A novel recursive algorithm for the calculation of the detailed identity coefficients.

Luis Alberto García-Cortés

doi:10.1186/s12711-015-0108-6

Abstract

BackgroundA recursive algorithm to calculate the fifteen detailed coefficients of identity is introduced. Previous recursive procedures based on the generalized coefficients of kinship provided the detailed coefficients of identity under the assumption that the two individuals were not an ancestor of each other.FindingsBy using gametic relationships to include three, four or two pairs of gametes, we can obtain these coefficients for any pair of individuals. We have developed a novel linear transformation that allows for the calculation of pairwise detailed identity coefficients for any pedigree given the gametic relationships. We illustrate the procedure using the well-known pedigree of Julio and Mencha, which contains 20 Jicaque Indians of Honduras, to calculate their detailed coefficients.ConclusionsThe proposed algorithm can be used to calculate the detailed identity coefficients of two or more individuals with any pedigree relationship.

Highlights

A recursive algorithm to calculate the fifteen detailed coefficients of identity is introduced
To obtain generalized kinship coefficients, Lange and Sinsheimer [5] described an alternative way, which can calculate the detailed coefficients of identity without this limitation
The detailed identity coefficients The 15 detailed coefficients of identity for individuals X and Y can be calculated from the generalized gametic relationships by a simple linear transformation

Summary

Introduction

A recursive algorithm to calculate the fifteen detailed coefficients of identity is introduced. Conclusions: The proposed algorithm can be used to calculate the detailed identity coefficients of two or more individuals with any pedigree relationship. This transformation provided the 9 condensed identity coefficients for any pair of individuals, but the 15 detailed identity coefficients can only be calculated using Karigl’s method under the assumption that neither of the two individuals is an ancestor of the other.

Results

Conclusion