  Pedigrees are directed acyclic graphs that represent ancestral relationships
between individuals in a population. Based on a schematic recombination
process, we describe two simple Markov models for sequences evolving on
pedigrees - Model R (recombinations without mutations) and Model RM
(recombinations with mutations). For these models, we ask an identifiability
question: is it possible to construct a pedigree from the joint probability
distribution of extant sequences? We present partial identifiability results
for general pedigrees: we show that when the crossover probabilities are
sufficiently small, certain spanning subgraph sequences can be counted from the
joint distribution of extant sequences. We demonstrate how pedigrees that
earlier seemed difficult to distinguish are distinguished by counting their
spanning subgraph sequences.
