Modeling extended lactations of dairy cows

Profitability Optimization of Dairy Farms: The Effect of Pregnancy Rate and Culling Decision

One of the most important decisions in dairy cattle production today is the correct choice of culling time for cows. In the culling decision process, the farmer has to take into account a number of factors, the complexity of which makes the decision-making task difficult. A crucial factor is the evolution of reproductive indicators. The aim of the research was to develop a microsimulation method that can be used to easily investigate the impact on profitability of increasing pregnancy rates and when the culling decision is made. In the microsimulation, the stock was examined without changing any other conditions. A microsimulation method has been developed to determine with high accuracy the effect of the pregnancy rate and the increase in culling days on the economic indicators of individual dairy farms. By microsimulation, the effect of changing these two parameters on the expected milk production of cows, the most important economic indicator for cattle farms, was investigated. The other parameters of economic importance were simulated using a cattle farm database. The purpose of microsimulation is to assist in producing certain managerial decisions in order to achieve better profitability and economic efficiency. In summary, the results showed that increasing the pregnancy rate can successfully reduce the length of the calving interval, but the improved pregnancy rate did not show a significant increase in milk production. In order to obtain results that can be used by farms, the authors intend to further develop the model in the future, adapting it to farms and taking into account their specificities.

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.

Genetics of Lifetime Reproductive Performance in Italian Heavy Draught Horse Mares

Simple Summary

Fertility is a very important fitness trait in animal production because of its significant economic importance, particularly in species with low reproductive efficiency. For this reason, it should be included as a breeding objective, particularly in horses, where the trait has received less interest than in other species. In this study, we attempted to identify a variable able to detect the lifetime reproductive performance of Italian Heavy Draught Horse (IHDH) mares and to analyze its possible implementation for breeding purposes, with the final aim to increase mares’ fertility efficiency. A phenotypic variable to be used early in life (at least after 3 breeding seasons) has been identified and validated in the study and its genetic component estimated. Results obtained indicated the proposed phenotypic measure of fertility as a good predictor of the lifetime reproductive success in IHDH mares and the variable showed high heritability (that is, the transmittable genetic component) for a fitness trait. Therefore, the use of the lifetime fertility rate proposed in this study for breeding purposes seems feasible, although some limitations could occur in the accuracy of individual breeding value estimates of mares and stallions.

Abstract

Our aims were to find a phenotypic variable to express mares’ lifetime reproductive performance after 6 breeding seasons (BS) in Italian Heavy Draught Horse breed (IHDH), and to estimate its heritability. At first, 1487 mares in a training dataset were used to implement and validate a set of predictive coefficients (LFR-C) or equations (LFR-E) to estimate a lifetime foaling rate (LFR) after 6 BS, i.e., the number of foals generated divided by the opportunities to do so. Then, 3033 mares in a dataset with at least 3 registered BS, was used to estimate LFR for mares with 3, 4, or 5 registered RS. This dataset contained actual (n = 1950) and estimated (n = 1443) LFR, obtained by LFR-C, and LFR-E; Arcsine transformation of LFR-C and LFR-E were also analyzed in single trait animal models to estimate heritability. Overall, the LFR showed a moderate but significant genetic variation, and the heritability of the trait was high (0.24) considering it is a fitness trait. The arcsine transformation of LFR did not show any improvement of heritability. The present study indicates the possible use of a linear LFR variable for breeding purposes in IHDH breed considering both complete and incomplete reproductive careers.

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.

Dynamic forecasting of individual cow milk yield in automatic milking systems

Accurate forecasting of dairy cow milk yield is useful to dairy farmers, both in relation to financial planning and for detection of deviating yield patterns, which can be an indicator of mastitis and other diseases. In this study we developed a dynamic linear model (DLM) designed to forecast milk yields of individual cows per milking, as they are milked in milking robots. The DLM implements a Wood's function to account for the expected total daily milk yield. It further implements a second-degree polynomial function to account for the effect of the time intervals between milkings on the proportion of the expected total daily milk yield. By combining these 2 functions in a dynamic framework, the DLM was able to continuously forecast the amount of milk to be produced in a given milking. Data from 169,774 milkings on 5 different farms in 2 different countries were used in this study. A separate farm-specific implementation of the DLM was made for each of the 5 farms. To determine which factors would influence the forecast accuracy, the standardized forecast errors of the DLM were described with a linear mixed effects model (lme). This lme included lactation stage (early, middle, or late), somatic cell count (SCC) level (nonelevated or elevated), and whether or not the proper farm-specific version of the DLM was used. The standardized forecast errors of the DLM were only affected by SCC level and interactions between SCC level and lactation stage. Therefore, we concluded that the implementation of Wood's function combined with a second-degree polynomial is useful for dynamic modeling of milk yield in milking robots, and that this model has potential to be used as part of a mastitis detection system.

Multiple-trait genomewide mapping and gene network analysis for scrotal circumference growth curves in Brahman cattle

Fertility traits are economically important in cattle breeding programs. Scrotal circumference (SC) measures are repeatable, easily obtained, highly heritable, and positively correlated with female fertility traits and sperm quality traits in males. A useful approach to summarize SC measures over time is using nonlinear models, which summarize specific measures of SC in a few parameters with biological interpretation. This approach facilitates the selection of bulls with larger SC and maturity index (K), that is, early maturing animals. Because SC is a sex-limited trait, identifying the underlying genomics of growth curve parameters will allow selection across both males and females. We reported the first multitrait genomewide association study (GWAS) of estimated growth curve parameters for SC data in Brahman cattle. Five widely used nonlinear models were tested to fit a total of 3,612 SC records, measured at 6, 12, 18, and 24 mo of age. The von Bertalanffy model, individually fitted for each animal, best fit this SC data. Parameter estimates SC at maturity (A) and K as well as SC at all ages were jointly analyzed in a GWAS to identify 1-Mb regions most strongly associated with each trait. Heritabilities were 0.25 for K and 0.32 for A and ranged from 0.51 to 0.72 for SC at 6 (SC6), 12 (SC12), 18 (SC18), and 24 mo of age (SC24). An overlapping window on chromosome 14 explaining around 0.8% of genetic variance for K, SC12, SC18, and SC24 was observed. The major positional candidate genes within 1 Mb upstream and downstream of this overlapping window were , , , and . Windows of 1 Mb explaining more than 0.4% of each trait on chromosomes 1, 3, 6, 7, 14, 17, 18, 24, 25, and 26 were identified. Pathways and net-work analyses were indicated through transcription factors playing a role on fertility traits: , , , , , , and . Further validation studies on larger populations or other breeds are required to validate these findings and to improve our understanding of the biology and complex genetic architecture of traits associated with scrotal growth and male fertility in cattle.

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.

Equid milk production: evaluation of Martina Franca jennies and IHDH mares by Wood’s model application

The present work aims to evaluate milk production aptitude of two equid species: horse and donkey. The trial was conducted on the Italian Heavy Draught breed horse (IHDH) and on the Martina Franca breed donkey. Data were collected from 23 multiparous nursing IHDH mares aged from 6 to 10 years, with an average bodyweight (BW) (mean ± s.d.) of 822.3 ± 61.8 kg and from 28 multiparous nursing donkeys of Martina Franca breed aged from 7 to 12 years, with an average BW (mean ± s.d.) of 389.5 ± 21.2 kg. Milk yield was recorded on 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165 and 180 days in milk (DIM). At each milk yield evaluation day, a milk sample was collected and its composition was analysed. All data were normalised according metabolic weight (MBW) of animals, so to make comparable results of the two considered species. Wood’s lactation model was used to describe milk, fat, protein and lactose yield. Peak lactation was reached on DIM 69 in IHDH horse and on DIM 48 in Martina Franca donkey with a milk production of 10.693 kg/100 kg MBW (R2 = 0.9139) and 5.264 kg/100 kg MBW (R2 = 0.9428), respectively. Persistency index of milk lactation curve was higher in Martina Franca donkey then in IHDH mares (7.0338 vs 6.2672). IHDH mares showed higher fat and protein production. Lactose curves showed a similar trend in both the species although IHDH’s curve was characterised by higher values. Data reported in the present work underline that both breeds considered are characterised by good milk production aptitude. Moreover, high R2 values obtained applying Wood’s model to milk, fat, protein and lactose production, calculated on the metabolic bodyweight basis, are indices of goodness of model fit.

Early lactation production, health, and welfare characteristics of cows selected for extended lactation

Some cows are able to achieve relatively high milk yields during extended lactations beyond 305 d in milk, and farmers may be able to use this potential by selecting the most suitable cows for an extended lactation. However, the decision to postpone insemination has to rely on information available in early lactation. The main objectives of this study were, therefore, to assess the association between the information available in early lactation and the relative milk production of cows on extended lactation, and to investigate if this information can be used to differentiate time of first insemination between cows. Data came from 4 Danish private herds practicing extended lactation in which some cows are selected to have a delayed time of planned first insemination. Average herd size varied from 93 to 157 cows, and milk yield varied from 7,842 to 12,315 kg of energy-corrected milk (ECM) per cow per year across herds. The analysis was based on 422 completed extended lactations (427 ± 87 d), and each lactation was assigned to 1 of 3 (low, medium, and high) milk performance groups (MPG) within parity group within herd based on a standardized lactation yield. For cows in the high MPG, peak ECM yield, and ECM yield at dry off were significantly greater, the relative reduction in milk yield between 60 and 305 d in milk was significantly smaller, and a smaller proportion had a body condition score (scale: 1-5) at dry off of 3.5 or greater compared with cows in low MPG. Previous lactation days in milk at peak ECM yield and ECM yield at dry off were higher, the relative reduction in milk yield between 60 and 305 d in milk was smaller, and the number of inseminations per conception was higher for multiparous cows in high MPG compared with low. Current lactation ECM yield at second and third milk recording were greater for cows in high MPG compared with low. A principal component analysis indicated that variables related to fertility, diseases, and milk yield explained most of the total variation between primiparous cows, whereas variables related to milk yield, fertility, and days in milk at peak yield were the most dominating for multiparous cows. Our study indicated that milk yields in previous lactation and at second and third milk recording correlate well with milk production potential, and therefore, may be promising indicators when selecting the most suitable cows for extended lactation.

The investigation of correlation among selected biochemical parameters and vital signs in dairy herd to design the bio-cybernetic dairy cow model

The paper presents investigations of the relationship between the biochemical parameters and vital signs in dairy cows. We analyzed the welfare and functioning of a dairy herd using biochemical parameters and vital signs. Life and biochemical parameters were examined. In the model indicators useful for monitoring the herd are: the age of the cows, the number of cows' lactating, daily amount of received milk, length of lactation period for cows in the herd, the length of inter-calving period for cows, the number of days to effective insemination, the amount of protein in the feed, the level of β-oxidation in leucocytes, glucose transport through red blood cells and plasma insulin. Based on the results the mathematical model was designed allowing the presentation of a cybernetic model of cow's organism. There was constructed a multi-equation model which determined the relationships between the selected variables describing the state of dairy cows in the herd and variables that characterize their welfare with its statistical verification.

Multi-Trait GWAS and New Candidate Genes Annotation for Growth Curve Parameters in Brahman Cattle

Understanding the genetic architecture of beef cattle growth cannot be limited simply to the genome-wide association study (GWAS) for body weight at any specific ages, but should be extended to a more general purpose by considering the whole growth trajectory over time using a growth curve approach. For such an approach, the parameters that are used to describe growth curves were treated as phenotypes under a GWAS model. Data from 1,255 Brahman cattle that were weighed at birth, 6, 12, 15, 18, and 24 months of age were analyzed. Parameter estimates, such as mature weight (A) and maturity rate (K) from nonlinear models are utilized as substitutes for the original body weights for the GWAS analysis. We chose the best nonlinear model to describe the weight-age data, and the estimated parameters were used as phenotypes in a multi-trait GWAS. Our aims were to identify and characterize associated SNP markers to indicate SNP-derived candidate genes and annotate their function as related to growth processes in beef cattle. The Brody model presented the best goodness of fit, and the heritability values for the parameter estimates for mature weight (A) and maturity rate (K) were 0.23 and 0.32, respectively, proving that these traits can be a feasible alternative when the objective is to change the shape of growth curves within genetic improvement programs. The genetic correlation between A and K was -0.84, indicating that animals with lower mature body weights reached that weight at younger ages. One hundred and sixty seven (167) and two hundred and sixty two (262) significant SNPs were associated with A and K, respectively. The annotated genes closest to the most significant SNPs for A had direct biological functions related to muscle development (RAB28), myogenic induction (BTG1), fetal growth (IL2), and body weights (APEX2); K genes were functionally associated with body weight, body height, average daily gain (TMEM18), and skeletal muscle development (SMN1). Candidate genes emerging from this GWAS may inform the search for causative mutations that could underpin genomic breeding for improved growth rates.

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.

Application of Wood's model to lactation curve of Italian Heavy Draft horse mares

The aim of this work was to study, using Wood's model, the lactation curve in Italian Heavy Draft horse (IHDH) mares, both for milk yield and composition. Interest in mare's milk has grown for use in human nutrition, as a substitute for human and cow milk for premature newborns and allergic children. For this study, 7 IHDH mares were used. Milk yield was evaluated from d 15 to 180 postpartum (every 15 d). Wood's lactation model was used to describe milk yield, fat, protein, and lactose lactation curves in the first 180 d in milk (DIM), with a prediction to 210 DIM. Mean values recorded across the considered lactation period for milk yield and constituents were 16.11 kg of milk/d, 11.38 g of fat/kg, 15.54 g of protein/kg, and 69.72 g of lactose/kg. The lactation curve showed a peak at 69 DIM, with a persistence index of 6.26. Fat (g/kg) and protein (g/kg) lactation curves decreased during the lactation period; instead, the lactose (g/kg) curve increased from the first to the last DIM. The coefficient of determination values indicated a good model fit by Wood's model application to IHDH mare lactation. The research showed good aptitude of a heavy horse breed, such as IHDH, for milk production.

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.

Use of test-day records beyond three hundred five days for estimation of three hundred five-day breeding values for production traits and somatic cell score of Canadian Holsteins

The Canadian Test-Day Model includes test-day (TD) records from 5 to 305 d in milk (DIM). Because 60% of Canadian Holstein cows have at least one lactation longer than 305 d, a significant number of TD records beyond 305 DIM could be included in the genetic evaluation. The aim of this study was to investigate whether TD records beyond 305 DIM could be useful for estimation of 305-d estimated breeding value (EBV) for milk, fat, and protein yields and somatic cell score. Data were 48,638,184 TD milk, fat, and protein yields and somatic cell scores from the first 3 lactations of 2,826,456 Canadian Holstein cows. All production traits were preadjusted for the effect of pregnancy. Subsets of data were created for variance-component estimation by random sampling of 50 herds. Variance components were estimated using Gibbs sampling. Full data sets were used for estimation of breeding values. Three multiple-trait, multiple-lactation random regression models with TD records up to 305 DIM (M305), 335 DIM (M335), and 365 DIM (M365) were fitted. Two additional models (M305a and M305b) used TD records up to 305 DIM and variance components previously estimated by M335 and M365, respectively. The effects common to all models were fixed effects of herd x test-date and DIM class, fixed regression on DIM nested within region x age x season class, and random regressions for additive genetic and permanent environmental effects. Legendre polynomials of order 6 and 4 were fitted for fixed and random regressions, respectively. Rapid increase of additive genetic and permanent environmental variances at extremes of lactations was observed with all 3 models. The increase of additive genetic and permanent environmental variances was at earlier DIM with M305, resulting in greater variances at 305 DIM with M305 than with M335 and M365. Model M305 had the best ability to predict TD yields from 5 through 305 DIM and less error of prediction of 305-d EBV than M335 and M365. Model M335 had smaller change of 305-d EBV of bulls over the period of 7 yr than did M305 and M365. Model M305a had the least error of prediction and change of 305-d EBV from all models. Therefore, the use of TD records of Holstein cows from 5 through 305 DIM and variance components estimated using records up to 335 DIM is recommended for the Canadian Test-Day Model.

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.

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.

A general bilinear model to describe growth or decline time profiles

Linear models are widely used because of their unrivaled simplicity, but they cannot be applied for data that have a turning-or rate-change-point, even if the data show good linearity sufficiently far from this point. To describe such bilinear-type data, a completely generalized version of a linearized biexponential model (LinBiExp) is proposed here to make possible smooth and fully parametrizable transitions between two linear segments while still maintaining a clear connection with the linear models. Applications and brief conclusions are presented for various time profiles of biological and medical interest including growth profiles, such as those of human stature, agricultural crops and fruits, multicellular tumor spheroids, single fission yeast cells, or even labor productivity, and decline profiles, such as age-effects on cognition in patients who develop dementia and lactation yields in dairy cattle. In all these cases, quantitative model selection criteria such as the Akaike and the Schwartz Bayesian information criteria indicated the superiority of the bilinear model compared to adequate less parametrized alternatives such as linear, parabolic, exponential, or classical growth (e.g., logistic, Gompertz, Weibull, and Richards) models. LinBiExp provides a versatile and useful five-parameter bilinear functional form that is convenient to implement, is suitable for full optimization, and uses intuitive and easily interpretable parameters.

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

Objectives of this study are to describe the biological basis for multiphasic milk production and to propose a new empirical model for the lactation curve. To illustrate this model, we used data on 3573 first-lactation Holsteins having lactations of various lengths (285, 345, 405, 465, and 525 d) and with various days open (45, 105, 165, 225, and 285 d). The model describes an increasing first phase of milk yield and a series of decreasing phases of yield. The increasing phase, described by an increasing logistic function of time, is associated with increase in number of active mammary gland cells and increase in yield per cell. The decreasing phases, described by three decreasing logistic functions of time, are associated with decreases in cell number due to apoptosis and in yield per cell due to pregnancy. The new model is [equation: see text] where yDIM is milk yield at each day in milk (DIM), a1 is upper level for the increasing first phase, and p2, p3, and p4 = (1 - p2 - p3) are proportions of a1 for the decreasing second, third, and fourth phases; b's are proportional to duration of each phase; and c's are time of maximum increase or decrease. Nonlinear regression was used to fit average milk yield for each of nine datasets, four with 180 d carried calf and five with 240 d carried calf. Average results indicated that for the first phase, upper level of milk yield was about 22 kg. Duration was about 120 d, centered on time of maximum increase, which was about 11 d before calving. For the second phase (first phase of apoptosis), decrease in yield was relatively large (about 20%) and duration was relatively long (about 375 d). Time of maximum decrease was about 107 d after calving. For the third phase (pregnancy), decrease in yield was relatively small (about 6%) and duration was relatively short (about 200 d). Time of maximum decrease was about 300 d after calving. For each additional day open, time of maximum decrease increased about 1 d. For the fourth phase (second phase of apoptosis), decrease in yield was relatively large (about 74%) and duration was relatively long (about 765 d). Duration for the lactation length of 525 d was exceptionally long. Time of maximum decrease was about 382 d after calving. For each additional day of lactation, duration increased about 5.4 d and day of maximum decrease increased about 0.82 d. We believe that it is possible to model empirically standard and extended lactation curves of dairy cows, based on biological theory and predicated on the multiphasic approach. Further research to understand better the biology of extended lactations, using the proposed multiphasic model, should use planned extended lactations that are at least 525 d in milk and have at least 240 d carried calf.

Lactation and gestation in dairy cows: flexibility avoids nutritional extremes

The modern dairy cow has been selectively bred to produce large amounts of milk. Partly as a result, food consumption is considerably less than milk energy output in early lactation. It is only at 2 months or more postpartum that intake increases to the point where positive energy balance is regained, the initial production being achieved by a substantial mobilisation of body reserves. These reserves are laid down before parturition, but it is certainly not the case that the pregnant cow will accumulate adipose tissue recklessly; in the last third of pregnancy well-fed cows in good body condition exhibit reduced, not increased, appetite. There is a fine balancing act to perform. Excessive body condition at parturition quickly leads to metabolic problems such as ketosis, but cows who subsequently become too thin have increased risk of metabolic diseases such as mastitis and lameness. The biological mechanisms regulating output of milk are reasonably well understood, those controlling appetite less well so, and there has been little attempt at systematic integration of the two. The transition from pregnancy to lactation represents a major challenge to homeostasis, made more complicated in multiparous cows by the fact that much of gestation is concurrent with lactation. Herein lies the potential for nutritionally-entrained flexibility. In the wild, concurrent pregnancy and lactation only occur when nutritional conditions are favourable. If conditions are poor, rebreeding will be delayed and lactation will continue, at an energetically-sustainable level, for much longer than its 'normal' duration. In this way the twin energetic burdens of pregnancy and lactation are separated, and extremes are avoided. Given the increasing public concern about stresses suffered by intensively-managed dairy cows, this case may be one where commercial dairying could learn useful lessons from nature.