Selection on Quantitative Traits and Predicting the Response
The breeder's equation predicts a one-generation change in a quantitative trait's mean: R = h²S, using narrow-sense heritability and the selection differential. Add R to the starting mean to predict the offspring mean. This is an approximate prediction under stated assumptions, not a universal rule for every selection process.
What a learner can do afterwards
- Predicts response and the next-generation mean from a selection differential and narrow-sense heritability under stated assumptions.
- Distinguishes directional, stabilising and disruptive selection by reproductive success across trait values, and describes expected effects on mean and spread.
- Explains possible causes of a selection plateau without treating the plateau alone as proof of its cause.
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S = selected parents' mean - population mean before selection. Narrow-sense heritability h² = V_A/V_P divides additive genetic variance by phenotypic variance. The breeder's equation predicts R = h²S, the change in mean. Add R to the starting mean for the predicted offspring mean. Under the model assumptions, positive S and positive h² predict a rise in mean. This equation does not predict the spread or identify a selection mode.
A plant population averages 40 cm, selected parents average 46 cm and h² = 0.4. S = 46 - 40 = 6 cm, so R = 0.4 × 6 = 2.4 cm. The predicted offspring mean is 42.4 cm. This approximate model assumes a roughly linear parent-offspring relationship based on additive inheritance, similar growing conditions and no strong effects from selection on other traits.
Selection modes describe which trait values have greater reproductive success. Directional selection favours one end of the range and can shift the mean towards that end; spread need not stay fixed. Stabilising selection favours intermediate values over both extremes and tends to narrow the spread. With a symmetric distribution and equal selection against both extremes, the mean can stay unchanged.
Disruptive selection favours both extremes over intermediate values. It can increase spread or produce two peaks. A symmetric pattern can leave the mean unchanged, but this is not required. These distribution effects are tendencies, not guarantees for each generation. A changed distribution alone cannot prove selection because environmental changes and other processes can also alter measured traits.
Repeated selection can reach a plateau, but not at a fixed time. With phenotypic variance fixed, declining additive genetic variance lowers h². For the same positive S, the predicted gain then shrinks. Opposing selection, health trade-offs or changed conditions can also limit gains. A plateau alone cannot identify its cause. Measure S, variance components and conditions again before predicting another generation.
Use narrow-sense h² in R = h²S, then add R to the starting mean. Identify selection by reproductive success. A plateau alone does not reveal its cause.
Lesson, questions and flashcards written for this dataset.
Readings and flashcards written for this dataset. Linked videos: Khan Academy, Natural selection and the owl butterfly and Variation in a species.
More to read
A response is a change, not a final mean
Suppose the population mean is 30 cm and the selected parents average 35 cm. The selection differential is S = 35 - 30 = 5 cm. With narrow-sense heritability h² = 0.2, the breeder's equation predicts R = 0.2 × 5 = 1 cm. The predicted offspring mean is therefore 31 cm.
The three measurements serve different roles. The population mean supplies the starting point. S describes how far the chosen parents differ from that starting population. R predicts how far the offspring mean will move.
Use h² = V_A/V_P, where V_A is additive genetic variance and V_P is phenotypic variance. Do not substitute broad-sense heritability just because it includes more genetic components.
The prediction is approximate. Its basic form assumes a roughly linear parent-offspring relationship based on additive inheritance, comparable conditions across generations and no strong effects from selection on other traits. It predicts a population mean, not each offspring's height.
Compare reproductive success across the range
Selection modes are defined by reproductive success across trait values. If one end of the range has greater success, selection is directional. If intermediate values exceed both extremes, selection is stabilising. If both extremes exceed the middle, selection is disruptive.
These definitions help interpret expected changes. Directional selection can move the mean towards a favoured extreme, but it does not require a constant spread. Stabilising selection tends to narrow the distribution. Disruptive selection can widen it or produce two peaks.
Whether the mean stays fixed depends on symmetry. Equal selection on both sides of a symmetric distribution can leave its mean unchanged. Unequal effects can also shift the mean.
A histogram alone does not identify the process. Nutrition, temperature or sampling can change the observed distribution. Evidence about which individuals survive and reproduce is needed to connect a pattern of trait values to selection.
What a plateau does and does not show
A breeding record may show smaller gains over time. Begin by checking the quantities in R = h²S. Has the difference between selected parents and the starting population changed? Has additive genetic variance changed relative to phenotypic variance?
If additive variance falls while phenotypic variance stays fixed, h² decreases. The same selection differential then predicts a smaller response. This is one possible explanation for a plateau, not a diagnosis supplied by the plateau itself.
Other explanations include selection opposing the breeder's target, health trade-offs associated with extreme values and changed conditions between measurements. A population can also retain genetic variation unrelated to the selected trait.
Measure the differential, variance components and conditions again. A flat record does not prove that all genetic variation is gone. Nor does repeated selection guarantee a plateau after a particular number of generations.
Keep the evolutionary claim specific
Choosing parents can create a selection differential even when their measured advantage is environmental. Plants growing in a richer patch may be taller without having an additive genetic advantage for height. Selecting those plants need not produce the inherited response expected from a genuinely heritable difference.
Artificial selection involves human choices about reproductive contributions. Natural selection involves differences in reproductive success under the organisms' conditions. Predicting a genetic response requires attention to inheritance in either case.
An absence of additive response for one trait does not mean that evolution throughout the population has stopped. Mutation, genetic drift and gene flow can change genetic composition. Selection may act on other traits.
State the limited conclusion supported by the measurements. No detected response in mean height is a different claim from no genetic change anywhere in the population.
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