Heritability is a central parameter for breeding, dating back to the foundation of quantitative genetics (Fisher (1918)). The current state-of-art to estimate heritabilities, as well as genetic correlations, is the use of REML (Thompson (2008)) with an “animal model”. Even though these estimation methods are now highly advanced, their applicability is limited to populations with recorded pedigrees, revealing an informative family structure, and preferably large size. In all other situations, i.e. populations with weak family structure, unrecorded pedigrees or small sample size, estimation of heritabilities and genetic correlations is impossible or very inaccurate.

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