Analysis of lactation shapes in extended lactations

Reference limits for blood gas analysis performed from coccygeal vessels of multiparous Holstein dairy cows: Effects of stage of lactation and season of sampling

Blood gas analysis is a great support to the diagnostic process of critically ill patients. Its correct application to the medicine of dairy cows depends on the availability of specific reference intervals that are still difficult to find in the literature. They may vary according to the type of blood sampled, animals' age and production stage, and climatic conditions. This study aimed at calculating the reference limits for some blood gas parameters in the blood collected from the coccygeal vessels of multiparous Holstein dairy cows. This site of sampling implies the risk of withdrawing blood of unknown origin (venous, arterial, or mixed), but has a high practical interest for the easy and quick performance and the minimal animal restraint required. Data from 379 cows were used, and reference limits were produced for pH, partial pressure of carbon dioxide (pCO2), bicarbonate concentration (HCO3), total carbon dioxide concentration (tCO2), oxygen saturation (sO2), hemoglobin (Hb), hematocrit (Hct), base excess (BE), glucose, Na, K, and ionized calcium (iCa). The effects of stage of lactation (5 to 60 vs. > 60 DIM) and season of sampling (cold vs. hot) were investigated, and specific reference limits were produced for each variable and each level of the factors whenever a significant effect was detected. The pH, sO2, K, and iCa were not influenced by season or stage of lactation. All the other blood gas parameters were significantly affected by season of sampling, and Hb, Hct, glucose, and Na were also affected by stage of lactation. Reference limits provided in this study are specific to the site of sampling (coccygeal vessels) and the animal category considered. Further studies are needed to produce reference intervals for other blood gas parameters, cow categories, and blood types.

Modeling daily yields of milk, fat, protein, and lactose of New Zealand dairy goats undergoing standard and extended lactations

This study aimed to assess the milk production data for New Zealand dairy goats in either a standard lactation (SL; ≤305 d in milk [DIM]) or extended lactation (EL; >305 and ≤670 DIM) using a random regression (RR) with third- and fifth-order Legendre polynomials, respectively. Persistency of EL was defined as (B/A) × 100, where A was the accumulated yield from d 1 to 305, and B was the accumulated yield from d 366 to 670. On average, goats in SL produced 1,183 kg of milk, 37 kg of fat, 37 kg of protein, and 54 kg of lactose. The average production of milk, fat, protein, and lactose in EL were 2,473 kg, 78 kg, 79 kg, and 112 kg, respectively. The average persistences for milk, fat, protein, and lactose yields during EL were 98%, 98%, 102%, and 96%, respectively. The relative prediction errors were close to 10% and the concordance correlation coefficients >0.92, indicating that the RR model with Legendre polynomials is adequate for modeling lactation curves for both SL and EL. Total yields and persistency were analyzed with a mixed model that included the fixed effects (year, month of kidding, parity, and proportion of Saanen) as covariates and the random effects of animal and residual errors. Effects of year, month of kidding, and parity were significant on the total yields of milk, fat, protein, and lactose for both SL and EL. The total milk yield of first-parity goats with SL was 946 kg and the total milk yield of second-parity goats with SL was 1,284 kg, making a total of 2,230 kg over 2 years. The total milk yield of a first-parity goat with EL was 2,140 kg. Thus, on average, a goat with SL for the first and second parity produced 90 kg more milk than a first-parity goat subjected to EL. However, a second-parity goat subjected to EL produced 43 kg more milk (2,639 kg) than a goat with SL following the second and third parity (1,284 kg + 1,312 kg). These data, along with the various other benefits of EL (e.g., fewer offspring born and reduced risk of mastitis, lameness, and metabolic problems in early lactation), indicate that EL as a management strategy holds the potential to improve dairy goat longevity and lifetime efficiency without compromising milk production.

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.

The effect of extended lactation on parameters of Wood's model of lactation curve in dairy Simmental cows

Objective

This study was focused on the estimation of parameters of Wood’s model and description of the lactation curve using the cows which were lactated over 24 months on the first lactation.

Methods

The database included 1,333 pure-bred dairy Simmental primiparous cows which lactated for 24 months (732 days). The initial dataset entering the procedure of assessment of parameters of Wood’s function included 35,826 milk yield records. Milk yield was recorded throughout lactation, with the earliest record taken on day 6 and the latest on day 1,348 of lactation. This dataset was used for the assessment of parameters a, b, c of Wood’s model using the non-linear statistical procedure. These parameters were estimated for different length of lactation. The assessed parameters were used for calculation of some characteristics of lactation curves.

Results

The lowest value of a parameter (15.2317) of Wood’s model of lactation curve was found out in lactations up to 305 days long, contrary to b and c parameters which were highest in those lactations (0.1029 and 0.0015, respectively). The maximum value of a parameter (17.4329) was found out in lactations up to 640 days long, unlike b and c parameters which were minimal in those lactations (0.0603 and 0.0010, respectively).

Conclusion

It can be concluded that the parameters of Wood’s model and the shape of lactation curve are changing with the growing number of milk yield records. Also, the assessed parameters revealed a significant milk production potential after 305 days of lactation.

Effect of mastitis on lactation curves in purebred Jersey cows

Mastitis is a most frequently occurring disease in dairy cattle which causes severe losses in milk production. In our study, we had collected 9960 weekly test day milk yield (WTDMY) records over a period of five years (2010– 2015) of 130 purebred Jersey cows reared at Central Cattle Breeding Farm, Sunabeda, Odisha under Ministry of Agriculture, Government of India. To study the lactation pattern of above milk data, we used six different lactation curve models, viz. Wilmink (WK), Wood (WD), Brody (BRD), Morant and Gnanasakthy (MG), Mitscherlich × Exponential (ME) and Ali and Schaeffer (AS). It was observed that in healthy and cows affected with mastitis, Ali and Schaeffer (AS) model showed best fit giving highest value of adjusted coefficient of determination (R2 adj.= 0.963) and lowest value of root mean square of error (0.303), Akaike’s information criterion (–97.887) and Schwartz Bayesian Information Criterion (–89.081). Testing of residuals was carried out by several tests, viz. the Shapiro- Wilk’s test, the run test and the Durbin-Watson (DW). Summary measures revealed that the loss of milk production due to mastitis with respect to healthy cows was 4.43%. Lactation persistency was estimated by ratio method and Mahadevan method. Higher persistency was observed in healthy cows.

Comparison of non-linear models to describe the lactation curves for milk yield and composition in buffaloes (Bubalus bubalis)

In order to describe the lactation curves of milk yield (MY) and composition in buffaloes, seven non-linear mathematical equations (Wood, Dhanoa, Sikka, Nelder, Brody, Dijkstra and Rook) were used. Data were 116,117 test-day records for MY, fat (FP) and protein (PP) percentages of milk from the first three lactations of buffaloes which were collected from 893 herds in the period from 1992 to 2012 by the Animal Breeding Center of Iran. Each model was fitted to monthly production records of dairy buffaloes using the NLIN and MODEL procedures in SAS and the parameters were estimated. The models were tested for goodness of fit using adjusted coefficient of determination (Radj(2)), root means square error (RMSE), Durbin-Watson statistic and Akaike's information criterion (AIC). The Dijkstra model provided the best fit of MY and PP of milk for the first three parities of buffaloes due to the lower values of RMSE and AIC than other models. For the first-parity buffaloes, Sikka and Brody models provided the best fit of FP, but for the second- and third-parity buffaloes, Sikka model and Brody equation provided the best fit of lactation curve for FP, respectively. The results of this study showed that the Wood and Dhanoa equations were able to estimate the time to the peak MY more accurately than the other equations. In addition, Nelder and Dijkstra equations were able to estimate the peak time at second and third parities more accurately than other equations, respectively. Brody function provided more accurate predictions of peak MY over the first three parities of buffaloes. There was generally a positive relationship between 305-day MY and persistency measures and also between peak yield and 305-day MY, calculated by different models, within each lactation in the current study. Overall, evaluation of the different equations used in the current study indicated the potential of the non-linear models for fitting monthly productive records of buffaloes.

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

Six classical growth functions (monomolecular, Schumacher, Gompertz, logistic, Richards, and Morgan) were fitted to individual and average (by parity) cumulative milk production curves of Canadian Holstein dairy cows. The data analyzed consisted of approximately 91,000 daily milk yield records corresponding to 122 first, 99 second, and 92 third parity individual lactation curves. The functions were fitted using nonlinear regression procedures, and their performance was assessed using goodness-of-fit statistics (coefficient of determination, residual mean squares, Akaike information criterion, and the correlation and concordance coefficients between observed and adjusted milk yields at several days in milk). Overall, all the growth functions evaluated showed an acceptable fit to the cumulative milk production curves, with the Richards equation ranking first (smallest Akaike information criterion) followed by the Morgan equation. Differences among the functions in their goodness-of-fit were enlarged when fitted to average curves by parity, where the sigmoidal functions with a variable point of inflection (Richards and Morgan) outperformed the other 4 equations. All the functions provided satisfactory predictions of milk yield (calculated from the first derivative of the functions) at different lactation stages, from early to late lactation. The Richards and Morgan equations provided the most accurate estimates of peak yield and total milk production per 305-d lactation, whereas the least accurate estimates were obtained with the logistic equation. In conclusion, classical growth functions (especially sigmoidal functions with a variable point of inflection) proved to be feasible alternatives to fit cumulative milk production curves of dairy cows, resulting in suitable statistical performance and accurate estimates of lactation traits.

Quantitative analysis of porcine reproductive and respiratory syndrome (PRRS) viremia profiles from experimental infection: a statistical modelling approach

Porcine reproductive and respiratory syndrome (PRRS) is one of the most economically significant viral diseases facing the global swine industry. Viremia profiles of PRRS virus challenged pigs reflect the severity and progression of infection within the host and provide crucial information for subsequent control measures. In this study we analyse the largest longitudinal PRRS viremia dataset from an in-vivo experiment. The primary objective was to provide a suitable mathematical description of all viremia profiles with biologically meaningful parameters for quantitative analysis of profile characteristics. The Wood's function, a gamma-type function, and a biphasic extended Wood's function were fit to the individual profiles using Bayesian inference with a likelihood framework. Using maximum likelihood inference and numerous fit criteria, we established that the broad spectrum of viremia trends could be adequately represented by either uni- or biphasic Wood's functions. Three viremic categories emerged: cleared (uni-modal and below detection within 42 days post infection(dpi)), persistent (transient experimental persistence over 42 dpi) and rebound (biphasic within 42 dpi). The convenient biological interpretation of the model parameters estimates, allowed us not only to quantify inter-host variation, but also to establish common viremia curve characteristics and their predictability. Statistical analysis of the profile characteristics revealed that persistent profiles were distinguishable already within the first 21 dpi, whereas it is not possible to predict the onset of viremia rebound. Analysis of the neutralizing antibody(nAb) data indicated that there was a ubiquitous strong response to the homologous PRRSV challenge, but high variability in the range of cross-protection of the nAbs. Persistent pigs were found to have a significantly higher nAb cross-protectivity than pigs that either cleared viremia or experienced rebound within 42 dpi. Our study provides novel insights into the nature and degree of variation of hosts' responses to infection as well as new informative traits for subsequent genomic and modelling studies.