What does "Linearized" mean when it's applied to the NRC 2001 model?... The short answer is that virually everything on the N fraction side that makes the NRC 2001 AA sub-model a reliable predictor of AA flows in field pratice has been stripped from the model. What is left will NOT predict the same EAA flows as the native, published model and is essentially useless for balancing diets for AA content.
Take a look at the plot in the right sidebar of this page.. What you see is a plot of predicted vs. measured flows of MP-Met. The measured AA flows come from 182 of the 199 diets that were used by the NRC committee to develop prediction equations for each individual EAA in order to predict the EAA profile of duodenal protein. From the EAA profile of duodenal protein, EAA flows were then calculated.That process was approached as follows. When the preliminary outputs of the theoretical framework of the AA sub-model had been evaluated and those framework output variables that best predicted the measured AA flows had been identified; individual equations for predicting EAA content in duodenal protein were developed that provided a "correction factor" to the prediction errors of the theoretical framework based on the relationship between preliminary framework outpus and the measured AA flows. Once these equations had been generated, the same diets in which EAA flows had been measured were entered into the NRC 2001 model and the resulting AA flow predictions plotted against the AA flows measured in the diets. As you can see from the plot, the prediction error for flows of MP-Met accross 182 diets was 1.3 grams/day (RMSPE=1.3).
That is exceptional predictive reliability within the experimental dataset used to develop the NRC 2001 AA sub-model. And, that exceptional reliability is the result of the dynamic, non-linear nature of the AA sub-model.
What makes the NRC AA sub-model dynamic?... In general, AA are subject to degradation in the rumen environment. One of the primary factors that determines the extent and magnitude of dietary AA degradation is the time feeds spend in the rumen environment. NRC 2001 segments CP into three fractions 1.) the A fraction which is considered to be wholly degraded in the rumen, 2.) the B fraction which is subject to degradation based on ruminal dwell time and 3.) the C fraction which is considered to pass through the rumen without degradation. What NRC predicts as Rumen Undegraded Protein (RUP) consists of the entire C fraction and the undegraded portion of the B fraction. The magnitude of B fraction degradation is determined by its rate of degradation (Kd) and its rate of passage through the rumen (Kp). Passage rate (Kp) is determined by two fundamental factors - level of dry matter intake (DMI) and diet composition.
Read that last sentence again - it's crucial to understanding what happens when a dynamic, non-linear AA sub-model is "linearized". Within the NRC 2001 model, CP is partitioned into rumen degraded protein (RDP) and rumen undegraded protein (RUP) on the basis of total A fraction, the degaded protion of the B fraction and the total C fraction with passage rate (Kp) determined by level of DMI and diet composition. Within the nutrient profiles of feeds in the NRC evaluation software, you will NOT find fields for RUP, RDP, MP or MP-AA. There are NO coefficients for these items. Why? Because they are dynamically determined ONLY within the context of a stipulated diet. With that fact in mind, consider this: The output variables of the NRC theoretical framework that were determined to be the best predictors of the EAA content of duodenal protein were the percenatage of each EAA in RUP and RUP as a percentage of duodenal protein. These are values that can ONLY be determined within the context of a stipulated diet. They CANNOT be entered into the nutrient profile of a feed because, outside the context of a diet, they CANNOT be known.
When NRC 2001 is linearized, ALL of these dynamic factors, that are the bedrock of the predictive reliability of the NRC AA sub-model, are stripped from it and are replaced with FIXED coefficients. So, if you're working with diet formulation software that claims to implement the NRC 2001 model, check the nutrient profiles of feeds within the software. If you find fields for RUP, RDP, MP and MP-AA and those fields contain coefficient values, you are NOT working with the NRC 2001 model as it was published. Instead, you are working with a linearization of NRC 2001 that WILL NOT reliably predcit AA supplies and therefore is essentially uselss for balancing diets for AA content. How do we know that? If you download and install the evaluation software provided with the published NRC 2001 model and review the nutrient profiles of feeds in the software, you will find neither fields nor coefficient values for NE(l), RDP, RUP, MP or MP-AA. NRC 2001 stipulates the AA composition of feeds as percentages of CP NOT as MP-AA. Why are these items and values missing? Because they are NOT fixed values and cannot be known on an individual ingredient bases; they can only be known within the context of a complete diet.
If you want further confirmation as to whether NRC 2001 has been linearized, enter the same diet with the same ingredients and the same forage analyses into the both NRC evaluation software and the software you're currently using and compare the predictions of EAA flows. That exercise will clearly illustrate how the software implementation of the model compares with the published model. And, if NRC has been linearized, it will be an eye-opening experience.
Why linearize NRC 2001? The dynamic nature of coefficients for RDP, RUP, MP and MP-AA, as well as digestibility and energy at productive level of intake, defines these segments of the NRC 2001 model as non-linear. Because these coefficients change during the solution process as diet composition changes, developing a solution approach for such a model can be a complex process and complexity translates into development time and development time is expensive - linearization is much less expensive. However, because it removes the dynamics of the AA sub-model, linearization also destroys the predictive reliability of the AA sub-model resulting in an implementation of NRC 2001 that is useless for AA balancing. The other side of the coin is that if NRC is not linearized but no model compliant solution process is put in place what results is an implementation of NRC 2001 incapable of providing meaningful model compliant optimization capabilities and instead requires manually iterated trial and error diet formulation.
Unfortunately, when NRC 2001 is linearized the biggest losers are cows and producers.
Bottom line... If you're working with diet formulation software that claims to implement NRC 2001 and you're struggling to get results from AA balancing, check your software to determine if coefficients for RDP, RUP, MP and MP-AA are present in feed nutrient profiles. If that is the case, what you are working with is a linearized implementation of NRC 2001 that has been stripped of everything that creates the excellent predictive reliability of the native NRC 2001 model. And, that's the primary reason why you're struggling with AA balancing.
While there are signigicant differences between NRC 2001 and CNCPS, nonetheless, CNCPS is a mixed linear, non-linear animal model as well and fares just as badly when "linearized".
Plots of predicted vs. measured flows of MP-Met from the dataset used to generate the NRC 2001 EAA profile equations. The prediction error across this entire, very diverse dataet of 199 diets was only 1.3 g day. Excellent predictive reliability!