Modification of the summative equation to estimate daily total digestible nutrients for bermudagrass pasture. Academic Article uri icon


  • In forage-animal nutrition modeling, diet energy is estimated mainly from the forage total digestible nutrients (TDN). As digestibility trials are expensive, TDN is usually estimated using summative equations. Early summative equations assumed a fixed coefficient to compute digestible fiber using the lignin-to-neutral detergent fiber (NDF) ratio. Subsequently, a structural coefficient (φ) was added to the summative equations to reflect an association between lignin and cell wall components. Additional modifications to the summative equations assumed a constant φ value, and they have been used as a standard method by many commercial laboratories and scientists. For feeds with nutritive values that do not change much over time, a constant φ value may suffice. However, for forages with nutritive values that keep changing during the grazing season owing to changes in weather and plant maturity, a constant φ value may add a systematic bias to prediction because it is associated with the variable lignin-to-NDF ratio. In this study, we developed a model to estimate φ as a function of the day of the year by using the daily TDN values of bermudagrass [Cynodon dactylon (L.) Pers.], a popular warm-season perennial grass in the southern United States. The variable φ model was evaluated by using it in the TDN equation and comparing the estimated values with the observed ones obtained from several locations. Values of the various measures of fit used-the Willmott index (WI), the modeling efficiency (ME), R2, root mean square error (RMSE), and percent error (PE)-showed that using the variable φ vis-à-vis the constant φ improved the TDN equation significantly. The WI, ME, R2, RMSE, and PE values of 0.94, 0.80, 0.80, 2.5, and 4.7, respectively, indicated that the TDN equation with the variable φ model was able to mimic the observed values of TDN satisfactorily. Unlike the constant φ, the variable φ predicted more closely the forage nutritive value throughout the grazing season. The variable φ model may be useful to forage-beef modeling in accurately reflecting the impacts of plant maturity and weather on daily forage nutritive value and animal performance.

author list (cited authors)

  • Woli, P., Rouquette, F. M., Long, C. R., Tedeschi, L. O., & Scaglia, G.

publication date

  • January 1, 2020 11:11 AM