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diaQTL: �QTL mapping in outbred tetraploid diallel populations

Jeffrey Endelman, University of Wisconsin-Madison

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Tools for Genomics-Assisted Breeding in Polyploids

January 15, 2021

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Joint Linkage Analysis & Selection in Autotetraploid Potato & Blueberry

USDA NIFA AFRI (2019–2023)

PolyOrigin for haplotype reconstruction

bioRxiv 2020.12.18.423519

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diaQTL for QTL mapping

bioRxiv 2020.12.18.423479

J. Endelman

R. Amadeu

C. Zheng

P. Muñoz

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By “diallel” we mean partial diallel

2006

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diaQTL

  • R package, maintained on GitHub
  • Multi-allelic QTL
  • Basic workflow: QTL Discovery 🡪 Haplotype Effects
  • Fit models with additive, dominance and polygenic effects
  • Include fixed effects for year, location, etc.
  • Tools for visualizing and selecting on haplotypes

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​

A.1

A.2

A.3

A.4

B.1

B.2

B.3

B.4

C.1

C.2

C.3

C.4

y1

1

​

1

​

1

1

​

​

​

​

​

​

y2

1

1

​

​

​

1

1

​

​

​

​

​

y3

1

​

​

1

​

​

​

​

1

1

​

​

y4

​

2

​

​

​

​

​

​

​

​

1

1

y5

​

​

​

​

​

1

1

​

​

1

​

1

Phenotype

Haplotype Dosage

A

B

C

3x3 half-diallel

Use regression to estimate additive effect for each haplotype

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Additive

Effect

Output from fitQTL function

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Each haplotype has an estimated effect, even though in reality,

# QTL alleles < # haplotypes

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Can hypothesize that haplotypes with similar effect contain the same QTL allele

A

B

C

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Dominance effects

  • Decomposed into digenic, trigenic, and quadrigenic components
    • Nice statistical properties (orthogonal effects)
    • Higher order terms tend to account for less variance

Effect

Predictor variable

Levels

(examples)

No. parameters in

3x3 half-diallel without selfing

additive

haplotype

A.1

A.2

B.1

12

digenic

diplotype

A.1+A.2

A.1+B.1

78

trigenic

triplotype

A.1+A.2+B.1

A.1+B.1+B.2

240

quadrigenic

tetratype

A.1+A.2+B.1+B.2

300

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Dominance effects

  • Decomposed into digenic, trigenic, and quadrigenic components
    • Nice statistical properties (orthogonal effects)
    • Higher order terms tend to account for less variance
  • When referring to a particular model, it includes all lower order effects

Model

Effects

additive

a

digenic

a + d

trigenic

a + d + t

quadrigenic

a + d + t + q

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Complete dominance

  •  

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Output from fitQTL

Above diagonal: digenic effects

Below diagonal: additive + digenic effects

 

 

In this Example:

C.4

C.3

C.2

C.1

B.4

B.3

B.2

B.1

A.4

A.3

A.2

A.1

C.4

C.3

C.2

C.1

B.4

B.3

B.2

B.1

A.4

A.3

A.2

A.1

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QTL Discovery

scan1 returns LOD score at each marker

Markers with LOD score above the threshold are declared significant

Need to control genome-wide false positive rate

  • Permutation test
  • Simulations without any QTL

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LOD threshold

Threshold increases with

  • number of parents
  • genome size

 

Simulated half-diallel populations

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Statistical Power

 

Simulated half-diallel populations

h2

​

0.2

​

0.1

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Accuracy of haplotype effect estimation also depends on pph

Accuracy = correlation between simulated and estimated effects

h2

​

0.2

​

0.1

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How does it work?

  • Due to the large number of model parameters, QTL effects are modeled as random
  • To allow for non-normal distribution, Bayesian regression models originally developed for genomic selection are used
    • R package BGLR (Pérez and de los Campos 2014)
  • Need to specify number of iterations for the algorithm
    • Function set_params provides guidance
  • Model fit vs. complexity assessed using DIC (deviance information criterion)
    • DIC = -2 (log likelihood@ posterior mean) + 2 (effective # parameters)
    • Lower is better

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Current version is 0.91

Consult NEWS file to see what changes have been made

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Vignette dataset

3x3 half-diallel

W6511-1R

VillettaRose

W9914-1R

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Input files

  • Three input files needed
    • Pedigree
    • Genotype
    • Phenotype

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Generate from PolyOrigin output using read_polyancestry

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specifies maximum possible dominance that will be fitted

dominance

Model

1

additive

2

digenic

3

trigenic

4

quadrigenic

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r2 = squared correlation between predicted and observed response variable

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deltaDIC = change in DIC relative to no-QTL model

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Haplotype effects

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Select the dominance model

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Proportion of variance

 

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Haplotype selection

​

A.1

A.2

A.3

A.4

B.1

B.2

B.3

B.4

C.1

C.2

C.3

C.4

id1

1

​

1

​

1

1

​

​

​

​

​

​

id2

1

1

​

​

​

1

1

​

​

​

​

​

id3

1

​

​

1

​

​

​

​

1

1

​

​

id4

​

2

​

​

​

​

​

​

​

​

1

1

id5

​

​

​

​

​

1

1

​

​

1

​

1

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Multiple QTL mapping

  • In the absence of epistasis, multiple QTL on different chromosomes can be detected adequately with scan1
  • For epistatic QTL on different chromosomes, both scan1 and fitQTL have the option of including a marker as a cofactor in the analysis
  • To resolve multiple QTL on the same chromosome, the best approach is a two-dimensional scan (scan2), which is under development and will be available soon

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Binary Traits: GLM with probit link function

id

LB-Resistant

W16215-100rus

N

W16215-101rus

Y

W16215-103rus

Y

W16215-105rus

Y

W16215-106rus

N

W16215-108rus

Y

W16215-109rus

Y

W16215-110rus

N

Code the trait as Y/N

Karki et al. (2021) doi:10.1101/2020.09.27.315812

QTL effects correspond to linear predictor of the GLM

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Binary Traits

id

LB-Resistant

W16215-100rus

N

W16215-101rus

Y

W16215-103rus

Y

W16215-105rus

Y

W16215-106rus

N

W16215-108rus

Y

W16215-109rus

Y

W16215-110rus

N

Code the trait as Y/N

diaQTL function fine_map

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Bayesian Credible Interval (CI)