Covariance functions are the ‘infinite-dimensional’ equivalents to covariance matrices for longitudinal data, i.e. many, ‘repeated’ records per individual taken over a period of time. Their properties are reviewed and illustrated with a numerical example. Restricted Maximum Likelihood estimation of genetic and phenotypic covariance functions fitting an animal model is described.

Two unconstrained procedures to ensure that intrabreed and interbreed genetic and environmental covariance estimates for multibreed populations are computed within the permissible ranges were developed. These procedures were called Partial Scoring and Cholesky Maximization. The Partial Scoring procedure uses partial steps to keep estimates of covariance matrices positive definite at each expect...

Determining how genetic variance changes under selection in natural populations has proved to be a very resilient problem in evolutionary genetics. In the same way that understanding the availability of genetic variance within populations requires the simultaneous consideration of genetic variance in sets of functionally related traits, determining how genetic variance changes under selection i...

One of the features of organisms that makes the study of biology so compelling is their apparent complexity. Molecular, cellular, developmental, physiological, neurological, and behavioral systems are each fascinating in and of themselves, but it is their interaction that generates what we see as the organism as a whole. By necessity, biologists have a tendency to break down organisms into thei...

The object of this paper is to indicate that the Pearson-Lawley selection rules form a plausible general theory for the simultaneous genetic analysis of means and covariance structure. Models are presented based on phenotypic selection and latent selection. Previously presented quantitative genetic models to decompose means and covariance structure simultaneously are reconsidered as instances o...

The relationship between multidimensional form of the adult mouse mandible and body size is examined from an ontogenetic perspective. The origin and ontogeny of phenotypic correlations are described in terms of genetic and environmental covariance patterns between adult skeletal morphology and growth in body weight. Different ontogenetic patterns are observed in the genetic correlations, and th...

INTRODUCTION Covariance matrices in quantitative genetic analyses have, by and large, been considered ‘unstructured’, i.e. for q random variables, there are q(q + 1)/2 distinct covariance components. This implies that the number of parameters to be estimated increases quadratically with the number of variables. Multivariate analyses involving more than a few traits have been hampered by computa...

We examined network properties of genetic covariance between average cortical thickness (CT) and surface area (SA) within genetically-identified cortical parcellations that we previously derived from human cortical genetic maps using vertex-wise fuzzy clustering analysis with high spatial resolution. There were 24 hierarchical parcellations based on vertex-wise CT and 24 based on vertex-wise SA...

in this study, the effect of maternal additive genetic and environment on body weight at 6 weeks (bwt6w), breast width (hbrs), carcass weight (carcwt), breast weight (brswt), blood hematocrit value (hem), residual feed intake (rfi), daily feed intake (dfi) and average daily gain (adg) were investigated in a commercial broiler dam line. with and without maternal effects, six different animal mod...