| In any breeding program the goal is to identify parents who will produce offspring with desired characteristics to improve the next generation. Rigorous selection of parents which can improve a trait in the short term has to be balanced in the long term with loss of genetic diversity, and possible inbreeding increase that could lead to consequences such as reduced resistance to pests and diseases or reduced adaptive potential. For our forest tree improvement program the trait of immediate interest is height: we have the heights of offspring from half-sib families, and information on survival. Our statistical analysis provides estimates of the genetic worth (often referred to as breeding values or combining abilities) of parents based on the observations of the offspring. These estimates can then be used to select the superior parents for breeding purposes.; We use a new model for height which includes parameters to measure any spatial correlation due to the micro-environment differences affecting growth, and to allow for the differing within family genetic variances. The maximum likelihood estimators for this model are then shown to be consistent, efficient, and asymptotically normal. Since the likelihood for our model is intractable we provide a procedure to approximate the maximum likelihood estimates using weighted linear mixed effects procedures to model the within family variances along with pseudo-likelihood and indirect estimation to account for the correlation. To take into account the presence of influential observations, due to contamination or possible measurement error, we also provide a robust version of our method. We also show how to incorporate estimates of family survival rates and measurements of genetic diversity into the selection process. Finally we use bootstrap methods to provide inference on the potential gain from selection and for the selection process itself. |
