Heritability & Quantitative Genetics Calculator
Calculate broad-sense heritability, narrow-sense heritability, response to selection, selection differential, and quantitative genetics variance components with clear steps and visuals.
Background
Quantitative genetics studies traits that vary continuously, such as height, crop yield, body size, milk production, or beak depth. Heritability estimates how much of the phenotypic variation in a population is associated with genetic variation. It does not tell you how “genetic” a single individual’s trait is.
How to use this calculator
- Use heritability from variance components when you have VA, VD, VI, VE, or VP.
- Use breeder’s equation when you want to solve for response to selection, heritability, or selection differential.
- Use realized heritability when you know the original mean, selected parent mean, and offspring mean.
- Use parent-offspring regression when your class gives you a regression slope or paired parent-offspring data.
How this calculator works
- Broad-sense heritability includes total genetic variance.
- Narrow-sense heritability uses additive genetic variance, which is most useful for predicting response to selection.
- Response to selection predicts how much the next generation’s mean changes after selection.
- Realized heritability is calculated from observed selection response.
- Parent-offspring regression estimates h² from the slope of offspring trait values plotted against parent or mid-parent values.
Formula & Equations Used
Phenotypic variance: VP = VG + VE + VG×E
Total genetic variance: VG = VA + VD + VI
Broad-sense heritability: H² = VG / VP
Narrow-sense heritability: h² = VA / VP
Breeder’s equation: R = h²S
Realized heritability: h² = R / S
Parent-offspring regression: h² = b for mid-parent regression, or h² = 2b for one-parent regression
Example Problems & Step-by-Step Solutions
Example 1 — Heritability from variance components
A trait has VA = 40, VD = 10, VI = 5, VE = 45, and VP = 100.
- Total genetic variance = 40 + 10 + 5 = 55
- Broad-sense heritability = 55 / 100 = 0.55, or 55%
- Narrow-sense heritability = 40 / 100 = 0.40, or 40%
Example 2 — Breeder’s equation
If h² = 0.4 and S = 5, then R = 0.4 × 5 = 2.
Example 3 — Realized heritability
A crop population has an original mean yield of 100 g. The selected parents average 110 g, and their offspring average 104 g.
- Selection differential: S = 110 − 100 = 10
- Response to selection: R = 104 − 100 = 4
- Realized heritability: h² = R / S = 4 / 10 = 0.40, or 40%
Frequently Asked Questions
Q: What does heritability mean?
Heritability estimates the proportion of variation in a trait within a population that is associated with genetic variation.
Q: Is heritability about individuals?
No. Heritability describes variation in a population, not how much of one individual’s trait is caused by genes.
Q: What is the difference between H² and h²?
Broad-sense heritability, H², includes total genetic variance. Narrow-sense heritability, h², includes only additive genetic variance.
Q: Why is narrow-sense heritability useful?
Narrow-sense heritability is especially useful because additive genetic variance predicts response to selection.
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