Reconstructing pedigrees using probabilistic analysis of ISSR amplification

Data obtained from ISSR amplification may readily be extracted but only allows us to know, for each gene, if a specific allele is present or not. From this partial information we provide a probabilistic method to reconstruct the pedigree corresponding to some families of diploid cultivars. This method consists in determining for each individual what is the most likely couple of parent pair amongst all older individuals, according to some probability measure. The construction of this measure bears on the fact that the probability to observe the specific alleles in the child, given the status of the parents does not depend on the generation and is the same for each gene. This assumption is then justified from a convergence result of gene frequencies which is proved here. Our reconstruction method is applied to a family of 85 living accessions representing the common broom {\it Cytisus scoparius}.