genomic_eigen_indices: Linear Molecular and Genomic Eigen Selection Index Methods...

In selection.index: Analysis of Selection Index in Plant Breeding

Linear Molecular and Genomic Eigen Selection Index Methods (Chapter 8)

Description

Implements the Linear Molecular and Genomic Eigen Selection Index methods from Chapter 8. These methods extend eigen-based selection to genomic/molecular data, maximizing the accuracy squared (rho_HI^2) through eigenvalue problems without requiring pre-specified economic weights.

Methods included: - MESIM : Molecular Eigen Selection Index Method (Section 8.1) - GESIM : Linear Genomic Eigen Selection Index Method (Section 8.2) - GW-ESIM : Genome-Wide Linear Eigen Selection Index Method (Section 8.3) - RGESIM : Restricted Linear Genomic Eigen Selection Index Method (Section 8.4) - PPG-GESIM: Predetermined Proportional Gain Genomic Eigen Selection Index (Section 8.5)

All implementations use C++ primitives (math_primitives.cpp) for quadratic forms and symmetric solves, while eigendecompositions use R's eigen() for correctness and compatibility with the existing package architecture.

Mathematical Foundation

Like the phenotypic ESIM (Chapter 7), these genomic eigen methods maximize the squared accuracy between the index and net genetic merit, but incorporate molecular markers, GEBVs, or genome-wide marker scores.

The general approach solves a generalized eigenproblem to find optimal index coefficients that maximize heritability without requiring economic weights.

References

Ceron-Rojas, J. J., & Crossa, J. (2018). Linear Selection Indices in Modern Plant Breeding. Springer International Publishing. Chapter 8.

selection.index documentation built on March 9, 2026, 1:06 a.m.