Determining the best predictive function to mathematically describe the lactation curve of primiparous Murcia does in Iran

Abstract

Dairy goats play a key role in production of dairy products in rural Iranian farming. This study has compared four general functions: Wood, Wilmink, 2-parameter Pollott function, and Dijkstra, to fit the lactation curves and also to predict total milk yield (TMY) using 11,451 test-day (TD) milk records from first-parity Murcia does (2018–2024). Two scenarios were analyzed: (1) using all does (with 4–8 TD) and fitting Wood, Wilmink, and Pollott functions, and (2) using does with full TDs (with 8 TD) and fitting all four functions. In the first scenario, Pollott function demonstrated the highest percentage of typical lactation curves (63.6%), followed by Wood (55.7%) and Wilmink (48.0%) functions. In the second scenario, Pollott function again outperformed the other functions, with 73.7% typical lactation curves. Based on the information criteria (IC), although Wood function performed well considering Akaike’s IC (AIC), Pollott function was the best regarding the corrected AIC (AICc) across both scenarios. Moreover, a comparison of the predicted lactation curves and the curve with real (observed) data, revealed that Pollott function more accurately predicted daily milk production, especially during the middle of lactation. Furthermore, the analysis of parameter correlations and variance inflation factors (VIF) indicated that the Pollott function effectively avoided multi-collinearity and over-fitting. It exhibited the lowest parameters correlations and VIF values among the fitted functions, with VIFs of 1.15 and 1.02 in the first and second scenarios, respectively, substantially lower than those of other functions. Consequently, based on comprehensive evaluation measures, including the number of typical curves, biological interpretation, IC, VIF and correlation of the parameters, and real and predicted data accordance; the Pollott function demonstrates robust performance and could be recommended for practical applications.