original ideas focused on rare & costly markers
models & methods refined as technology advanced

• single marker regression
• QTL (quantitative trait loci)
  • single locus models: interval mapping for QTL
  • QTL model search: QTLs & epistasis
• polygenes (association mapping)
  • adjust for population structure
  • capture "missing heritability"
• genome-wide selection

use statistical modeling to predict how a plant will perform
before it is field-tested

• genomic selection (GS)
  • marker assisted selection (MAS)
  • genome-wide selection (GS)
• other uses of word (relevent to systems genetics)
  • natural selection: survival of the fittest
  • model selection: search for QTLs
  • selection bias: overestimate of QTL effects

• trait is highly polygenic (genetically variable)
  • influenced by a few key genomic regions
  • high heritability (low environmental variation)
• measuring trait is costly
  • difficult or expensive process (technology)
  • measuring tool may be highly variable
  • time-consuming (plant has to grow first)
  • desire to streamline multi-year selection

• forms of genome-wide selection
  • marker-assisted: with phenotypes
  • marker-based: without phenotypes
• use markers to improve selection for complex traits
  • predict phenotype from marker genotype
  • select candidates based on best marker genotypes
  • use training set to predict test set of individuals

• 1990s & 2000s: markers were expensive
• economic strategy:
  • first identify significant markers (QTL analysis)
  • use best markers to genotype selection candidates
• estimate marker effects by multiple regression
  • treat genetic effects as fixed and few
  • \(E(y)= \mu_q, q=(q_1,q_2,q_3)\)

www.21stcentech.com/heard-marker-assisted-breeding/

• new paradigm with technology advances
  • improved statistical methods and software
  • cheap markers
• using only significant markers to predict trait …
  • gives good estimates (maybe) of markers …
  • but does not maximize accuracy
• simple but effective approach
  • treat marker effects as random
  • use all markers (away from QTL if any)

MAS approach \(y = \mu_q + e, V(e) = \sigma^2I\)

• estimate fixed QTL effects \(\hat{\mu}_q\) (MLEs)
• predict phenotype using fixed effects \(\hat{y}=\hat{\mu}_q\)

GS approach \(y = \mu + g + e, V(g) = \sigma_g^2K\)

• estimate kinship \(K\) from all markers \(M\) as for poly
• predict random effect \(\hat{g}\) using BLUP
• predict phenotype \(\hat{y}=\hat{g}\)

• DO example
• rrBLUP fit without QTL
• correlation 0.79

• DO example
• rrBLUP fit with QTL
• correlation 0.74