Relationship between lactation curve function and phenotypic variance in random regression Test Day models

In Random Regression models (RRM), the most updated version of Test Day (TD)
models, the lactation curve is split into a fixed average curve and a random animal specific part (deviation from
the average curve) (Schaeffer, 2004). The variance component of the RR coefficients determines the (co) variance
function of each pair of days in milk (DIM) (Pool and Meuwissen, 2000). Very different patterns of variance
functions have been reported in literature, and several authors pointed out a possible rule of the type of
function chosen as RR sub-model and data structure (Kettunenet al., 2000; Meyer, 1998). Aim of this work is to investigate some possible reasons for such results, in particular the effects of the mathematical function and of the possible occurrence of different shapes of lactation curve (regular and atypical).