Accurate mathematical models to describe the lactation curve of Lacaune dairy sheep under intensive management

Abstract

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 5 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 application of a mechanistic model to analyze the factors that affect the lactation curve parameters of dairy sheep in Mexico

“…The substantial difference of parameters that define the patterns of lactation curve and milk yield between lactation numbers are probably related to the biology of the mammary gland.. By interpreting the biological parameters from Pollott´s model, it can be established that the maximum TMY reached in third lambing is associated with lower decline in the udder cells (DR). This disagrees with the results from the Awassi (Pollott and Gootwine, 2004) and Lacaune sheep (Elvira et al, 2013a), both studies showed that milk yield declined as the ewes aged. Also DR increased and MS declined as lambing number increased.…”

“…Flock 1 had the highest TMY, lowest DR (0.12, P = 0.03) and a trend to have the highest level of MSmax (3.43 L, P = 0.08). Hence, higher milk yields are associated with higher MSmax and lower rate of decreasing number of mammary cell due to apoptosis (DR) (Elvira et al, 2013a); fortunately, these parameters were negatively correlated (r = -0.35). MSmax is highly correlated with the peak yield (r = 0.99) (Pollott and Gootwine, 2004).…”

“…This mechanistic model mimics three processes that occur during pregnancy and lactation: differentiation of mammary secretory cells, programmed secretory cell death (apoptosis) and milk secretion cell per cell (Pollott, 2000). Pollott's model has been compared to empirical and mechanistic models of lactation curve fitting (Angeles-Hernandez et al, 2013;Elvira et al, 2013a;Pollott and Gootwine, 2000) and this model have been found to be the bestfit method using sheep's milk yield records; also, it has the advantage that it provides parameters which can have biological interpretation.…”

Diversity of dairy goat lactation curves in France

“…Research on shape of the lactation curve has mainly addressed milk persistency, trying to find indicator criteria of the slope of the curve after the peak of lactation (Gengler, 1996), or modeling of overall curve shape. Some authors have focused on finding mathematical models that describe the biological processes of milk production by mammary gland cells (Pollott, 2000;Elvira et al, 2013a). Others have proposed a statistical approach by modeling the shape of the curve from elementary controls such as random regression testday models including genetic and nongenetic effects (Menéndez-Buxadera et al, 2010;Mucha et al, 2014;Brito et al, 2017) or by using methods such as principal component analysis (PCA) to sum up the information contained in the data (Carta et al, 2014).…”

Potentials of using milk performance data and FAMACHA score as indicators for Targeted Selective Treatment in Lacaune dairy sheep in Switzerland

“…In Lacaune dairy sheep the lactation peak occurs between the 27 th and 48 th day postpartum depending on the lactation number. Until the 90 th day, 50 % of the total milk yield is usually produced ( Elvira et al, 2013 ). Thus, in this study we covered only the two last thirds of the lactation period where milk yield is already decreasing.…”