Probability inheritance algorithm and its implementation

Abstract

An algorithm for functional evaluation of the likelihood of paternal and maternal recombination fractions for pedigree data is proposed. The idea behind the algorithm is that the probability of affected status and certain marker genotypes of ancestors is inherited by their descendants along with the inheritance of certain haplotypes. In this algorithm, the likelihood is evaluated by a single recursive call for each terminal sibling set along with the inheritance flow. The advantage of the algorithm is not only the simplicity of its implementation, but also its functional form of evaluation. The likelihood is obtained as a polynomial of the recombination fractions, making it easier to validate the likelihood more carefully, resulting in a more accurate localization of the disease locus. We report an experimental implementation of this algorithm in R, together with several practical applications.

Keywords:

• pedigree analysis
• pedigree graph
• probability inheritance
• functional evaluation
• polynomial

Acknowledgements

We would like to express our sincere gratitude to Dr Ian Saunders in CSIRO for proofreading our manuscript.