Genetic Models

This page provides detailed information about the genetic models available in Binx for GWAS analysis.

Overview

Genetic models define how allele dosage relates to phenotype. Binx implements models from GWASpoly (Rosyara et al., 2016) that accommodate various inheritance patterns in diploids and polyploids.

Diploid Models (ploidy=2)

Additive

The standard additive model assumes each allele copy contributes equally to the trait.

Use when: Trait value scales linearly with allele count.

binx gwas --ploidy 2 --models additive ...

1-dom-ref (Reference Dominant)

Tests if the reference allele (A) is dominant.

Use when: One copy of B is sufficient to express the B phenotype.

binx gwas --ploidy 2 --models 1-dom-ref ...

1-dom-alt (Alternate Dominant)

Tests if the alternate allele (B) is dominant.

Use when: Two copies of B are needed to express the B phenotype.

binx gwas --ploidy 2 --models 1-dom-alt ...

Tetraploid Models (ploidy=4)

Additive

Linear dosage effect across all five genotype classes.

Use when: Each B allele adds equally to trait value.

General (4 degrees of freedom)

No assumption about inheritance pattern. Estimates separate effects for each genotype class.

Use when: Exploring inheritance pattern; hypothesis generation.

Note: Performs a single joint test of all 4 dummy variables simultaneously, using more degrees of freedom. This reduces power compared to additive but can detect complex inheritance patterns.

1-dom (Simplex Dominant)

One copy of B is sufficient for effect. Using 1-dom tests both 1-dom-ref and 1-dom-alt.

Use when: Trait exhibits complete dominance; presence/absence effect.

binx gwas --ploidy 4 --models 1-dom ...

2-dom (Duplex Dominant)

Two copies of B are sufficient for effect. Using 2-dom tests both 2-dom-ref and 2-dom-alt.

Use when: Partial dominance; two copies needed for effect.

binx gwas --ploidy 4 --models 2-dom ...

diplo-additive (Diploidized Additive)

Treats the tetraploid as if it were diploid.

Use when: Expecting diploid-like inheritance in autopolyploid.

binx gwas --ploidy 4 --models diplo-additive ...

diplo-general (Diploidized General)

Diploid-style general model in tetraploid context (heterozygotes collapsed).

Use when: Expected diploid-like inheritance with unknown dominance.

binx gwas --ploidy 4 --models diplo-general ...

Hexaploid Models (ploidy=6)

Similar patterns extend to hexaploids:

Choosing Models

Recommended Strategy

1. Start broad: Run additive + general models
2. Compare results: Look for QTLs significant in one but not other
3. Refine hypotheses: Test specific dominance models
4. Validate: Check if model assumptions match biology

Model Selection Guide

Multiple Testing Considerations

Running multiple models increases false positive rate:

• Apply correction across all tests
• Or use Bonferroni within each model separately
• Consider the general model as a single 4-df test

Statistical Details

Effect Estimation

For each model, Binx estimates:

y = μ + Xβ + u + ε

Where:

• y = phenotype
• μ = intercept
• X = design matrix (model-specific)
• β = fixed marker effect
• u = random polygenic effect
• ε = residual

Testing

The null hypothesis (H₀: β = 0) is tested using a Wald test:

W = β² / Var(β)

Which follows a χ² distribution with degrees of freedom depending on the model.

Examples

Compare Additive vs Dominant

# Run both models
binx gwas \
  --geno geno.tsv \
  --pheno pheno.csv \
  --trait yield \
  --ploidy 4 \
  --models additive,1-dom \
  --out results.csv

# Find markers significant in one but not other
awk -F',' 'NR==1 {print; next}
  {key=$1","$2","$3; if(key in seen) {
    if(($4=="additive" && $5>5 && seen[key]<5) ||
       ($4!="additive" && $5<5 && seen[key]>5))
      print key, "differs"
  }
  seen[key]=$5}' results.csv

All Tetraploid Models

binx gwas \
  --geno geno.tsv \
  --pheno pheno.csv \
  --trait yield \
  --ploidy 4 \
  --models additive,general,1-dom,2-dom,diplo-additive,diplo-general \
  --out all_models.csv

References

1. Rosyara, U.R., De Jong, W.S., Douches, D.S., & Endelman, J.B. (2016). Software for genome-wide association studies in autopolyploids and its application to potato. The Plant Genome 9(2).

2. Endelman, J.B. (2011). Ridge regression and other kernels for genomic selection with R package rrBLUP. The Plant Genome 4:250-255.

See Also

• binx gwas - GWAS command reference
• Working with Polyploids - Polyploid tutorial