Reconstructing pedigrees: some identifiability questions for a recombination-mutation model

TL;DR

This paper investigates whether pedigrees can be reconstructed from genetic sequence data using Markov models, providing partial results on identifiability when crossover probabilities are small.

Contribution

It introduces two Markov models for sequence evolution on pedigrees and offers partial identifiability results based on counting spanning subgraph sequences.

Findings

Identifiability is possible for small crossover probabilities.

Counting spanning subgraph sequences helps distinguish pedigrees.

Partial results improve understanding of pedigree reconstruction.

Abstract

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.