A novel method of estimating milking interval-adjusted 24-h milk yields in dairy cattle milked in automated milking systems

Mechanistic models are valuable tools for studying the underlying mechanisms of complex biological phenomena. For example, cow lifespan models can be used to identify differences in resource acquisition and allocation strategies between individuals, which is relevant for decision-making in breeding programs. In such models, differences in simulated traits between individuals are consequences of the parameter set that represents the genetic potential of each animal and its interaction with the environment. This indicates that the identification of these differences is essentially a search for individual parameters. In mechanistic models, this search is generally a non-convex problem that has different local minima because the parameters interact within these models. Due to this and to the simulation time length (e.g. years), there is uncertainty associated with the inference of the parameter values for each individual. This uncertainty can be quantified using Bayesian inference since this approach treats the model parameters as random variables with an underlying probability distribution that describes them. The objective of this work was to employ the Delayed Rejection Adaptive Metropolis (DRAM) algorithm to identify the parameters of a cows’ lifespan model using two datasets of Holstein cows. The datasets contain periodic measurements of Milk Yield (MY), BW, and Body Condition Score (BCS). Additionally, one of the two datasets has information of BW from birth to first calving. The average Mean Absolute Percentage Error (MAPE) minimisation between the simulated and experimental data (MY, BW and BCS) was used as the objective function for parameter search. The Bayesian inference performance was compared with four optimisation metaheuristic approaches: Differential Evolution, Genetic Algorithm, Particle Swarm Optimisation, and Simulated Annealing. Although the results show that all methods are efficient in finding parameter values that reduce the distance between the simulated and experimental data (MAPE < 10%), the DRAM method is more efficient in terms of computational cost, and the parameter distributions obtained with this method offer more information about the statistical properties of each parameter (e.g. median).

Various studies with growing ruminants report increases in nitrogen use efficiency (NUE) when feeding oscillating (OS) dietary CP, whereas limited research with lactating dairy cows demonstrates a lack of improvement in NUE when feeding OS diets. We hypothesised that a total mixed ration (TMR) delivering OS CP (48-h phases of 134 and 171 g CP/kg DM, respectively) compared to a static CP TMR (ST; 152 g CP/kg DM) would result in similar or increased urinary purine derivative excretion (as a marker of microbial protein synthesis (MPS)) and greater urinary nitrogen excretion in lactating dairy cows. Responses in intake, production, apparent total tract digestibility (ATTD), nutrient balance, and estimated MPS were evaluated using faecal and urine collection in 12 multiparous cows (172 ± 39 d in milk) in a randomised complete block design, where total urinary output was estimated indirectly. All measurements were taken during d 8 (at 1700) to d 16 (at 1700) of the 16-d study that followed a 28-d period in which cows already received their respective treatments. Dry matter intake, yields of milk, protein, fat, lactose, and fat- and protein-corrected milk were similar for ST and OS. Milk composition, BW, and body condition score also did not differ between treatments, except for a tendency for increased milk urea concentration with OS (13.7 vs 12.4 mg/dL). Feed efficiency, NUE and ATTD of organic matter, NDF, CP and gross energy did not differ, but ATTD of crude fat (658 vs 627 g/kg) and starch (980 vs 975 g/kg) increased, and ATTD of DM (702 vs 691 g/kg) tended to increase with OS. Milk energy as a proportion of digested energy tended to decrease with OS (34.6 vs 37.1%), but other energy metabolism variables were not affected by treatment. Estimated urinary nitrogen excretion increased (165 vs 144 g/d), estimated urinary nitrogen as a proportion of nitrogen intake tended to increase (25.3 vs 22.7%), and milk nitrogen as a proportion of digested nitrogen decreased (47.3 vs 51.8%) in response to OS. Estimated urinary excretion of creatinine (184 vs 165 mmol/d), uric acid (29 vs 20 mmol/d) and urea (3.1 vs 2.5 mol/d) increased, but other nitrogen metabolism parameters were not affected by OS. Overall, oscillating dietary CP content did not affect lactational performance, milk NUE, or estimated MPS. However, ATTD of some nutrients increased, postabsorptive energy use for milk synthesis tended to decrease, and estimated urinary nitrogen losses increased with OS.

Irregular milking intervals in automated milking systems contribute to additional variation in daily milk yield records in comparison to those derived from systems using regular milking intervals. Various methods have been developed to estimate 24-h adjusted milk yields, though they are not well suited for the evaluation of serial milk yield data, particularly when milking intervals span calendar days. The objective of this study was to develop a methodology to estimate serial 24-h milk yields by adjusting for irregular milking intervals. Using data collected from an automated milking system (AMS), the total yield at a given milking event and the elapsed time from the previous entry into the AMS were used to calculate the milking interval and the average rate of milk secretion over that interval. Milking intervals and associated milk secretion rates were then realigned to calendar days to allow the proportional distribution of milk yield when milking intervals spanned more than one day. Using this method, variation in daily milk yield was decreased and adjusted estimates of 24-h milk yield were visually more similar to those typically observed in milking systems with regular milking intervals. Estimates of interval-adjusted milk yields were strongly correlated to those calculated using moving averages, suggesting that this method can yield comparable results to established methods for estimation of test-day milk yield.