Dry matter intake in US Holstein cows: Exploring the genomic and phenotypic impact of milk components and body weight composite

Large datasets allow estimation of feed required for individual milk components or body maintenance. Phe-notypic regressions are useful for nutrition management, but genetic regressions are more useful in breeding programs. Dry matter intake records from 8,513 lactations of 6,621 Holstein cows were predicted from phenotypes or genomic evaluations for milk components and body size traits. The mixed models also included DIM, age-parity subclass, trial date, management group, and BW change during 28-and 42-d feeding trials in mid lactation. Phenotypic regressions of DMI on milk (0.014 ± 0.006), fat (3.06 ± 0.01), and protein (4.79 ± 0.25) were much less than corresponding genomic regressions (0.08 ± 0.03, 11.30 ± 0.47, and 9.35 ± 0.87, respectively) or sire genomic regressions multiplied by 2 (0.048 ± 0.04, 6.73 ± 0.94, and 4.98 ± 1.75). Thus, marginal feed costs as fractions of marginal milk revenue were higher from genetic than phenotypic regressions. According to the ECM formula, fat production requires 69% more DMI than protein production. In the phenotypic regression, it was estimated that protein production requires 56% more DMI than fat. However, the genomic regression for the animal showed a difference of only 21% more DMI for protein compared with fat, whereas the sire genomic regressions indicated approximately 35% more DMI for fat than protein. Estimates of annual maintenance in ki-lograms DMI/kilograms BW per lactation were similar from phenotypic regression (5.9 ± 0.14), genomic regression (5.8 ± 0.31), and sire genomic regression multiplied by 2 (5.3 ± 0.55) and are larger than those estimated by the National Academies for Science, Engineering, and Medicine based on NE L equations. Multiple regressions on genomic evaluations for the 5 type traits in body weight composite (BWC) showed that strength was the type trait most associated with BW and DMI, agreeing with the current BWC formula, whereas other traits were less useful predictors, especially for DMI. The Net Merit formula used to weight different genetic traits to achieve an economically optimal overall selection response was revised in 2021 to better account for these estimated regressions. To improve profitability, breeding programs should select smaller cows with negative residual feed intake that produce more milk, fat, and protein.


INTRODUCTION
Dry matter intake plays a major role in characterizing feed efficiency in dairy cattle (Li et al., 2016) and has been widely used in dairy nutrition research.As feed represents the largest operating cost in dairy production (Shalloo et al., 2004;Ho et al., 2013;Manzanilla-Pech et al., 2016), feed efficiency has gained increased attention for genetic selection.Improved feed efficiency contributes to farm profitability by reducing input costs and to environmental sustainability by reducing greenhouse gas emissions (Knapp et al., 2014;Hurley et al., 2017) and land needed for feed production (von Keyserlingk et al., 2013).Since 1990, feed efficiency has been considered as a potential goal of national dairy breeding objectives around the world, with records of feed intake for individual cows assessed for genetic evaluation (Van Arendonk et al., 1991;Nieuwhof et al., 1992;Veerkamp et al., 1994;Veerkamp, 1998).Feed efficiency of the US dairy herd has already improved 3-fold since the 1920s, and methane emissions also decreased by 39% over 8 decades (Garcia, 2013).In 2007, the dairy cow population consisted of 9.1 million cows, with an average weight of 635 kg and annual milk production reaching 9,096 kg.In contrast, the 1924 population included 21.4 million cows, with an average weight of 454 kg and annual milk production of 1,888 kg.More recently, despite a 24.9% increase in total milk production between 2007 and 2017, greenhouse gas emissions from US dairy cattle increased by only 1.0% (Capper and Cady, 2020).That study also emphasized noticeable reductions in the resources required for milk production in 2017 compared with 2007, encompassing cattle, feedstuffs, land, and water usage.These improvements can be attributed to advancements in genetics, feeding practices, nutrition, and overall cow health (Place and Mitloehner, 2010;Knapp et al., 2014).
Selecting for feed efficiency is a challenging task, with the major drawback being the substantial expense to collect feed intakes of individual animals (Pryce et al., 2015).Currently, most feed intake data are collected in research or nucleus herds, resulting in a very limited number of records being generated per year, thereby making it difficult to predict genetic merit for feed efficiency accurately or estimate genetic parameters reliably (Veerkamp et al., 2012).Yet the global dairy industry is highly motivated to improve feed efficiency (Berry et al., 2014;de Haas et al., 2015).Therefore, a greater emphasis is being directed to collect more feed intake data from multiple data sources to better characterize the genetic basis of feed intake in dairy cattle (Li et al., 2016).
The main components affecting feed efficiency in lactating cows are feed intake, milk production, maintenance costs, and changes in BW.Nutritionists often convert total feed energy to digestible energy by subtracting undigested fecal energy, then to ME by subtracting urinary and gas energy output, then to NE L by assuming a constant biological efficiency of 0.66 (NRC, 2001).Modern dairy cattle average approximately 25% of NE L for body maintenance functions and 75% for milk components, with changes in BW being minor but occasionally important (VandeHaar et al., 2016).Individual cows may convert more of their intake energy or protein into milk energy or protein due to phenotypic or genetic differences in any of these biological functions.
Although NRC (2001) specified that NE L for maintenance was 0.08 × metabolic body weight (MBW; measured as kg BW 0.75 ), this requirement was recently updated to 0.10 × MBW (NASEM, 2021).Selection for overall conformation in earlier decades tended to increase the body size and BW of Holsteins in the United States (Hansen, 2000), but since 2000, the Net Merit index (NM$) has favored smaller cows to improve feed efficiency (VanRaden et al., 2021).To accelerate the improvement of feed efficiency in the dairy industry, the genetic, economic, and biological effect of BW should be properly considered.Although Freeman (1975) reported a positive genetic correlation between BW and milk production, he also pointed out that heavier dairy cows are not necessarily desirable because of negative phenotypic and genetic correlations with feed efficiency.A study on 5,000 Holsteins in mid lactation demonstrated zero or negative genetic correlation between BW and milk energy output (VandeHaar et al., 2014).Selecting cows with smaller BW can decrease maintenance costs and improve health, fertility, and feed efficiency without negative consequences for milk production (Hansen, 2000).
The maintenance requirement estimated by NASEM (2021) and its previous editions, such as NRC (2001), are based on phenotypic data.Before incorporating feed intake data into feed efficiency genetic evaluation, accurate assessments of the genetic relationship of BW with maintenance feed costs are required (Visscher et al., 1994).However, BW data of individual cows on commercial farms are often unknown and rarely captured in centralized databases that span multiple farms.Since 2000, the NM$ index has used body weight composite (BWC) as a breeding objective in its formula, and it has been predicted by using 5 different linear type traits (i.e., stature, strength, body depth, dairy form, and rump width).One of the limitations of using BWC is that it is an imperfect proxy for BW.The NM$ predicts lifetime profit and includes other incomes and costs associated with BW, such as newborn calf value, variable cost of raising replacements, cost of growth after first calving, loss from cow death rate, and income from cull price.Of the 15 major national selection indexes analyzed, 7 indexes showed no direct selection for or against body size or BW.Among the 7 indexes that selected against body size, New Zealand had the largest penalty on BW, with a relative value of −11%.On average, the relative values for body size traits across these 7 indexes amounted to −5.6% of the total absolute value.Only 1 index (Canada) exhibited positive selection for body size (Toghiani and VanRaden, 2021).
Increased feed efficiency can be accomplished by selecting for lower residual feed intake (RFI), which is defined as the difference between actual and predicted DMI (Berry and Crowley, 2013;Connor, 2015).Genomic selection for feed efficiency can be reported in a variety of ways, such as DMI, RFI, and Feed Saved, and has been already implemented in national selection programs in Australia (Pryce et al., 2015), the Netherlands (Veerkamp et al., 2014), the United States (VanRaden et al., 2021), and the United Kingdom (Li et al., 2021).Beyond using RFI as an indicator for feed efficiency, the optimal level of milk production relative to BW must also be considered as a crucial selection indicator for feed efficiency (VandeHaar et al., 2016).Thus, a reasonable approach to improve feed efficiency is to use an index to select for lower BWC and lower RFI while selecting for greater milk production and improved milk components, along with healthier and more fertile cows (Pryce et al., 2015).
One of the objectives of this study was to use updated feed intake data from US Holstein dairy research herds to develop prediction models for DMI and BW from phenotypic and genomic regression of key energy sink traits.In addition, the intention of this study was to show how these predictions for effects of BWC and milk components on DMI can be used along with estimates of feed cost in deriving selection indexes.

Data Collection
This study used the US feed efficiency database for lactating Holstein cows, primarily sourced from 6 research stations: Iowa State University (Ames, Iowa), Michigan State University (East Lansing, MI), the University of Florida (Gainesville, FL), the University of Wisconsin-Madison (Madison, WI), the United States Dairy Forages Research Center (Madison, WI), and the USDA Animal Genomics and Improvement Laboratory (Beltsville, MD).This comprehensive database consists of daily phenotypic records, including milk yield compo-nents (milk, fat, and true protein yield), DMI, BW, MBW, DIM, age-parity class, experimental trials, changes in BW, and herd-year class.Records were primarily collected during mid lactation (between 50 and 200 DIM) due to the relative stability of DMI and BW within this period of lactation.Few cows had additional data before 50 or after 200 DIM, due to the high cost of data collection and desire to phenotype more cows instead of more days per cow.Daily phenotypic records were edited and compiled to form a single 28-d or 42-d average phenotypic record within each lactation, following procedures outlined in Tempelman et al. (2015).Records received as of April 2023 from the contributing institutions underwent further editing and compilation by the Council of Dairy Cattle Breeding (CDCB, Bowie, MD), following the same established methods.Subsequently, this dataset was merged with a CDCB official genomic evaluation database (https: / / uscdcb .com/genomic -evaluations/ ), which included GEBV for milk components, BWC, and 5 type traits contributing to BWC formation.The final dataset was used for DMI and BW prediction and consisted of a total 8,513 lactations (3,859 primiparous and 4,654 multiparous) from 6,621 Holstein dairy cows.More detailed information about the process of collecting phenotypes for developing the US feed efficiency database can be found in Tempelman et al. (2015).A summarized description of DMI and BW is presented in Table 1.

Mixed Model Analyses
To predict DMI from energy sink variables and to predict BW from conformation traits, a total of 6 linear mixed models using PROC MIXED of SAS (version 9.4; SAS Institute Inc.) were implemented for DMI (4 models) and BW (2 models) predictions.The mixed models used for DMI prediction were differentiated based on including phenotypic, sire's genomic, and cow's genomic regressions of energy sink variables to construct the model.
The following 4 linear mixed models were used for predicting DMI: [1] and The following 2 linear mixed models (Equations 5 and 6) were used for predicting BW: and where y ij is the observed DMI or BW trait in kg for animal i in all given models, μ is the overall intercept, age_lack j represents the categorical fixed effect for the group j consisting of age subclass in the month (3 levels: low, medium, high) and parity (6 levels: 1, 2, 3, 4, 5, >5), DIM i represents days in milk variable for animal i, DeltaBW_kg i is the average daily change in BW variable for animal i, and MBW i is the metabolic body weight variable of animal i, which is derived by raising its actual BW to the power of 0.75.All these variables are associated with their corresponding regression coefficients (β i ) and are common across 6 mixed models except for the MBW variable, which is specific to Equation 1.
The rest of the variables corresponding to fixed effects in all given models are specific and unique, where milk_kg i , fat_kg i , and prot_kg i are phenotypic milk, fat, and protein yield variables in kilograms for animal i, respectively (Equation 1); BWC_EBV i , milk_EBV i , fat_EBV i , and prot_EBV i denote the genomic variable of BWC, milk yield, fat yield, and protein yield for animal i, respectively (Equation 2); ST_EBV i , SR_EBV i , DR_EBV i , BD_EBV i , and RW_EBV i represent genomic variables of stature, strength, dairy form, body depth, and rump width for animal i, respectively (Equation 3); and Sire_BWC_EBV i , Sire_milk_EBV i , Sire_fat_EBV i , and Sire_prot_EBV i denote the sire's genomic variables of BWC, milk yield, fat yield, and protein yield for animal i, respectively (Equation 4).For predicting BW (in kg), 2 linear mixed models (Equations 5 and 6) were used in which the genomic variables of milk, fat, and protein yield were excluded from the fixed effects in both Equations 5 and 6 to mainly estimate the genomic effect of BWC and its related type traits on BW for lactating cows.In addition, similar random effects were used for all mixed models, in which mgt i is the random effect of herd-year for animal i, trial i is random effect of experiment trial for animal i, and e ij is the random residual effect assumed normally distributed.Due to possible collinearity between fixed effects in linear mixed models, the multicollinearity diagnostics have been implemented in all existing models to remove problematic predictors if the variance inflation factor (VIF) exceeds 10, implying that the highest VIF provides redundant information about the response variable in the presence of other predictors in the model.A summary description of the response and explanatory variables used in the mixed model analyses is presented in Table 1.
To minimize the potential confounding of the random effects associated with both herd-year and experiment trail variables in our linear mixed models, 3 specific criteria were evaluated: correlation analysis, variance partitioning, and model fit assessment.The correlation analysis yielded a weak negative correlation coefficient of −0.28 for both random variables, indicating limited confounding.Variance partitioning demonstrated independent contributions of both random variables to the variability in the response variable (DMI or BW), with no dominant factor.Furthermore, a model fit comparison between models with and without random effects revealed a substantial improvement when both random effects were incorporated, capturing unique sources of variability.These findings supported the inclusion of both head-year and experiment trail variables as random effects without high confounding in our models.
National GEBV for production and conformation are not a completely independent source of data because those GEBV include the research cow phenotypes, and the resulting phenotypic covariances might bias the genomic regression estimates upward.Validation and cross-validation methods often exclude the animal's own phenotype to obtain unbiased estimates.Initial testing used the published national GEBV for yield traits, but to check for and remove potential bias, the test was recomputed after excluding phenotypes from the research cows that were measured for DMI.

Empirical Equations Used by Nutrient Requirement Models to Predict Feed Intake
Statistical models for DMI prediction in dairy cattle regress on variables related to energy and protein sinks (i.e., milk production and components, MBW, BW change; Byskov et al., 2017).However, the inclusion of variables in the model depends on the availability of data and the hypotheses being tested.Diet-related variables were not included in the models in this study, which focused solely on animal-related variables (i.e., age, parity, DIM, and energy sinks).The rationale for using only animal-related variables is 2-fold.First, the composition of the diet is unknown in many studies within the database.Second, cows within a cohort received the same mixed ration.Nonetheless, group effects were estimated if cows within the same trial received different treatments.Additionally, it is worth noting that the effects of diet-related variables may vary depending on the lactation stage of the cows (Allen, 2014;de Souza et al., 2019) where Parity is an indicator variable (1 for multiparous and 0 for primiparous cows), MilkE is milk energy (Mcal/d, as defined by heats of enthalpy of components), BW is body weight (kg), BCS is body condition score, and DIM is days in milk for lactating Holstein cows; however, the effect of DIM is most important in the first 30 d and has little impact after 100 d.Most previous studies tried to separate genetic from environmental effects using only the records from the research farms; in the current study, we use estimated genetic effects from the much larger national dataset for production and conformation traits.The use of national data for traits with high reliability and intense genetic selection provides much more accurate estimates of genetic effects and genetic trends than using only a few thousand research cows having phenotypes over a decade.

Marginal Revenue and Cost
Progress for each trait in a selection index depends on incomes, costs, and covariances among the traits.To guide future index development, revenues from milk components and marginal costs of feed needed to produce those components are provided as examples from VanRaden et al. (2021).The assumed milk component revenues were $4.62/kg for fat, $5.26/kg for protein, and $0.043/kg for milk volume.The assumed feed cost in dollars was $0.24/kg for DMI.Progress for yield traits compared with other traits depends on the profit from additional yield compared with the costs or revenues from other traits.Marginal revenues and costs of feed to produce 100 kg of standardized milk with 3.5% fat and 3.0% protein were also calculated as (100 × milk + 3.5 × fat + 3.0 × protein) to indicate how overall progress for yield traits can be affected by the differing regression estimates.

Feed Intake for Yield Components
Feed intakes associated with milk components were examined by using phenotypic (Equation 1), GEBV (Equation 2), and sire GEBV (Equation 4) regressions.Table 2 represents the required feed amount for milk, fat, and protein and estimated marginal feed cost in dollar value to produce 100 kg of standardized milk with 3.5% fat and 3.0% protein across different methods.The estimated regression coefficients of milk components from genomic and sire genomic regressions were multiplied by 305-d kg to predict the required daily DMI (kg), and only the latter regression for milk components was further multiplied by 2 because sires contributed only half of the genes.The SE of regression coefficients were small for phenotypic regressions but about 4 times larger for genomic regressions and about 8 times larger for sire SE.A diagnostic test for multicollinearity was conducted on Equations 1, 2, and 4 to assess the likelihood of elevated VIF scores associated with milk, fat, and protein.The VIF scores exceeding 10 indicate high collinearity and could lead to instability in estimates when predicting DMI.However, the collinearity of milk, fat, and protein both phenotypically and genomically in the equations above, was found to be within acceptable limits, not exceeding the threshold.Specifically, collinearity was identified in the phenotypic regression of milk (6.08), fat (2.24), and protein (6.88) in Equation 1, the genomic regression of milk (2.33), fat (1.41), and protein (2.89) in Equation 2, and sire's genomic regression of milk (2.41), fat (1.55), and protein (3.18) in Equation 4.
Across the models used to predict DMI in the current study, the phenotypic regressions on milk components (Equation 1) estimated that 56% more feed was needed to produce protein than fat on a mass basis, and 163% more feed to produce 1 Mcal of milk protein than 1 Mcal of milk fat.The genomic regression gave an opposite estimate with 21% more feed required to produce fat than protein.The fat-to-protein ratio from genomic regression agrees more closely with the assumed ratio in the ECM method but with much less feed intake required for milk yield than in the ECM method.Furthermore, the sire genomic regression estimated 35% more feed required for fat than protein.All 3 regression methods estimated that much less DMI was required to produce milk volume (mostly water, lactose, and minerals) than was previously assumed in NM$ 2018.
Using our presumed prices for feed and milk, the marginal feed cost from phenotypic regression on the 3 components together totaled $6.35/100 kg for standardized milk and was much lower than (only 17%) of the marginal milk revenue of $36.37/100 kg.The genomic regression of the cow resulted in a markedly higher total marginal feed cost ($18.14/100kg) compared with the phenotypic regression whereas genomic regression of the sire yielded just over half the marginal feed cost of cow's genomic regression ($10.40/100kg) as expected.The inconsistent regressions for fat versus protein precluded any large changes to those ratios assumed in NM$ 2021, but consistent regressions indicating that lactose is less expensive to produce led to an increased value of milk in NM$ 2021.
For many years, only the theoretical study of Dado et al. (1994) was available, which assumed protein input is more limited than energy in most US rations because of its higher cost.Nutritionists often calculated intake and output based only on the energy in individual milk components.Thus, nearly all other countries assumed that feed costs for each milk component were proportional to ECM (Peter Amer, AbacusBio, New Zealand, personal communication, 2020) based on the suggested feed energy requirement by various editions of NRC, such as NRC (2001) and NASEM (2021).

Feed Intake for Maintenance
Maintenance per lactation was estimated by regressing DMI kg/d on phenotypic MBW, genomic BWC, and sire genomic BWC for this study and compared across different methods (Table 3).Conversion from daily to lactation basis assumed 305 d per lactation analogous to yield traits plus 60-d dry periods.The days of maintenance cost were assumed to be 365 d for simplicity and can be equivalent to the maintenance cost per year.To translate MBW and BWC into BW to calculate maintenance cost per year, an increase of l kg of MBW converts to a change of about 6.67 kg in BW for cows with normal BW ranging from 550 to 850 kg.In addition, the new estimates from regression of BW on genomic BWC in this study showed a change of 17.28 kg in BW per unit of BWC compared with 18.14 kg from Manzanilla-Pech et al. (2016) used previously in NM$ 2018.
Phenotypic regression on MBW gave 0.108 kg DMI/ kg BW 0.75 /d, and this coefficient was multiplied by 365 and divided by 6.67 to estimate that heavier cows have an increase in lactation maintenance of 5.9 kg DMI/kg BW per lactation.This value is higher than that estimated from NRC (2001) and NASEM (2021) based on NE L equations but less than that of NASEM (2021) based on DMI equations.In NRC ( 2001) based on DMI equations, the DMI predicted from BW was 0.0968 kg DMI/ kg BW 0.75 per day, which calculates to an increase in maintenance of 5.3 kg DMI/kg BW per lactation as BW increases.However, in NASEM (2021) based on DMI equations, the portion of DMI predicted from BW was 0.022 kg DMI/ kg BW per day, which translates to 8.0 kg DMI/kg BW per lactation as BW increases.If one uses the energy requirements for maintenance from NRC and assumes that cows must eat more over a lactation to meet the maintenance, and that a standard lactating diet is 1.7 Mcal NE L /kg, then heavier cows would eat an extra 4.3 kg DMI/kg BW per lactation using NRC (2001) and 5.3 kg DMI/kg BW per lactation using (NASEM, 2021).
Genomic regression of DMI on cow's BWC evaluation gave 0.275 kg DMI/d.Multiplying that by 365 and dividing by 17.28 to convert BWC to BW gives 5.8 kg DMI/kg BW per lactation, which is nearly the same as for phenotypic regression.Sire genomic regression on BWC gave 0.126 kg DMI/d, which was about half the regression on cow estimated breeding value as expected.Thus, the coefficient of sire genomic BWC multiplied by 2 and 365 and divided by 17.28 to obtain 5.3 kg DMI/ kg BW per lactation, which agrees with estimates from cow's phenotypic and genomic regression.

Feed Needs Based on Nutritional Calculations
When evaluating the cost of feed related to changes in milk production and BW, it is worth considering the calculations used in nutrition.NASEM ( 2021), along with many other nutrition models, provides calculations for predicting DMI (chapter 2) and for the energy and protein requirements (chapters 3 and 5) of dairy cows.As milk production increases relative to BW, the actual nutrient requirements increase at a faster rate than the predicted intake.Thus, higher-producing cows are fed diets with greater energy and protein density than lowerproducing cows.(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015)(2016).These cows were part of the database used in our current DMI prediction, but the current predictions used nearly 3 times the number of animals and with the same animal variables except for BCS.By utilizing BCS and a nonlinear function of DIM, NASEM (2021) predicted that the portion of DMI attributed to BW was 0.022 kg DMI/ kg BW per day, which translates to 8.0 kg DMI/lactation for every 1 kg increase in BW in a modern Holstein cow; this estimate is substantially greater than the predictions from our current regressions.The current regressions have values similar to those from NRC (2001), where the portion of DMI predicted from BW was 0.0968 kg DMI/kg BW 0.75 per day.This translates to an increase in maintenance of 5.2 kg DMI/lactation for a 1 kg heavier Holstein.The database to predict feed intake based on animal and feed factors had insufficient information and variation for BW to predict feed associated with maintenance.For the feed intake associated with milk production, the NASEM equation using only animal factors predicts that an additional kilogram of standard milk (3.5% fat), When utilizing the NASEM intake prediction equation that incorporates both animal and feed factors, the marginal feed intake for additional milk is influenced by the NDF digestibility of forages.For example, if the forage NDF digestibility is 38%, an extra 1 kg of milk leads to a 0.186 kg increase in DMI.However, if forage NDF digestibility is 58%, the same increase in milk results in a higher DMI of 0.264 kg.If we assume that DMI predictions reflect the marginal feed required for additional milk, then these calculations present a clear contradiction, as the more digestible diet would contain more NE L per kilogram, so that less feed is needed per kilogram of milk.However, it is important to note that this intake equation was developed to predict voluntary feed consumption, not feed requirements.The equation originates from a meta-analysis conducted by Allen et al. (2019); as the authors of that study point out, higher energy (more digestible) diets generally increase the predicted voluntary feed intake in high-producing cow because their ability to consume enough feed to meet their milk production needs is limited by gut distention.Allen et al. (2019) also discovered that milk volume exhibited a stronger correlation with feed intake than did milk energy output, suggesting that mammary glucose uptake (and thus lactose output) could be a major driver of appetite.Another approach to calculate feed needs for changes in cow BW and milk yield is by utilizing energy requirements for maintenance and milk production.In NASEM (2021), the NE L requirement for maintenance is 0.1 Mcal per unit BW 0.75 , which translates to 0.015 Mcal NE L /kg of BW in the 550 to 850 kg BW range.If we assume that cows need to consume more feed over lactation to meet maintenance requirements and that the average diet over a lactation cycle using NASEM contains 1.7 Mcal NE L / kg, then heavier cows would consume an additional 3.2 kg of DMI/kg BW per year.This is 25% higher than the value in NRC ( 2001) and is likely still underestimated.As shown by Moraes et al. (2015), estimated energy requirements associated with BW and milk and estimated feed NE L values must be from the same models.Compared with previous NRC models and to models based on cows from the United Kingdom, Ireland, and the Netherlands (Strathe et al., 2011), NASEM (2021) increased the NE L requirement for maintenance by 25% and also increased the calculated NE L density of diets by ~8%; hence, the feed needed for maintenance increase by ~19%. the NASEM committee cited data from Moraes et al. (2015) suggesting the maintenance requirement might be even higher.Evidently, our efforts to enhance milk production over the past century have led to breeding cows that necessitate a larger amount of feed for their maintenance.
In NASEM (2021), similar to previous NRC guidelines, the NE L value of a feed (Mcal/kg DM) is defined as the amount of milk gross energy that an additional 1 kg of feed can support after fulfilling the maintenance requirement.Milk energy is determined by summing the heats of enthalpy of its components and is defined in NASEM (2021, Equation 3 Mcal/kg) can be used for maintenance, milk production, body gain, or other functions.The digestibility of feeds, particularly forages, exhibits considerable variability and has a substantial impact on the NE L value; however, digestibility can be measured.Assuming a standard lactating diet with an NE L value of 1.7 Mcal/kg and standard milk composition of 3.5% fat, 3.0% protein, and 4.85% lactose, an additional 1 kg of milk/d would necessitate an incremental 0.407 kg of DMI/d.As all the energy in a feed must be allocated somewhere and given that the losses of feed GE can be reasonably predicted, the amount of feed required to produce 1 kg of standard milk should fall within a 20% range of 0.407 kg according to the laws of thermodynamics.
One issue with using energy requirements to predict the feed needed for increased milk production is that the regressions predict milk energy output based on feed energy input, which runs contrary to the direction required for genetic selection of cows that eat less feed per unit milk.Theoretically, however, the additional feed required to produce more milk should match the incremental milk that can be generated from the additional feed.Feed protein requirements should also be considered when estimating the feed costs associated with milk components.In the United States, feed costs for NM$ have been determined, in part, based on the theoretical study conducted by Dado et al. (1994).This study assumed that protein input is typically more limited than energy in most US rations due to its higher cost.An alternative approach for calculating feed costs is to consider both the energy and protein requirements for each milk compo- nent.Subsequently, calculated costs for feed energy and protein can be used, taking into consideration the prices of commonly used feeds.This method allows for a more comprehensive assessment of the feed costs associated with milk production.In terms of energy requirements, the feed NE L requirements for each milk component are determined based on their respective enthalpies, as outlined by NASEM (2021).Regarding protein requirements, assuming that the quantity of feed protein in lactating diets is influenced by milk protein output and that fat and lactose output do not have a meaningful protein requirement, it can be inferred that 1 g of milk protein requires 1 g of feed net protein, which is equivalent to 1.43 g MP based on a 70% conversion rate from MP to net protein.Feed protein and energy costs are subject to variation based on location and time, but reasonable prices can be estimated at $12/100 Mcal NE L and $73/100 kg MP.Using these prices, the feed cost for 1 kg of protein, fat, and lactose are $1.74, $1.11, and $0.47, respectively.As demonstrated by Dado et al. (1994), the cost for protein is substantially higher than that of fat or lactose.By employing this approach, the feed cost for standard milk with 3.5% fat and 3.0% protein is calculated to be $11.44/100 kg.This cost is considerably higher than the phenotypic regression estimates and lower than the genomic regression estimate.However, it results in increased feed cost for protein relative to fat compared with both regression approaches and is identical to the feed cost used in NM$ 2021.

Feed Expense to Use in Selection Indexes
In addition to the nutritional methods used previously, the new estimates from phenotypic, cow's genomic, and sire's genomic regression methods, as used in this study, could provide a better understanding of predicting the feed required for milk components.Variations in SE for yield components emphasize the divergences between phenotypic and genomic regressions, prompting the necessity for biological explanations.Marginal feed costs associated with milk, fat, and protein are directly subtracted from yield trait revenues to obtain net income in selection index formulas.
As shown in Table 3, the maintenance cost resulting from all 3 regression methods was almost 2 and 3 times higher than the estimated values based on NE L equations in NRC 2001 and NM$ 2018, respectively.The cost of maintenance in NM$ 2018 from Table 3 had been too low because it was estimated as a dollar value in 2000 and not updated for inflation until the 2021 revision.The assumed maintenance cost per year used in NM$ 2021 was 4.5, resulting from averaging the maintenance estimates of NRC 2021 and all regression methods.Using the NM$ 2021 value for maintenance cost, the direct selec-tion emphasis in NM$ 2021 is now 9.4% against BWC, which represents a 77% increase compared with the 5.4% emphasis against BWC used in NM$ 2018.The current study used more cow records to estimate regressions than in NM$ 2021 and provides further comparisons to standard nutritional recommendations.At the next revision of the NM$ or other indexes, experts should balance the SE of the differing estimates and consider other published recommendations to deliver more precise economic values that will be better understood and lead to further improvements in feed efficiency.

Effects of BWC Components on DMI and BW
The results from Equation 2showed that the regression coefficient on genomic BWC was significant for predicting DMI (0.275 ± 0.015; P < 0.001) and BW (17.28 ± 0.26; P < 0.001).This highlights the importance of BWC in predicting both DMI and BW, factors directly associated with maintenance costs.Because the BWC formula comprises 5 type traits, substituting the genomic information of these traits with genomic BWC provides insight into which type traits are influential in predicting DMI and BW.Given the potential high correlation between type traits, a multicollinearity diagnostic test was conducted on Equation 6 to assess the possibility of a large VIF score, which could lead to unstable estimates when predicting both DMI and BW.This diagnostic test revealed that body depth trait had the largest VIF score in both DMI and BW models (Figure 1), suggesting that body depth offers redundant information for DMI and BW in the presence of the other type traits.The estimates of genomic type traits, before and after implementing the multicollinearity diagnostic for DMI and BW, are presented in Table 4.
After excluding genomic body depth from both the DMI and BW models, strength was the most statistically significant (P < 0.001) predictor associated with DMI and BW.This finding aligns with the current BWC formula published by the Holstein Association (2017), whereas other type traits were not statistically significant predictors, especially for DMI.In addition to strength, dairy form was the second most statistically significant (P < 0.001) predictor after body depth was excluded from the BW model and it showed a stronger negative association with BW (−12.71) as opposed to when body depth was included in the model (−3.48).The significance and direction of regression coefficients for strength and dairy form traits in the original BWC formula are supported by the estimates of both type traits and their associations with BW (Table 4).Although the inclusion of genomic BWC alone in Equation 5 for predicting DMI and BW was statistically significant (P < 0.001), utilizing the 4 most genomically independent type traits (stature, strength, dairy form, and rump width) derived from genomic BWC to predict both DMI and BW resulted in a lower Akaike information criterion compared with solely using genomic BWC in the model.This suggests that the model, which decomposed BWC into its constituent type traits, provides a better fit for the data.
Potential biases of including the phenotypes of the research cow in the regressions on national GEBV were minor because those GEBV changed very little after excluding the phenotypes of the research cows from the GEBV (Table 5).A cow's phenotype for yield receives little emphasis compared with the enormous national data included in the GEBV, and the same is true for conformation traits.For yield traits, GEBV correlations were >0.99,SD ratios were close to 1.0, and the reliability gains were small by including rather than excluding pose of providing specific information and does not imply recommendation or endorsement by the USDA.The USDA is an equal opportunity provider and employer.No human or animal subjects were used, so this analysis did not require approval by an Institutional Animal Care and Use Committee or Institutional Review Board.The authors have not stated any conflicts of interest.

Figure 1 .
Figure 1.Distribution of variance inflation factor (VIF) scores for all predictors in DMI (A) and BW (B) model using multicollinearity diagnostic test.Predictors with VIF >10 are subjected to potential collinearity issues in the model.Abbreviations used for all predictors in both models: age_lact = age subclass in the month and parity; DeltaBW_kg = average daily change in kg of BW; DIM = days in milk; milk_ebv = genomic estimated breeding value of milk yield; fat_ebv = genomic estimated breeding value of fat yield; prot_ebv = genomic estimated breeding value of protein yield; ST_ebv = genomic estimated breeding value of stature; SR_ebv = genomic estimated breeding value of strength; DF_ebv = genomic estimated breeding value of dairy form; BD_ebv = genomic estimated breeding value of body depth; RW_ebv = genomic estimated breeding value of rump width.

Table 1 .
Summary statistics of response and explanatory variables used in mixed models Toghiani et al.: PREDICTION MODELS FOR DRY MATTER INTAKE

Table 2 .
Toghiani et al.: PREDICTION MODELS FOR DRY MATTER INTAKE Required feed amount (kg) for milk, fat, and protein and estimated marginal feed cost in dollar value across different methods

Table 3 .
Toghiani et al.: PREDICTION MODELS FOR DRY MATTER INTAKE Estimates of lactation maintenance cost across different methods Toghiani et al.: PREDICTION MODELS FOR DRY MATTER INTAKE