Comparison of three mathematical models to estimate lactation performance in dairy cows.

Milk yield dynamics and production performance reflect how dairy cows cope with their environment. To optimize farm management, time-series of individual cow milk yield have been studied in the context of precision livestock farming, and many mathematical models have been proposed to translate raw data into useful information for the stakeholders of the dairy chain. To gain better insights on the topic, this study aimed at comparing 3 recent methods that allow to estimate individual cow potential lactation performance, using daily data recorded by the automatic milking systems of 14 dairy farms (7 Holstein, 7 Italian Simmental) from Belgium, the Netherlands, and Italy. An iterative Wood model (IW), a perturbed lactation model (PLM), and a quantile regression (QR) were compared in terms of estimated total unperturbed (i.e., expected) milk production and estimated total milk loss (relative to unperturbed yield). The IW and PLM can also be used to identify perturbations of the lactation curve and were thus compared in this regard. The outcome of this study may help a given end-user in choosing the most appropriate method according to their specific requirements. If there is a specific interest in the post-peak lactation phase, IW can be the best option. If one wants to accurately describe the perturbations of the lactation curve, PLM can be the most suitable method. If there is need for a fast and easy approach on a very large data set, QR can be the choice. Finally, as an example of application, PLM was used to analyze the effect of cow parity, calving season, and breed on their estimated lactation performance.

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.

Milking Temperament and Its Association with Test-Day Milk Yield in Bulgarian Murrah Buffaloes.

The goal of this research was to evaluate milking temperament and its relationship with test-day milk (TDMY0) yield in Bulgarian Murrah buffaloes. This study involved 90 buffalo cows reared under a tie-stall production system which were milked twice a day with a milking pipeline. The behavioral responses of the buffaloes were reported during preparation for milking and during actual milking. The average temperament score during preparation for milking was 1.83, and 1.93 during milking itself. The most common reaction was leg lifting (18.9%), followed by cows moving on the stall bed (10%), definite kicking (9.9%), and 13.3% managing to remove the milking cluster during milking. The frequency of buffaloes showing adverse reactions (scores 4 and 5) increased considerably during milking compared to preparation for milking. Repeated scoring of temperament during the same lactation did not show a significant difference in the frequency of temperament assessments both in preparation for milking and during milking. The minimal difference may be due to the accuracy of the assessment or a momentary change in the condition of the animals during the two scorings. Cows with the most unwanted milking behavior (scores 5 and 4) had the highest LS means for TDMY, 8.18 kg and 7.65 kg, respectively. The reasons for these buffaloes remaining until later lactations was their high milk yield and the injection of oxytocin before milking, which helps them to be fully milked.

Assessing Environmental Effects upon Modeling the Individual Lactation Curve of a Local Goat Population in a Pastoral System.

The present study aims to use Wood's model to determine the parameters of individual lactation curves in a local goat population and their factors of variation under a pastoral system. A total of 137,927 records from 432 local goats were collected to assess the impact of litter size, year and month of kidding, herd and the age of the dam on lactation curve parameters. Wood's model parameters were estimated using non-linear regression, and individual curves were fitted. The characteristics of the lactation curves were computed. The initial yield (A), rate of increase (B) and rate of decline (C) parameters in Wood's model for local goats were 730 g, 0.26 and 0.09 respectively. The values of peak milk production (PP), peak date (PD) and persistency (PC) were 931.88 g/d, 23.39 days and 91.50%, respectively. Persistence was higher in goats with simple births, while peak production increased by around 0.3 kg for each additional kid. The curve parameters "A" and "C" differed according to the herd and month of kidding (p < 0.05); the age of the dam only had an impact on parameter "A" (p < 0.01). Parameter "B" was not significantly influenced by any of the factors considered (p > 0.05). Correlation coefficients among lactation curve characteristics were ranged from -0.20 to 0.89. Due to a significant negative correlation, selecting for parameter "A" may have an adverse effect on parameter "B", resulting in a shorter time to reach peak production and less persistency, but an increase in peak production among goats. The curves derived from Wood's model suggest that the shape of the curve may serve as a basis for herd management planning and to improve local population potentialities.

Lactation traits and reproductive performances of Sahraoui female camel in two breeding systems at Algerian Sahara.

The main objective of this study is to determine the impact of the camel livestock system on individual and herd performances of milk production, lactation curve, fats, and protein concentrations. For this purpose, 13 she-camels of Sahraoui breed from the south eastern Algeria and belonging and semi-intensive system (N = 6) and intensive system (N = 7) were studied. Recording and sampling of milk were carried out at regular intervals during a full lactation. The lactation curve was estimated using Wood's gamma function and the t-test of independent groups was carried out to compare lactation performances, lactation curve, and reproductive parameters. The overall average daily milk (DMY), fat (DFY), and protein (DPY) yield were 6.77 ± 0.82 kg/day, 4.15 ± 0.91%, and 4.49 ± 0.20%, respectively. The mean of total milk yield (TMY) was 2696.39 ± 343.86 kg during a mean lactation length (LL) of 398.38 ± 20.65 days. The peak of milk production (6.79 ± 0.68 kg) was reached at 93.9 ± 55.8 days after calving. The open day (DO) and inter-calving interval (ICI) recorded in this study were 348.38 ± 30.33 and 723.38 ± 30.33 days, respectively. There is no significant difference (p > 0.05) between intensive and semi-intensive breeding systems for TMY (2795.39 ± 261.88 kg vs. 2580.89 ± 414.43 kg), DMY (6.96 ± 0.66 kg vs. 6.55 ± 1.00 kg), and LL (402.14 ± 21.18 days vs. 394 ± 21.03 days). However, the total amount of fat was significantly higher in intensive system (182.02 ± 33.91 kg) and the DPY content was significantly higher in semi-intensive system (4.60 ± 0.13%). The parameters α, ß, and γ of lactation, fat, and protein curves between the two systems showed a highly significant difference (p < 0.01) for the parameters (α and ß) for the milk production curve, significant (p < 0.05) for the time to reach peak yield, and no significance for the other parameters. The corresponding values of the coefficient of determination (R2) were 0.62, 0.35 for milk yield (p > 0.05), 0.12, 0.13 (p > 0.05) for fat, and 0.03, 0.11 (p < 0.05) for protein, in the intensive and semi-intensive systems, respectively. In addition, DO and ICI were not significantly different between the livestock systems, but were higher in the intensive system than the semi-intensive system (337.17 ± 26.26 vs. 712.17 ± 26.26, respectively). The study concluded that the intensive system had a higher milk performance with a more efficient lactation curve. The incomplete gamma model (Wood) used in this study was inappropriate for estimating milk yield, but acceptable for fat and protein.

Lactation curves of Montbéliarde-sired and Viking Red-sired crossbred cows and their Holstein herdmates in commercial dairies.

Lactation curves were estimated for Montbéliarde (MO) × Holstein (HO) and Viking Red (VR) × HO 2-breed crossbred cows and for MO × VR/HO and VR × MO/HO 3-breed crossbred cows and their HO herdmates from test-day observations in 7 high-performance herds that participated in a designed study. Cows calved from 2010 to 2017. Test-day observations from milk recording were used to fit the lactation curves of cows in their first 3 lactations. Lactations of cows were required to have at least 250 DIM and to have at least 6 test days ≤265 DIM. Lactation curves from random regression (RR) were compared for 305-d production (kg), peak production (kg), peak day of production, and production from 4 to 103 DIM (kg), from 104 to 205 DIM (kg), and from 206 to 305 DIM (kg) for milk, fat, and protein. Also, the persistency of production was compared. First-lactation versus second- and third-lactation cows were analyzed separately for both the 2-breed and 3-breed crossbred cows and their respective HO herdmates. Legendre polynomial RR had the best goodness of fit for the lactation curves compared with Ali-Schaeffer and Wilmink RR from the test-day observations of milk, fat, and protein production. For fluid milk production of first-lactation cows, the MO × HO 2-breed crossbreds were not different from their HO herdmates for any of the lactation-curve characteristics, except persistency. However, the VR × HO 2-breed crossbreds had less fluid milk production compared with their HO herdmates. For first lactation, the MO × HO 2-breed crossbreds had more persistency of milk, fat, and protein production compared with their HO herdmates. The first-lactation MO × VR/HO 3-breed crossbreds had more persistency of fluid milk production compared with their HO herdmates. For second and third lactations, both the MO × HO and the VR × HO 2-breed crossbreds had higher fat production compared with their HO herdmates. Furthermore, the MO × HO 2-breed crossbreds had more protein production (kg) in all 3 periods of lactation compared with their HO herdmates. Crossbred cows may have advantages over HO cows for persistency of production in high-performance herds.

The marker effects of a single-step random regression model for 4 test-day traits in German Holsteins.

The single-step genomic model has become the golden standard for routine evaluation in livestock species, such as Holstein dairy cattle. The single-step genomic model with direct estimation of marker effects has been proven to be efficient in accurately accounting for millions of genotype records. For diverse applications including frequent genomic evaluation updates on a weekly basis, estimates of the marker effects from the single-step evaluations play a central role in genomic prediction. In this study we focused on exploring the marker effect estimates from the single-step evaluation. Phenotypic, genotypic, and pedigree data were taken from the official evaluation for German dairy breeds in April 2021. A multilactation random regression test-day model was applied to more than 242 million test-day records separately for 4 traits: milk, fat, and protein yields, and somatic cell scores (SCS). Approximately one million genotyped Holstein animals were considered in the single-step genomic evaluations including ∼21 million animals in pedigree. Deregressed multiple across-country breeding values of Holstein bulls having daughters outside Germany were integrated into the national test-day data to increase the reliability of genomic breeding values. To assess the stability and bias of the marker effects of the single-step model, test-day records of the last 4 yr were deleted, and the integrated bulls born in the last 4 yr were truncated from the complete phenotypic dataset. Estimates of the marker effects were shown to be highly correlated, with correlations ∼0.9, between the full and truncated evaluations. Regression slope values of the marker-effect estimates from the full on the truncated evaluations were all close to their expected value, being ∼1.03. Calculated using random regression coefficients of the marker effect estimates, drastically different shapes of the genetic lactation curve were seen for 2 markers on chromosome 14 for the 4 test-day traits. The contribution of individual chromosomes to the total additive genetic variances seemed to follow the polygenic inheritance mode for protein yield and SCS. However, chromosome 14 was found to make an exceptionally large contribution to the total additive genetic variance for milk and fat yields because of markers near the major gene DGAT1. For the first lactation test-day traits, we obtained ∼0 correlations of chromosomal direct genomic values between any pair of the chromosomes; no spurious correlations were found in our analysis, thanks to the large reference population. For trait milk yield, chromosomal direct genomic values appeared to have a large variation in the between-lactation correlations among the chromosomes, especially between first and second or third lactations. The optimal features of the random regression test-day model and the single-step marker model allowed us to track the differences in the shapes of genetic lactation curves down to the individual markers. Furthermore, the single-step random regression test-day model enabled us to better understand the inheritance mode of the yield traits and SCS (e.g., variable chromosomal contributions to the total additive genetic variance and to the genetic correlations between lactations).

Updating test-day milk yield factors for use in genetic evaluations and dairy production systems: a comprehensive review.

Various methods have been proposed to estimate daily yield from partial yields, primarily to deal with unequal milking intervals. This paper offers an exhaustive review of daily milk yields, the foundation of lactation records. Seminal advancements in the late 20th century concentrated on two main adjustment metrics: additive additive correction factors (ACF) and multiplicative correction factors (MCF). An ACF model provides additive adjustments to two times AM or PM milk yield, which then becomes the estimated daily yields, whereas an MCF is a ratio of daily yield to the yield from a single milking. Recent studies highlight the potential of alternative approaches, such as exponential regression and other nonlinear models. Biologically, milk secretion rates are not linear throughout the entire milking interval, influenced by the internal mammary gland pressure. Consequently, nonlinear models are appealing for estimating daily milk yields as well. MCFs and ACFs are typically determined for discrete milking interval classes. Nonetheless, large discrete intervals can introduce systematic biases. A universal solution for deriving continuous correction factors has been proposed, ensuring reduced bias and enhanced daily milk yield estimation accuracy. When leveraging test-day milk yields for genetic evaluations in dairy cattle, two predominant statistical models are employed: lactation and test-day yield models. A lactation model capitalizes on the high heritability of total lactation yields, aligning closely with dairy producers' needs because the total amount of milk production in a lactation directly determines farm revenue. However, a lactation yield model without harnessing all test-day records may ignore vital data about the shapes of lactation curves needed for informed breeding decisions. In contrast, a test-day model emphasizes individual test-day data, accommodating various intervals and recording plans and allowing the estimation of environmental effects on specific test days. In the United States, the patenting of test-day models in 1993 used to restrict the use of test-day models to regional and unofficial evaluations by the patent holders. Estimated test-day milk yields have been used as if they were accurate depictions of actual milk yields, neglecting possible estimation errors. Its potential consequences on subsequent genetic evaluations have not been sufficiently addressed. Moving forward, there are still numerous questions and challenges in this domain.

Proposed methods for estimating loss of saleable milk in a cow-calf contact system with automatic milking.

Cow-calf contact (CCC) systems, although beneficial in many respects, introduce additional challenges to collect reliable data on milk production, which is important to assess individual cow efficiency and dairy farm profitability. Apart from weighing calves before and after each feeding, the amount of saleable milk lost due to calf suckling is practically impossible to measure. Here, we assess 2 indirect methods for estimating loss of saleable milk when housing cows and calves together in a robotic milking unit. In our study, treatment (CCC) cows and calves were kept together full time until the calves were 127 ± 6.6 d old (mean ± SD). Control cows were separated from their calves within 12 h of birth and then kept in the same unit as the treatment cows but with no access to either their own or treatment calves. Milk yield recording of both groups was performed from calving until pasture release at 233 ± 20 d in milk. The first estimation method relied on observed postseparation milk yield data, which were fed into a modified Wilmink regression model to determine the best-fitting lactation curve for the preseparation period. The second method was based on the cows' daily energy intake postseparation, calculated by measuring the daily feed intake and analyzing the energy content of the ration. The calculated energy intake was used to determine the average ratio between energy intake and the observed milk yield the following day for each individual cow, assuming constant rates of mobilization and deposition of body fat. The obtained ratio was then used to calculate the expected daily milk yield based on daily energy intake data during the preseparation period. In this paper, we analyzed data from 17 CCC cows kept together with their calves and 16 control cows; both groups calved from September to October 2020 and were followed up until release to pasture in May 2021. Saleable milk yield was lower in CCC cows than in control cows, both before and after separation. The 2 methods were used on data for control cows and showed milk yield loss using the lactation curve method (average of -3.4 ± 2.8 kg/d) and almost no loss using energy intake data (average of -1.4 ± 2.7 kg/d). Milk yield loss for CCC cows was estimated at average 11.3 ± 4.8 and 7.3 ± 6.6 kg milk/d, respectively. The proposed lactation curve estimation method tends to overestimate milk yield loss, whereas the method based on energy intake is more accurate. However, collecting detailed energy intake data per individual cow requires additional effort and equipment, which is not always feasible on commercial farms. Further research is needed to improve milk loss estimation and to better understand trade-offs in CCC systems.

Modelling Lactation Curves for Dairy Sheep in a New Zealand Flock.

Lactation curves were modelled for dairy sheep in a New Zealand flock, providing information on the lactation yields of milk, fat, protein, and lactose, corrected for 130 days of milking. From 169 ewes, a total of 622 test-day records were obtained during the milk production season of 2021-2022 (from October to January). The flock produced an average of 86.1 kg of milk, 5.1 kg of fat, 4.5 kg of protein, and 4.1 kg of lactose, and moderate to large coefficients of variation were observed (27-31%) for these traits. The lactation persistency of milk, fat, protein, and lactose yields ranged from 52.3 to 72.7%. Analyses of variance for total yield and persistency were performed with an animal model that included the fixed effects of age (parity number), litter size, coat colour, and milking frequency (days in twice-a-day milking) and random residuals. Age and milking frequency were the only factors that significantly affected the yields of milk, fat, protein, and lactose. Age significantly affected the lactation persistency of milk and lactose yields, whereas litter size affected the persistency of protein, and milking frequency affected the persistency of fat. This study on this single flock provides valuable experience for a larger-scale animal breeding programme in New Zealand.

An investigation of extracellular vesicles in bovine colostrum, first milk and milk over the lactation curve.

Extracellular vesicles (EVs) in milk have claimed benefits ranging from conveying immunological privilege to infants to being suitable as natural delivery vehicles for therapeutic drugs. However, a longitudinal study of bovine EVs quantities and characteristics in colostrum (COL), first milk (FM) and throughout the lactation curve of mature milk (MM) had never been performed and so was our aim. COL, FM and 9 months of MM samples were collected. Caseins -overlapping size with EVs- were removed. EVs were collected by density gradient ultracentrifugation and characterised by SDS-PAGE, Bradford assay, nanoparticle tracking analysis, immunoblotting, imaging flow cytometry analysis, and transmission electron microscopy. COL and FM had substantially more EVs than MM, with COL enriched in small EVs. No significant differences were observed between months 1-9 of MM. Altogether, although COL and FM are particularly rich sources of EVs, mature milk throughout the lactation curve is also an abundant source of intact EVs.

Genetic aspects of Wood's lactation curve parameters in Jersey crossbred cattle using Bayesian approach.

The study was undertaken to estimate the genetic parameters of lactation curve parameters of Wood's function in Jersey crossbred cattle using the Bayesian approach. Data on 33,906 fortnightly test day milk yields of 1,718 lactation records of Jersey crossbred cows, maintained at the ICAR-National Dairy Research Institute in West Bengal, were collected over a period of 40 years. The lactation curve parameters including 'a' (initial milk yield after calving), 'b' (ascending slope up to peak yield) and 'c' (descending slope after peak yield) and lactation curve traits, peak yield (ymax), time of peak yield (tmax) and persistency of milk yield (P) of individual cow for each lactation were estimated using the incomplete gamma function (Wood's model) by fitting the Gauss-Newton algorithm as an iteration method using PROC NLIN procedure of SAS 9.3. Variance components and genetic parameters of lactation curve parameters/traits were estimated by a repeatability animal model using the Bayesian approach. Estimates of heritabilities were found to be 0.18 ± 0.05, 0.09 ± 0.03 and 0.11 ± 0.04 for parameters 'a', 'b' and 'c', respectively and 0.24 ± 0.05, 0.12 ± 0.04, and 0.15 ± 0.05 for ymax, tmax and P, respectively. Repeatability estimates were 0.31 ± 0.03, 0.21 ± 0.04 and 0.30 ± 0.04 for parameters 'a', 'b' and 'c' respectively and 0.39 ± 0.03, 0.24 ± 0.03 and 0.37 ± 0.03 for ymax, tmax and p, respectively. Genetic correlations among lactation curve parameters/traits ranged from -0.75 to 0.95. Existence of genetic correlations among lactation curve parameters/traits indicated substantial genetic and physiological relationships among lactation curve parameters/traits of Jersey crossbred cattle.

Exploring milk loss and variability during environmental perturbations across lactation stages as resilience indicators in Holstein cattle.

Genetic selection for resilience is essential to improve the long-term sustainability of the dairy cattle industry, especially the ability of cows to maintain their level of production when exposed to environmental disturbances. Recording of daily milk yield provides an opportunity to develop resilience indicators based on milk losses and fluctuations in daily milk yield caused by environmental disturbances. In this context, our study aimed to explore milk loss traits and measures of variability in daily milk yield, including log-transformed standard deviation of milk deviations (Lnsd), lag-1 autocorrelation (Ra), and skewness of the deviations (Ske), as indicators of general resilience in dairy cows. The unperturbed dynamics of milk yield as well as milk loss were predicted using an iterative procedure of lactation curve modeling. Milk fluctuations were defined as a period of at least 10 successive days of negative deviations in which milk yield dropped at least once below 90% of the expected values. Genetic parameters of these indicators and their genetic correlation with economically important traits were estimated using single-trait and bivariate animal models and 8,935 lactations (after quality control) from 6,816 Chinese Holstein cows. In general, cows experienced an average of 3.73 environmental disturbances with a milk loss of 267 kg of milk per lactation. Each fluctuation lasted for 19.80 ± 11.46 days. Milk loss traits are heritable with heritability estimates ranging from 0.004 to 0.061. The heritabilities differed between Lnsd (0.135-0.250), Ra (0.008-0.058), and Ske (0.001-0.075), with the highest heritability estimate of 0.250 ± 0.020 for Lnsd when removing the first and last 10 days in milk in a lactation (Lnsd2). Based on moderate to high genetic correlations, lower Lnsd2 is associated with less milk losses, better reproductive performance, and lower disease incidence. These findings indicate that among the variables evaluated, Lnsd2 is the most promising indicator for breeding for improved resilience in Holstein cattle.

Neurophysiology of Milk Ejection and Prestimulation in Dairy Buffaloes.

The present review aims to integrate the anatomical characteristics of the mammary gland and the neurophysiology of milk ejection to understand the milking capacity of the water buffalo. Since one of the main uses of this species is milk production, this article will analyze the controversies on the use of oxytocin as a stimulant during milking as well as the existing alternatives that farmers apply to promote correct stimulation during milk letdown. According to the available literature, the efficiency of the milking process, the quality of the milk, and the health of the animals are elements that require the consideration of species-specific characteristics to enhance the performance of buffaloes. The incorporation of technological innovations and competitive strategies could contribute to a better understanding of water buffalo in the milk industry.

Optimal value for the exponential term of Wilmink's function according to current Holstein lactation curves in Japan.

We compared values of Wilmink's exponential term to describe the lactation curves of Holstein cows in Japan. Data were a total of 100,971,798 test-day records from the first through fifth parities during 1991 through 2018. The lactation curve model used fourth-order Legendre polynomials and Wilmink's exponential term. In total, 810 analyses were executed to compare six values (-0.02, -0.03, …, -0.07) for the exponential term to select the one that yielded the smallest root mean square error. For all parities, daily milk yield and lactation persistency increased consistently and peak lactation days occurred later from year to year. For the years evaluated, the optimal exponential term was -0.05 for first and second parities, -0.04 for third parity, and -0.03 for fourth and fifth parities. The change in the exponential parameter with increasing year was related to delays in peak lactation.

Herd level economic comparison between the shape of the lactation curve and 305 d milk production.

Herd milk production performance is generally evaluated using the herd's average 305-day milk production (HM305). Economic comparisons between herds are also often made using HM305. Comparing herds is thus based on summarized milk production, and not on the form of the lactation curves of the cows within the herd. Cow lactation curve characteristics can be aggregated on a calendar year basis to herd lactation curve characteristics (HLCC) (herd magnitude, herd time to peak yield and herd persistency). Thus far, no literature has evaluated whether the shape of the lactation curve (described by HLCC) is better able to explain the economic variation of herds than summarized milk production such as HM305 does. This study aims to determine whether HM305 or HLCC is better able to explain the variation in economic performance between herds. To do so, we evaluated 8 years of Dutch longitudinal data on milk production and the financial accounts of 1,664 herds. Cow lactation curve characteristics were calculated through lactation curve modeling and aggregated to HLCC on a calendar year basis for two parity groups (primiparous cows and multiparous cows). Using income over feed cost per cow (IOFC-cow) or per 100 kg milk (IOFC-milk) as the dependent variable separately, we developed four linear mixed models. Two models were used to analyse the association between herd economic performance and HLCC; the other two models were used to analyse the association between herd economic performance and HM305. A Cox test and J test were used to compare two non-nested models to investigate whether HM305 or HLCC better explain IOFC. The average IOFC-cow was €2,305 (SD = 408) per year, while the average IOFC-milk was €32.1 (SD = 4.6). Results showed that HLCC and HM305 explain the same amount of variance of IOFC-cow or IOFC-milk. IOFC-cow was associated with HM305 and HLCC (except herd time to peak yield for primiparous cows). Herd magnitude was most strongly associated with IOFC-cow, followed by herd persistency and herd time to peak yield of multiparous cows. IOFC-milk was not associated with HM305 or HLCC (except for a weak negative association with herd persistency for primiparous cows). IOFC-cow and IOFC-milk were driven most by time effects. In conclusion, HLCC and HM305 explain the same amount of variance in IOFC-cow or IOFC-milk. HLCC is more computationally expensive, while HM305 is more readily available.

Investigating the effect of temporal, geographic, and management factors on US Holstein lactation curve parameters.

We fit the Wood's lactation model to an extensive database of test-day milk production records of US Holstein cows to obtain lactation-specific parameter estimates and investigated the effects of temporal, spatial, and management factors on lactation curve parameters and 305-d milk yield. Our approach included 2 steps as follows: (1) individual animal-parity parameter estimation with nonlinear least-squares optimization of the Wood's lactation curve parameters, and (2) mixed-effects model analysis of 8,595,413 sets of parameter estimates from individual lactation curves. Further, we conducted an analysis that included all parities and a separate analysis for first lactation heifers. Results showed that parity had the most significant effect on the scale (parameter a), the rate of decay (parameter c), and the 305-d milk yield. The month of calving had the largest effect on the rate of increase (parameter b) for models fit with data from all lactations. The calving month had the most significant effect on all lactation curve parameters for first lactation models. However, age at first calving, year, and milking frequency accounted for a higher proportion of the variance than month for first lactation 305-d milk yield. All parameter estimates and 305-d milk yield increased as parity increased; parameter a and 305-d milk yield rose, and parameters b and c decreased as year and milking frequency increased. Calving month estimates parameters a, b, c, and 305-d milk yield were the lowest values for September, May, June, and July, respectively. The results also indicated the random effects of herd and cow improved model fit. Lactation curve parameter estimates from the mixed-model analysis of individual lactation curve fits describe well US Holstein lactation curves according to temporal, spatial, and management factors.

Comparison of models for lactation curves of Holstein, Brown Swiss, and F1 crossbred cows under subtropical conditions.

Tropical and subtropical milk production herds in Mexico generally generate different types of milk-yield records as milk yield per month and mean production per month. Lactation curves generated by these types of records may contribute to understand milk production in the tropical regions of Mexico. The aim of this study was to compare five lactation-curve models fitted to two types of milk-yield records of Holstein, Brown Swiss, and F1 crossbred cows under subtropical conditions. The two types of records (n = 3756) used were: (1) milk yield per month (TR) and 2) mean production per months (MR). Goodness-of-fit statistics, including Akaike's information criterion (AIC) and root mean square error (RMSE), were applied to compare the models for each type of records. The Brody model provided the best goodness-of-fit when using monthly milk-yield records, while the Wilmink model provided the best goodness-of-fit for lactation milk-yield records. The RMSE and AIC values were similar between datasets. The final third of the lactation curve showed a little difference between model predictions in both datasets. The comparison of several models was useful to better describe the actual lactation curves of the herd. The Wood model may be adequate to compare information as a reference with other models for decision making process at milk production.

Genetic parameters of milk and lactation curve traits of dairy cattle from research farms in Thailand.

OBJECTIVE: This study was aimed to estimate the genetic parameters, including genetic and phenotypic correlations, of milk yield, lactation curve traits and milk composition of Thai dairy cattle from three government research farms. METHODS: The data of 25,789 test-day milk yield and milk composition records of 1,468 cattle from lactation 1 to 3 of Holstein Friesian (HF) and crossbred HF dairy cattle calved between 1990 and 2015 from three government research farms in Thailand were analysed. 305-day milk yield was estimated by the Wood model and a test interval method. The Wood model was used for estimating cumulative 305-day milk yield, peak milk yield, days to peak milk yield and persistency. Genetic parameters were estimated using linear mixed models with herd, breed group, year and season of calving as fixed effects, and animals linked to a pedigree as random effects, together with a residual error. Univariate models were used to estimate variance components, heritability, estimated breeding values (EBVs) and repeatability of each trait, while pairwise bivariate models were used to estimate covariance components and correlations between traits in the same lactation and in the same trait across lactations. RESULTS: The heritability of 305-day milk yield, peak milk yield and protein percentage have moderate to high estimates ranging from 0.19 to 0.45 while days to peak milk yield, persistency and fat percentage have low heritability ranging from 0.08 to 0.14 in lactation 1 cows. Further, heritability of most traits considered was higher in lactation 1 compared with lactations 2 and 3. For cows in lactation 1, high genetic correlations were found between 305-day milk yield and peak milk yield (0.86±0.07) and days to peak milk yield and persistency (0.99±0.02) while estimates of genetic correlations between the remaining traits were imprecise due to the high standard errors. The genetic correlations within the traits across lactation were high. There was no consistent trend of EBVs for most traits in the first lactation over the study period. CONCLUSION: Both the Wood model and test interval method can be used for milk yield estimates in these herds. However, the Wood model has advantages over the test interval method as it can be fitted using fewer test-day records and the estimated model parameters can be used to derive estimates of other lactation curve parameters. Milk yield, peak milk yield and protein percentage can be improved by a selection and mating program while days to peak milk yield, persistency and fat percentage can be improved by including into a selection index.

Analysis of Non-Genetic Factors Affecting Wood's Model of Daily Milk Fat Percentage of Holstein Cattle.

This research paper aimed to explore the characteristics of Holstein cattle's milk fat percentage lactation curve and its influencing factors. The Wood model was used for fitting the lactation curve of 398,449 DHI test-day milk fat percentage records of Holstein cows from 2018 to 2020 in 12 dairy farms in Jiangsu province, and the influencing factors­including farm size, parity, calving season, calving interval, and 305-days milk production­on the parameters of the lactation curve were analyzed. The results showed that the non-genetic factors such as dairy farm size, calving season, parity, calving interval, and 305-days milk yield have a significant impact on milk fat percentage (p < 0.01); the average R2 of the daily milk fat percentage curve was 0.9699; the lowest milk fat percentage was 3.54%; the time to reach the lowest milk fat percentage was 126 days; and the persistence of milk fat percentage was 3.59%. All of these factors explored in this study fit at different levels above 0.96. The Wood model performed well in the fitting and analysis of the milk fat percentage curve of Holstein cattle in Jiangsu Province. This study provides a reference for improving the milk fat percentage of Holstein cattle.