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Selection Index

Multi-Trait Selection Index

Rank parents by a weighted combination of standardized traits — pick the right crosses.

How it works

The Smith–Hazel selection index combines multiple traits into a single score using economic or breeder-defined weights. We z-standardize each trait so weights are comparable across units, compute the index per parent, and rank the top pairwise crosses by mid-parent value. This translates messy multi-trait data into a clean shortlist of crosses to plant.

Formula

I = Σ w_i · z(trait_i), where z is the per-trait z-score across the population.

What you get

  • ▸Ranked parent list with index score
  • ▸Top pairwise crosses by mid-parent index
  • ▸Per-trait z-scores for diagnostic inspection

When to use it

  • ▸You measure multiple traits and need a single ranking
  • ▸You're planning crosses for next season
  • ▸You want to balance yield with quality or disease resistance

Inputs

Trait table
CSV: `id` + one numeric column per trait
Weights
JSON/CSV mapping trait → weight (economic value or breeder preference)

Parameters

NameDefaultDescription
Standardisationz-scoreOptionally switch to min-max scaling for bounded traits.
DirectionautoPer-trait higher-is-better / lower-is-better flag.
Top-N crosses50Number of parent pairs to return, ranked by mid-parent index.

Workflow

  1. 1. Standardise
    Per-trait z-scores across the population.
  2. 2. Weighted sum
    I_i = Σ w_j · z_ij with breeder-supplied weights.
  3. 3. Rank parents
    Sort descending; ties broken by primary trait weight.
  4. 4. Score crosses
    Mid-parent index for every parent pair; top-N returned.

Interpreting results

  • ▸Inspect per-trait z-scores of the top-ranked parents — a single dominant trait can carry a mediocre profile.
  • ▸Sensitivity check: rerun with ±20% on the largest weight; unstable rankings need better weight elicitation.

Common pitfalls

  • ✕Unstandardised traits let the largest-scale trait dominate regardless of weight.
  • ✕Ignoring trait direction (lower-is-better) silently flips a weight's sign.

Worked example

Wheat yield + protein + rust
Weights (0.5, 0.3, 0.2). Top cross combines a high-yield parent (z = 1.8) with a rust-resistant, above-average parent (z_rust = 1.4, z_yield = 0.7). Mid-parent index 1.1.

Try it — interactive example

Estimate response to selection for a single trait using the breeder's equation: ΔG = i · h² · σp.

Expected outputs
ΔG per cycle
7.02 units
ΔG per year
1.755 units/yr
Response as % of σp
70.2%

Numbers are quick analytical estimates for planning — actual runs incorporate the full data, covariates, and QC pipeline.

References

Run Selection Index on your data

Open the module and upload a CSV.

Open module