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

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

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

The main objective of this study was to compare the performance of different ‘nonlinear quantile regression’ models evaluated at the τth quantile (0·25, 0·50, and 0·75) of milk production traits and somatic cell score (SCS) in Iranian Holstein dairy cows. Data were collected by the Animal Breeding Center of Iran from 1991 to 2011, comprising 101 051 monthly milk production traits and SCS records of 13 977 cows in 183 herds. Incomplete gamma (Wood), exponential (Wilmink), Dijkstra and polynomial (Ali & Schaeffer) functions were implemented in the quantile regression. Residual mean square, Akaike information criterion and log-likelihood from different models and quantiles indicated that in the same quantile, the best models were Wilmink for milk yield, Dijkstra for fat percentage and Ali & Schaeffer for protein percentage. Over all models the best model fit occurred at quantile 0·50 for milk yield, fat and protein percentage, whereas, for SCS the 0·25th quantile was best. The best model to describe SCS was Dijkstra at quantiles 0·25 and 0·50, and Ali & Schaeffer at quantile 0·75. Wood function had the worst performance amongst all traits. Quantile regression is specifically appropriate for SCS which has a mixed multimodal distribution.

The study reported in this Research Communication was carried out to examine how parity and milking time affected donkey milk yield under a typical Chinese production system. Eighteen Jiangyue breed donkeys with good health condition, aged between 6 and 9 years, and with parities 3 and 4, were selected. Milk production was measured commencing from the fourth week post-foaling, with a total data collection of 170 d in milk (lactation length). Mean milk yield of the donkeys used in this study was 3·0 kg/donkey/d. Results showed milk yield decreased with days in milk from 3·3 kg/donkey/d at the start of the study, to 2·2 kg/donkey/d by the end of the 170 d. Parity 3 donkeys produced 22% more milk than parity 4 donkeys (3·3 kg/donkey/d vs 2·7 kg/donkey/d). The information provided by this study should aid producers in estimating the expected milk yields from individual donkey, and better predict milk yield over the course of a production cycle.

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

This study investigated factors affecting milk production and lactation curves from complete lactations of Lacaune dairy sheep. Animals were part of a single flock under intensive management and were milked twice daily starting at lambing. The results of the analyses of 7788 complete lactations showed an average total milk yield of 434±183 l from lactations 234±63 d long, with an average lambing interval of 302±65 d. A Pollott additive mathematical model was used to estimate complete lactation curves. Clustering analysis identified four lactation types among Lacaune dairy sheep differing mainly in productivity i.e. milk yield per lactation (MY) and length of lactation (DIM). The so-called SL type involved short, less productive lactations (n=2137; 27·4%; MY=222±75·5 l and DIM=182±52·9 d). The SN type involved short lactations of normal productivity (n=2039; 26·2%; MY=396±73·7 l and DIM=205±33·1 d). The LP type involved long and productive lactations (n=2169; 27·9%; MY=487±70·5 l and DIM=265±40·7 d), while the LVP type included long and extremely productive lactations (n=1443; 18·5%; MY=694±114·0 l and DIM=295±54·7 d). Sheep showing the best lactation curves were usually younger than other sheep, and they had higher yield during the previous lactation, a shorter previous dry period (55±50·4 for LP and 61±55·0 d for LVP types) and longer lambing intervals. In addition, they tended to be born in September and to lamb in March, October and December. Sheep were remarkably stable in their lactation curve behaviour: the curve type observed for the first lactation was highly likely to persist in subsequent lactations (P<0·0001). These results suggest that farmers can use the shape of the first lactation curve to guide their selection of ewes for breeding and retention on the farm, thereby improving flock productivity.

Although the intensive production system of Lacaune dairy sheep is the only profitable method for producers outside of the French Roquefort area, little is known about this type of systems. This study evaluated yield records of 3677 Lacaune sheep under intensive management between 2005 and 2010 in order to describe the lactation curve of this breed and to investigate the suitability of different mathematical functions for modeling this curve. A total of 7873 complete lactations during a 40-week lactation period corresponding to 201 281 pieces of weekly yield data were used. First, five mathematical functions were evaluated on the basis of the residual mean square, determination coefficient, Durbin Watson and Runs Test values. The two better models were found to be Pollott Additive and fractional polynomial (FP). In the second part of the study, the milk yield, peak of milk yield, day of peak and persistency of the lactations were calculated with Pollot Additive and FP models and compared with the real data. The results indicate that both models gave an extremely accurate fit to Lacaune lactation curves in order to predict milk yields (P = 0.871), with the FP model being the best choice to provide a good fit to an extensive amount of real data and applicable on farm without specific statistical software. On the other hand, the interpretation of the parameters of the Pollott Additive function helps to understand the biology of the udder of the Lacaune sheep. The characteristics of the Lacaune lactation curve and milk yield are affected by lactation number and length. The lactation curves obtained in the present study allow the early identification of ewes with low milk yield potential, which will help to optimize farm profitability.

The objective of this study was to describe the lactation curve of dairy cattle in Kenya using a suitable lactation function in order to facilitate inclusion of partial lactations in national dairy cattle evaluation and to assess the effect of data characteristics on lactation curve parameters. Six functions were fitted to test day (TD) milk yield records from six parities of Ayrshire, Guernsey, Holstein Friesian, Jersey and Sahiwal cattle. Five datasets: DS-1 (12-TD dataset with randomly missing records), DS-2 (10-TD dataset without missing records), DS-3 (10-TD dataset with randomly missing records), DS-4 (7-TD dataset, with only TD 4 to 10 records) and DS-5 (7-TD dataset, with TD 1 to 4, 6, 8 and 10 records) depicting various recording circumstances were derived to assess the effects of data characteristics on lactation curves and to assess the feasibility of reducing the number of TD samples per lactation. The fit of the functions was evaluated using adjusted R2 and their predictive abilities were compared using mean square prediction error, percentage of squared bias and the correlation between the predicted and actual milk yield. These criteria plus the changes in the parameters of curve functions and their associated standard errors were used in determining the effects of data characteristics on lactation curves. The mechanistic functions of Dijkstra (DIJ) and Pollott (APOL), and the incomplete gamma function of Wood (WD) had the highest adjusted R2 > 0.75. The APOL function was eliminated due to convergence failures when analysis of individual lactations within breeds was carried out. Both DIJ and WD had good predictive ability, although DIJ performed slightly better. Convergence difficulties were noted in some DIJ analysis where data were limiting. Missing records, especially at the beginning of a lactation, greatly influenced parameters a and b of the functions. It also resulted in estimates with large standard errors. Missing records in later lactation hardly affected the parameter estimates. The WD and DIJ functions showed superior fit to the data. The WD function demonstrated higher adaptability to various data characteristics than DIJ and could be used in situations where animal recording is not consistently practised and where recording of animal performance is routinely practised. DIJ function had high data requirements, which restricts it to dairy systems with consistent recording, despite easy physiological interpretation of its parameters. The number of TD per lactation could be reduced by minimising sampling frequency in the later lactation while maintaining the monthly sampling frequency in early lactation.

An investigation of the shape of the lactation curve and the mastitis incidence was conducted to identify whether management interventions of the lactation curve constitute a potential for reducing incidence of mastitis at herd level. Lactation curves were estimated to describe the variation of daily milk yield during the 305-d lactation period in Norwegian Red cows. Associations between mastitis incidence at herd level and lactation curve characteristics such as production level at onset of lactation, magnitude and time of peak milk yield, and increase and decrease of milk yield rates were studied. Data from 250 303 lactations occurring during 2005 and 2006 from 14 766 herds were obtained from the Norwegian Dairy Herd Recording System. Besides veterinary treatments, the records included information on monthly test-day milk yields. The shapes of the lactation curves at herd level were parameterized using a modified Wilmink model in two separate mixed model analyses. In the first analysis a subset of lactations with no records of veterinary treatments was used. Lactation curves from herds with high (>0·31 cases/305-d lactation) and low (<0·07 cases/305-d lactation) herd mastitis incidence rate were parameterized and compared for three separate strata of parity. The result showed that high herd mastitis incidence rate was associated with a low intercept (P<0·05), a steep slope before peak milk yield (P<0·01) and a rapid decline after peak milk yield (P<0·01). In the second analysis a subset of high-yielding lactations with veterinary treatments of mastitis only and lactations with no records of veterinary treatment were compared. This was done to investigate whether the findings at herd level were also reflected at cow level. These results showed that lactation curves from lactations with mastitis cases were associated with a steep slope before peak milk yield (P<0·05) in second and later parities and a rapid decline after peak milk yield (P<0·01) in all three parity groups.

Early lactation parameters are difficult to estimate from commercial dairy records due to the small number of records available before the peak of production. A biological model of lactation was used with weekly milk records from a single Holstein herd to estimate these early lactation parameters and the secretion rate of milk from the average cell throughout lactation. A genetic analysis of the lactation curve parameters, calculated curve characteristics and secretion rate traits was undertaken. Early lactation traits were found to have little genetic variation and effectively zero heritability. Secretion rate traits for milk, protein, lactose and water were all moderately heritable and highly genetically correlated (>0.87) but fat secretion rate had lower genetic correlations with the other secretion rates. A similar pattern of correlations was seen between total lactation yield traits for fat, protein, lactose and water. The genetic correlations between the lactation curve traits and the secretion rate traits were calculated. Total milk yield, peak yield and maximum secretion potential were all highly correlated with milk, lactose and water secretion rates but less so with fat and protein secretion rates. In particular, fat secretion rate had a moderate to low genetic correlation with these lactation curve traits. Persistency of lactation was highly correlated with fat and protein secretion rates, more persistent lactations being associated with lower rates of secretion of these milk components. Similar levels of heritability were found, where trait genetic parameters were directly equivalent to those derived from the same dataset by random regression methods. However, by using a biological model of lactation to analyse lactation traits new insights into the biology of lactation are possible and ways to select cows on a range of lactation traits may be achieved.

The aim of the work is to evaluate the effects of different forage to concentrate rations on milk yield, composition and renneting properties of milk of Jonica breed goats. Twenty-four Jonica goats received diets with forage to concentrate ratio of 35/65, 50/50 or 65/35, providing respectively a low, medium and high energy level. Goats were divided into three homogenous groups and confined in individual pens for 152 days to assess the daily feed intake and milk yield and composition. The main conclusions show that animal body weight did not change significantly with the increasing levels of forage, whereas significant differences (P<0·05) for daily dry matter intake were observed in relation to the evolution of lactation. Milk production was influenced (P<0·05) by dietary treatments and was higher in the diet with the greatest energy level. Forage to concentrate ratios did not significantly affect milk characteristics, milk renneting properties, initial production, rate of increase until reaching the peak and rate of decline after peak production. However, the day of peak production and peak production of goats were linearly reduced when the level of forage increased within the diet. In conclusion, the results indicate that both forage to concentrate ratio and energy level improve goat's production without influencing the milk composition.

Weekly locomotion scores on a scale of 1 to 5 were used to investigate the relationship between cattle lameness, management systems and the impact of lameness on milk production. The data were 14026 locomotion scores from 248 Holstein-Friesian cows. Cows were managed in two groups, XE (high-concentrate feed and housed indoors all year) and XM (low-concentrate feed and outdoors in summer). Analysis was performed using residual maximum likelihood. Results indicated that the most significant variables affecting locomotion were time of year when the animal was locomotion scored and management group. Cows scored during February and August had increased locomotion problems. Cows in the more intensively managed group had significantly poorer locomotion compared with those in the more extensive group. Older animals were more susceptible to lameness than heifers. Body weight, body condition score and days in milk (DIM) also accounted for significant variation in locomotion score. Poor locomotion was associated with a significant reduction in the milk yield of later lactation cows. There was a significant difference in the shape of the lactation curve depending on whether or not the cow was lame during lactation. Average persistency was greater for the group of cows never lame throughout lactation compared with those lame before 60 DIM.

A large number of environmental factors affect the daily milk production of a cow. Lactation curves included in the French test-day model are modelled as a function of days in milk with semi-parametric curves (splines). The proper modelling of environmental effects in the test-day analysis was investigated using test-day records collected from the first three lactations of French Montbéliarde cows from 1988 to 2005. Four lactation-curve effects describing calving month, length of dry period, age at calving and gestation defined within parity-class were fitted. The shape of lactation curves did not depend on year of calving, which can be modelled as a constant over the whole lactation. To reduce computational requirements and time, data were pre-adjusted in a first step for fixed effects with no year interaction, and then used for genetic evaluation. Correlations for each lactation between 305-day estimates of genetic and permanent environment effects computed using pre-adjustment factors obtained at a 4-year interval were virtually one. The use of a two-step procedure had a very limited impact on the estimates of genetic and permanent environment effects. The minimum correlations with values estimated with a one-step procedure were 0.9984 and 0.9974, respectively. The knowledge of systematic environmental effects affecting the cow daily yield through lactation curves offers interesting perspectives to predict future daily milk production.

Milk production and reproductive performance of pluriparous dairy cows was compared for cows whose lactations were induced by hormonal treatment or followed natural calving. The study was conducted on 179 high-yielding dairy cows in a large dairy operation in a hot arid environment of northern Mexico, where bovine somatotropin (bST) was routinely used in all cows. To induce lactation, 98 cows that had previously failed to become pregnant were treated with 500 mg bST on days 1, 8 and 21. From days 2 to 8, cows were treated with oestradiol cypionate (0·30 mg/kg live weight (LW) per day) and progesterone (0·28 mg/kg LW per day). From days 9 to 15, oestradiol cypionate alone was given. PGF2α was given on day 16. Nothing was administered on days 17 and 18, and 15 mg flumetasone was administered from days 19 to 21. Lactation was induced successfully in all 98 cows subjected to the hormone treatment. All cows received 500 mg bST every 14 days throughout lactation from 63±7 days after lactation had started. Cows with induced lactations produced less (P<0·01) milk per 305-day lactation (9599±1387 kg) than controls (12 302±1245 kg). Proportion of cows pregnant was similar in induced cows and non-treated cows (71 v. 75%). Induction of lactation was associated with increased numbers of services per pregnancy (5·8±4·0 v. 4·22±2·98; P<0·01) compared with controls; however, impaired reproduction might not necessarily have been related to the hormonal treatment to induce lactation, but due to the nature of the cows utilized for this treatment group. This protocol can be used on dairy farms where bST treatment and prolonged steroid administration of dairy cows is legally permitted.

Test day records of milk yield (38765), fat and protein contents (11357) of Sarda goats (the most numerous Italian goat breed) were analysed with mixed linear models in order to estimate the effects of test date (month and year of kidding for fat and protein contents) parity, number of kids born, altitude of location of flocks (<200 m asl, 200–500 m asl, >500 m asl), flocks within altitude and lactation stage (eight days-in-milk intervals of 30 d each) on milk production. All factors considered in the models affected milk traits significantly. Milk yield was lower in first parity goats than in higher parities whereas fat and protein contents showed an opposite trend. Goats with two kids at parturition had a higher milk yield than goats with one kid and tended to have lower fat and protein percentages. Repeatability between test days within lactation was 0·34, 0·17 and 0·45 for milk yield, fat content and protein content, respectively. Lactation curves of goats farmed at different altitudes were clearly separated, especially for milk yield. Results of the present study highlight differences in milk production traits among the three subpopulations that have been previously identified within the Sarda breed on the basis of the morphological structure of animals and altitude of location of flocks.

Advantages of the use of test-day records for genetic evaluation of dairy cattle are now widely accepted. In particular, longitudinal models such as random regression avoid using ad hoc extrapolation procedures to reconstruct complete lactations as they provide individual predictions even for incomplete data. However, these predictions and parameter estimates obtained in the model do not take into account the lactation length. This can be an important drawback for phenotypic and genetic analysis of milk production of cows with shorter lactations. The aim of this paper is to propose a methodology that would correct these predictions, weighting them by the probability at each point in time of each cow being dried off. The proposed procedure is easy to implement and calculations are fast to compute. A simulation study and an application on real data for daily milk records show that the proposed methodology provides a more accurate estimation for individual cumulative production as well as genetic values, and avoids predicting negative productions at the end of the lactation as is often the case with random regression models.

Milk yields of 66 nursing does recorded in Zaria, Nigeria were used to characterize the lactation curve and study the influencing factors in Red Sokoto goats. Lactation curve parameters obtained by fitting the model: Yt = atbe –ct were subjected to statistical analysis, using herd, season, parity, litter size and litter composition of dams.

The results indicate that the lactation curve of these goats was characterized by milk production increasing in early lactation, attaining a peak at approximately 2 to 5 weeks post partum and thereafter declining slowly to the end of lactation. The observed total yield, peak yield, peak day and the estimated persistency defined as c–( b + 1) was 79·3 kg, 1·2 kg, 20·5 and 143·2, respectively. Parameters ‘ a‘ and ‘ c‘ were strongly but negatively correlated ( r = –0·53; P < 0·01). The curve parameters ‘ a‘ and ‘ c‘ differed by herd and season ( P < 0·05); and parity only affected ( P < 0·01) parameter ‘ a‘. None of the factors significantly influenced parameter ‘ b‘ ( P > 0·05).

The significant herd and season effects may have practical implications in determining optimal feeding management and season of breeding to maximize total lactation yield.

Despite milk being an important product from sheep, there are very few reports of milk production from the complete lactation of dairy sheep. The Improved Awassi in Israel is kept under an intensive system of management with lambs being weaned soon after birth. Records from one such flock were analysed to investigate the suitability of various mathematical functions for describing milk yield from the complete lactations of dairy sheep. This included a consideration of whether the functions could cope with short lactations, a characteristic of dairy sheep, and a limited number of test-day records per lactation.

Four non-linear mathematical functions were investigated (Wood, Morant, Grossman and Pollott), two of which could also be fitted in a linear and a linear weighted form (Wood and Morant). These functions were fitted to weekly data from a ‘typical Awassi lactation curve’, represented by least squares means of daily milk yield from each week of a 40-week lactation derived from an analysis of 25605 test day records. Characteristics of the lactation were calculated from the functions, such as total milk yield, day and level of peak yield and persistency. These functions were also fitted to 1416 individual lactation records of up to 10 test-day records per lactation. The value of the functions was investigated using the residual mean square (RMS) of the fitted curve as an indicator of how well each function described the lactation. Forms of these functions with a reduced number of parameters were also investigated.

The non-linear functions always fitted the data with a lower RMS than their linear equivalent and the weighted form of the linear functions always had a lower RMS than the unweighted form. Of the linear functions, Morant fitted better than Wood. Of the non-linear functions Grossman, Morant and Pollott (additive and multiplicative) fitted the data equally as well but better than Wood. The various functions predicted characteristics of the lactation curve differently; the Wood functions tended to overestimate yield in early lactation and the Morant functions underestimated peak yield.

No function was better suited to short lactations than another. However the three-parameter function of Morant, Pollott multiplicative and Pollott additive were considered to be the most suitable for describing the complete lactation of dairy sheep.

Five published equations were compared on their ability to adjust different patterns of lactation curves. The equation y(t) = a exp(b1t'2/2 + b2/t – c(l + t'/2)t') with t' = (t – 21·4)/l00 (i) was retained because of the quality of the adjustment and the absence of convergence problems when applied on individual curves. Including an effect of season (SE) and an effect of pregnancy (PE) improved the quality of individual adjustments (no. = 339). The final equation was equal to (i) + SE + PE with SE = a + b cos (2π(wc + w - l)/52) + c sin(2n(wc + w - 1)/52), with wc= week of the year at calving, w = week after calving and a = 0·0065, b = -1·26 and c = 0·374, and PE = a (wp –18) e-bwp, with w p = week of pregnancy and a, b fixed parameters. Individual cow characteristics were used to analyse equation (i) parameters. The predictions obtained with this equation and several predictive functions of the equation (i) parameters, which differed in the way they included or not the potential of production, were compared. With no indication of this potential, the prediction was very poor. With the initial production (mean production of the 4th, 5th and 6th days of lactation) as an estimate of this potential, 75% of the lactations had the median of absolute values of errors less than 2·95 kg/day. The results were highly improved by using the yield during the 5th week of lactation. The threshold of 2·95 was reduced to about 2 kg/day. The quality of the individual prediction was better for primiparous than for multiparous cows, and for French Friesian and Montbeliarde cows than for pure or crossbred Holstein cows. Although individual predictions were not always satisfactory, they provided excellent agreement when averaged per group (20 cows).