Title : Ancestral Relationships Using Metafounders : Finite Ancestral 1 Populations and across Population Relationships

23 Recent use of genomic (marker-based) relationships shows that relationships exist within 24 and across base population (breeds or lines). However, current treatment of pedigree 25 relationships is unable to consider relationships within or across base populations, although 26 such relationships must exist due to finite size of the ancestral population and connections 27 between populations. This complicates the conciliation of both approaches and, in 28 particular, combining pedigree with genomic relationships. We present a coherent 29 theoretical framework to consider base population in pedigree relationships. We suggest a 30 conceptual framework that considers each ancestral population as a finite-sized pool of 31 gametes. This generates across-individual relationships and contrasts with the classical view 32 where each population is considered as an infinite, unrelated pool. Several ancestral 33 populations may be connected and therefore related. Each ancestral population can be 34 represented as a “metafounder”, a pseudo-individual included as founder of the pedigree 35 and similar to an “unknown parent group”. Metafounders have selfand across36 relationships according to a set of parameters, which measure ancestral relationships, i.e. 37 homozygozities within populations and relationships across populations. These parameters 38 can be estimated from existing pedigree and marker genotypes using maximum likelihood or 39 a method based on summary statistics, for arbitrarily complex pedigrees. Equivalences of 40 genetic variance and variance components between the classical and this new 41 parameterization are shown. Segregation variance on crosses of populations is modeled. 42 Efficient algorithms for computation of relationship matrices, their inverses, and inbreeding 43 coefficients are presented. Use of metafounders leads to compatibility of genomic and 44