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A large number of environmental factors affect the shape of lactation curves. The association of these factors in groups of effects can be a good alternative for a better modelling of these factors of variations. Lactation curves for milk yield, fat and protein percentages of 5649 Tunisian Holstein-Friesian cows were modelled with the Wilmink's function. The effects of environmental grouped factors, calving age-parity, herd-calving year and calving season on the main lactation curve traits for milk yield, fat and protein percentages were analysed. The effect of calving age -parity was highly significant (p<0.01) for all lactation curve parameters for milk yield (expect for b), whereas for fat percentage, this factor affected significantly (p<0.01) the DIM of peak, the persistency and total fat yield (Y305). For protein percentage, peak yield, DIM of peak and persistency were significantly influenced (P<0.01). The herd-calving year effect was highly significant (p<0.01) for all parameters of the lactation curve of the daily milk yield and fat percentage except for parameter b and persistency. For protein, this effect was significant (P<0.05) for parameter b and persistency, and no significant for parameter c and total protein yield, and highly significant for other traits. Parameter b (for milk, fat and protein), Y305 (for fat) and persistency (for fat and protein) were independent to calving season (P>0.05). The association of the environmental factors into groups of effects allows a better description of the lactation curves and cow's performance. For example calving age- parity allowed fit and follow the individual lactation curve of the animals according to their parity in relation to their calving age. This aspect permits to reduce the number of factors and the levels of each factor in the models of analyses.
Keywords: dairy cows - lactation curve - grouped environmental effect - Wilmink's function
The association of environmental factors into effects group allows a better interpretation and description of parameters variation and lactation curve shape. For the parity and calving age effects we noticed the strong relationship between these two factors, thus for same calving age class we remarked the existence of several animals having different parities (table 1). So, it is interesting to consider the parity in relation to the calving age in an effect group. Several references have studied the variation factors of the lactation curve. However, numerous studies (Macciotta et al., 2006, Marisela et al., 2005, Tekerli et al., 2000) have been interested much more to the milk yield. On the other hand, studying mathematical properties of lactation curve provides summarized information about dairy cattle production, which is important for decisions on herd management (Silvester et al., 2006; Lin and Togashi, 2005 and Macciotta et al., 2005) and selection strategies and is a key element in determining optimum strategies for insemination and replacement of dairy cows (Vargas et al., 2000). Furthermore, analysis of lactation curve shape is important as it helps to identify feeding and management problems within a dairy herd (Epaphrase, 2004; Tekerli et al., 2000). Wood (1969) already commented on the fact that the shape of the lactation curve in cows is affected by not only biological factors such as age and fertility of the cow, but also by various environmental factors. Previous studies have reported the effects of environmental factors such as season, parity, age, pregnancy, feed and different management practices (Wood, 1972; Congleton and Everett, 1980; Grossman et al., 1986; Stanton et al., 1992; Tekerli et al., 2000 and Leclerc et al., 2008). Jamrozik and Schaeffer (1997) specified that test day yields for Holstein dairy cows are affected by factors such as breed, region, how the herd is managed, day of the year, parity, age at calving, month of calving, days in milk, pregnancy status, medical treatments and number of milking times per day.
The main objectives of the present research were to fit and estimate the parameters of lactations curves using Wilmink's function and to investigate the effects of some grouped environmental factors on the lactation curves components in Holstein dairy cattle of Tunisia.
Materials and Methods
A sample of 259,776 test-day records of 5649 Holstein-Friesian cows were collected by the National Centre of Genetic Improvement of Tunisia (CNAG: Sidi Thabet, Tunis). The original data concerned 188 herds during years 1994 to 2002. The data of cows having a lactation less than 305 days, were removed. On the other hand, when the lactation of a cow was longer than 305 days, only 305 day milk yield was used in the analyses. The data of cows having illnesses, which affect milk yield and those with very low milk productions or aberrant values for protein and /or fat contents were also excluded from the analyses.
Lactation curve Model
The exponential model of Wilmink (1987) was used to fit individual lactation curves with the main grouped factors:
The parameter K is connected to the time of lactation peak and usually assumes a fixed value, derived from a preliminary analysis made on average production Wilmink (1987). In a preliminary analysis, K was estimated at 0.065 for milk and 0.10 for fat and protein. When one has a mathematical model to fitting lactation, the peak yield (Peak) and the time to which one observes this maximum (DIMP) are obtained respectively like ordinate and X- coordinate of the point where the derivative of the mathematical function is cancelled from the equation of the model these parameters can be calculated as follows:
Persistency for milk, fat and protein yields is defined as the milk, fat and protein yields at one test expressed as a percentage at an earlier test, adjusted to a 30-day interval between tests. The Total of milk, protein and fat yields (Y305) was calculated by Fleischmann method.
Factors affecting the shape of lactation curves
To fit and study factors which affect the shape of lactation curves, data used in this work were grouped according to following factors:
Groups according to the calving age associated with parity
Six groups were edited according to calving age and parity (Table 1). Effects of calving age on milk production were generally studied to facilitate comparison of cow differing in maturity (Leclerc et al., 2008). According to Grossman et al. (1986), the effect of the calving age on the shape of lactation curves is explained by a difference of lactation number between the first lactation and the following one.
Groups according to Herds - calving year
Jensen (2001) recommended including the herd effect for modelling of lactation curves. Smith et al.(1962), Wiggans and Van Vleck (1979) and Grossman et al. (1986) reported that the level of dairy production of the herd affects lactation curves. Three groups of cows were formed according to the level of production of the herds on calving years.
Groups according to calving season
The calving months were grouped in 4 seasons: winter (December - February), spring (Mars - May), summer (June - August), and fall (September - November) (Tekerli et al., 2000; Rekik et al., 2003). The effects of calving age-parity, herds-calving year, calving season and first test-day date on lactation curves traits were analysed by a general linear model:
Where: a lactation curve trait of milk or its composition (fat and protein) based on observation n in calving age - parity group i (i=1,2,3,4,5,6), belonging to group of herd - calving year (j=1,2,3) and has calving season k (k=1,2,3,4); = overall mean; =effect of calving age - parity ; HCY= effect of herd- calving year; S= effect of calving season; b= regression coefficient; TD= first test day (co-variable) and e= random residual with an expected value of zero and a variance of .
Results and Discussion
Factors affecting the shape of lactation curves
The ANOVA mean squares of calving age-parity herd-calving year, calving season and DIM at first test-day on lactation curve traits are presented in table 2. Moreover the least square means of level effects and the coefficient of regression on DIM at first test-day are expressed by table 2. The coefficient of determination ranged from 0.03 for a (factors associated with the inclining slope of the lactation curves for protein percentage) to 0.55 for peak yield (for milk yield). These results are similar to some other previous findings (Tekerli et al., 2000; Rekik et al., 2003). The effect of calving age-parity was highly significant (P<0.01) for all lactation curve traits (except for b) of milk yield. This effect was not significant (P>0.05) on b and c for fat and protein percentage, but significant (P<0.05) on a for fat and protein percentage, peak yield for fat and Y305 for protein and highly significant (P<0.01) for the other traits. The effect of herd-calving year was highly significant (P<0.01) for all lactation curve traits of milk yield except for b and persistency. This effect was significant (P<0.05) on b and persistency for protein, with any effect on b and persistency (for fat) and on c and Y305 (for protein). The remaining traits (table 2) were strongly significant (P<0.01) for the indicated effect. Parameter b (for milk, fat and protein), Y305 (for fat) and persistency (for fat and protein) were independent to the calving season (P>0.05). The total yield (Y305) for milk and protein were significant (P<0.05) and the remaining parameters were highly significant (P<0.01) for the calving season effect. The DIM at first test-day was highly significant (P< 0.01) for all lactation curves traits of milk yield, except for persistency degree and total milk yield. This factor did not have any effect on a and persistency degree (for fat) and on a, b, c, persistency and Y305 (for protein).
The least squares means (table 3) of the calving age-parity shows a significant difference between the first and the other calving age groups associated with the parity. This difference is characterized at first by the parameter a, which expresses the increasing phase of lactation, the parameter c which expresses the decreasing phase of lactation and by the peak yield, DIM at peak, persistency degree and total milk yield at 305 days of lactation for milk, and different primarily by the parameter a, peak yield, persistency and Y305 for the fat percentage, whereas for protein percentage of only the peak of production and the persistency which expresses this difference.
The three groups of herds formed by classes of calving year present the same parameter b which expresses the ascending phase of the dairy production and were of the same level of persistency and different for the other lactation curve traits (for milk, fat and protein).
The least square means of lactation curves parameters according to the calving season (tables 3 and 4), show that the cows initiate their lactation in a different way (parameter a) for milk and fat, then this production evolves in the same way during the ascending phase (parameter b) showing the independence of this phase of the calving season for milk, with a light difference for fat and protein percentage. Then the cows reach their peak of production has slightly different dates (with a difference especially between winter and fall calving seasons for milk, winter-fall and spring- summer for fat and winter- fall, spring and summer for protein), but produce different yields with the peak, between spring, summer, winters and fall calving seasons for milk, completely different for fat and a difference enters winter-spring and summer-fall for protein. In spite of this difference of the variation of the shape of the lactation curve between calving seasons, animals produce similar 305 days milk yield with the same level to persistency for winters, fall and spring and different only from the summer calving seasons for milk, and the same yield and persistency for fat.
Goodness to fit and the average of individual lactation curves traits with main grouped effects
The Wilmink's model shows a good description of the data following quality of adjustment obtained expressed by the coefficient of determination (R2) which varies from 0.97 to 0.98 for milk, 0.97 for fat percentage and 0.99 for protein percentage The averages of the absolute error (RES) are from 1.68 to 2.34; 0.37 to 0.41 and 0.16 to 0.17 respectively for milk yield, fat and protein percentage.
The percentage of the atypical curves varies from 17.93 to 21.4 % for milk yield, and from 29.84 to 37.45 % and 16.54 to 29.69 % for fat and protein percentage, respectively. For studies on milk yield, Tekerli et al. (2000) reported 26.3% of atypical curves on a total of 1278 lactation; Rekik et al. (2003) reported 15% to 42 % atypical curves in different types of herds in Tunisia, and Shanks et al. (1981) reported 840 atypical lactations of 113705 lactation. Silvester et al. (2008) reported that curves for fat and protein percentage showed the reversed standard shape in 62.4 and 66.4% of the lactations ,respectively, followed by standard shape (23.7 and 19.4% respectively).
The cows of the first group (associated with calving age-parity) produced lower milk, fat and protein yields than the other groups. However, we reported a difference in 668 kg of milk, 28 and 25 kg of fat and protein compared to the maximum of the production recorded in the others groups. Thus the cows of this group reach their peak later (at 7 to 8 weeks of lactation) and produce less with the lactation peak, but they are more persistent for milk, fat and protein. Indeed, 97.09% of the cows of this group are in first parity (primiparous) and whose calving age varies from 16 to 36 months. This aspect is explained by the fact that the tissues of milk secreting in the animals to take more time to reach its maximum activity among primiparous cows (Rao and Sundaresan, 1979). The peak yield is obtained with the third group made up of 76.79% of the cows in the third parity (calving age from 50 to 62 months). For milk composition this peak yield for milk protein percentage is obtained among younger animals, belonging to the second group of which 88.24% of the cows are in the second parity (calving age from 37 to 49 months) and obtained for milk fat percentage among cows with more advanced calving age (75 to 87 months) and whose group of association is made of 23.77 % of the cow in 4th parity and 65.72 % have reach their 5th parity. The 305 day milk yield (6041 kg) is allowed by cows of which calving age is ranging from 63 to 74 months, mainly in 4th parity (69.73 %) and 21.31 % are in third parity. The total fat yield is allowed by older animals, that is to say 204 and 205 kg respectively for the 5th and the 6th group (corresponding to calving age from 75 to 164 months) and whose majority of the animals are between 5th (65.72 %) and 6th (43.49 %) parity. Finally, the total protein yield (Y305 = 178 kg) is recorded with cow of the third group (76.76 % in third parity) and 4th group (21.31 % in third parity and 69.72 % in 4th parity) and with a calving age ranging between 63 and 74 months. The cows of the 4th, 5th and 6th groups aged more than 5 years had the lower persistency for milk production, fat and protein. The averages of the individual lactation curve parameters belonging to the second group of herd effect associated with calving years shows that calving years 1994; 1996; 1999 and 2002 were more favourable to the dairy production, which results in the highest milk and fat yields produced over 305 days of lactation, with a difference in 283 kg of milk and 20 kg of fat. Moreover, cows of this group produce more at the peak compared to the herds of the first group which have the minimal productions. For protein, the cows of the second and third groups gave more quantity of protein compared to the first group, but the third group was more persistent and produces more at lactation peak.
The averages of individual lactations (tables 5 and 6) according to the calving season showed a seasonal variation of the parameters of the lactation curves. Similar results were reported for this effect on the milk yield (Shanks et al., 1981; Tekerli et al., 2000; Rekik et al., 2003). Seasonal effect on lactation curves for fat and protein have been described (Stanton et al., 1992) by a mixed model. Indeed, the cows which calved in winters and in autumn had the highest yields at the lactation peak and produced more milk, fat and protein than those calving in spring and summer. Calving of winters is more persistent than the other calving season for milk, fat and protein. The weakest persistency degree of fat (84.21 %) is obtained among cows which calved in summer.
Fitted lactation curves for different grouped environment effects
Fitting lactation curve with various grouped effects is expressed by figures 1, 2 and 3, respectively for calving age-parity; herds-calving years and calving season effects. This result shows a variation of the shape of the lactation curves with the described effects. For the calving age-parity effect, the lactation curve for cows of first group (primparous) distinguished clearly from other groups with more flattened general form, lactation begins with a low level from initial production (roughly 18 kg against 23 to 24 kg for the other groups), then the production increases slowly to reach the peak of production and finally this production falls with a rhythm of decrease slower than the other groups. This evolution of form confirms the results obtained with numerical values indicating the primiparous cows are more persistent. Between 200 and 305 DIM of lactation, the lactation curves of various groups approach, and the cows of the first and second groups (mainly in second and the third lactation) finish their lactation with the highest level of production. Whereas, animals of the 6th group (calving age > 8 years) give the lower level of production at the end of lactation (12 kg at 305 days of lactation).
The shape of the lactation curves of 2nd, 3rd, 4th, 5th and 6th groups presents one similar general pace, in the form of bundles with superior limit the lactation curves of the cows of the third group and the curve of the cows of the 6th group like inferior limit, intercalated by the curves of the other groups.
For fat and protein percentage, the inferior curve is that of the first group like the milk yield, but the superior curve is that of the second group. Lactations are initiated with a similar level of milk composition (in fat and protein) with the highest initial percentage is obtained with cows of second group. The decreasing phase follows the same space for the various groups, but different before reaching the peak and finally the shape of the curve different between groups. According to the figures 1-b and 1-c, the milk richest in fat and protein during the duration of lactation is obtained with the cows in second lactation (88.24 %) and from calving age varies from 37 to 49 months. Figure 3, expresses the effect of the calving season on the shape of the lactation curve. For milk yield the form is different during the phases: initial, increasing and decrease passing by a peak of production different, then the curves approach at the 240 days from lactation. For the fat and protein percentage calving season involves different forms from the lactation curve but which is remarkable the summer season involves a complete modification of the shape of the lactation curve for fat percentage what gives an atypical form.
Herd - calving year affects the shape of the lactation curves (figure 2) for milk yield and its composition involving a modification of various phases of the shape of the lactation curve. This variation can be explained by several factors such as the climatic conditions which change according to the years and which affects the food of the cows by the quantity and the quality of forage produced and the management practices of the breeding change between the herds, what affects the level of production of the cows.
Wilmink's function was used to evaluate the effects of some environmental factors affecting lactation curve parameters as well as some production characteristics of Tunisian Holstein-Friesian cows. It seems that the Wilmink's model allows a good description of the data by good quality of adjustment obtained for the milk yield and for fat and protein percentages shown by the values obtained from coefficient of determination and the residual. The use of the groups which associates the factors of environment makes it possible to better study the effect of these factors on the parameters and the shape of the curve of lactation. According to the results obtained with the data used in this study, primparous cows produced lower milk, fat and protein yields, reach their peak later (at 7 to 8 week of lactation) and produce less with the lactation peak, but they are more persistent for milk, fat and protein. The peak yield is obtained among cows with cows in the third lactation (calving age 50 to 62 month) for milk; 4th to 5th parity (calving age 75 to 87 month) for fat and in second parity (calving age 37 to 49 month) for protein. The maximum of total 305 day yield is recorded by cows: for milk and protein (3rd to 4th parity; calving age 63-74 month), for fat (5th to 6th parity; calving age 75-164 month). The averages of individual lactations according to the calving season showed a seasonal variation of the shape of the lactation curves.