Selection and response to selection
The breeder's equation and genetic gain: selection differential, heritability, intensity, accuracy and generation interval, with worked sums.
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Every generation, breeders choose which animals become parents. If the chosen animals are better than average for milk yield, growth or egg production, and if part of their superiority is genetic, their offspring will be better too. How much better is predicted by one of the most useful equations in agriculture, the breeder's equation, and its extension to genetic gain per year. These ideas explain why dairy cows today produce far more milk than their ancestors, why broilers grow several times faster than chickens of the 1950s, and why genomic selection has accelerated progress.
Selection response is a core topic in animal breeding, plant breeding and quantitative genetics exams.
The breeder's equation
- Selection differential (S): the difference between the mean of the selected parents and the mean of the population they were chosen from.
- Heritability (h2): the proportion of the variation in the trait that is due to additive genetic effects, which parents pass to offspring.
- Response to selection (R): the change in the mean of the next generation.
Because the size of S depends on how variable the trait is and how strictly parents are chosen, it is often written using the intensity of selection (i), the selection differential in standard deviation units:
where σP is the phenotypic and σA the additive genetic standard deviation. Selection intensity depends only on the proportion selected: about 0.80 if the best 50 per cent are kept, 1.40 for 20 per cent, 1.76 for 10 per cent and 2.67 for 1 per cent.
Genetic gain per year
Livestock improvement is usually measured per year, which depends on the generation interval (L), the average age of parents when their offspring are born:
where r is the accuracy of selection, the correlation between the estimated and true breeding value. Gain is increased by:
- selecting more intensely (fewer, better parents), especially among males, since one sire has many offspring;
- raising accuracy with records on relatives, progeny testing and genomic information;
- shortening the generation interval, by breeding young animals.
In dairy cattle, A. Rendel and A. Robertson (1950) showed that genetic gain comes through four pathways: sires to breed bulls, sires to breed cows, dams to breed bulls and dams to breed cows, with most gain through the selection of sires. Progeny testing gave high accuracy but long generation intervals of about six years. Genomic selection, introduced in dairy cattle around 2009, gives fairly accurate breeding values for young bulls from their DNA, roughly halving the generation interval and about doubling the rate of genetic gain in many countries.
Methods of selection
- Individual (mass) selection on the animal's own performance: effective for highly heritable traits measured in both sexes, such as growth rate.
- Pedigree selection on ancestors' records, useful early in life.
- Family and sib selection, for traits measured only in one sex or after slaughter.
- Progeny testing: judging a sire by his daughters' performance; accurate but slow.
- For several traits: tandem selection (one trait at a time), independent culling levels (minimum standards for each trait) and the selection index, generally the most efficient.
Limits and complications
- Low heritability traits, such as fertility and disease resistance (often h2 below 0.1), respond slowly; selection uses indexes and large datasets.
- Correlated responses: selecting for one trait changes others; strong selection for milk yield reduced fertility in dairy cows until fertility was added to selection indexes.
- Environment: response measured in one environment may not fully appear in another (genotype × environment interaction).
- Inbreeding: intense selection among few animals raises inbreeding, which reduces fitness and long-term response.
- Selection index: combining several traits weighted by their economic value gives the best overall improvement.
Predicting response
A herd averages 6,000 kg of milk per lactation, with a phenotypic standard deviation of 1,000 kg. Heritability of milk yield is 0.3.
Keeping the best half as parents. Intensity i = 0.80, so S = 0.80 × 1,000 = 800 kg.
- R = h2 × S = 0.3 × 800 = 240 kg per generation.
- With a generation interval of 5 years: 48 kg per year.
Keeping only the best 10 per cent (i = 1.76): S = 1,760 kg, R = 0.3 × 1,760 ≈ 528 kg per generation.
Shortening the generation interval from 5 to 2.5 years with genomic selection, at the same intensity and accuracy, doubles annual gain: 48 kg becomes 96 kg per year.
In practice, intense selection is applied mainly to sires: a few top bulls produce thousands of daughters through AI, while most cows must be kept as replacements.
Key points
- Selection differential S = mean of selected parents − population mean.
- Breeder's equation: R = h2 × S; equivalently R = i h2 σP.
- Selection intensity: about 0.80 (best 50 per cent), 1.40 (20 per cent), 1.76 (10 per cent), 2.67 (1 per cent).
- Gain per year = i r σA ÷ L: raise intensity and accuracy, shorten the generation interval.
- Four pathways in dairy cattle; most gain through sires; genomic selection roughly doubles gain.
- Watch correlated responses, genotype × environment interaction and inbreeding.
What the exams ask
- School-leaving and entrance papers: what selection is and why heritability matters.
- Degree and research-fellowship entrances: the breeder's equation, selection intensity, accuracy, generation interval, gain per year, correlated response and selection indexes.
- Professional examinations: designing breeding programmes, progeny testing versus genomic selection, and balancing gain with inbreeding.
Described in general terms: the kind of examination, not a past paper. Laisha never reproduces exam questions.
Questions people ask
Why do offspring regress toward the average?
Part of the parents' superiority is due to favourable environment or non-additive gene effects, which are not passed on. Only the additive genetic part, measured by heritability, is inherited.
Why select mostly on males?
A male can have many more offspring than a female, especially with AI, so fewer males are needed and they can be selected far more intensely.
Does genomic selection replace recording animals?
No. Genomic predictions are trained on large reference populations with recorded performance. Continued recording keeps predictions accurate.
Sources
- Falconer, D. S. and Mackay, T. F. C. Introduction to Quantitative Genetics, 4th edition. Longman, 1996. Chapters 11–13.
- Rendel, J. M. and Robertson, A. "Estimation of genetic gain in milk yield by selection in a closed herd of dairy cattle." Journal of Genetics 50, 1–8 (1950).
- Schaeffer, L. R. "Strategy for applying genome-wide selection in dairy cattle." Journal of Animal Breeding and Genetics 123, 218–223 (2006).
- García-Ruiz, A. et al. "Changes in genetic selection differentials and generation intervals in US Holstein dairy cattle as a result of genomic selection." Proceedings of the National Academy of Sciences 113, E3995–E4004 (2016).
- Bourdon, R. M. Understanding Animal Breeding, 2nd edition. Prentice Hall, 2000.
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