QGQuantitative Genetics Tool
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Version 1.2 · Interactive Breeding Story

Can you breed wheat with more solid stems?

Join wheat breeder Martha and follow a real-world breeding story: increasing stem solidness across generations to strengthen plants and improve resistance to wheat stem sawfly.

1Solidness Explorer 2Crossing Specialist 3Data Analyst 4Heritability Thinker 5Wheat Breeder
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Your breeding challenge

Martha is improving wheat stem solidness, scored from 0% (completely hollow) to 100% (fully pith-filled). Your job is to explain the variation, compare breeding families, estimate heritability, and predict the gain from selecting plants with more solid stems.

Why solid stems matter

Wheat stem sawfly is a serious pest of wheat in western North America. The female deposits eggs inside wheat stems, where the larva feeds and develops.

Near maturity, the larva can weaken or cut the stem near its base. Damaged stems may lodge—fall over—making harvest difficult and increasing yield loss.

Solid-stemmed wheat contains more pith inside the stem. This physical trait can interfere with larval survival and has been used in breeding programs as an important form of host-plant resistance.

More solid stems may also improve mechanical strength, helping plants remain standing. In this teaching model, solidness is expressed on a simple 0–100% scale.

From hollow to solid

The cross-sections below illustrate the simple 0–100% scale used in this lesson.

0% · Hollow
50% · Partly solid
100% · Solid

Learning Objectives

By the end of this lesson, you should be able to:

  • Explain why wheat stem solidness shows continuous variation.
  • Distinguish genetic and environmental effects.
  • Predict how stem-solidness variation in the F₂ differs from the F₁.
  • Interpret an ANOVA.
  • Explain the meaning of heritability.
  • Predict the response to selection for increased stem solidness.
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Field Observation

The stems are not equally solid

Begin by separating genetic and environmental effects on stem solidness.

1Why stem solidness differs

Your mission: Determine whether differences in stem solidness could come from genes, the environment, or both.
Phenotype means the trait we can observe or measure. In this lesson, the phenotype is wheat stem solidness, scored from 0% (hollow) to 100% (fully solid or pith-filled).
Stem solidness depends on both genotype and environment. Two plants with similar genes may still develop different amounts of pith because growing conditions and developmental timing can influence how strongly the trait is expressed.
Phenotype = Genetic effect + Environmental effect

Explore stem solidness in a population

Check your understanding:

What happens when environmental variation in stem development increases?

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The Cross

Cross a hollow-stem line with a solid-stem line

Follow stem solidness through the P₁, P₂, F₁, and F₂ generations.

2Make a cross

Your mission: Cross a low-solidness line with a high-solidness line and identify which generation contains the greatest variation.
Parental lines are the two original lines used in a cross. The F₁ is their first offspring generation. The F₂ is produced when F₁ individuals reproduce.
The F₁ plants are relatively similar because they receive the same general combination of parental alleles. In the F₂, alleles affecting pith development segregate into many combinations, producing a wider range of stem-solidness scores.
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Check your understanding:

Why is the F₂ usually more variable than the F₁?

Learn more: transgressive segregation

Some F₂ individuals may have lower solidness than the hollow parent or higher solidness than the solid parent. This can happen when offspring inherit complementary combinations of alleles that produce values beyond both parental averages.

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Family Trial

Which families truly differ?

Use ANOVA to compare mean stem solidness among breeding families.

3Compare families

Your mission: Decide whether differences among families are large enough to justify selecting the most solid-stemmed material.
Analysis of variance, or ANOVA, asks whether the differences among group means are large compared with the variation among individuals inside those groups.
Imagine several wheat breeding families grown under similar conditions. ANOVA helps us decide whether their average stem-solidness scores differ more than expected from ordinary plant-to-plant variation.
Show ANOVA calculations
Check your understanding:

If ANOVA is significant, what can we conclude?

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Inheritance Question

How much variation can selection use?

Partition variance and interpret heritability.

4What heritability means

Your mission: Estimate how much of the observed variation in stem solidness can help predict offspring performance.
Heritability describes how much of the variation among individuals in a particular population and environment is associated with genetic differences.
Heritability does not tell us what percentage of one plant's solid stem was “caused by genes.” It describes variation among plants in a specific population and environment.
Broad-sense heritability, H²

Uses all genetic variance, including additive and dominance effects.

Narrow-sense heritability, h²

Uses only additive genetic variance, which is especially useful for predicting response to selection.

Broad-sense heritability
H² = 0.64
Narrow-sense heritability
h² = 0.51
Check your understanding:

What happens to heritability if environmental variance increases while genetic variance stays the same?

Learn more: why narrow-sense heritability matters

Additive allele effects are transmitted predictably from parents to offspring. That is why narrow-sense heritability is used in the breeder's equation.

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Breeding Decision

Select the most solid-stemmed plants

Predict improvement in stem solidness with the breeder’s equation.

5Select the most solid-stemmed plants

Your mission: Select plants with the most solid stems and predict the mean solidness of the next generation.
Selection differential, S, is the difference between the mean of the selected parents and the mean of the original population.
Response to selection, R, is the expected change in the offspring generation.
When narrow-sense heritability is high, selected parents tend to pass more of their stem-solidness advantage to their offspring.
Response to selection = Narrow-sense heritability × Selection differential
Final check:

Which situation should produce the largest response to selection?

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Martha’s breeding cycle completed!

You followed Martha’s wheat program from stem scoring to a prediction of increased solidness in the next generation.

Concepts mastered

  • Continuous variation
  • Polygenic inheritance
  • ANOVA
  • Heritability
  • Response to selection
Final outcome: You can now explain variation in wheat stem solidness, evaluate breeding families, interpret heritability, and predict whether selection can increase solidness across generations.
Achievement unlockedYou completed a lesson step.