Statistical models for estimating the genetic basis of repeated measures and other function-valued traits

The genetic analysis of characters that are best considered as functions of some independent and continuous variable, such as age, can be a complicated matter, and a simple and efficient procedure is desirable. Three methods are common in the literature: random regression, orthogonal polynomial approximation, and character process models. The goals of this article are (i) to clarify the relationships between these methods; (ii) to develop a general extension of the character process model that relaxes correlation stationarity, its most stringent assumption; and (iii) to compare and contrast the techniques and evaluate their performance across a range of actual and simulated data. We find that the character process model, as described in 1999 by Pletcher and Geyer, is the most successful method of analysis for the range of data examined in this study. It provides a reasonable description of a wide range of different covariance structures, and it results in the best models for actual data. Our analysis suggests genetic variance for Drosophila mortality declines with age, while genetic variance is constant at all ages for reproductive output. For growth in beef cattle, however, genetic variance increases linearly from birth, and genetic correlations are high across all observed ages.