Lactation curve model with explicit representation of perturbations as a phenotyping tool for dairy livestock precision farming

Abstract

24Background 25Understanding the effects of environment on livestock provides valuable information on how 26 farm animals express their production potential, and on their welfare. Ruminants are often 27 confronted with perturbations that affect their performance. Evaluating the effect of these 28 perturbations on animal performance could provide metrics to quantify how animals cope 29 with their environment and therefore better manage them. In dairy systems, milk production 30 records can be used to evaluate this effect because (1) they are easily accessible, (2) the 31 overall dynamics throughout the lactation process have been widely described, and (3) 32 perturbations often occur and cause milk loss. In this study, a lactation curve model with 33 explicit representation of perturbations was developed. 34 Methods 35The perturbed lactation model is composed of two components. The first one describes a 36 theoretical unperturbed lactation curve (unperturbed lactation model), and the second 37 describes deviations from the unperturbed lactation model. The model was fitted on 319 38 complete lactation data from 181 individual dairy goats allowing the characterization of 39 individual perturbations in terms of their starting date, intensity, and shape. 40 Results 41The fitting procedure detected a total of 2354 perturbations with an average of 7.40 42 perturbations per lactation. Loss of production due to perturbations varied between 2 % and 43 19 %. Results show that it is not the number of perturbations is not the major factor 44 explaining the loss in milk yield over the lactation, suggesting that there are different types of 45 animal response to disturbing factors. 46 Conclusions 47 * ( ) = • • − • 128where * ( ) is the unperturbed daily milk yield in kg, is the time in days after parturition 129 and , , are positive parameters that determine the shape of the lactation curve ( scales the 130 general level of the curve, controls the type and magnitude of the curvature of the function, 131 and regulates the rate of decrease in milk yield after the lactation peak). Values of these 132 parameters can be used to calculate some essential features of the lactation curve such as the 133 time of peak yield ( ⁄ , in days), the lactation persistency, i.e., the extent to which peak yield 134 is maintained (−( + 1) • ( ) in kg.d -1 ), or the peak yield ( • ( ⁄ ) • − in kg) [16]. 135Perturbation model 136

The geometry of the lactation curve based on Wood's equation: a two-step prediction

“…We choose equation 1 because of its flexibility and feasibility to mimic lactation records as demonstrated by several authors (Dijkstra et al, 2010;Ferreira et al, 2015;López et al, 2015;Ahmed et al, 2019). The geometric properties of equation 1 are nonlinear functions of its parameters.…”

“…In addition, we can use those parametric estimates to predict the impact of long-term environmental constraints over milk production trends (Wood, 1972), e.g., the attenuation or worsening of the effects of the oxidative stress over the secretory capacity of the mammary gland, and the consequent result in milk production (Bernabucci et al, 2002(Bernabucci et al, , 2005. Other solutions may be of use for shortterm effects that dramatically alter the lactation trends (Ahmed et al, 2019).…”

“…Nevertheless, there are literature reports that present the difficulty of some mathematical models to fit atypical lactation profiles, which include profiles with an insufficient number of records to characterize the entire lactation, concave-shaped profiles, as well as those profiles that present an irregular distribution of milk records over time. Furthermore, some studies have emphasized that genetics, diet, parity order, season, metabolic disorders, diseases, and other environmental aspects are responsible for the occurrence of atypical lactation profiles (Wood, 1968(Wood, , 1970(Wood, , 1972(Wood, , 1976(Wood, , 1980Grossman and Koops, 1988;Olori et al, 1999;Rekik and Ben Gara, 2004;Dijkstra et al, 2010;Hossein-Zadeh, 2016;Ahmed et al, 2019). These factors might explain why some models are unsuccessful in fitting some lactation records.…”

“…These types of lactation profiles occurred for groups BPO 41 and BPO 43 , which might be associated with the poor dairy temperament of Zebu breeds and its crossbreeds with dairy breeds (Bangar and Verma, 2017). Sometimes, even cows that exhibited a typical convex-shaped lactation profile in a previous lactation fail to present a peak milk yield in a further lactation, because of environmental factors such as metabolic disorders, mastitis, other diseases, and nutritional or other management errors (Wood, 1968(Wood, , 1970(Wood, , 1972(Wood, , 1976(Wood, , 1980Macciotta et al, 2005;Hossein-Zadeh, 2016;Ahmed et al, 2019). Nevertheless, the cows that presented typical convex-shaped lactation profiles were those that produced more milk in the entire course of lactation than their counterparts did.…”

Developing smart fitting algorithms to identify random perturbations in time-series data

“…In dairy systems, it is well known that milk yield can be affected by problems such as udder health problems [1], lameness [2], heat stress [3] or nutritional challenges [4]. Such problems induce perturbations in the course of the lactation process and result in a serrated shape pattern in the lactation curve.…”