Modeling extended lactation curves of dairy cattle: a biological basis for the multiphasic approach

Fitting mathematical functions to extended lactation curves and forecasting late-lactation milk yields of dairy cows

A 305-d lactation followed by a 60-d dry period has traditionally been considered economically optimal, yet dairy cows in modern intensive dairy systems are frequently dried off while still producing significant quantities of milk. Managing cows for an extended lactation has reported production, welfare, and economic benefits, but not all cows are suitable for an extended lactation. Implementation of an extended lactation strategy on-farm could benefit from use of a decision support system, based on a mathematical lactation model, that can identify suitable cows during early lactation that have a high likelihood of producing above a target milk yield (MY) at 305 d in milk (DIM). Therefore, our objectives were (1) to compare the suitability of 3 commonly used lactation models for modeling extended lactations (Dijkstra, Wood, and Wilmink) in primiparous and multiparous cows under a variety of lactation lengths, and (2) to determine the amount of early-lactation daily MY data needed to accurately forecast MY at d 305 by using the most suitable model and determine whether this is sufficient for identifying cows suitable for an extended lactation before the end of a typical voluntary waiting period (50-90 d). Daily MY data from 467 individual Holstein-Friesian lactations (DIM >305 d; 379 ± 65-d lactation length [mean ± SD]) were fitted by the 3 lactation models using a nonlinear regression procedure. The parameter estimates of these models, lactation characteristics (peak yield, time to peak yield, and persistency), and goodness-of-fit were compared between parity and different lactation lengths. The models had similar performance, and differences between parity groups were consistent with previous literature. Then, data from only the first i DIM for each individual lactation, where i was incremented by 30 d from 30 to 150 DIM and by 50 d from 150 to 300 DIM, were fitted by each model to forecast MY at d 305. The Dijkstra model was selected for further analysis, as it had superior goodness-of-fit statistics for i= 30 and 60. The data set was fit twice by the Dijkstra model, with parameter bounds either unconstrained or constrained. The quality of predictions of MY at d 305 improved with increasing data availability for both models and assisting the model fitting procedure with more biologically relevant constraints on parameters improved the predictions, but neither was reliable enough for practical use on-farm due to the high uncertainty of forecasted predictions. Using 90 d of data, the constrained model correctly classified 66% of lactations as being above or below a target MY at d 305 of 25 kg/d, with a probability threshold of 0.95. The proportion of correct classifications became smaller at lower targets of MY at d 305 and became greater when using more lactation days. Overall, further work is required to develop a model that can forecast late-lactation MY with sufficient accuracy for practical use. We envisage that a hybridized machine learning and mechanistic model that incorporates additional historical and genetic information with early-lactation MY could produce meaningful lactation curve forecasts.

Comparison and estimation of different linear and nonlinear lactation curve submodels in random regression analyses on dairy cattle

In the random regression model (RRM) for milk yield, by replacing empirical lactation curves with the five-order Legendre polynomial to fit fixed groups, the RRM can be transformed to a hierarchical model that consisted of a RRM in the first hierarchy with Legendre polynomials as individuals’ lactation curves resolved by restricted maximum likelihood (REML) software, and a multivariate animal model for phenotypic regression coefficients in the second hierarchy resolved by DMU software. Some empirical lactation functions can be embedded into the RRM at the first hierarchy to well fit phenotypic lactation curve of the average observations across all animals. The functional relationship between each parameter and time can be described by a Legendre polynomial or an empirical curve usually called submodel, and according to three commonly used criteria, the optimal submodels were picked from linear and nonlinear submodels except for polynomials. The so-called hierarchical estimation for the RRMs in dairy cattle indicated that more biologically meaningful models were available to fit the lactation curves; moreover, with the same number of parameters, the empirical lactation curves (MIL1, MIL5, and MK1 for 3, 4, and 5 parameters, respectively) performed higher goodness of fit than Legendre polynomial when modelling individuals’ phenotypic lactation curves.

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.

Associations between feed efficiency and aspects of lactation curves in primiparous Holstein dairy cattle

Genetic selection for improved feed efficiency in dairy cattle has received renewed attention over the last decade to address the needs of a growing global population. As milk yield is a critical component of feed efficiency metrics in dairy animals, our objective was to evaluate the associations between feed efficiency in primiparous Holstein cattle and parameters of a mathematical model describing individual lactation curves. The Dijkstra lactation curve model was fit to individual lactation records from 34 Holstein heifers with previously estimated measures of feed efficiency. We found that the optimal fit of the Dijkstra model was achieved using daily milk yield records up to 21 d in milk to capture the rise to peak milk yield and using monthly dairy herd improvement records for the remainder of lactation to accurately characterize lactation persistency. In the period of lactation before peak milk yield, improved feed efficiency was associated with a faster increase in daily milk yield over a shorter period of time at the expense of increased mobilization of body reserves; this serves to reinforce the concept that dairy cattle are primarily capital breeders versus income breeders. Feed efficiency in the period following peak lactation, as measured by gross feed efficiency, return over feed costs, and net energy efficiency of lactation, was positively associated with higher peak milk yield. The findings in early lactation suggest that estimates of feed efficiency could be improved by evaluating feed efficiency relative to conception, rather than parturition and lactation, to better account for the energy stored and released from body reserves in capital breeding.

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.

Effects of micronutrient supplementation on performance and epigenetic status in dairy cows

The postpartum period is crucial in dairy cows and is marked by major physiological and metabolic changes that affect milk production, immune response and fertility. Nutrition remains the most important lever for limiting the negative energy balance and its consequences on general health status in highly selected dairy cows. In order to analyze the effect of a commercial micronutrient on intrinsic parameters, performances and the epigenome of dairy cows, 2 groups of 12 Holstein cows were used: 1 fed a standard diet (mainly composed of corn silage, soybean meal and non-mineral supplement) and the other 1 fed the same diet supplemented with the commercial micronutrient (µ-nutrient supplementation) for 4 weeks before calving and 8 weeks thereafter. Milk production and composition, BW, body condition score (BCS), DM intake (DMI) and health (calving score, metritis and mastitis) were recorded over the study period. Milk samples were collected on D15 and D60 post-calving for analyses of casein, Na+ and K+ contents and metalloprotease activity. Milk leukocytes and milk mammary epithelial cells (mMECs) were purified and counted. The viability of mMECs was assessed, together with their activity, through an analysis of gene expression. At the same time points, peripheral blood mononuclear cells (PBMCs) were purified and counted. Using genomic DNA extracted from PBMCs, mMECs and milk leukocytes, we assessed global DNA methylation (Me-CCGG) to evaluate the epigenetic imprinting associated with the µ-nutrient-supplemented diet. The µ-nutrient supplementation increased BCS and BW without modifying DMI or milk yield and composition. It also improved calving condition, reducing the time interval between calving and first service. Each easily collectable cell type displayed a specific pattern of Me-CCGG with only subtle changes associated with lactation stages in PBMCs. In conclusion, the response to the µ-nutrient supplementation improved the body condition without alteration of global epigenetic status in dairy cows.

Genome-wide association studies for genetic effects that change during lactation in dairy cattle

Genetic effects on milk production traits in dairy cattle might change during lactation. However, most genome-wide association studies (GWAS) for milk production traits assume that genetic effects are constant during lactation. This assumption might lead to missing these quantitative trait loci (QTL) whose effects change during lactation. This study aimed to screen the whole genome specifically for QTL whose effects change during lactation. For this purpose, 4 different GWAS approaches were performed using test-day milk protein content records: (1) separate GWAS for specific lactation stages, (2) GWAS for estimated Wilmink lactation curve parameters, (3) a GWAS using a repeatability model where SNP effects are assumed constant during lactation, and (4) a GWAS for genotype by lactation stage interaction using a repeatability model and accounting for changing genetic effects during lactation. Separate GWAS for specific lactation stages suggested that the detection power greatly differs between lactation stages and that genetic effects of some QTL change during lactation. The GWAS for estimated Wilmink lactation curve parameters detected many chromosomal regions for Wilmink parameter a (protein content level), whereas 2 regions for Wilmink parameter b (decrease in protein content toward nadir) and no regions for Wilmink parameter c (increase in protein content after nadir) were detected. Twenty chromosomal regions were detected with effects on milk protein content; however, there was no evidence that their effects changed during lactation. For 5 chromosomal regions located on chromosomes 3, 9, 10, 14, and 27, significant evidence was observed for a genotype by lactation stage interaction and thus their effects on milk protein content changed during lactation. Three of these 5 regions were only identified using a GWAS for genotype by lactation stage interaction. Our study demonstrated that GWAS for genotype by lactation stage interaction offers new possibilities to identify QTL involved in milk protein content. The performed approaches can be applied to other milk production traits. Identification of QTL whose genetic effects change during lactation will help elucidate the genetic and biological background of milk production.

Extended lactation in high-yielding dairy cows. I. Effects on reproductive measurements

The objective of this prospective field study was to evaluate the effects of extending the lactation period on various reproductive measurements of high-yielding Holstein cows. On 40 d in milk (DIM), cows were gynecologically examined (transrectal palpation, sonography, vaginoscopy). Cows without signs of clinical endometritis were blocked by parity and were randomly allocated to 1 of 3 experimental groups with a voluntary waiting period (VWP) of 40, 120, and 180 d, respectively (G40, n = 135; G120, n = 141; G180, n = 139). Cows of G120 and G180 were reexamined at the end of the VWP. If natural estrus was detected within 46 d after the end of the VWP, an artificial insemination was performed. If no estrus was detected, the respective cows were synchronized by applying the classical Ovsynch protocol. We found no difference in the proportion of cows in which estrus was detected between 40 to 86 DIM or in the days to first estrus between the 3 groups. Estrus detection in this period was lower in cows with body condition score <3 on 90 DIM compared with body condition score ≥3 (61.5 vs. 76.0%) and in cows with high energy-corrected milk production (ECM) on 92 DIM [58.6 vs. 70.1%, for cows with higher and lower than the median (39.9 kg) ECM, respectively]. The proportion of cows that estrus was detected within 46 d after the VWP was greater in G120 (88.9%) and G180 (90.8%) compared with G40 (70.4%). These effects were more apparent in cows with high ECM. The rate of estrus detection and of becoming pregnant in this period was greater for G120 (hazard ratio = 2.2 and 1.6, respectively) and for G180 (hazard ratio = 2.4 and 1.8) compared with G40. Cows in both groups with extended lactation had greater overall first service conception rates (G120 = 48.9%; G180 = 49.6%) and a lower number of services per pregnant cow (G120 = 1.56 ± 0.1; G180 = 1.51 ± 0.1) compared with G40 (36.6%; 1.77 ± 0.1). We observed no difference in pregnancy loss or in the proportion of cows culled up to 305 d of lactation between the 3 groups. The number of Ovsynch protocols per 1,000,000 kg of ECM was reduced by 75% in G180 and by 74% in G120 compared with G40 (5.9 vs. 7.1 vs. 25.1). In conclusion, extending the lactation of dairy cows can improve main reproductive measurements in high-yielding cows.

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.

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.

Fitting milk production curves through nonlinear mixed models

The aim of this work was to fit and compare three non-linear models (Wood, Milkbot and diphasic) to model lactation curves from two approaches: with and without cow random effect. Knowing the behaviour of lactation curves is critical for decision-making in a dairy farm. Knowledge of the model of milk production progress along each lactation is necessary not only at the mean population level (dairy farm), but also at individual level (cow-lactation). The fits were made in a group of high production and reproduction dairy farms; in first and third lactations in cool seasons. A total of 2167 complete lactations were involved, of which 984 were first-lactations and the remaining ones, third lactations (19 382 milk yield tests). PROC NLMIXED in SAS was used to make the fits and estimate the model parameters. The diphasic model resulted to be computationally complex and barely practical. Regarding the classical Wood and MilkBot models, although the information criteria suggest the selection of MilkBot, the differences in the estimation of production indicators did not show a significant improvement. The Wood model was found to be a good option for fitting the expected value of lactation curves. Furthermore, the three models fitted better when the subject (cow) random effect was considered, which is related to magnitude of production. The random effect improved the predictive potential of the models, but it did not have a significant effect on the production indicators derived from the lactation curves, such as milk yield and days in milk to peak.

A review of the genetic and non-genetic factors affecting extended lactation in pasture-based dairy systems

Milk production per cow has significantly increased over the last 50 years due to the strong genetic selection for increased milk production; associated with this increased production has been a decline in reproductive performance. As a result, superior-yielding cows that have failed to get into calf in a traditional 12-month calving system may be carried over and milked continuously for another 6 months instead of being culled. Studies indicate that cows are able to achieve lactations greater than 305 days and up to 670 days under pasture-based systems, with and without the use of supplementary feeds. Extended lactations of 16 months are most common and economically viable in Australian dairy systems. These findings indicate a potential role for extended lactation in countries such as Australia, where pasture-based dairy systems in which Holstein-Friesian dairy cows predominate. However, variation between cows in their milk yield profiles and the ability of cows to reach a planned dry-off date over an extended lactation occurs depending on the cow’s genetic strain, nutrition and environmental interactions, with certain strains of cow being better suited to extended lactation than others. The focus of this review is to examine the scope for genetic improvement as well as important considerations (non-genetic factors) when selecting suitable animals for extended lactation in pasture-based dairy systems, with an emphasis on Australian systems. These considerations include the impacts of cow strain, nutrition, milk production, and biological and economical costs associated with extended lactation. Methods for modelling extended lactation and estimating genetic parameters of lactation persistency, milk yield and component traits under extended lactation will be addressed and future directions for further research suggested.

Comparative 2D-DIGE proteomic analysis of bovine mammary epithelial cells during lactation reveals protein signatures for lactation persistency and milk yield

Mammary gland is made up of a branching network of ducts that end with alveoli which surrounds the lumen. These alveolar mammary epithelial cells (MEC) reflect the milk producing ability of farm animals. In this study, we have used 2D-DIGE and mass spectrometry to identify the protein changes in MEC during immediate early, peak and late stages of lactation and also compared differentially expressed proteins in MEC isolated from milk of high and low milk producing cows. We have identified 41 differentially expressed proteins during lactation stages and 22 proteins in high and low milk yielding cows. Bioinformatics analysis showed that a majority of the differentially expressed proteins are associated in metabolic process, catalytic and binding activity. The differentially expressed proteins were mapped to the available biological pathways and networks involved in lactation. The proteins up-regulated during late stage of lactation are associated with NF-κB stress induced signaling pathways and whereas Akt, PI3K and p38/MAPK signaling pathways are associated with high milk production mediated through insulin hormone signaling.

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.

Brain growth of the domestic pig (Sus scrofa) from 2 to 24 weeks of age: a longitudinal MRI study

An animal model with brain growth similar to humans, that can be used in MRI studies to investigate brain development, would be valuable. Our laboratory has developed and validated MRI methods for regional brain volume quantification in the neonatal piglet. The aim of this study was to utilize the MRI-based volume quantification technique in a longitudinal study to determine brain growth in domestic pigs from 2 to 24 weeks of age. MRI data were acquired from pigs 2-24 weeks of age using a 3-dimensional magnetization-prepared gradient echo sequence on a Magnetom Trio 3-tesla imager. Manual segmentation was performed for volume estimates of total brain, cortical, diencephalon, brainstem, cerebellar and hippocampal regions. Logistic modeling procedures were used to characterize brain growth. Total brain volume increased 130% (±12%) and 121% (±7%) from 2 to 24 weeks in males and females, respectively. The maximum increase in total brain volume occurred about the age of 4 weeks and 95% of whole brain growth occurred by the age of 21-23 weeks. Logistical modeling suggests there are sexually dimorphic effects on brain growth. For example, in females, the cortex was smaller (p = 0.04). Furthermore, the maximum growth of the hippocampus occurred about 5 weeks earlier in females than males, and the window for hippocampal growth was significantly shorter in females than males (p = 0.02, p = 0.002 respectively). These sexual dimorphisms are similar to what is seen in humans. In addition to providing important data on brain growth for pigs, this study shows pigs can be used to obtain longitudinal MRI data. The large increase in brain volume in the postnatal period is similar to that of human neonates and suggests pigs can be used to investigate brain development.

Analysis of lactation shapes in extended lactations

In order to describe the temporal evolution of milk yield (MY) and composition in extended lactations, 21 658 lactations of Italian Holstein cows were analyzed. Six empirical mathematical models currently used to fit 305 standard lactations (Wood, Wilmink, Legendre, Ali and Schaeffer, quadratic and cubic splines) and one function developed specifically for extended lactations (a modification of the Dijkstra model) were tested to identify a suitable function for describing patterns until 1000 days in milk (DIM). Comparison was performed on individual patterns and on average curves grouped according to parity (primiparous and multiparous) and lactation length (standard ≤305 days, and extended from 600 to 1000 days). For average patterns, polynomial models showed better fitting performances when compared with the three or four parameters models. However, LEG and spline regression, showed poor prediction ability at the extremes of the lactation trajectory. The Ali and Schaeffer polynomial and Dijkstra function were effective in modelling average curves for MY and protein percentage, whereas a reduced fitting ability was observed for fat percentage and somatic cell score. When individual patterns were fitted, polynomial models outperformed nonlinear functions. No detectable differences were observed between standard and extended patterns in the initial phase of lactation, with similar values of peak production and time at peak. A considerable difference in persistency was observed between 200 and 305 DIM. Such a difference resulted in an estimated difference between standard and extended cycle of about 7 and 9 kg/day for daily yield at 305 DIM and of 463 and 677 kg of cumulated milk production at 305 DIM for the first- and second-parity groups, respectively. For first and later lactation animals, peak yield estimates were nearly 31 and 38 kg, respectively, and occurred at around 65 and 40 days. The asymptotic level of production was around 9 kg for multiparous cows, whereas the estimate was negative for first parity.

Mapping quantitative trait loci (QTL) in sheep. IV. Analysis of lactation persistency and extended lactation traits in sheep

Background

In sheep dairy production, total lactation performance, and length of lactation of lactation are of economic significance. A more persistent lactation has been associated with improved udder health. An extended lactation is defined by a longer period of milkability. This study is the first investigation to examine the presence of quantitative trait loci (QTL) for extended lactation and lactation persistency in sheep.

Methods

An (Awassi × Merino) × Merino single-sire backcross family with 172 ewes was used to map QTL for lactation persistency and extended lactation traits on a framework map of 189 loci across all autosomes. The Wood model was fitted to data from multiple lactations to estimate parameters of ovine lactation curves, and these estimates were used to derive measures of lactation persistency and extended lactation traits of milk, protein, fat, lactose, useful yield, and somatic cell score. These derived traits were subjected to QTL analyses using maximum likelihood estimation and regression analysis.

Results

Overall, one highly significant (LOD > 3.0), four significant (2.0 < LOD < 3.0) and five suggestive (1.7 < LOD < 2.0) QTL were detected across all traits in common by both mapping methods. One additional suggestive QTL was identified using maximum likelihood estimation, and four suggestive (0.01 < P < 0.05) and two significant (P < 0.01) QTL using the regression approach only. All detected QTL had effect sizes in the range of 0.48 to 0.64 SD, corresponding to QTL heritabilities of 3.1 to 8.9%. The comparison of the detected QTL with results in cattle showed conserved linkage regions. Most of the QTL identified for lactation persistency and extended lactation did not coincide. This suggests that persistency and extended lactation for the same as well as different milk yield and component traits are not controlled by the same genes.

Conclusion

This study identified ten novel QTL for lactation persistency and extended lactation in sheep, but results suggest that lactation persistency and extended lactation do not have a major gene in common. These results provide a basis for further validation in extended families and other breeds as well as targeting regions for genome-wide association mapping using high-density SNP arrays.

Relationship between the milk yield response to short-term bovine somatotropin treatment and the lipolytic response to adrenaline in dairy cows

The aim of this experiment was to determine if the milk yield response of dairy cows to short-term treatment with bovine somatotropin (bST) was correlated with the non-esterified fatty-acid (NEFA) response to an adrenaline challenge. Twenty-six multiparous Holstein cows (58+/-5.4 days postpartum) received daily sub-cutaneous injections of saline for 7 days followed by sub-cutaneous injections of 20mg/day of bST for 14 days. On day 7 of the saline treatment and day 14 of the bST treatment the cows were given an intravenous injection of adrenaline (1.4 microg/kg body weight). Blood samples were taken before and after the adrenaline challenge. The difference in milk yield between the saline and the second week of bST treatment (MYR) varied considerably between animals (from -0.4 to +8.0 kg/day). MYR was positively correlated with the change in the basal concentration of NEFA between the saline and second week of bST treatment, as well as with the change in the area under the profile of NEFA above basal values following the adrenaline challenge. It remains to be established whether the greater lipolytic responses to adrenaline of the cows with the greater MYR reflects the deeper negative energy that these animals also experienced or a fundamental difference in the physiology of their adipose tissue.

Feed supplementation prevents post-conception decline in milk progesterone concentrations associated with production stress in dairy buffaloes (Bubalus bubalis)

The onset of pregnancy may be associated with hormonal changes and decline in milk yield of buffaloes. To investigate this, forty lactating buffaloes from 1st to 23rd weeks post-conception were selected. The animals were assigned to three treatments: PRT, PRS, NPRT and three milk yielding groups HMY, 66 to 75 l/week, n = 12; MMY, 56 to 65 l/week, n = 16; LMY, 46 to 55 l/week, n = 12). Milk samples were collected on alternate weeks and analyzed with ultrasonic milk analyzer. EIA was used for milk progesterone concentrations. Group means were compared and correlation analysis was conducted. Progesterone concentrations increased in almost similar pattern with the advancing weeks post-conception. The high and low yielder showed greater progesterone concentrations in the supplemented than the animals on traditional ration (P < 0.001). Progesterone concentrations correlated positively with fat (%), negatively with milk yield, protein (%) and lactose (%). Decline in milk yield became drastic when progesterone concentrations rose above 6.44 ng/ml. The pregnant animals on traditional ration exhibited a sharper decline in milk yield with the increasing progesterone concentrations as compared to pregnant animals with supplemented ration. It is concluded that concentrates supplementation induced a raise in progesterone levels. Progesterone concentrations and milk yield showed an inverse relationship.

Extended lactation in dairy cows: effects of milking frequency, calving season and nutrition on lactation persistency and milk quality

Twelve spring-calving and twelve winter-calving cows were managed for extended lactation cycles of 18-months duration, with the former group then completing a second extended lactation. Half of the cows were fed according to standard management practice for the herd; the other half received supplementary concentrate from week 9 of lactation onwards. Commencing at the same time, half of the udder of each cow was subjected to increased milking frequency (thrice daily rather than twice daily). Lactation persistency (and hence total milk yield) was significantly increased by frequent milking. Winter calving cows and supplemented cows also exhibited better persistency, but this was only evident up until the point of re-breeding, at around lactation week 33. Milk composition was measured in the spring-calving cows in both their first and second extended lactations. Composition altered during the course of the lactation, protein and fat percentages increasing and lactose percentage decreasing, irrespective of treatment. The quality of the milk for processing into cheese, fermented products, heat-treated products and cream liqueurs was assessed by calculation of casein number (casein protein as a proportion of total protein). Processing quality declined across the course of lactation in those groups that showed poor persistency but not in those that maintained a persistent lactation. Milk hygienic quality (somatic cell counts) showed parallel changes. Body condition score increased during the course of lactation but was not affected by supplementation; none of the cows became excessively fat. All cows remained healthy throughout the extended lactations and the majority (33/36) re-bred successfully. By demonstrating that lactation persistency is plastic and can be improved by simple management interventions, the results lend support to the economic arguments in favour of extended lactation cycles. The likely welfare benefits of extended lactation are also discussed.

Modeling extended lactations of Holsteins

Modeling extended lactations for the US Holsteins is useful because a majority (>55%) of the cows in the present population produce lactations longer than 305 d. In this study, 9 empirical and mechanistic models were compared for their suitability for modeling 305-d and 999-d lactations of US Holsteins. A pooled data set of 4,266,597 test-day yields from 427,657 (305-d complete) lactation records from the AIPL-USDA database was used for model fitting. The empirical models included Wood (WD), Wilmink (WIL), Rook (RK), monophasic (MONO), diphasic (DIPH), and lactation persistency (LPM) functions; Dijkstra (DJ), Pollott (POL), and new-multiphasic (MULT) models comprised the mechanistic counterparts. Each model was separately tested on 305-d (>280 days in milk) and 999-d (>800 days in milk) lactations for cows in first parity and those in third and greater parities. All models were found to produce a significant fit for all 4 scenarios (2 parity groups and 2 lactation lengths). However, the resulting parameter estimates for the 4 scenarios were different. All models except MONO, DIPH, and LPM yielded residuals with absolute values smaller than 2 kg for the entire period of the 305-d lactations. For the extended lactations, the prediction errors were larger. However, the RK, DJ, POL, and MULT models were able to predict daily yield within a +/- 3 kg range for the entire 999-d period. The POL and MULT models (having 6 and 12 parameters, respectively) produced the lowest mean square error and Bayesian information criteria values, although the differences from the other models were small. Conversely, POL and MULT were often associated with poor convergence and highly correlated, unreliable, or biologically atypical parameter estimates. Considering the computational problems of large mechanistic models and the relative predictive ability of the other models, smaller models such as RK, DJ, and WD were recommended as sufficient for modeling extended lactations unless mechanistic details on the extended curves are needed. The recommended models were also satisfactory in describing fat and protein yields of 305-d and 999-d lactations of all parities.

The declining phase of lactation: peripheral or central, programmed or pathological?

In most species the functional activity of the mammary gland during lactation follows a biphasic developmental pattern. This pattern starts with a rapid increase in milk output that occurs with secretory activation and continues with a more gradual increase until the point of peak lactation is reached. Following this gain-of-function phase, the ability of the gland to produce milk decreases. This decrease occurs even if the lactation is prolonged by the presence of continued suckling stimulus and complete milk removal. This review describes the current state of our knowledge concerning the factors that regulate milk synthesis capacity by the mammary gland during the lactation cycle. The review describes four potential alternatives as mechanisms governing the process, which we refer to as secretory diminution. These alternatives are not presented as mutually exclusive of each other or other possible mechanisms, but are proposed as potential contributing mechanisms.

Productive life including all lactations and longer lactations with diminishing credits

Alternative measures of productive life (PL) were compared, and life expectancy factors were updated to replace estimates from 1993. Alternatives were proposed with extra credits for lactations longer than 10 mo and beyond 84 mo of age and for each calving so that an extremely long lactation would not receive more credits than multiple shorter lactations with dry periods between. Maximum credits per lactation of 10 mo (original PL), 12 mo, and unlimited were compared. The unlimited credits option either included or excluded a calf value equal to 2 mo of production and had credits given for all days either uniformly or based on lactation curves (diminishing credits). Standard lactation curves (first, second, and greater lactations) were estimated based on the test-day yields of Holstein cows remaining in lactation from a set of 903,579 lactation records. For the diminishing credits alternative, credit for a given day of a parity was derived using the predicted yield of the day proportional to the average daily yield of the first 305 d of second parity. Daily yields were deviations from a baseline of 13.62 kg. Heritabilities and genetic correlations were estimated by multitrait REML for alternative measures of PL, for longevity censored at various ages, and for yield traits and SCS in first parity. Data for REML analysis included records from 1,098,329 Holsteins born from 1994 through 1997 from 5,109 sires, and a relationship matrix among sires was included in the model. Lactations beyond 84 mo added little information. Heritability of PL was 0.073 with 10 mo, 0.069 with 12 mo, 0.068 and 0.067 with unlimited (uniform) lactation credits (with and without calf credits, respectively), and 0.070 with unlimited diminishing credits. Corresponding correlations among predicted transmitting abilities for PL and protein yield were 0.07, 0.06, 0.12, 0.23, and 0.09, all much lower than the 0.46 estimated in 1993. Heritability of PL with diminishing credits improved from 0.017 to 0.070 when censoring age increased from 36 to 96 mo. There was no further increase in heritability beyond 96 mo. Genetic correlation with the final PL was 0.87 when PL was censored at 36 mo, but the estimate increased steadily with the censoring age. The PL with diminishing credits, which was favorable in both economic and genetic aspects, was desirable in crediting cows for complete lactations.

Economic Value of Pregnancy in Dairy Cattle

The objective of this study was to estimate the value of pregnancy for dairy cows. Effects of the stage of gestation, stage of lactation, lactation number, milk yield, milk price, replacement heifer cost, probability of pregnancy, probability of involuntary culling, and breeding decisions were studied. A bioeconomic model was used, and breeding and replacement decisions were optimized. A general Holstein herd in the United States was modeled. The average value of a new pregnancy was $278. The value of a new pregnancy increased with days in milk early in lactation but typically decreased later in lactation. Relatively high-producing cows and first-lactation cows reached greater values, and their values peaked later in lactation. The average cost of a pregnancy loss (abortion) was $555. The cost of a pregnancy loss typically increased with gestation length. Sensitivity analyses showed that an increased probability of pregnancy, an increased persistency of milk yield, and a smaller replacement heifer cost greatly reduced the average value of a pregnancy. The value of a new pregnancy was negative for relatively high-producing first-lactation cows when persistency of lactation and the probability of pregnancy were increased. Breeding was delayed when the value of pregnancy was negative. Changes in milk price, absolute milk yield, and probability of involuntary culling had less effect on the value of pregnancy. The value of pregnancy and optimal breeding decisions for individual cows were greatly dependent on the predicted daily milk yield for the remaining period of lactation. An improved understanding of the value of pregnancy may support decision making in reproductive management when resources are limited.

Influence of milking frequency on the productivity of dairy cows

Benefits and issues of changing milking frequency from the traditional twice a day are reviewed. Increased efficiency through dairy automation and mechanisation, and the desire to utilise advances in genetic selection, have made milking more frequently than twice a day an attractive option for some farmers. The size of the response to increased milking frequency appeared not to be related to existing milk yield, with the average response to increasing the frequency from 2 to 3 times a day being 3.5–3.8 kg/day. Labour is the single most important cost associated with the decision to increase milking frequency. For this reason, automated milking systems may hold the key to the long-term profitability of challenging cows to produce to their genetic potential. In contrast, reducing milking frequency to once a day has been used to reduce stress on underfed cows or for lifestyle and/or labour considerations. Short-term experiments indicate an average production loss of 21% for once daily relative to twice daily milking. Full lactation experiments suggest greater losses of 35–50%, but there is evidence that cows can adapt to longer milking intervals and this, coupled with increased stocking rate and care to maximise milk removal, may restrict yield losses to less than 10% on a whole-farm basis.

Economic and Environmental Feasibility of a Perennial Cow Dairy Farm

More efficient and economical production systems are needed to improve the sustainability of dairy farms. One concept to consider is using perennial cows. Perennial cows are those that maintain a relatively high milk production for >or=2 yr without going through the typical dry period followed by calving. Farm records show that some cows have produced over 20 kg/d after 4 yr of continuous lactation. A farm simulation model was used to evaluate the long-term performance, environmental impact, and economics of a conceptual perennial cow production system on a typical dairy farm in Pennsylvania. Compared with a traditional 100-cow farm with replacement heifers produced on the farm, a perennial herd of 100 cows and purchased replacements provided environmental benefit but sustained a substantial economic loss. However, increasing the perennial herd to 128 cows better utilized the feed produced on the farm. Compared with the traditional 100-cow farm, use of the perennial 128-cow herd reduced supplemental protein and mineral feed purchases by 38%, increased annual milk sales by 21%, reduced nitrogen losses by 17%, maintained a phosphorus balance, and increased annual net return to farm management by 3200 dollars. A traditional 120-cow dairy farm with purchased replacements also used a similar amount of farm-produced feed. Compared with this option, the farm with 128 perennial cows reduced protein and mineral feed purchases by 36%, maintained similar annual milk sales, increased manure production by 7%, reduced N losses by 10%, and increased annual net return by 12,700 dollars. The economic feasibility of the perennial-cow dairy farm was very sensitive to the milk production maintained by the perennial herd and market prices for milk and perennial replacement animals. The analysis was relatively insensitive to the assumed useful life of perennial cows as long as they could be maintained in the herd for at least 3 yr. Thus, a perennial cow production system can improve the economic and environmental sustainability of a traditional dairy farm if a similar level in annual milk production per cow can be maintained.

Detection of different shapes of lactation curve for milk yield in dairy cattle by empirical mathematical models

The study of relationships between mathematical properties of functions used to model lactation curves is usually limited to the evaluation of the goodness of fit. Problems related to the existence of different lactation curve shapes are usually neglected or solved drastically by considering shapes markedly different from the standard as biologically atypical. A deeper investigation could yield useful indications for developing technical tools aimed at modifying the lactation curve in a desirable fashion. Relationships between mathematical properties and lactation curve shapes were analyzed by fitting several common functions (Wood incomplete gamma, Wilmink's exponential, Ali and Schaeffer's polynomial regression, and fifth-order Legendre polynomials) to 229,518 test-day records belonging to 27,837 lactations of Italian Simmental cows. Among the best fits (adjusted r(2) higher than 0.75), the 3-parameter models (Wood and Wilmink) were able to detect 2 main groups of curve shape: standard and atypical. Five-parameter models (Ali and Schaeffer function and the Legendre polynomials) were able to recognize a larger number of curve shapes. The higher flexibility of 5-parameter models was accompanied by increased sensitivity to local random variation as evidenced by the bias in estimated test-day yields at the beginning and end of lactation (border effect). Meaning of parameters, range of their values and of their (co) variances are clearly different among groups of curves. Our results suggest that analysis based on comparisons between parameter values and (co)variances should be done carefully. Comparisons among parameter values and (co)variances could yield more robust, reliable, and easy to interpret results if performed within groups based on curve shape.