Prediction of first lactation total milk yield using part lactation performance trait in Hariana cattle

Introduction

Hariana cattle, one of India's prominent dual-purpose zebu breeds, play a central role in the dairy economy of northern states owing to their adaptability, disease resistance, and suitability for smallholder production systems. The native breeding tract of Hariana cattle encompasses a large part of Rohtak, Hisar and Gurgaon districts of Haryana (Joshi et al., 1995) [1] . Although the breed is valued for its resilience, its milk production levels are considerably influenced by early-life growth, reproductive performance, and management conditions. Among the various production traits, First Lactation Total Milk Yield (FLTMY) remains a critical benchmark because it provides the earliest and most dependable indication of an animal's future milkyielding ability. Reliable prediction of FLTMY is therefore essential for informed selection, scientific heifer replacement decisions, and maximising genetic progress in Hariana herds. Conventional selection tools for FLTMY often rely on pedigree-based estimates or single-trait assessments, which may overlook the complex interactions that shape milk performance in indigenous breeds. Hariana cattle display considerable variation in reproductive milestones, lactation dynamics, and environmental adaptability, making trait prediction more challenging but also more important. Daily milk production is a readily available and widely recorded parameter on farms adopting smart technologies, making it a primary focus of analysis (Song et al., 2025) [5] . With the increasing availability of herd-level data, advanced statistical and computational approaches offer new possibilities to quantify trait relationships more accurately. Prediction models built on multivariate trait associations integrating reproductive parameters, early-lactation indicators, and biometric measures can provide a practical, fieldoriented tool for forecasting FLTMY before calving.

As per Wisnieski et al. (2019) [2] predictive modeling is a data-driven approach that efficiently integrates the most influential variables and their interactions to forecast current or future outcomes. Such models help identify promising heifers at an early stage, reduce uncertainty in breeding decisions, and improve economic efficiency for farmers and breeding organisations. The present study focuses on developing and evaluating robust prediction models specifically for Hariana cattle, with the aim of identifying potent predictor traits and generating reliable, easy-to-use equations for field applications. This work acknowledges the unique biological and management characteristics of the breed and contributes to data-driven improvement strategies for India's indigenous cattle resources.

Materials and Methods

Data source and traits studied

The present study was conducted using first-lactation performance records of Hariana cattle maintained at the Livestock Farm Complex (LFC), DUVASU, Mathura, over an extended period from 1964 to 2025. Only animals with complete and reliable first-lactation records were included in the analysis. The traits considered were age at first calving (AFC, days), first lactation length (FLL, days), 30-days milk yield (30DMY, litre) and first lactation total milk yield (FLTMY, litre). FLTMY was treated as the dependent variable, whereas AFC, FLL and 30DMY were considered as predictor variables for developing prediction models.

Data editing and preliminary analysis

Prior to statistical analysis, the data were screened to remove records with missing values or biologically inconsistent observations. Descriptive statistics including mean, standard deviation and range were computed for all traits. Outliers, when detected, were handled using the ± 3 standard deviation criterion. To ensure uniformity in scale and improve model stability, all variables were standardised before regression analysis.

Development of prediction models

Multiple linear regression models were developed to predict FLTMY using different combinations of predictor traits. The general linear regression model applied was:

Where Y represents FLTMY, X₁, X₂ and X₃ denote AFC, FLL and 30 DMY in various combinations, β₀ is the intercept, βᵢ are the regression coefficients and ε is the random error term. Seven models were evaluated, including single-trait, two-trait and three-trait combinations of AFC, FLL and 30DMY. Regression coefficients were estimated using the least squares method.

Assessment of collinearity and model diagnostics

Multicollinearity among predictor variables was assessed using Variance Inflation Factor (VIF) and tolerance values.

Model evaluation criteria

The predictive performance of different models was compared using coefficient of determination (R²) as suggested by Saunders et al. (2012) [4] , root mean square error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE) and Theil's U statistic as suggested by Maheta (2019) [3] . The best-fitting model was identified based on higher adjusted R² values coupled with lower error statistics, particularly RMSE and U values.

Software used

All statistical analyses and regression modelling were carried out using R, Microsoft Excel and SPSS, employing standard linear modelling procedures and diagnostic tools.

Results and Discussion

Multicollinearity among predictor variables

Multicollinearity among the independent variables considered for prediction of first lactation total milk yield (FLTMY) was assessed using the Variance Inflation Factor (VIF). The VIF values for first lactation length (1.236), age at first calving (1.008) and 30-days milk yield (1.235) were well below the critical threshold, indicating absence of serious multicollinearity among predictor traits. These low VIF values confirm the stability of regression coefficients and reliability of parameter estimates in the developed prediction models. 2. Among the single-trait models, FLL was the most important predictor of FLTMY, explaining 56.94 per cent of the total variation. The model based on 30DMY accounted for 33.15 per cent variation, whereas AFC alone exhibited very poor predictive ability (R² = 0.50%). These results indicate that lactation-related traits contribute more effectively to prediction of FLTMY than reproductive traits when used independently. the AFC and 30DMY model showed inferior performance.

The three-trait model including AFC, FLL and 30DMY yielded a slightly higher coefficient of determination (64.98%). However, the gain in R² was negligible compared to the two-trait model, while requiring inclusion of an additional predictor variable. The superiority of this model highlights the biological significance of lactation length and early milk yield in determining total lactation performance. First lactation length reflects milk persistency, while 30-days milk yield serves as an early indicator of lactation potential. These findings suggest that early lactation traits can be effectively utilised for early selection and genetic improvement programmes in Hariana cattle.

References

1. Joshi BK, Tantia MS, Kumar P, Gupta N, Vij PK, Nivsarkar AE, et al. Hariana cattle: A monograph on breed charcteristics, National Bureau of Animal Genetic Resources; 1995.
2. Wisnieski L, Norby B, Pierce SJ, Becker T, Sordillo LM. Prospects for predictive modeling of transition cow diseases. Animal Health Research Reviews. 2019 Jun;20(1):19-30.
3. Maheta D. Forecasting nifty and sensex series using Theil's U statistic. International Journal of Advanced Science and Technology. 2019;28(16):246-251.
4. Saunders LJ, Russell RA, Crabb DP. The coefficient of determination: what determines a useful R2 statistic?. Investigative Ophthalmology & Visual Science. 2012 Oct 1;53(11):6830-6832.
5. Song JW, Lee M, Cho H, Lee DH, Seo S, Lee WH. Development of individual models for predicting cow milk production for real-time monitoring. Computers and Electronics in Agriculture. 2025 Jan 1;228:109698.