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 complicate d matter, and a simple and efficient procedure is desirable. Three methods are common in the literature: random regression, orthogonal polynomial appr oximation, and character process models. The goals of this article are (i) to clarify the relationships between these methods; (ii) to develop a gener al extension of the character process model that relaxes correlation statio narity, its most stringent assumption; and (iii) to compare and contrast th e techniques and evaluate their performance across a range of actual and si mulated data. We find that the character process model, as described in 199 9 by Fletcher 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 b est models for actual data. Our analysis suggests genetic variance for Dros ophila mortality declines with age, while genetic variance is constant at a ll ages for reproductive output. For growth in beef cattle, however, geneti c variance increases linearly from birth, and genetic correlations are high across all observed ages.