English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Many computations with SNP data including genomic evaluation, parameter estimation, and genome-wide association studies use an inverse of the genomic relationship matrix. The cost of a regular inversion is cubic and is prohibitively expensive for large matrices. Recent studies in cattle demonstrated that the inverse can be computed in almost linear time by recursion on any subset of ∼10,000 individuals. The purpose of this study is to present a theory of why such a recursion works and its implication for other populations. Assume that, because of a small effective population size, the additive information in a genotyped population has a small dimensionality, even with a very large number of SNP markers. That dimensionality is visible as a limited number of effective SNP effects, independent chromosome segments, or the rank of the genomic relationship matrix. Decompose a population arbitrarily into core and noncore individuals, with the number of core individuals equal to that dimensionality. Then, breeding values of noncore individuals can be derived by recursions on breeding values of core individuals, with coefficients of the recursion computed from the genomic relationship matrix. A resulting algorithm for the inversion called "algorithm for proven and young" (APY) has a linear computing and memory cost for noncore animals. Noninfinitesimal genetic architecture can be accommodated through a trait-specific genomic relationship matrix, possibly derived from Bayesian regressions. For populations with small effective population size, the inverse of the genomic relationship matrix can be computed inexpensively for a very large number of genotyped individuals.

Inexpensive Computation of the Inverse of the Genomic Relationship Matrix in Populations with Small Effective Population Size