On the analysis of Canadian Holstein dairy cow lactation curves using standard growth functions

Genetic association between fat-to-protein ratio and traits of economic interest in early lactation Holstein cows in Brazil

The aims of this study were to estimate the genetic parameters for fat-to-protein ratio (F:P) within the first 90 days of lactation and to examine their genetic associations with daily milk yield (MY), somatic cell score (SCS), and calving interval between the first and second calving (IFSC) and between the second and third calving (ISTC) during the first three lactations of Holstein cows. We utilized 200,626 production-related data officially recorded from 77,436 cows milked two or three times a day from 2012 to 2022, sourced from the Holstein Cattle Breeders Association of Paraná State, Brazil. The (co)variance components were estimated using animal models, adopting the restricted maximum likelihood (REML) method with single-trait analysis (for heritability and repeatability) and two-trait analysis (for genetic and phenotypic correlations), per lactation. Regardless of lactation number, heritability estimates were relatively low, ranging from 0.08 ± 0.005 to 0.10 ± 0.003 for F:P; 0.08 ± 0.01 to 0.18 ± 0.005 for MY; 0.04 ± 0.01 to 0.07 ± 0.004 for SCS; and 0.03 ± 0.01 for both IFSC and ISTC. Repeatability estimates within the same lactation were low for F:P (ranging from 0.17 ± 0.002 to 0.19 ± 0.03), high for MY (between 0.50 ± 0.003 and 0.53 ± 0.002), and moderate to high for SCS (between 0.39 ± 0.003 and 0.44 ± 0.004). Genetic correlations between F:P and MY ranged from -0.26 ± 0.03 to -0.15 ± 0.02; F:P and SCS, from -0.06 ± 0.03 to -0.03 ± 0.08; F:P and IFSC, 0.31 ± 0.01; F:P and ISTC, 0.20 ± 0.01; MY and IFSC, 0.24 ± 0.05; and MY and ISTC, 0.13 ± 0.08. The fat-to-protein ratio during early lactation showed low genetic variability, regardless of lactation number. Furthermore, it was genetically correlated with MY, IFSC, and ISTC, although there is an antagonistic and unfavorable correlation between traits that can limit genetic progress.

Comparison of nonlinear functions to describe lactation curves for cumulative milk production in buffalo

The aim of this study was to examine the suitability of different growth functions (linear, sinusoidal, Gompertz, Schumacher and Richards) to fit cumulative milk production data from buffalo cows. Cumulative milk production at each day in milk was calculated from two published datasets reporting (i) fortnightly test-day milk yield records of the first lactation of Murrah buffalo that had calved during 1977-2012 and (ii) the first lactation records of Jaffarabadi buffalo collected from history-cum-pedigree registers for each quinquennium between 1991 and 2010. Each function was fitted to the lactation curves using nonlinear regression procedures. The Richards and sinusoidal equations provided the smallest root mean square error values, Akaike's and Bayesian information criteria and, therefore, the best fit for the cumulative lactation curves for milk yield. The Richards equation appeared to provide the most accurate estimate of the cumulative milk production at peak milk yield. Sinusoidal and flexible classical growth functions are appropriate to describe cumulative milk production curves and estimate lactation traits in buffalo.

Relationships between body- and udder-related type traits with somatic cell counts and potential use for an early selection method for water buffaloes (Bubalus bubalis)

Water buffalo milk is a reliable source of high-quality nutrients; however, the susceptibility of mastitis in buffaloes must be taken into consideration. An animal with somatic cell count (SCC) of greater than 250,000 cells/mL is reported to be likely to have mastitis which has serious adverse effects on animal health, reproduction, milk yield, and milk quality. Type traits (TTs) of water buffalo can affect SCC in animal milk to some extent, but few reports on the correlation between SCC and TTs are available. In this study, a total of 1908 records collected from 678 water buffaloes were investigated. The general linear model was used to identify factors associated with phenotypic variation of the somatic cell score (SCS) trait, including parity, lactation length, calving year, and calving season as fixed effects. Using PROC CORR analysis method, taking calving year and lactation length as covariates, the correlation co-efficient between TT and SCS was obtained. Our results showed that correlation co-efficients between the 45 TTs with SCS ranged from 0.003 to 0.443 (degree of correlation). The correlation between udder traits and SCS was greater than that between body structure traits and SCS. Among udder traits, distance between teats (including front and rear teat distance [r = 0.308], front teat distance [r = 0.211], and teat crossing distance [r = 0.412]) and teat circumference (r = 0.443) had the highest correlation with SCS, followed by the leg traits including rear leg height (r = -0.354) and hock bend angle (r = -0.170). Animal with high rear legs (>48 cm) and short teat crossing distance (<17 cm), and narrow teat circumference (<11 cm) exhibited low SCS. Using four nonlinear models (Von Bertalanffy, Brody, Logistic, and Gompertz), the optimal growth curves of the TTs highly correlated with the SCS (rear leg height and teat crossing distance) were fitted, and the correction co-efficients of these two TTs rear leg height and teat crossing distance of animal from young age (2 mo old) to first lactation (35 mo old) were attained for establishment of early selection method for water buffaloes with low SCS. This study provides theoretical support for early selection of low-SCS water buffaloes and lays a foundation for improving milk quality and promoting healthy development of water buffalo's dairy industry.

Modelling growth in dairy heifers based on linear body measurements (withers height) using non-linear functions

This research communication reports a study to model the growth curves for withers height (WH) and body weight (BW) to withers height ratio (BW:WH) using monthly records (from 1 to 24 months of age) for three breeds of dairy heifer (Holstein, Jersey and Brown Swiss). The data sets used were those reported by the Dairy Heifer Evaluation Project of Penn State Extension (USA) between 1991 and 1992. Four growth functions (monomolecular and Michaelis-Menten, both with diminishing returns behaviour, and Schumacher and López, both with asymptotic sigmoidal behaviour) were fitted using the non-linear regression procedure of the SigmaPlot software and the parameters estimated. The models were judged for goodness of fit using adjusted coefficient of determination ($R_{{\rm adj}}^2 $), root mean square error (RMSE), Akaike's information criterion (AIC) and Bayesian information criterion (BIC). Assessing the goodness of fit by $R_{{\rm adj}}^2 $ (>0.99 in all cases) reveals the generally appropriate fit of the models to the data. The non-sigmoidal functions (i.e. Michaelis-Menten and monomolecular) provided the best fits giving the lowest values of RMSE, AIC and BIC. Based on the chosen statistical criteria, the Schumacher and López equations provided acceptable fits to the WH and BW:WH growth curves, but showed points of inflexion at times before birth, indicating that these growth curves are not sigmoidal. In conclusion, evaluation of the different non-linear growth functions used in this study indicated their potential for modelling growth patterns in dairy heifers.

Random Regression Model for Genetic Evaluation and Early Selection in the Iranian Holstein Population

Simple Summary

The objective of this study was to use a model to predict breeding values for sires and cows at an early stage of the first lactation of cows and progeny groups in the Iranian Holstein population to support the early selection of sires. Our results show that we can select sires according to their daughters’ early lactation performance before they finish first lactation. Cross-validation results show that early selection accuracy can be high, and such an early selection can decrease the generation interval and lead to an increased genetic gain in the Iranian Holstein population.

Abstract

The objective of this study was to use a model to predict breeding values for sires and cows at an early stage of the first lactation of cows and progeny groups in the Iranian Holstein population to enable the early selection of sires. An additional objective was to estimate genetic and phenotypic parameters associated with this model. The accuracy of predicted breeding values was investigated using cross-validation based on sequential genetic evaluations emulating yearly evaluation runs. The data consisted of 2,166,925 test-day records from 456,712 cows calving between 1990 and 2015. (Co)-variance components and breeding values were estimated using a random regression test-day model and the average information (AI) restricted maximum likelihood method (REML). Legendre polynomial functions of order three were chosen to fit the additive genetic and permanent environmental effects, and a homogeneous residual variance was assumed throughout lactation. The lowest heritability of daily milk yield was estimated to be just under 0.14 in early lactation, and the highest heritability of daily milk yield was estimated to be 0.18 in mid-lactation. Cross-validation showed a highly positive correlation of predicted breeding values between consecutive yearly evaluations for both cows and sires. Correlation between predicted breeding values based only on records of early lactation (5–90 days) and records including late lactation (181–305 days) were 0.77–0.87 for cows and 0.81–0.94 for sires. These results show that we can select sires according to their daughters’ early lactation information before they finish the first lactation. This can be used to decrease generation interval and to increase genetic gain in the Iranian Holstein population.

Modelling Extended Lactations in Polish Holstein-Friesian Cows

Simple Summary

Mathematical models of lactation curves are functions that describe milk production on each day of lactation. These models are able to predict milk yields as well as provide valuable information applicable in breeding and management decisions. The aim of the present study was to examine different shapes of lactation curves for milk traits (i.e., milk, fat, protein and lactose yields and urea content in milk) modelled by the Wilmink function and by linear or squared functions between 306 and 400 days in milk (DIM). The results suggested that the course of extended lactations could be modelled by a nonlinear model, for example, the Wilmink function, for up to 305 DIM, and the linear or squared function could be more appropriate afterwards.

Abstract

The objectives of this study were (1) to examine different shapes of lactation curves for milk, fat, protein and lactose yields and urea content in milk fitted by the Wilmink function using the test-day (TD) records and (2) to find the function that best describes test-day records beyond 305 days in milk (DIM) for Polish Holstein–Friesian cows. The data were 6,955,768 TD records from the 702,830 first six lactations of 284,193 Polish Holstein–Friesian cows. Cows calved in 19,102 herds between 2001 and 2018. The following functions were fitted to TD data from each lactation: (1) Wilmink model fitted to the whole lactation, (2) Wilmink model fitted to TD records from 5 to 305 DIM and linear function fitted to TD records from 306 to 400 DIM, (3) Wilmink model fitted to TD records from 5 to 305 DIM and squared function fitted to TD records from 306 to 400 DIM. The present study showed that urea content in milk was modelled slightly worse than other milk traits. The results suggested that the course of lactation could be successfully modelled by a nonlinear model, for example, the Wilmink function, for up to 305 DIM, and by the linear or squared function afterwards.

Genomic studies of milk-related traits in water buffalo (Bubalus bubalis) based on single-step genomic best linear unbiased prediction and random regression models

Genomic selection has been widely implemented in many livestock breeding programs, but it remains incipient in buffalo. Therefore, this study aimed to (1) estimate variance components incorporating genomic information in Murrah buffalo; (2) evaluate the performance of genomic prediction for milk-related traits using single- and multitrait random regression models (RRM) and the single-step genomic best linear unbiased prediction approach; and (3) estimate longitudinal SNP effects and candidate genes potentially associated with time-dependent variation in milk, fat, and protein yields, as well as somatic cell score (SCS) in multiple parities. The data used to estimate the genetic parameters consisted of a total of 323,140 test-day records. The average daily heritability estimates were moderate (0.35 ± 0.02 for milk yield, 0.22 ± 0.03 for fat yield, 0.42 ± 0.03 for protein yield, and 0.16 ± 0.03 for SCS). The highest heritability estimates, considering all traits studied, were observed between 20 and 280 d in milk (DIM). The genetic correlation estimates at different DIM among the evaluated traits ranged from -0.10 (156 to 185 DIM for SCS) to 0.61 (36 to 65 DIM for fat yield). In general, direct selection for any of the traits evaluated is expected to result in indirect genetic gains for milk yield, fat yield, and protein yield but also increase SCS at certain lactation stages, which is undesirable. The predicted RRM coefficients were used to derive the genomic estimated breeding values (GEBV) for each time point (from 5 to 305 DIM). In general, the tuning parameters evaluated when constructing the hybrid genomic relationship matrices had a small effect on the GEBV accuracy and a greater effect on the bias estimates. The SNP solutions were back-solved from the GEBV predicted from the Legendre random regression coefficients, which were then used to estimate the longitudinal SNP effects (from 5 to 305 DIM). The daily SNP effect for 3 different lactation stages were performed considering 3 different lactation stages for each trait and parity: from 5 to 70, from 71 to 150, and from 151 to 305 DIM. Important genomic regions related to the analyzed traits and parities that explain more than 0.50% of the total additive genetic variance were selected for further analyses of candidate genes. In general, similar potential candidate genes were found between traits, but our results suggest evidence of differential sets of candidate genes underlying the phenotypic expression of the traits across parities. These results contribute to a better understanding of the genetic architecture of milk production traits in dairy buffalo and reinforce the relevance of incorporating genomic information to genetically evaluate longitudinal traits in dairy buffalo. Furthermore, the candidate genes identified can be used as target genes in future functional genomics studies.

Serum retinol, β-carotene, and α-tocopherol as biomarkers for disease risk and milk production in periparturient dairy cows

The effectiveness of using serum vitamin concentrations as biomarkers to predict diseases in dairy cows during the periparturient period is not well known. The objective of this study was to evaluate the association between serum β-carotene, retinol, and α-tocopherol concentrations and periparturient cow diseases in commercial dairies. We measured serum concentrations of these vitamin-active compounds at dry-off and during close-up (approximately 3 wk before calving) and early lactation (approximately 7 d post-calving), and we examined their association with clinical diseases in the first 30 d in milk. Diseases were diagnosed by trained personnel and recorded using database software. Blood samples were taken from 353 cows from 5 different farms over a 3-yr period. Blood samples were analyzed for β-carotene, retinol, α-tocopherol, and cholesterol. We built separate mixed logistic regression models for each disease outcome: hyperketonuria, lameness, mastitis, uterine diseases (retained placenta or metritis), and an aggregate outcome. For the aggregate outcome, a cow was considered positive if she had one or more of the following: hyperketonuria, lameness, mastitis, uterine disease, pneumonia, milk fever, or displaced abomasum. Concentrations of all 3 fat-soluble vitamins decreased significantly in early lactation relative to the 2 prepartum sampling times. Serum retinol concentrations at close-up and early lactation were negatively associated with odds of developing postpartum hyperketonuria. At early lactation, cows with uterine disease had lower serum retinol concentrations than cows without uterine disease. Similarly, lower serum retinol concentrations were associated with greater odds of having any one disease in the aggregate outcome. First-test 305-d mature-equivalent milk yield was positively correlated with increased serum α-tocopherol and negatively correlated with β-carotene concentrations. This study demonstrates the potential for serum β-carotene, retinol, and α-tocopherol to serve as biomarkers for disease risk.

Short communication: The lag response of daily milk yield to heat stress in dairy cows

Previous studies suggest that there exists a lag relationship between daily milk yield and heat stress. The values of heat stress indicators (e.g., temperature-humidity index and ambient temperature) before test day have a simple correlation with daily milk yield on test day. However, the simple correlation might not be the best description because daily milk yield and heat stress indicators have a nature of time series in common, and their correlations are cross correlations that could be affected by autocorrelations. We hope to give a more reliable estimation on the lag relationship of daily milk yield via excluding autocorrelations with transfer function modeling. In this study, we found a lag relationship between daily milk yield and heat stress indicators based on transfer function modeling. Heat stress indicators included ambient temperature and temperature-humidity index. The daily milk yield data from 123 cows were obtained during a consecutive 63-d period (July 10-September 10, 2016). The mean daily milk yield (MY) and the maximum daily ambient temperature (TA_max) satisfied the stationary hypothesis, and the cross correlation between them was calculated. Before excluding autocorrelation, MY at 0 to 4 d after test day had significant cross correlations with TA_max on test day. After excluding the influence of autocorrelations, MY at 1 to 3 d after the test day had significant cross correlations with TA_max on test day. This result suggested that MY would respond to TA_max 1 d after the test day. In addition, the strength of cross correlations between MY and TA_max decreased from 1 to 3 d in sequence, implying a declining lag response of MY that would last for 3 d. The transfer function model for MY and TA_max is written as: MY_t = 16.90 + 0.74MY_{t- 1} - 0.25TA_max_{t- 1} + N_t, where N_t is white noise. This model can be used to track and predict the dynamic response of MY to TA_max.

Bayesian Analysis of the Association between Casein Complex Haplotype Variants and Milk Yield, Composition, and Curve Shape Parameters in Murciano-Granadina Goats

Considering casein haplotype variants rather than SNPs may maximize the understanding of heritable mechanisms and their implication on the expression of functional traits related to milk production. Effects of casein complex haplotypes on milk yield, milk composition, and curve shape parameters were used using a Bayesian inference for ANOVA. We identified 48 single nucleotide polymorphisms (SNPs) present in the casein complex of 159 unrelated individuals of diverse ancestry, which were organized into 86 haplotypes. The Ali and Schaeffer model was chosen as the best fitting model for milk yield (Kg), protein, fat, dry matter, and lactose (%), while parabolic yield-density was chosen as the best fitting model for somatic cells count (SCC × 103 sc/mL). Peak and persistence for all traits were computed respectively. Statistically significant differences (p < 0.05) were found for milk yield and components. However, no significant difference was found for any curve shape parameter except for protein percentage peak. Those haplotypes for which higher milk yields were reported were the ones that had higher percentages for protein, fat, dry matter, and lactose, while the opposite trend was described by somatic cells counts. Conclusively, casein complex haplotypes can be considered in selection strategies for economically important traits in dairy goats.

Clustering and Characterization of the Lactation Curves of Dairy Cows Using K-Medoids Clustering Algorithm

Simple Summary

A lactation curve (LC) provides valuable insights in planning appropriate management strategies related to health, nutrition, and breeding in dairy cows. A clustering based approach on LC patterns analysis is presented. The k-medoids algorithm is adopted for the clustering. This approach generates several clusters which have similar milking characteristics of total milk yield, peak milk yield, and days in milk at peak yield. The LCs of some groups represent characteristics of atypical milking patterns which are not considered much in previous approaches, whereas LCs of the other groups show the typical LC patterns similar to the results of previous methods. This approach could be used as a tool to manage an abnormal herd of cows.

Abstract

The aim of the study was to group the lactation curve (LC) of Holstein cows in several clusters based on their milking characteristics and to investigate physiological differences among the clusters. Milking data of 330 lactations which have a milk yield per day during entire lactation period were used. The data were obtained by refinement from 1332 lactations from 724 cows collected from commercial farms. Based on the similarity measures, clustering was performed using the k-medoids algorithm; the number of clusters was determined to be six, following the elbow method. Significant differences on parity, peak milk yield, DIM at peak milk yield, and average and total milk yield (p < 0.01) were observed among the clusters. Four clusters, which include 82% of data, show typical LC patterns. The other two clusters represent atypical patterns. Comparing to the LCs generated from the previous models, Wood, Wilmink and Dijsktra, it is observed that the prediction errors in the atypical patterns of the two clusters are much larger than those of the other four cases of typical patterns. The presented model can be used as a tool to refine characterization on the typical LC patterns, excluding atypical patterns as exceptional cases.

Nutritional, behavioral and performance parameters of F1 Holstein x Zebu cows at different lactation stages

ABSTRACT The objective of this study was to evaluate the different lactation stages of F1 Holstein x Zebu cows on intake and digestibility of nutrients, nitrogen use efficiency, feeding behavior and performance. Thirty-six F1 Holstein × Zebu cows with initial body weight (BW) of 482±43kg were used. The early, mid and late lactation stages were characterized after 50±13, 111.5±11.75 and 183.0±17.5 days in milk, respectively. A completely randomized design with three lactation stages and 12 cows in each treatment group was used. Dry matter intake (P=0.01) was higher in late lactation. Milk yield (P<0.01) was 24.17% higher in early lactation than in other stages. Body weight was lowest in mid-lactation cows (465.63kg; P<0.01). The feed efficiency was 23.36% higher in early lactation than in other stages (0.82kg of milk/kg of DM). F1 Holstein x Zebu cows have increased dry matter intake in late lactation. Milk yield and feed efficiency in early lactation were benefited by changes in feeding behavior, such as increased rumination time.

Introducing a sinusoidal equation to describe lactation curves for cumulative milk yield and composition in Holstein cows

The aim of the work reported here was to investigate the appropriateness of a sinusoidal function by applying it to model the cumulative lactation curves for milk yield and composition in primiparous Holstein cows, and to compare it with three conventional growth models (linear, Richards and Morgan). Data used in this study were 911 144 test-day records for milk, fat and protein yields, which were recorded on 834 dairy herds from 2000 to 2011 by the Animal Breeding Centre and Promotion of Animal Products of Iran. Each function was fitted to the test-day production records using appropriate procedures in SAS (PROC REG for the linear model and PROC NLIN for the Richards, Morgan and sinusoidal equations) and the parameters were estimated. The models were tested for goodness of fit using adjusted coefficient of determination $\lpar {R_{{\rm adj}}^2 } \rpar $, root mean square error (RMSE), Akaike's information criterion (AIC) and the Bayesian information criterion (BIC). $R_{{\rm adj}}^2 $ values were generally high (>0.999), implying suitable fits to the data, and showed little differences among the models for cumulative yields. The sinusoidal equation provided the lowest values of RMSE, AIC and BIC, and therefore the best fit to the lactation curve for cumulative milk, fat and protein yields. The linear model gave the poorest fit to the cumulative lactation curve for all production traits. The current results show that classical growth functions can be fitted accurately to cumulative lactation curves for production traits, but the new sinusoidal equation introduced herein, by providing best goodness of fit, can be considered a useful alternative to conventional models in dairy research.

Genome-wide association for milk production and lactation curve parameters in Holstein dairy cows

The aim of this study was to identify genomic regions associated with 305‐day milk yield and lactation curve parameters on primiparous (n = 9,910) and multiparous (n = 11,158) Holstein cows. The SNP solutions were estimated using a weighted single‐step genomic BLUP approach and imputed high‐density panel (777k) genotypes. The proportion of genetic variance explained by windows of 50 consecutive SNP (with an average of 165 Kb) was calculated, and regions that accounted for more than 0.50% of the variance were used to search for candidate genes. Estimated heritabilities were 0.37, 0.34, 0.17, 0.12, 0.30 and 0.19, respectively, for 305‐day milk yield, peak yield, peak time, ramp, scale and decay for primiparous cows. Genetic correlations of 305‐day milk yield with peak yield, peak time, ramp, scale and decay in primiparous cows were 0.99, 0.63, 0.20, 0.97 and −0.52, respectively. The results identified three windows on BTA14 associated with 305‐day milk yield and the parameters of lactation curve in primi‐ and multiparous cows. Previously proposed candidate genes for milk yield supported by this work include GRINA, CYHR1, FOXH1, TONSL, PPP1R16A, ARHGAP39, MAF1, OPLAH and MROH1, whereas newly identified candidate genes are MIR2308, ZNF7, ZNF34, SLURP1, MAFA and KIFC2 (BTA14). The protein lipidation biological process term, which plays a key role in controlling protein localization and function, was identified as the most important term enriched by the identified genes.

Lactation curves and model evaluation for feed intake and energy balance in dairy cows

A good health status of high-performing dairy cows is essential for successful production. Feed intake affects the metabolic stability of dairy cows and can be used as a measurement for energy balance. By implementing feed intake and energy balance into the breeding goal, these traits provide great potential for an improvement in the health of dairy cows by breeders. In this study, fixed and random regression models were tested to establish appropriate models for a further analysis of this approach. A total of 1,374 Holstein-Friesian cows and 327 Simmental cows (SI) from 12 German research farms participating in a collaboration called optiKuh were phenotyped. Feed intake data recording was standardized across farms, and energy balance was calculated using phenotypic information on milk yield, milk ingredients, live weight, gestation stage, and feed intake. The phenotypic data set consisted of a total of 40,012 Holstein-Friesian and 16,996 SI with average weekly dry matter intakes of 21.8 ± 4.3 and 20.2 ± 3.6 kg/d, respectively. Observations of days in milk 1 to 350 were used to evaluate the best-fitting models and to estimate the repeatability and correlations between cow effects at different stages for feed intake and energy balance. Four parametric functions (Ali and Schaeffer and Legendre polynomials of second, third, and fourth degree) were compared to model the lactation curves. Based on the corrected Akaike information criterion and the Bayesian information criterion, the goodness of fit was evaluated to choose the best-fitting model for the finest description of lactation curves for the traits energy balance and feed intake. Legendre polynomial fourth degree was the best-fitting model for random regression models. In contrast, Ali and Schaeffer was the best choice for fixed regression models. Feed intake and energy balance acted as expected: the feed intake increased slowly at the beginning of lactation and the negative energy balance switched to a positive range around 40 to 80 d of lactation. The repeatabilities of both traits were quite similar and the repeatabilities for SI were the highest for both traits. Additionally, correlations between cow effects were closest between early days in milk. These results emphasize the possibility that the unique optiKuh data set can be used for further genetic analyses to enable genomic selection for feed intake or energy balance.

Sinusoidal function to describe the growth curve of dairy heifers

The objective of the present study is to introduce a sinusoidal function into dairy research and production by applying it to bodyweight records (from 1 to 24 months) from six dairy cow breeds reported by the Dairy Heifer Evaluation Project of Penn State Extension (USA) from 1991 to 1992. The function was evaluated with regard to its ability to describe the relationship between bodyweight and age in dairy heifers, and then compared with seven standard growth functions, namely monomolecular, logistic, Gompertz, von Bertalanffy, Richards, Schumacher and Morgan. The models were fitted to monthly bodyweight records of dairy heifers using non-linear regression to derive estimates of the parameters of each function. The models were tested for goodness of fit by using adjusted coefficient of determination, root mean square error, Akaike’s information criterion and Bayesian information criterion. Values of adjusted coefficient of determination were generally high for all models, suggesting the generally appropriate fit of the models to the data. The sinusoidal function provided the best fit of the growth curves for Brown Swiss, Guernsey and Milking Shorthorn breeds due to the lowest values of root mean square error, Akaike’s information criterion and Bayesian information criterion. According to the chosen statistical criteria, the Richards function provided the best fit for Ayrshire heifers, and the monomolecular the best for Holstein and Jersey. The least accurate estimates were obtained with the logistic. In conclusion, the sinusoidal function introduced here can be considered as an appropriate alternative to standard growth functions when modelling growth patterns in dairy heifers.

Evaluating lifetime nitrogen use efficiency of dairy cattle: A modelling approach

The increased nitrogen (N) use efficiency in cattle farming is proposed as a key action to improve N management and reduce the environmental impact of cattle farming systems. Most attention has been given to lactating cow nutrition, excluding the elements of fertility, disease, and the non-lactating animals within the herd. Therefore, the aim of the current study was to develop a herd-level simulation model incorporating these elements to assess dairy farm N use efficiency. We developed a cattle N use efficiency (CNE) model with six primary compartments: (i) heifer growth, (ii) heifer removal, (iii) pregnancy, (iv) cow removal, (v) disease and fertility, and (vi) milk production. The CNE model calculates N loss or gain for each compartment, and then calculates the lifetime N loss or gain taking into account the replacement rate (rep) and/or the corresponding number of lactations in a herd (Lact = 1/rep). Finally, three N use efficiencies were estimated: (i) ReplNE: replacement cattle N use efficiency, (ii) LactNE: lifetime N use efficiency for lactation, and (iii) LNE: lifetime N use efficiency. The sensitivity of the model to variation in farm- and animal-related input values was evaluated using Monte Carlo simulation. Values for a model dairy farm were used based on published data reflecting typical dairy farming practices in the United Kingdom. To assist reporting net values of main N outputs, a dairy herd of 100 lactating cows was modelled. Productive N outputs (1000s of kg) over the course of an animal’s lifetime, partitioned into milk and meat, were dominated by milk production (89% of total N output). We estimated a mean ReplNE of 23.7%, affected most by the last stage of heifer growth. The Monte Carlo sensitivity analysis suggested that variation in time to first calving (T_1stCal) might cause larger changes on ReplNE than variation in feed. The sensitivity analysis revealed a strong positive correlation between dietary oriented milk N use efficiency (MNE) and LactNE and LNE (r = 0.99 and 0.97 for LactNE and LNE, respectively). However, our study highlighted two other model variables that affected LNE. Variation in calving interval (CI; r = −0.15) and T_1stCal (r = −0.15) may cause measurable reductions of overall LNE. The first is an indicator of lactating cattle fertility, and the second an indicator of replacement cattle growth and fertility efficiency. In conclusion, with the current study we provided a dairy cattle herd model that is sensitive in elements of diet, fertility and health. Lifetime N use efficiency of dairy cattle is dominated by MNE, but we detected specific non-diet related variables that affect ReplNE, LactNE and LNE.

A new standard model for milk yield in dairy cows based on udder physiology at the milking-session level

Milk production in dairy cow udders is a complex and dynamic physiological process that has resisted explanatory modelling thus far. The current standard model, Wood’s model, is empirical in nature, represents yield in daily terms, and was published in 1967. Here, we have developed a dynamic and integrated explanatory model that describes milk yield at the scale of the milking session. Our approach allowed us to formally represent and mathematically relate biological features of known relevance while accounting for stochasticity and conditional elements in the form of explicit hypotheses, which could then be tested and validated using real-life data. Using an explanatory mathematical and biological model to explore a physiological process and pinpoint potential problems (i.e., “problem finding”), it is possible to filter out unimportant variables that can be ignored, retaining only those essential to generating the most realistic model possible. Such modelling efforts are multidisciplinary by necessity. It is also helpful downstream because model results can be compared with observed data, via parameter estimation using maximum likelihood and statistical testing using model residuals. The process in its entirety yields a coherent, robust, and thus repeatable, model.