001, and ns, not significant at the α = 0.01 level.

**Table 6.**Evaluation of models used to describe percent N remaining of belowground biomass of hairy vetch and cereal rye cover crops at Exp. 1 in 2015. Data were from no-till plots at Carbondale, IL.

Model ^{1} | Crop | Adj. R^{2} | RMS ^{2} | SEE ^{3} | PRESS ^{4} | AIC ^{5} | Normality ^{6} | Variance ^{7} | D-W Statistic ^{8} | Parameter Estimates | ||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

a | b | c | d | yₒ | ||||||||||

1 | Hairy vetch | 0.84 | 184.6 | 13.6 | 8239.3 | 229.0 | Fail, P < 0.001 | Pass, P = 0.331 | Fail, 1.461 | 102.23 ** | 0.00 3** | - | - | - |

Cereal rye | 0.48 | 557.2 | 23.6 | 30,410.2 | 339.6 | Fail, P = 0.712 | Pass, P = 0.302 | Fail, 2.135 | 88.35 ** | 0.0007 ** | - | - | - | |

2 | Hairy vetch | 0.88 | 141.8 | 11.9 | 6445.3 | 219.0 | Fail, P = 0.012 | Fail, P = 0.013 | Fail, 1.832 | 94.98 ** | 0.004 ** | - | - | 12.59 |

Cereal rye | 0.53 | 505.9 | 22.5 | 27,841.2 | 335.8 | Pass, P = 0.103 | Pass, P = 0.155 | Pass, 2.262 | 72.83 ** | 0.002 ** | - | - | 27.03 | |

3 | Hairy vetch | 0.89 | 132.3 | 11.5 | 6002.7 | 216.0 | Pass, P = 0.055 | Pass, P = 0.066 | Pass, 1.889 | 5.89ns | 1402.55ns | 474.64ns | - | - |

Cereal rye | 0.54 | 496.4 | 22.3 | 27,334.6 | 334.7 | Pass, P = 0.067 | Pass, P = 0.131 | Pass, 2.269 | 17.40ns | 1400.68ns | 785.27ns | - | - | |

4 | Hairy vetch | 0.88 | 135.5 | 11.6 | NAN ^{9} | 218.5 | Pass, P = 0.097 | Pass, P = 0.125 | Pass, 1.819 | 1393.69ns | 0.156ns | 47.91ns | 0.001ns | - |

Cereal rye | 0.54 | 499.5 | 22.3 | 26,909.2 | 336.4 | Pass, P = 0.107 | Pass, P = 0.219 | Pass, 2.271 | 65.16 ** | 0.0004 * | 427.10ns | 0.119ns | - | |

5 | Hairy vetch | 0.89 | 133.9 | 11.6 | NAN | 219.6 | Pass, P = 0.114 | Pass, P = 0.108 | Pass, 1.918 | 301.95ns | 0.090ns | 48.43ns | 0.002ns | 7.61 |

Cereal rye | 0.53 | 506.9 | 22.5 | 27,949.1 | 338.7 | Pass, P = 0.074 | Pass, P = 0.180 | Pass, 2.292 | 53.09ns | 0.0009 ** | 5394.02ns | 0.249ns | 18.38 | |

6 | Hairy vetch | 0.88 | 140.7 | 11.9 | 6555.7 | 220.1 | Fail, P = 0.032 | Pass, P = 0.310 | Pass, 1.836 | 88.52 ** | 0.006** | −0.005ns | - | 20.96 |

Cereal rye | 0.53 | 504.8 | 22.5 | 28,582.6 | 337.0 | Pass, P = 0.112 | Pass, P = 0.160 | Pass, 2.252 | 52.88 ** | 0.005ns | −0.012ns | - | 52.64 | |

7 | Hairy vetch | 0.89 | 129.5 | 11.4 | 5745.2 | 213.7 | Fail, P = 0.032 | Pass, P = 0.071 | Pass, 1.889 | 114.21 ** | 144.17 ** | - | - | - |

Cereal rye | 0.54 | 495.3 | 22.3 | 26,961.6 | 333.7 | Pass, P = 0.420 | Pass, P = 0.675 | Pass, 2.284 | 98.97** | 658.49 ** | - | - | - | |

8 | Hairy vetch | 0.89 | 131.2 | 11.5 | 5936.5 | 215.6 | Pass, P = 0.067 | Pass, P = 0.088 | Pass, 1.891 | 113.4 ** | 120.39 * | - | - | 3.27 |

Cereal rye | 0.54 | 499.2 | 22.3 | 27,227.1 | 334.6 | Pass, P = 0.071 | Pass, P = 0.131 | Pass, 2.273 | 88.50 ** | 346.70ns | - | - | 15.56 |

^{1}Decay models: 1, y = ae

^{−bx}; 2, y = ae

^{−bx}+ yₒ; 3, y = ae

^{b}

^{/(c + x)}; 4, y = ae

^{−bx}+ ce

^{−dx}; 5, y = ae

^{−bx}+ ce

^{−dx}+ yₒ; 6, y = ae

^{−bx}+ cx + yₒ; 7, y = ab/(b + x); 8, y = ab/(b + x) + yₒ.

^{2}Residual mean square of the model.

^{3}Standard error of estimate of the model parameters.

^{4}Predicted residual sum of squares estimate of the model.

^{5}Akaike information criterion value of the model.

^{6}Shapiro-Wilk test for normality of the data where pass and fail assumptions were made at α ≤ 0.05.

^{7}Constant variance test using Spearman rank correlation where a pass or fail assumptions were made at α ≤ 0.05.

^{8}Durbin-Watson test of independence of residuals where a pass or fail assumptions were made at α ≤ 0.05.

^{9}Not-a-number notation for non-finite residuals. * t-test significant at α ≤ 0.01, ** at α ≤ 0.001, and ns, not significant at the α = 0.01 level.

**Table 7.**Evaluation of models used to describe percent N remaining of aboveground hairy vetch and cereal rye cover crops at Exp. 2 in 2017 and 2018 at Carbondale, IL. Data were pooled across tillage treatments, replicates, and years.

Model ^{1} | Crop | Adj. R^{2} | RMS ^{2} | SEE ^{3} | PRESS ^{4} | AIC ^{5} | Normality ^{6} | Variance ^{7} | D-W Statistic ^{8} | Parameter Estimates | ||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

a | b | c | d | yₒ | ||||||||||

1 | Hairy vetch | 0.84 | 112.6 | 10.6 | 15264.9 | 627.8 | Fail, P < 0.001 | Fail, P < 0.001 | Pass, 1.550 | 90.99 ** | 0.002 ** | - | - | - |

Cereal rye | 0.49 | 307.9 | 17.5 | 39938.3 | 737.6 | Fail, P = 0.008 | Fail, P = 0.007 | Fail, 0.452 | 86.49 ** | 0.0006 ** | - | - | - | |

2 | Hairy vetch | 0.90 | 71.4 | 8.5 | 9665.5 | 568.7 | Fail, P < 0.001 | Fail, P < 0.001 | Pass, 1.880 | 89.97 ** | 0.004 ** | - | - | 13.41 |

Cereal rye | 0.58 | 254.5 | 16.0 | 32876.8 | 714.3 | Fail, P = 0.002 | Fail, P < 0.001 | Fail, 0.479 | 63.44 ** | 0.002 ** | - | - | 37.03 | |

3 | Hairy vetch | 0.92 | 56.5 | 7.5 | 7612.2 | 537.8 | Fail, P < 0.001 | Pass, P = 0.090 | Pass, 1.821 | 6.30 ** | 1409.78 ** | 489.94 ** | - | - |

Cereal rye | 0.59 | 252.8 | 15.8 | 32027.1 | 713.5 | Fail, P = 0.006 | Fail, P < 0.001 | Fail, 0.463 | 26.31 ** | 857.15 * | 622.09 * | - | - | |

4 | Hairy vetch | 0.93 | 51.8 | 7.2 | 7126.0 | 527.6 | Fail, P < 0.030 | Pass, P = 0.333 | Pass, 1.710 | 51.3 ** | 0.001 ** | 68.47 ** | 0.014 ** | - |

Cereal rye | 0.58 | 256.4 | 16.0 | 33265.5 | 716.4 | Fail, P = 0.003 | Fail, P < 0.001 | Fail, 0.475 | 60.28 ** | 0.003 * | 40.70 * | 0.0005ns | - | |

5 | Hairy vetch | 0.93 | 50.2 | 7.1 | 6966.6 | 524.4 | Fail, P = 0.006 | Pass, P = 0.072 | Pass, 1.777 | 54.58 ** | 0.002 ** | 63.35 ** | 0.020 * | 6.77 |

Cereal rye | 0.58 | 255.2 | 16.0 | 33569.6 | 717.0 | Fail, P = 0.006 | Fail, P < 0.001 | Fail, 0.463 | 19.57ns | 0.013ns | 52.88 * | 0.002ns | 34.54 | |

6 | Hairy vetch | 0.92 | 58.0 | 7.6 | 7843.6 | 542.5 | Fail, P = 0.003 | Fail, P = 0.034 | Pass, 1.761 | 81.38 ** | 0.007 ** | −0.011 ** | - | 29.64 |

Cereal rye | 0.58 | 256.5 | 16.0 | 32265.5 | 716.4 | Fail, P = 0.003 | Fail, P < 0.001 | Fail, 0.476 | 60.86 ** | 0.003 * | −0.002ns | - | 40.04 | |

7 | Hairy vetch | 0.92 | 54.5 | 7.4 | 7285.9 | 531.9 | Fail, P = 0.008 | Fail, P < 0.001 | Pass, 1.855 | 112.18 ** | 158.74 ** | - | - | - |

Cereal rye | 0.55 | 270.5 | 16.4 | 34908.2 | 721.0 | Fail, P = 0.027 | Fail, P = 0.002 | Fail, 0.426 | 95.64 ** | 876.72 ** | - | - | - | |

8 | Hairy vetch | 0.92 | 53.8 | 7.3 | 7231.4 | 531.4 | Fail, P < 0.001 | Fail, P = 0.038 | Pass, 1.825 | 112.07 ** | 136.27 ** | - | - | 2.80 |

Cereal rye | 0.58 | 252.9 | 15.9 | 32553.8 | 713.5 | Fail, P = 0.007 | Fail, P < 0.001 | Fail, 0.462 | 79.50 ** | 323.88 * | - | - | 25.28 |

^{1}Decay models: 1, y = ae

^{−bx}; 2, y = ae

^{−bx}+ yₒ; 3, y = ae

^{b}

^{/(c + x)}; 4, y = ae

^{−bx}+ ce

^{−dx}; 5, y = ae

^{−bx}+ ce

^{−dx}+ yₒ; 6, y = ae

^{−bx}+ cx + yₒ; 7, y = ab/(b + x); 8, y = ab/(b + x) + yₒ

^{2}Residual mean square of the model.

^{3}Standard error of estimate of the model parameters.

^{4}Predicted residual sum of squares estimate of the model.

^{5}Akaike information criterion value of the model.

^{6}Shapiro-Wilk test for normality of the data where pass and fail assumptions were made at α ≤ 0.05.

^{7}Constant variance test using Spearman rank correlation where a pass or fail assumptions were made at α ≤ 0.05.

^{8}Durbin-Watson test of independence of residuals where a pass or fail assumptions were made at α ≤ 0.05. * t-test significant at α ≤ 0.01, ** at α ≤ 0.001, and ns, not significant at the α = 0.01 level.

**Table 8.**Evaluation of models using combined data from Exp. 1 and 2 for percent mass remaining of aboveground hairy vetch and cereal rye cover crops in Carbondale, IL.

Model ^{1} | Crop | Adj. R^{2} | RMS ^{2} | SEE ^{3} | PRESS ^{4} | AIC ^{5} | Normality ^{6} | Variance ^{7} | D-W Statistic ^{8} |
---|---|---|---|---|---|---|---|---|---|

1 | Hairy vetch | 0.87 | 101.8 | 10.1 | 19,406.7 | 873.3 | Fail, P < 0.001 | Fail, P < 0.001 | Fail, 1.139 |

Cereal rye | 0.55 | 296.7 | 17.2 | 54,460.9 | 1040.2 | Fail, P = 0.015 | Pass, P = 0.837 | Fail, 0.753 | |

2 | Hairy vetch | 0.92 | 63.7 | 8.0 | 12,171.6 | 786.3 | Fail, P < 0.002 | Pass, P = 0.126 | Fail, 1.474 |

Cereal rye | 0.58 | 273.2 | 16.5 | 50,114.3 | 1026.2 | Fail, P < 0.001 | Fail, P < 0.027 | Fail, 0.764 | |

3 | Hairy vetch | 0.94 | 50.4 | 7.1 | 9605.9 | 724.0 | Fail, P < 0.001 | Pass, P = 0.340 | Fail, 1.499 |

Cereal rye | 0.59 | 265.6 | 16.3 | 48,616.8 | 1021.2 | Fail, P < 0.001 | Fail, P < 0.001 | Fail, 0.758 | |

4 | Hairy vetch | 0.94 | 47.6 | 6.9 | 9206.8 | 732.5 | Fail, P < 0.001 | Pass, P = 0.358 | Fail, 1.438 |

Cereal rye | 0.61 | 264.8 | 16.0 | 47,033.4 | 1016.3 | Fail, P = 0.009 | Fail, P < 0.001 | Fail, 0.767 | |

5 | Hairy vetch | 0.94 | 46.6 | 6.8 | 9079.3 | 729.5 | Fail, P < 0.001 | Pass, P = 0.186 | Fail, 1.508 |

Cereal rye | 0.61 | 258.5 | 16.1 | 47,500.3 | 1018.4 | Fail, P = 0.007 | Fail, P < 0.001 | Fail, 0.767 | |

6 | Hairy vetch | 0.94 | 51.6 | 7.2 | 9857.2 | 747.5 | Fail, P < 0.001 | Pass, P = 0.453 | Fail, 1.436 |

Cereal rye | 0.61 | 258.3 | 16.1 | 47,266.8 | 10.17.1 | Fail, P = 0.016 | Fail, P < 0.001 | Fail, 0.767 | |

7 | Hairy vetch | 0.94 | 47.9 | 6.9 | 9080.3 | 731.4 | Fail, P < 0.001 | Pass, P = 0.220 | Fail, 1.510 |

Cereal rye | 0.59 | 270.9 | 16.5 | 49,594.2 | 1023.6 | Fail, P = 0.003 | Pass, P = 0.071 | Fail, 0.757 | |

8 | Hairy vetch | 0.94 | 48.0 | 6.9 | 9134.1 | 732.9 | Fail, P < 0.001 | Pass, P = 0.382 | Fail, 1.499 |

Cereal rye | 0.61 | 257.8 | 12.3 | 48,442.0 | 1015.5 | Fail, P < 0.001 | Fail, P < 0.001 | Fail, 0.758 |

^{1}Decay models: 1, y = ae

^{−bx}; 2, y = ae

^{−bx}+ yₒ; 3, y = ae

^{b}

^{/(c + x)}; 4, y = ae

^{−bx}+ ce

^{−dx}; 5, y = ae

^{−bx}+ ce

^{−dx}+ yₒ; 6, y = ae

^{−bx}+ cx + yₒ; 7, y = ab/(b + x); 8, y = ab/(b + x) + yₒ.

^{2}Residual mean square of the model.

^{3}Standard error of estimate of the model parameters.

^{4}Predicted residual sum of squares estimate of the model.

^{5}Akaike information criterion value of the model.

^{6}Shapiro-Wilk test for normality of the data where pass and fail assumptions were made at α ≤ 0.05.

^{7}Constant variance test using Spearman rank correlation where a pass or fail assumptions were made at α ≤ 0.05.

^{8}Durbin-Watson test of independence of residuals where a pass or fail assumptions were made at α ≤ 0.05.

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## Share and Cite

**MDPI and ACS Style**

Dhakal, M.; Singh, G.; Cook, R.L.; Sievers, T.
Modeling Hairy Vetch and Cereal Rye Cover Crop Decomposition and Nitrogen Release. *Agronomy* **2020**, *10*, 701.
https://doi.org/10.3390/agronomy10050701

**AMA Style**

Dhakal M, Singh G, Cook RL, Sievers T.
Modeling Hairy Vetch and Cereal Rye Cover Crop Decomposition and Nitrogen Release. *Agronomy*. 2020; 10(5):701.
https://doi.org/10.3390/agronomy10050701

**Chicago/Turabian Style**

Dhakal, Madhav, Gurbir Singh, Rachel L. Cook, and Taylor Sievers.
2020. "Modeling Hairy Vetch and Cereal Rye Cover Crop Decomposition and Nitrogen Release" *Agronomy* 10, no. 5: 701.
https://doi.org/10.3390/agronomy10050701