Genetic Evaluation of Murrah buffaloes by fitting Random Regression Models using B-spline function - Ranjan, Ashish; Dr. ANAND JAIN; Dr. ARCHANA VERMA; Dr. RANJANA SINHA; Dr. POOJA JOSHI; Dr. G. R GOWANE (The Indian Journal of Animal Sciences, 2026)
In the present study, random regression models with both random and ﬁxed effect regressions ﬁtted by B-spline functions were used to estimate genetic parameters with 5 knots. The common effects for all models were month of recording, year of recording as ﬁxed regressions on daily milk yield records and random regressions for additive genetic and permanent environmental effects. Among model studied with B-spline functions considering homogeneity and heterogeneity of residual variances, the model that best fit the data was BSQ5H1 (quadratic B-spline model of polynomial order 6 with homogenous residual variance) having knot at 5th, 80th ,155th, 230th  and 305th  DIM for the first lactation daily milk yield records of Murrah buffaloes. For BSQ5H1, the R2 value with estimated arithmetic mean of daily milk yield for first lactation was 93.7%. The highest values of additive genetic (1.22kg2) and permanent environment variance (5.27kg2) were observed in the initial (5th) and last (305th) DIM of lactation. Heritability estimates ranged from 0.07±0.05 to 0.21±0.07. It was observed that the heritability estimates were higher in early and late lactation while lower in mid of lactation (DIM 110 to 154). The estimated value of genetic correlation ranged from -0.50 (DIM 5 with DIM 174 to DIM 187) to 1.00. The DIM 5 had negative genetic correlations with peak yield DIM 65 to DIM 243. The rank correlation between sires with 6th order of Legendre polynomial function (RLP6) with BSQ5H1 was more than 0.99 and highly significant (P