Analysis of the inheritance, selection and evolution of growth trajectories.

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Abstract
We present methods for estimating the parameters of inheritance and selection that appear in a quantitative genetic model for the evolution growth trajectories and other "infinite-dimensional" traits that we recently introduced. Two methods for estimating the additive genetic covariance function are developed, a "full" model that fully fits the data and a "reduced" model that generates a smoothed estimate consistent with the sampling errors in the data. By decomposing the covariance function into its eigenvalues and eigenfunctions, it is possible to identify potential evolutionary changes in the population's mean growth trajectory for which there is (and those for which there is not) genetic variation. Algorithms for estimating these quantities, their confidence intervals, and for testing hypotheses about them are developed. These techniques are illustrated by an analysis of early growth in mice. Compatible methods for estimating the selection gradient function acting on growth trajectories in natural or domesticated populations are presented. We show how the estimates for the additive genetic covariance function and the selection gradient function can be used to predict the evolutionary change in a population's mean growth trajectory.