Estimation of Spring Forage Quality for Alfalfa in New York State

David Parsons, Jerome H. Cherney, and Hugh G. Gauch, Jr., Department of Crop and Soil Sciences, Cornell University, Ithaca, NY 14853

Abstract

Equations were developed to estimate alfalfa neutral detergent fiber (NDF) concentration in spring growth in New York State, using easily available variables and a typical cutting height used by growers. Models with two or three explanatory variables had greater predictive accuracy than models containing more variables. Models combining alfalfa height, growing degree days, and Julian date offer the greatest potential to increase predictive accuracy. Stage of maturity did not improve prediction accuracy. Predictions using the predictive equations for alfalfa quality (PEAQ) with alfalfa sampled in New York were biased, possibly due to differences in cutting height between observations used to fit the equation, and typical cutting heights in New York State. An equation previously fit to New York, using only the explanatory variable alfalfa height, was less biased.

Introduction

Timing of spring forage harvest is critical to obtain optimal quality for animal production. For forage that serves as the primary fiber source in the diet, the concentration of neutral detergent fiber (NDF) is a key forage quality variable. The optimal forage NDF for high-producing dairy cows is approximately 45% for alfalfa silage (2). Considering quality losses during harvest, storage, and feed-out, optimal NDF for standing alfalfa forage may be closer to 38%. Regardless of the value selected as "optimal" there is a relatively small acceptable range in optimal alfalfa NDF (3), emphasizing the need for quick and accurate methods for determining NDF. Numerous methods have been developed to estimate alfalfa NDF, including predictive equations based on weather, chronological age, and plant morphology (5). The most widely used of these are the predictive equations for alfalfa quality (PEAQ) models (8) which consider plant height and maturity stage. Although the initial NDF model was calibrated for Wisconsin, equations have been validated for other regions of the United States, including Ohio (10) and New York (1). Objectives of this study were to evaluate predictive accuracy of existing equations for estimation of spring alfalfa NDF concentration under New York growing conditions, and estimate additional prediction equations based on data easily accessible to growers.

Estimation of Alfalfa NDF Concentration

Stands of pure first-cut alfalfa were sampled in growers’ fields in 19 New York counties during May and June 2004 and 2005. Additional samples were taken from various field experiments that included alfalfa near Dryden and Ithaca, NY. Fields with alfalfa height of at least 12 inches were identified and a representative sampling area was visually identified in 2004. In 2005 a 36-inch diameter hoop was used to define a representative portion of the field as the sample area. Height of the tallest alfalfa stem in the sample area was measured to the terminal bud (MAXHT). The maturity categories of Kalu and Fick (8) were used to assign a numerical value to the most mature stem in the sample area (MAXSTAGE). A representative sample of 1 to 1.5 lb of alfalfa was hand clipped from the sample area at a height of 4 inches to approximate typical alfalfa harvest height. The time of sampling was recorded and converted to a 24-hour decimal time (TIME). The date of sampling was transformed to Julian date, the number of days from the beginning of the year (JDATE). The altitude of the field was recorded (ALTF). The geographic co-ordinates, which were not used as explanatory variables, were overlayed with the co-ordinates of all New York State weather stations using Manifold (Enterprise Edition 6.50, CDA International Ltd., San Mateo, CA). Voronoi cells were created to enable determination of the nearest weather station for each field and its altitude (ALTWS) was used as a potential predictor. Accumulated growing degree days were calculated for each site using base 32°F (GDD32) and base 41°F (GDD41). Growing degree day accumulation was initiated when the mean temperature exceeded the base for five consecutive days.

In total, 109 samples of alfalfa were taken. The aim of the study was to develop robust equations for estimation of alfalfa NDF concentration. Therefore samples were collected by numerous people over a wide geographic area and two climatically different years from fields having variable alfalfa and weed densities and different alfalfa varieties.

Samples were analyzed for NDF concentration based on the procedure described by Van Soest et al. (12), using the ANKOM fiber analyzer with filter bags. Selection of explanatory variables was performed using PROC RSQUARE and regression analysis was performed using PROC GLM (SAS for Windows Release 9.1, SAS Institute Inc., Cary, NC).

Prediction Equations for Alfalfa NDF Estimation

In Table 1 the best three models are included for equations containing one to eight variables. Model evaluation was based on several statistics. The coefficient of determination (R²) is the proportion of the variation explained by variables in the model and estimates goodness of fit of the model to the data. Root mean square error (RMSE) is the standard deviation around the regression line and is another measure of goodness of fit. In model development RMSE gives a measure of calibration error of the model and has the same units as the variable predicted, in this case NDF as a percentage of dry matter concentration. A good model therefore has a high R² and a low RMSE. However, R² and RMSE assess model accuracy in terms of the data used to construct the model; neither of these statistics assesses predictive accuracy of the model for independent data sets. The Schwarz Bayesian criterion (SBC) is a statistic that has components relating to both the fit of the model and the number of parameters in the model and, in contrast to R² and RMSE, is a better assessment of predictive accuracy. Statistics such as R² and RMSE tend to overfit the data used for model construction at the expense of accuracy for new data (6).

Table 1. Variable selection procedure summary, listing the three best models for each number of variables, sorted by Schwarz Bayesian criterion (SBC).

Number of variables	R²	RMSE	SBC	Variables in model
1	0.88	1.87	144	MAXHT
1	0.58	3.56	284	GDD41
1	0.58	3.60	286	GDD32
2	0.92	1.61	115	GDD41 MAXHT
2	0.91	1.62	116	GDD32 MAXHT
2	0.90	1.71	128	JDATE MAXHT
3	0.92	1.57	113	GDD32 ALTWS MAXHT
3	0.92	1.57	113	GDD41 ALTWS MAXHT
3	0.92	1.58	115	GDD32 ALTF MAXHT
4	0.92	1.54	113	JDATE GDD41 ALTWS MAXHT
4	0.92	1.56	115	JDATE GDD41 ALTF MAXHT
4	0.92	1.57	116	JDATE GDD32 ALTWS MAXHT
5	0.92	1.54	117	JDATE GDD41 ALTWS TIME MAXHT
5	0.92	1.55	117	JDATE GDD41 ALTWS MAXSTAGE MAXHT
5	0.92	1.55	117	JDATE GDD32 GDD41 ALTWS MAXHT
6	0.93	1.55	121	JDATE GDD41 ALTWS TIME MAXSTAGE MAXHT
6	0.92	1.55	121	JDATE GDD32 GDD41 ALTWS TIME MAXHT
6	0.92	1.55	121	JDATE GDD41 ALTF ALTWS TIME MAXHT
7	0.93	1.55	125	JDATE GDD32 GDD41 ALTWS TIME MAXSTAGE MAXHT
7	0.93	1.55	125	JDATE GDD41 ALTF ALTWS TIME MAXSTAGE MAXHT
7	0.93	1.55	125	JDATE GDD32 GDD41 ALTF ALTWS TIME MAXHT
8	0.93	1.56	129	JDATE GDD32 GDD41 ALTF ALTWS TIME MAXSTAGE MAXHT

The results in Table 1 will first be considered in terms of how many predictor variables should be included in the model. Focusing on the best model for each number of variables, R² with one variable in the model is 0.88 and increases with more variables in the model to a maximum value of 0.93. The best one-variable model has an RMSE of 1.87 and initially decreases with extra variables, with a minimum of 1.54 reached with four or five variables models. After this point, the RMSE begins to rise slightly and the 8-variable model has an RMSE of 1.56. The best one-variable model has an SBC value of 144. The minimum SBC value of 113 is reached with three variables in the model. As further variables are added SBC begins to rise and has a value of 129 for the eight-variable model. We interpret these results that although models with a high number of variables increase the goodness of fit of the model, predictive accuracy is optimized with just three variables. This outcome exemplifies a widely-observed response called Ockham’s hill wherein models with too few parameters underfit real signal whereas models with too many parameters overfit spurious noise, so a relatively parsimonious model is most predictively accurate (6).

Regarding the most useful variables for alfalfa NDF prediction, the best one-variable model is based on MAXHT, with an R² of 0.88, RMSE of 1.87 and an SBC of 144 (Table 1). The next best one-variable model, based on GDD41, has a much lower R² (0.58), and values of RMSE (3.56) and SBC (286) almost two times that of the previous model. The best two-variable model includes both MAXHT and GDD41 and results in a SBC of 115, lower than the best one-variable model. The best three-variable model includes MAXHT, either GDD41 or GDD32, and ALTWS, and the corresponding SBC of 113 is the lowest of all models.

Model Selection for Use by Producers

In choosing models for use by growers, both the predictive accuracy of a parameter and the accessibility of the parameter data should be considered. For example, we interpret from the results in Table 1 that alfalfa NDF estimation models can be improved by incorporating growing degree day data; however this information is not always readily available to growers, particularly data from a weather station in close proximity to the farm. As an alternative, Julian date is a much more accessible variable, and thus equations including JDATE should be considered even though they may be less accurate than those including growing degree days. Table 2 lists some potentially useful equations for growers. The model incorporating only alfalfa height (Eq. 1) may be of sufficient accuracy to meet the goal of farmers, which is to estimate the standing alfalfa NDF to aid in determining when the alfalfa is ready for spring harvest. The advantage of a simple one-variable model is that calculations could easily be made by the farmer in the field, using a stick with NDF estimates on the side, or alternatively just a calculator. If increased model accuracy is desired and the information is available, growing degree days could be added to the model (Eq. 2). In addition, if growing degree day information is available it is likely that the altitude of the weather station is also known, and thus a three-variable model with the best predictive accuracy could be used (Eq. 4). However, if growing degree data was not available a farmer could improve predictive accuracy by incorporating Julian date in the model (Eq. 3) and possibly also the altitude of the field (Eq. 5).

Table 2. Practical equations for estimating alfalfa NDF in New York State.

Equation number	R²	RMSE	SBC	Model
1	0.88	1.87	144	6.77 + 1.03(MAXHT)
2	0.92	1.61	115	6.89 + 0.0076(GDD41) + 0.85(MAXHT)
3	0.90	1.71	128	-7.03 + 0.11(JDATE) + (0.94)MAXHT
4	0.92	1.57	113	6.38 + 0.0072(GDD41) + 0.00090(ALTWS) + 0.84(MAXHT)
5	0.91	1.63	121	-8.00 + 0.11(JDATE) + 0.0013(ALTF) + 0.95(MAXHT)

The Value of Alfalfa Maturity in Estimation of Alfalfa NDF

Equations proposed by Hintz and Albrecht (8) and validated by Sulc et al. (11) focused on the use of both alfalfa height and maturity in estimating alfalfa NDF. Results of the variable selection procedure in this study (Table 1) confirmed the usefulness of MAXHT, but failed to demonstrate the usefulness of MAXSTAGE. MAXSTAGE was added to a model containing MAXHT to further determine whether MAXSTAGE is a significant variable in estimating alfalfa NDF. When MAXSTAGE is added to the model the R² rises from 0.88 to 0.89, and the RMSE drops from 1.87 to 1.86, which is negligible from a forage quality standpoint. However when MAXHT is already in the model, MAXSTAGE does not significantly (P > 0.13) contribute to further explaining any variation in alfalfa NDF. In addition the SBC increases from 144 to 147, suggesting that the predictive accuracy of the model may actually decrease with MAXSTAGE in the model. Although it is recognized that with a larger number of samples MAXSTAGE is more likely to be statistically significant, the value of MAXSTAGE in a model for farmer use is questionable.

These results confirm the work of Cherney (1) that an equation with MAXHT alone is acceptable for New York State, possibly because alfalfa in the Northeast often remains vegetative for prolonged periods with little change in the maturity stage (3). In addition to making calculations more complex for the farmer, these results suggest that the addition of MAXSTAGE contributes little additional information and is possibly detrimental to the predictive accuracy of the model.

Validation of the PEAQ Equation and Other Models

Validation tests described by Fick & Janson (4) were applied to the PEAQ model (8) and also to an equation derived by Cherney (1) for New York State, hereafter referred to as NYPQ. Equations were tested by regressing the actual laboratory measurements on the estimated values from the predictive equations. A nearly perfect prediction equation would have an intercept a = 0, a slope b = 1, R² near 1 and nil error (RMSE). Results in Table 3 show that both models are similar in their goodness of fit, with R²of 0.88 for both models and RMSE of 1.89 for PEAQ and 1.87 for NYPQ. The b-values of 1.37 for PEAQ and 1.31 for NYPQ were of similar magnitude, with slopes significantly different from 1. Both models also had y-intercepts significantly different from 0, although the a-value for NYPQ (-9.3) was less than that of PEAQ (-16.0), indicating less bias in the NYPQ model. The relationships between predicted and actual NDF for the PEAQ and NYPQ models (Fig. 1 and 2) indicate bias in both models. Gauch et al. (7) proposed the partitioning of mean squared deviation (MSD) into squared bias (SB), nonunity slope (NU) and lack of correlation (LC) as an alternative method to better understand the appropriateness of a statistical model. The three components add up to MSD and have distinct meanings, with SB, NU and LC relating to translation, rotation and scatter, respectively. PEAQ has a much larger overall MSD (19.98) than NYPQ (4.98) (Fig. 3). The LC component for PEAQ (3.49) denoting scatter of the data, is very similar to that for NYPQ (3.44) and both are within acceptable levels. The NU component for PEAQ (1.93) denoting rotation, is greater than that for NYPQ (1.46) and again both are within acceptable levels. Finally, the SB component for PEAQ (14.56) denoting translation, is much greater than that for NYPQ (0.09). We interpret the results that the NYPQ model predicts NDF better than PEAQ for these data, primarily due to a much lower SB. The high SB of the PEAQ model means that its use would regularly result in overestimation of NDF values. Although there are numerous possible reasons for this, one possibility is the cutting heights used for the models. The PEAQ equation was based on a cutting height of 1.5 inch, whereas the NYPQ model and this study were based on a cutting height of 4 inches, representing a typical cutting height. Sampling lower would include material of higher NDF near the base of the plant; however the effect of this extra 2.5 inches would be diluted with increasing plant height. This may account for the larger NU in the PEAQ equation and the increasing underestimation of NDF for low values of NDF.

Table 3. Coefficient of determination (R²), root mean square error (RMSE), slope (b), and y-intercept (a), derived from the regressions of PEAQ and NYPQ estimates on observed forage quality values.

	R²	RMSE	b	SE_b	Prob b=1.0	a	SE_a	Prob a=o
PEAQ	0.88	1.89	1.37	0.048	*	-16.0	1.59	*
NYPQ	0.88	1.87	1.31	0.046	*	-9.3	1.35	*

* Significant at a probability level of 0.001.

Fig. 1. Relationship between predicted and actual neutral detergent fiber (NDF) using the PEAQ model.

Fig. 2. Relationship between predicted and actual neutral detergent fiber (NDF) using the NYPQ model.

Fig. 3. Components of mean squared deviation (MSD) for the PEAQ and NYPQ models. The three components are squared bias (SB), non-unity slope (NU), and lack of correlation (LC).

Conclusions

Accurate estimation of first-cut alfalfa NDF for New York can be achieved with few variables. In addition to traditional statistics to assess model accuracy, a measure of predictive accuracy, such as SBC, can result in the selection of more parsimonious models. Alfalfa height alone is a good predictor of alfalfa NDF; however, model accuracy can be increased by including another variable in the model, such as growing degree days or Julian date. However, including alfalfa maturity did not increase model accuracy. The PEAQ equation was biased for New York State fields when alfalfa is harvested at a 4-inch stubble height. Ultimately farmers are only interested in knowing the NDF concentration of the portion of the plant that they will harvest. Thus we conclude that the NYPQ equation, using only alfalfa height, is a more appropriate model for New York State conditions. With further validation, the additional models in this paper offer potential for improved accuracy of predicting alfalfa NDF concentration.

Acknowledgments

The authors thank Sam Beer, Kai Ming Zhao, Molly Lebowitz, Jen Beckman, Peter Barney, Aaron Gabriel, Jeff Miller, Bruce Tillapaugh, Rick Faucett, Michael Hunter, Michael Davis, Aysin Bilgili, and Leon Hatch for assistance with harvesting and analysis. This research was supported by a Kieckhefer Adirondack Fellowship.

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