BREEDING VALUE AND VARIANCE COMPONENT ESTIMATION FROM DATA CONTAININGINBRED INDIVIDUALS - APPLICATION TO GYNOGENETIC FAMILIES IN COMMON CARP (CYPRINUS-CARPIO L)

Under gynogenetic reproduction, offspring receive genes only from thei r dams and completely homozygous offspring are produced within one gen eration. When gynogenetic reproduction is applied to fully inbred indi viduals, homozygous clone lines are produced. A mixed model method was developed for breeding value and variance component estimation in gyn ogenetic families, which requires the inverse of the numerator relatio nship matrix. A general method for creating the inverse for a populati on with unusual relationships between animals is presented, which redu ces to simple rules as is illustrated for gynogenetic populations. The presence of clones in gynogenetic populations causes singularity of t he numerator relationship matrix. However, clones can be regarded as r epeated observations of the same genotype, which can be accommodated b y modifying the incidence matrix, and by considering only unique genot ypes in the estimation procedure. Optimum gynogenetic sib family sizes for estimating heritabilities and estimates of their accuracy were de rived and compared to those for conventional full-sib designs. This wa s done by means of a deterministic derivation and by stochastic simula tion using Gibbs sampling. Optimum family sizes were smallest for gyno genetic families. Only for low heritabilities, there was a small advan tage in accuracy under the gynogenetic design.