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Alternative Ways of Computing the Numerator Relationship Matrix.

Mohammad Ali Nilforooshan1, Dorian Garrick2, Bevin Harris1

  • 1Livestock Improvement Corporation, Hamilton, New Zealand.

Frontiers in Genetics
|August 16, 2021
PubMed
Summary
This summary is machine-generated.

New methods significantly reduce computation time for calculating the additive genetic relationship matrix (A), crucial for animal breeding and genetic studies. Optimized algorithms achieve faster A matrix construction than A inverse calculation, even for large pedigrees.

Keywords:
Cholesky decompositionconjugate gradientinbreeding coefficientinversenumeric relationship matrixparallel computingpedigree

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Area of Science:

  • Animal Genetics
  • Quantitative Genetics
  • Computational Biology

Background:

  • The additive genetic relationship matrix (A) is fundamental in quantitative genetics for understanding genetic merit and population structure.
  • Calculating the inverse of A (A^-1) is computationally intensive, posing challenges for large animal populations.
  • Existing methods for A matrix computation have limitations in speed and efficiency, especially for large datasets.

Purpose of the Study:

  • To develop and compare novel computational methods for efficiently calculating the additive genetic relationship matrix (A).
  • To minimize the computational time and memory usage for constructing the A matrix in large pedigrees.
  • To evaluate the performance of new algorithms against existing methods using simulated animal populations.

Main Methods:

  • Development of new algorithms including the Array-Tabular method and iterative updates for Thompson's method.
  • Implementation of methods in the R programming language, incorporating parallel computing for performance enhancement.
  • Simulation of pedigrees with varying sizes (20K, 180K animals) and litter sizes to test computational efficiency.

Main Results:

  • Optimized algorithms significantly reduced computation time for A matrix construction, outperforming A^-1 calculation.
  • For a 180K pedigree, the optimized method achieved A matrix construction in 17 minutes and 3 seconds.
  • Calculating inbreeding coefficients was found to be extremely fast, even for large pedigrees (<0.2s for 180K).

Conclusions:

  • New computational strategies offer substantial improvements in calculating the additive genetic relationship matrix (A) for large populations.
  • The developed methods provide faster and more efficient alternatives for constructing the A matrix compared to existing approaches.
  • Archiving relationship coefficients and using external files for successive updates can mitigate memory and disk space limitations.