Comparison between bivariate models for 56-day nonreturn and interval from calving to first insemination in Norwegian red

A bivariate threshold-linear (TL) and a bivariate linear-linear (LL) model were assessed for the genetic analysis of 56-d nonreturn (NR56) and interval from calving to first insemination (CFI) in first-lactation Norwegian Red (former Norwegian Dairy Cattle) (NRF). Three different datasets were used to infer genetic parameters and to predict transmitting abilities for NRF sires. Mean progeny group sizes were 147.8, 102.7, and 56.5 daughters, and the corresponding number of sires were 746, 743, and 742 in the 3 datasets. Otherwise, the structures of the 3 datasets were similar. When the TL model was used, heritability of liability to NR56 was 2.8% in the 2 larger datasets and 3.8% in the smallest dataset. In the LL model, the heritability of NR56 in the largest dataset and in the 2 smaller datasets was 1.2 and 0.9%, respectively. For CFI, the heritability was similar in TL and LL models, ranging from 2.4 to 2.7%. The small heritability of the 2 reproductive traits implies that most of the variation is environmental and that large progeny groups are required to get accurate sire PTA. The point estimates of the genetic correlation between NR56 and CFI were near zero in both models. The 2 bivariate models were compared in terms of predictive ability using logistic regression and a χ² statistic based on differences between observed and predicted outcomes for NR56 in a separate dataset. Comparison was also with respect to ranking of sires and correlations between sire posterior means (TL model) and PTA (LL model). We found very small differences in ability to predict NR56 between the 2 bivariate models, regardless of the dataset used. Correlations between sire posterior means (TL) and sire PTA (LL) and rank correlations between sire evaluations were all >0.98 in the 3 datasets. At present, the LL model is preferred for sire evaluations of NR56 and CFI in NRF. This is because the LL model is less computationally demanding and more robust with respect to the structure of the data than TL.     

Measurement, modelling and prediction of equilibrium moisture content in Pinus radiata heartwood and sapwood

heartwood and sapwood specimens was measured and modelled statistically under conditions of adsorption and desorption over a range of values of temperature and humidity typically encountered in in-service use. Two mathematical models (Day and Nelson 1965; W. Simpson 1971) were fitted to the data using non-linear least squares. To obtain statistically valid estimates and predictions, a logarithmic transformation was needed. Re-parameterisations of the models are given which reduce the correlations between parameters to reasonable levels, reduce the number of parameters needed to accommodate the different wood types and sorption conditions, and make it possible to fit the model to limited size datasets. Predictions from the model are estimated to have a relative error of 0.6% (about 10 times more accurate than the raw data) of the predicted value for wood with properties similar to the samples tested. The results are compared to the USDA Wood handbook (USDA Forest Service 1974) values for sitka spruce and some differences noted.     

Use and impact of usual intake models on dietary exposure estimate and risk assessment of chemical substances: a practical example for cadmium,acrylamide and sulphites

To estimate of food and nutrient intakes, 24-h recalls are frequently used in dietary assessment. However intake data collected for a short period are a limited estimator of long-term usual intake. An important limitation of such data is that the within-person variability tends to inflate the intake distribution leading to a biased estimation of extreme percentiles. Statistical models, named usual-intake models, that separate the within-person variability from the between-persons variability, have lately been implemented. The main objectives of this study were to highlight the potential impact that usual-intake models can have on exposure estimate and risk assessment and to point out which are the key aspects to be considered in order to run these models properly and be sure to interpret the output correctly. To achieve the goal we used the consumption data obtained by the French dietary survey INCA2 and the concentration data collected during the French TDS2, using Monte Carlo Risk Assessment (MCRA) software, release 8.0. For the three substances included in this study (cadmium, acrylamide and sulphites), the exposure of the upper percentiles was significantly reduced when using usual-intake models in comparison with the results obtained in the observed individual mean models, even if in terms of risk assessment the impact of using usual-intake models was limited. From the results it appears that the key aspects to consider when using usual-intake models are: (1) the normality of the log-transformed intake distribution, (2) the contribution per single food group to the total exposure, and (3) the independency of food consumption data on multiple days. In conclusion, usual-intake models may have an impact on exposure estimates although, referring to the results, it did not bring any changes in terms of risk assessment, but further investigations are needed.     

Prediction of nitrogen excretion in dairy farms located in north Florida: a comparison of three models

The increasing N concentrations in surface and groundwater in north Florida emphasize the need to identify sources of N loss and ways to reduce them. The amount of N excretion produced by dairy farms and deposited into the Suwannee River agro-ecosystem is being heavily scrutinized by regulatory agencies because it is believed to contribute significantly to the high N concentrations in water. Models developed by Van Horn and the USDA-Natural Resource and Conservation Service are used to estimate N balances on dairy farms. This study explores ways to improve these estimates by using dynamic simulation of N excretion over time. The Livestock Dynamic North Florida Dairy Farm model (LiDyNoFlo), which was created for this purpose, is described. The amount of N excretion on a dairy farm depends on crude protein in the diet, milk production, the presence of mature bulls and heifers, and seasonality of production. The LiDyNoFlo considered more variables than earlier models, and estimates of N excretion differed from those of other models. Comparisons consistently showed the LiDyNoFlo predictions of N excretion were between those predicted by the Van Horn model (upper end) and the Natural Resource and Conservation Service model (lower end). The LiDyNoFlo predicted that a 1,000-cow operation produced 324 kg of N excretion/d in February and 307 kg of N excretion/d in August because of seasonal milk production and herd dynamics. Seasonal differences in N excretion are important because they determine the opportunity for N recycling in the crop fields such that total N losses into the Suwannee River agro-ecosystem may be minimized.     

Estimates of calf starter energy affected by consumption of nutrients. 1. Evaluation of models to predict changing digestion on energy content in calf starters

Apparent total-tract digestibility data from 3 published studies with calves from 0 to 4 mo of age were used to evaluate National Research Council (2001) estimates of metabolizable energy (ME) in calf starters (CS). Calves (n = 83) or pens of calves (n = 24) were used in model development. In each study, 48 Holstein bull calves (2 to 3 d of age at initiation of each study) were fed varying amounts of milk replacer with CS and water for ad libitum consumption. Calf starters varied in nutrient content and form (pelleted, texturized, or mixed with 5% grass hay and fed as a total mixed ration). Apparent total-tract digestibility was measured at various ages from 3 to 16 wk. Feed and feces were collected from 20 calves per trial during 5-d collection periods during the first 56 d of each trial. In 2 studies, calves were grouped in pens (4 calves/pen) for a second 56-d measurement period. Fecal collections were repeated occasionally during the second period. Total-tract digestibilities (n = 207) of neutral detergent fiber, nonfiber carbohydrates, crude protein, and fat were used to calculate digestible energy (DE) and ME in CS using equations from the 2001 Dairy National Research Council. Three modeling approaches were constructed to evaluate changing digestion of nutrients, DE, and ME in CS, including linear mixed models, broken-line regression, and exponential models. Linear mixed models provided best model fit statistics for digestion of crude protein, ether extract, neutral detergent fiber, and ME. Exponential models were optimal for digestion of dry matter and nonfiber carbohydrates. Linear mixed models were selected for evaluation of effects of intake on changing nutrient digestion from CS and amount of DE and ME available at various ages.     

Statistical method to assess usual dietary intakes in the European population

Food consumption data are a key element of EFSA’s risk assessment activities, forming the basis of dietary exposure assessment at the European level. In 2011, EFSA released the Comprehensive European Food Consumption Database, gathering consumption data from 34 national surveys representing 66,492 individuals from 22 European Union member states. Due to the different methodologies used, national survey data cannot be combined to generate European estimates of dietary exposure. This study was executed to assess how existing consumption data and the representativeness of dietary exposure and risk estimates at the European Union level can be improved by developing a ‘Compiled European Food Consumption Database’. To create the database, the usual intake distributions of 589 food items representing the total diet were estimated for 36 clusters composed of subjects belonging to the same age class, gender and having a similar diet. An adapted form of the National Cancer Institute (NCI) method was used for this, with a number of important modifications. Season, body weight and whether or not the food was consumed at the weekend were used to predict the probability of consumption. A gamma distribution was found to be more suitable for modelling the distribution of food amounts in the different food groups instead of a normal distribution. These distributions were combined with food correlation matrices according to the Iman–Conover method in order to simulate 28 days of consumption for 40,000 simulated individuals. The simulated data were validated by comparing the consumption statistics of the simulated individuals and food groups with the same statistics estimated from the Comprehensive Database. The opportunities and limitations of using the simulated database for exposure assessments are described.     

Fitting a lognormal distribution to enumeration and absence/presence data

To fit a lognormal distribution to a complex set of microbial data, including detection data (e.g. presence or absence in 25g) and enumeration data (e.g. 30cfu/g), we compared two models: a model called M(CLD) based on data expressed as concentrations (in cfu/g) or censored concentrations (e.g. <10cfu/g, or >1cfu/25g) versus a model called M(RD) that directly uses raw data (presence/absence in test portions, and plate colony counts). We used these two models to simulated data sets, under standard conditions (limit of detection (LOD)=1cfu/25g; limit of quantification (LOQ)=10cfu/g) and used a maximum likelihood estimation method (directly for the model M(CLD) and via the Expectation-Maximisation (EM) algorithm for the model M(RD). The comparison suggests that in most cases estimates provided by the proposed model M(RD) are similar to those obtained by model M(CLD) accounting for censorship. Nevertheless, in some cases, the proposed model M(RD) leads to less biased and more precise estimates than model M(CLD).     

High Exposure from Summary Statistics (HESS): application to the EFSA comprehensive European food consumption database

While intake and exposure assessments can be readily carried out for a number of countries using complete datasets, the majority of European intake data are only available in the form of summary statistics published by the European Food Safety Authority (EFSA). Only EFSA have access to the complete datasets which are used in scientific opinions it issues. The proposed High Exposure from Summary Statistics (HESS) method is derived from first principles, and compared to existing models used to estimate high consumer exposures from the EFSA Comprehensive European Food Consumption Database. The method is applied to recent US consumption data to test its usefulness for deterministic and probabilistic exposure models, where comparisons between model results and detailed exposure assessments are possible. HESS is shown to provide a modest overestimation of the actual high consumer exposure, with a level of consistency and predictability that is much better than existing methods used with the EFSA Comprehensive European Food Consumption Database.     

Estimates of calf starter energy affected by consumption of nutrients. 2. Effect of changing digestion on energy content in calf starters

Apparent total-tract digestibility data from 3 published studies with calves from 0 to 4 mo of age were used to evaluate National Research Council (NRC; 2001) estimates of digestible energy (DE) and metabolizable energy (ME) in calf starters (CS). Calves (n = 83) or pens of calves (n = 24) were used in model development. In each study, 48 Holstein bull calves (2–3 d of age at initiation of each study) were fed varying amounts of milk replacer with CS and water for ad libitum consumption. Calf starters varied in nutrient composition and physical form (pelleted, textured, or mixed with 5% grass hay and fed as a total mixed ration). Apparent total-tract digestibility was measured at various ages. Feed and feces were collected from 20 calves per trial during 5-d collection periods during the first 56 d of each trial. In 2 studies, calves were grouped in pens (4 calves/pen) for a second 56-d measurement period. Fecal collections were repeated occasionally during the second period. Total-tract digestibilities (n = 207) of neutral detergent fiber, nonfiber carbohydrates (NFC), crude protein (CP), and fat were used to calculate ME in CS using equations from the 2001 Dairy NRC. Contributions of digestible CP and fat from milk replacer before weaning were estimated using nonlinear regression and removed from estimates of fat and CP digestibility in CS. Digestion of most nutrients in CS and calculated DE and ME in CS were low early in life and increased with increasing cumulative NFC intake. The natural logarithm of cumulative NFC intake, measured from d 0 to the end of each digestibility period, accounted for more variation in CS nutrient digestibilities, DE and ME estimates compared with daily NFC intake or intake of other nutrients, intake of milk replacer, or age of calf. Calculated ME values in CS were similar to those predicted by NRC after calves consumed approximately 15 kg of cumulative NFC or 28 kg of cumulative dry matter intake (assuming 53% NFC in CS). Current estimates of energy in CS fed to 4 mo of age may overestimate contribution of dry feed to overall energy metabolism in young calves.     

Several MPN models for serial dilutions with suppressed growth at low dilutions

Most probable number (MPN) estimates of microbial concentrations from serial dilutions employ a usual model of probabilities of the various possible outcomes. Outcomes challenge the usual model when they occur at markedly different rates from what the usual model predicts. Too many outcomes that suggest suppression of growth at low dilutions have occurred in some foods. These challenge the usual model and suggest new models. This paper provides four new models: growth suppression by a toxicant released from the food product by sample preparation; interference by a non-target species of microbe; disaggregation of clumped microbes at a single dilution step; disaggregation spread evenly over several dilution steps. The assumptions and discussion of how to find the maximum likelihood estimate for the parameters are given.     

Comparing experimental design schemes in predictive food microbiology: Optimal parameter estimation of secondary models

In predictive food microbiology, full factorial designs are still more the rule than the exception, despite the huge experimental workload and cost related to this method. In this study, two simulation studies for secondary square-root-type models are performed to compare several experimental designs with respect to four criteria: (i) number of experiments, (ii) goodness-of-fit statistics with respect to the original model structure, and (iii) accuracy and (iv) uncertainty of the parameter estimates. In addition, the effect of data quality, quantified as the error related to plate count measurements, is assessed on the relation between model structure and experimental design. Full factorial, reduced full factorial, central composite, Latin-square and Box-Behnken designs are evaluated and compared to randomly selected datasets.     

Identification of non-linear microbial inactivation kinetics under dynamic conditions

In this study dynamic microbial inactivation experiments are exploited for performing parameter identification of a non-linear microbial model. For that purpose microbial inactivation data are produced and a differential equation exhibiting a shoulder and a loglinear phase is employed. The derived parameter estimates from this method were used to perform predictions on an independent experimental set at fluctuating temperature. Joint confidence regions and asymptotic confidence intervals of the estimated parameters were compared with previous studies originating from parameter identification under isothermal conditions. The developed approach can provide more reliable estimates for realistic conditions compared to the usual or standard two step approach.     

Detection of mastitis in dairy cattle by use of mixture models for repeated somatic cell scores: a Bayesian approach via Gibbs sampling

The distribution of somatic cell scores could be regarded as a mixture of at least two components depending on a cow's udder health status. A heteroscedastic two-component Bayesian normal mixture model with random effects was developed and implemented via Gibbs sampling. The model was evaluated using datasets consisting of simulated somatic cell score records. Somatic cell score was simulated as a mixture representing two alternative udder health statuses ("healthy" or "diseased"). Animals were assigned randomly to the two components according to the probability of group membership (Pm). Random effects (additive genetic and permanent environment), when included, had identical distributions across mixture components. Posterior probabilities of putative mastitis were estimated for all observations, and model adequacy was evaluated using measures of sensitivity, specificity, and posterior probability of misclassification. Fitting different residual variances in the two mixture components caused some bias in estimation of parameters. When the components were difficult to disentangle, so were their residual variances, causing bias in estimation of Pm and of location parameters of the two underlying distributions. When all variance components were identical across mixture components, the mixture model analyses returned parameter estimates essentially without bias and with a high degree of precision. Including random effects in the model increased the probability of correct classification substantially. No sizable differences in probability of correct classification were found between models in which a single cow effect (ignoring relationships) was fitted and models where this effect was split into genetic and permanent environmental components, utilizing relationship information. When genetic and permanent environmental effects were fitted, the between-replicate variance of estimates of posterior means was smaller because the model accounted for random genetic drift.     

Calving ease (Co)variance components for a sire-maternal grandsire threshold model

Variance components for a sire-maternal grandsire (MGS) threshold model were estimated from subsets of the US calving ease (CE) database, which includes over 10 million calving records with CE scored 1 (no problem) to 5 (extreme difficulty). Selected records included sire and MGS among the 2601 most frequently appearing bulls. The data were further restricted by requiring at least 20 records in each herd year. Five mutually exclusive sample datasets of approximately 200,000 records each were created based on herd code. The model included random herd-year, sire, MGS, and residual effects and fixed year-season, parity-sex, and birth year of sire and MGS effects. Fewer than 50 iterations were required to reach convergence. The (co)variance component estimates from the five replicates were quite similar. The set of estimates (0.438, herd-year; 0.022, sire; 0.016, MGS; 0.009, sire-MGS) that yielded among the highest heritabilities (0.086, direct; 0.048, maternal) and a correlation of direct and maternal effects near the mean (-0.12) was selected for use in the implementation of a sire-MGS model for CE.     

Evaluation of different feed intake models for dairy cows

The objective of the current study was to evaluate feed intake prediction models of varying complexity using individual observations of lactating cows subjected to experimental dietary treatments in periodic sequences (i.e., change-over trials). Observed or previous period animal data were combined with the current period feed data in the evaluations of the different feed intake prediction models. This would illustrate the situation and amount of available data when formulating rations for dairy cows in practice and test the robustness of the models when milk yield is used in feed intake predictions. The models to be evaluated in the current study were chosen based on the input data required in the models and the applicability to Nordic conditions. A data set comprising 2,161 total individual observations was constructed from 24 trials conducted at research barns in Denmark, Finland, Norway, and Sweden. Prediction models were evaluated by residual analysis using mixed and simple model regression. Great variation in animal and feed factors was observed in the data set, with ranges in total dry matter intake (DMI) from 10.4 to 30.8 kg/d, forage DMI from 4.1 to 23.0 kg/d, and milk yield from 8.4 to 51.1 kg/d. The mean biases of DMI predictions for the National Research Council, the Cornell Net Carbohydrate and Protein System, the British, Finnish, and Scandinavian models were −1.71, 0.67, 2.80, 0.83, −0.60 kg/d with prediction errors of 2.33, 1.71, 3.19, 1.62, and 2.03 kg/d, respectively, when observed milk yield was used in the predictions. The performance of the models were ranked the same, using either mixed or simple model regression analysis, but generally the random contribution to the prediction error increased with simple rather than mixed model regression analysis. The prediction error of all models was generally greater when using previous period data compared with the observed milk yield. When the average milk yield over all periods was used in the predictions of feed intake, the increase in prediction error of all models was generally less than when compared with previous period animal data combined with current feed data. Milk yield as a model input in intake predictions can be substantially affected by current dietary factors. Milk yield can be used as model input when formulating rations aiming to sustain a given milk yield, but can generate large errors in estimates of future feed intake and milk production if the economically optimal diet deviates from the current diet.     

Genetic analysis of days from calving to first insemination and days open in Danish Holsteins using different models and censoring scenarios

The objectives of this study were to estimate genetic parameters and evaluate models for genetic evaluation of days from calving to first insemination (ICF) and days open (DO). Data including 509,512 first-parity records of Danish Holstein cows were analyzed using 5 alternative sire models that dealt with censored records in different ways: 1) a conventional linear model (LM) in which a penalty of 21 d was added to censored records; 2) a bivariate threshold-linear model (TLM), which included a threshold model for censoring status (0, 1) of the observations, and a linear model for ICF or DO without any penalty on censored records; 3) a right-censored linear model (CLM); 4) a Weibull proportional hazard model (SMW); and 5) a Cox proportional hazard model (SMC) constructed with piecewise constant baseline hazard function. The variance components for ICF and DO estimated from LM and TLM were similar, whereas CLM gave higher estimates of both additive genetic and residual components. Estimates of heritability from models LM, TLM, and CLM were very similar (0.102 to 0.108 for ICF, and 0.066 to 0.069 for DO). Heritabilities estimated using model SMW were 0.213 for ICF and 0.121 for DO in logarithmic scale. Using SMC, the estimates of heritability, defined as the log-hazard proportional factor for ICF and DO, were 0.013 and 0.009, respectively. Correlations between predicted transmitting ability from different models for sires with records from at least 20 daughters were far from unity, indicating that different models could lead to different rankings. The largest reranking was found between SMW and SMC, whereas negligible reranking was found among LM, TLM, and CLM. The 5 models were evaluated by comparing correlations between predicted transmitting ability from different data sets (the whole data set and 2 subsets, each containing half of the whole data set), for sires with records from at least 20 daughters, and χ² statistics based on predicted and observed daughter frequencies using a cross validation. The model comparisons showed that SMC had the best performance in predicting breeding values of the 2 traits. No significant difference was found among models LM, TLM, and CLM. The SMW model had a relatively poor performance, probably because the data are far from a Weibull distribution. The results from the present study suggest that SMC could be a good alternative for predicting breeding values of ICF and DO in the Danish Holstein population.     

Estimation of primary and secondary particulate matter intake fractions for power plants in Georgia

Air pollution benefit-cost analyses depend on dispersion models to predict population exposures to pollutants, but it is difficult to determine the reasonableness of the model estimates. This is in part because validation with field measurements is not feasible for marginal concentration changes and because few models can capture the necessary spatial and temporal domains with adequate sophistication. In this study, we use the concept of an intake fraction (the fraction of a pollutant or its precursor emitted that is eventually inhaled) to provide insight about population exposures and model performance. We apply CALPUFF, a regional-scale dispersion model common in health benefits assessments, to seven power plants in northern Georgia, considering both direct emissions of fine particulate matter (PM2.5) and secondarily formed ammonium sulfate and ammonium nitrate particles over a domain within 500 km of Atlanta. We estimate emission-weighted average intake fractions of 6 x 10(-7) for primary PM2.5, 2 x 10(-7) for ammonium sulfate from SO2, and 6 x 10(-8) for ammonium nitrate from NOx, with no effect of SO2 on ammonium nitrate. To provide insight about model strengths and limitations, we compare our findings with those from a frequently applied source-receptor (S-R) matrix. Using S-R matrix over an identical domain, the corresponding intake fractions are 5 x 10(-7), 2 x 10(-7), 3 x 10(-8), and -2 x 10(-8), respectively, with the values approximately doubling if the domain is expanded to cover the continental United States. Evaluation of model assumptions and comparison of past intake fraction estimates using these two models illustrates the importance of assumptions about the relative concentrations of ammonia, sulfate, and nitrate, which significantly influences ammonium nitrate intake fractions. These findings provide a framework for improved understanding of the factors that influence population exposures to particulate matter.     

Proceedings of the workshop on food-consumption surveys in developing countries: general approaches to estimation of dietary exposure to contaminants

The initial steps in estimating dietary exposure to contaminants include gathering the necessary expertise, clarifying the intent and purpose of the work, selecting a dietary exposure model, and gathering available pertinent information. Expertise is generally needed in chemistry, agriculture, toxicology, statistics, nutritional epidemiology, and computer software development. The goal might be to determine the average exposure of a population to contaminants, to identify demographic groups within a population that are especially vulnerable to a contaminant, to evaluate the regulation of agricultural and food-manufacturing practices, or to determine compliance with standards for local and/or imported foods. Examples of dietary exposure models include the core food model, directed core food model, large database model, raw agricultural commodity (RAC) model, regional diet model, duplicate diet model, and total diet composite model. Each model has advantages and disadvantages and different costs and resource requirements. Consideration of the sources and flow of selected contaminants though the food supply may help identify the best exposure model to use. Pertinent information that may already be available includes analytical data on contaminants in foods or commodities, government regulations pertaining to the levels of contaminants in foods, food-consumption data, data on the average body weights of age-gender groups (to express exposure on a body weight basis), and biochemical measures of contaminants or their residues/metabolites. Collecting available information helps to clearly define what critical information is missing so that the planned research can be most effective. Careful documentation of decisions and assumptions allows for recalculating exposure estimates with the same model using different decisions and assumptions; documentation also allows others to understand what was done and how to use the resulting intake estimates properly. Clearly identifying the limitations of the exposure model may provide justification for additional resources to further refine and improve the model.     

Accounting for energy and protein reserve changes in predicting diet-allowable milk production in cattle

Current ration formulation systems used to formulate diets on farms and to evaluate experimental data estimate metabolizable energy (ME)-allowable and metabolizable protein (MP)-allowable milk production from the intake above animal requirements for maintenance, pregnancy, and growth. The changes in body reserves, measured via the body condition score (BCS), are not accounted for in predicting ME and MP balances. This paper presents 2 empirical models developed to adjust predicted diet-allowable milk production based on changes in BCS. Empirical reserves model 1 was based on the reserves model described by the 2001 National Research Council (NRC) Nutrient Requirements of Dairy Cattle, whereas empirical reserves model 2 was developed based on published data of body weight and composition changes in lactating dairy cows. A database containing 134 individually fed lactating dairy cows from 3 trials was used to evaluate these adjustments in milk prediction based on predicted first-limiting ME or MP by the 2001 Dairy NRC and Cornell Net Carbohydrate and Protein System models. The analysis of first-limiting ME or MP milk production without adjustments for BCS changes indicated that the predictions of both models were consistent (r² of the regression between observed and model-predicted values of 0.90 and 0.85), had mean biases different from zero (12.3 and 5.34%), and had moderate but different roots of mean square errors of prediction (5.42 and 4.77 kg/d) for the 2001 NRC model and the Cornell Net Carbohydrate and Protein System model, respectively. The adjustment of first-limiting ME- or MP-allowable milk to BCS changes improved the precision and accuracy of both models. We further investigated 2 methods of adjustment; the first method used only the first and last BCS values, whereas the second method used the mean of weekly BCS values to adjust ME- and MP-allowable milk production. The adjustment to BCS changes based on first and last BCS values was more accurate than the adjustment to BCS based on the mean of all BCS values, suggesting that adjusting milk production for mean weekly variations in BCS added more variability to model-predicted milk production. We concluded that both models adequately predicted the first-limiting ME- or MP-allowable milk after adjusting for changes in BCS.