Response to selection
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Response to selection (R) is the change in the mean of a quantitative trait from one generation to the next that follows a choice of parents. The breeder's equation, R = h2S, predicts it from the selection differential S and the narrow-sense heritability h2. The differential is the amount by which the chosen parents exceed the mean of their population.[1] The prediction can be made before any selection is done. The response itself is measured in the offspring. The ratio of the two quantities afterwards gives a realised heritability.[1]
In a Dutch study of fibre hemp published in 1994, mass selection proved efficient for bast fibre content and reduced THC content. Its author wrote that no realised or narrow-sense heritability had been reported for the crop before.[2] Hemp lines in Ukraine have since been selected for cannabigerol and against other cannabinoids in Cannabis.[3][4]
The equation
Parents chosen from a randomly mating population differ from its mean. On average their offspring differ from it by a fraction of that amount. The fraction is the slope of the regression of offspring on the mean of their two parents, the mid-parent. That slope is the covariance of offspring and mid-parent, ½σA2, divided by the variance of the mid-parent, ½σP2. It therefore equals σA2/σP2, the additive genetic variance over the phenotypic variance, which is h2.[1] Multiplying the slope by the differential gives R = h2S.
The response depends on the average phenotype of the chosen parents and not on how they are mated.[5] Quantitative genetics began trying to predict it in the 1930s: J.B.S. Haldane computed the intensity of selection from the tails of the normal curve in 1930, and Jay Lush carried the methods into livestock breeding with Animal Breeding Plans in 1937.[6] He defined the response in 1940. The formula is known as Lush's breeder's equation.[1][7]
The regression on individual parents is difficult to apply directly in plant breeding. Plant breeders usually select among entries grown in replicated plots across many environments. The plants they measure for the response may be several generations removed from the plants they selected.[1] The general form is R = βSRS, where βSR is the regression of the response units on the selection units. Hanson defined heritability in 1963 to fit this form. A heritability so defined has little meaning unless its selection units and response units are named.[1]
Selection intensity
When parents are the top fraction of a normally distributed trait, their differential follows from that fraction alone. In standard deviations it is the selection intensity i, and S = iσP, so R = ih2σP.[1][8]
| Share of the population kept as parents | Selection intensity i |
|---|---|
| 50 per cent | 0.798 |
| 20 per cent | 1.400 |
| 10 per cent | 1.755 |
| 5 per cent | 2.063 |
| 1 per cent | 2.665 |
| 0.1 per cent | 3.367 |
Take a population of mice with a mean weight of 20 g, a standard deviation of 2 g and a heritability of 0.3. Breeding from the top 10 per cent gives a differential of 3.52 g and an expected offspring mean of about 21.06 g.[8] Gain does not rise in step with the number of candidates. Choosing 10 parents out of 1,000 where 10 out of 100 were chosen before gives 52 per cent more gain for ten times the candidates.[9] Keeping fewer parents also raises the intensity, but a smaller breeding population loses additive variance sooner.[10]
Selecting one sex
The two sexes enter the equation separately: R = ½h2(Sf + Sm). The differential to use is the simple average of the two, even when different numbers of each sex are kept. If one sex is taken at random, its term falls to zero and the response is half that of selecting both.[5]
In dioecious cannabis most useful products come from female plants, which makes favourable traits hard to recognise in a male, and selection on economic traits is usually limited to females.[11]: 299, 303 Work on bast fibre published in 1924 was an early exception: male plants with a low fibre yield were removed before they flowered.[12]
Source of the gain
Selection on a trait raises the frequency of the alleles that increase it. Summed over loci, these changes in allele frequency come to ih2σP, the whole of the predicted response. The gain is therefore expected to last when selection stops.[10] Truncation selection also creates linkage disequilibrium. It places alleles that increase the trait in repulsion, which lowers the variance of the next generation. Bulmer gave an approximation for this effect between unlinked loci in 1971. The usual prediction ignores it and holds h2 and σP at their starting values, which gives the same response in each generation.[10]
Clayton and colleagues tested the prediction at Edinburgh in 1957 on the number of abdominal bristles in Drosophila, a highly heritable trait with mostly additive variance. R = h2S predicted the early generations quite well. Most of the response stayed when selection was relaxed. With selection continued for many generations, both the high and low lines moved outside the range of the base population.[7]
Realised heritability
Dividing an observed response by the selection applied gives h2 = R/iσ, the realised heritability.[1] Douglas Falconer introduced the term in 1952 to describe responses in selection experiments.[7] Hetzer and Harvey selected pigs in two directions for backfat. Their high and low lines came to differ by 68 per cent of the starting mean in one breed, over 10 generations, and by 44 per cent in another, over eight. The realised heritabilities agreed with estimates of the trait from variance components.[7]
Gain per year
Plant breeders commonly write the equation with an accuracy term and a time term: ΔG = σair/L. Here σa is the additive genetic standard deviation of the population, r the accuracy of selection and L the years per breeding cycle. Eberhart added the denominator in 1970, to express the response as change over time.[9] Cobb and colleagues called cycle time the cheapest and most powerful of these terms to change. They argued that raising heritability beyond about 0.5 to 0.7 is rarely worth the added testing locations. Recurrent selection in Brazilian upland rice gained 3.6 per cent a year over three cycles and in irrigated lowland rice 1.98 per cent.[9]
Hemp in the field often flowers only two to four months after sowing in Europe and North America. Under artificial light, in a speed-breeding protocol published in 2022, a generation from seed to seed takes under nine weeks, which allows five generations a year. The protocol is meant for crosses, mapping populations and new cultivars. These figures are generation times and not gains from selection.[13] Cobb and colleagues expected shorter cycles from rapid generation advance and genomic selection.[9] Genomic prediction has been tried on cannabinoids: in drug-type accessions genotyped at 250,000 markers, a random forest model predicted THC, CBD and their precursors best of the models compared.[14]
Other traits and other environments
Breeders understood that the equation holds only for the trait being selected.[7] Hazel used the genetic correlation between traits in 1943. Robertson then showed in 1966, from the culling of dairy cattle, that the change in a trait equals its genetic covariance with fitness, and Price generalised that result in 1970. Lande generalised the breeder's equation itself in 1979, in terms of selection gradients.[7] In the long-term artificial selection of maize at the University of Illinois, the populations selected for kernel oil differ in a range of correlated traits, and the high-oil line yields poorly.[15][16]
One trait measured in two environments can be treated as two correlated traits. Falconer extended the genetic correlation to this case in 1952 and showed that selection in a poorer environment might give a larger response in a good one than selection in the good one itself.[7] Cooper and colleagues wrote this into the breeder's equation for crops in 2023. They added a term for the additive genetic correlation between a programme's trials and its target environments, which runs from +1 where the two are well aligned to −1 where they are poorly aligned. For the grain yield of 15 wheat genotypes in two sets of environments, the correlation was 0.70.[17] Petit and colleagues judged hemp traits with a large genotype-by-environment interaction poor targets for breeding.[18]
Departures from the prediction
Beavis and colleagues teach that realised gains are always less than predicted ones. Heritabilities estimated from half-sib and other family data carry a bias from epistatic variance, which overestimates the predicted gain.[1]
A changing environment can hide a response or be mistaken for one. Natural selection may oppose the breeder, so that the response reaches a plateau with additive variance still present. Genetic drift in a finite population eventually removes that variance.[10] Fitness-related traits in the Edinburgh experiments were predicted more poorly than bristle number and reached plateaus.[7]
Over many generations the prediction for one cycle gives way to a limit. Under the infinitesimal model, in which many loci each have a small effect, the ratio of the selection limit to the first generation's response is 2Ne, twice the effective population size. Results from many Drosophila experiments fit this ratio well once mutation is allowed for, though they separate it poorly from other models of gene effects. Annual selection in the Illinois maize lines has run for more than 100 generations. Its responses are not inconsistent with the infinitesimal model if mutation is allowed for.[7]
In natural populations
Evolutionary biologists use the equation to predict adaptation in the wild, where its assumptions are harder to meet. The univariate form assumes that the trait is not correlated with other traits that affect fitness. The multivariate form assumes that all such traits have been measured. Morrissey and colleagues argued in 2010 that studies of natural selection are likely to violate both and recommended the Robertson–Price identity in their place.[19] In Soay sheep on St Kilda the breeder's equation predicted increasing size in four morphological traits. The sheep were not getting larger. Robertson's theorem did not predict that they would.[20] Benoit Pujol and colleagues wrote in 2018 that a lack of the expected response appears to be the norm in long-term studies of wild populations, even where genetic variation and selection have both been found.[21]
Selection in cannabis
Sebastiaan Hennink scored 252 hemp plants in 1991 and their half-sib progenies in 1992. He used selection to test the heritabilities he estimated from them. Bast fibre content was highly heritable and mass selection for it had no undesirable influence on other characters. Flowering date, plant height and stem diameter had disadvantages when used to select indirectly for bast fibre yield.[2] The other results below are changes in a line or cultivar over years of breeding.
| Trait | Material and method | Result |
|---|---|---|
| Bast fibre content | G. Bredemann's hemp, male plants low in fibre removed before flowering; work published in 1924 | From about 12 to about 24 per cent, on the breeders' figures of 1956[12] |
| Bast fibre content | Hemp breeding from the 1920s to about 1990 | From about 12–15 per cent to 25–35 per cent[2] |
| THC content | Selections of existing French cultivars, from the 1980s | Below 0.07 per cent, from 0.1–0.3 per cent[2] |
| Male plants, THC and yield | Monoecious cultivar Henola, 11 years of mass selection against male plants and high THC, and for yield | Cultivar released[22] |
| CBD, THC and cannabinol | Ukrainian monoecious hemp, selfing of plants without these compounds, 2009–2019 | Contents reduced to complete absence; families without them from the first selfed generation[3] |
| Cannabigerol (CBG) | Selfed lines of Hlukhivski 58 above 0.5 per cent CBG, selected to the sixth generation and combined into the cultivar Vik 2020 | 1.034 per cent, against 0.002 per cent in the standard cultivar Hliana[4] |
| Resistance to the root-knot nematode Meloidogyne hapla | Mass selection in Kompolti Sárgaszárú, by Hennink and Dieleman | Little progress, put down to limited genetic variation[23] |
Horkay found in 1982 that selection for more bark fibre raised the number of both primary and secondary fibre cells, the secondary more, and that textile quality suffered because secondary fibres are less strong.[24] Breeders in Hungary and France stopped selecting for higher fibre content for this reason, though high fibre levels do paper no harm.[2] In two Ukrainian cultivars and their selfed lines, CBD and THC contents were correlated at 0.71 to 0.90. Serhii Mishchenko concluded that this eases selection against all cannabinoids and hampers selection for high CBD with low THC. The correlations were weaker in inbred plants than in the original breeding material.[3]
From broad-sense estimates in clones of 119 drug-type genotypes, Naim-Feil and colleagues judged that cannabinoid composition would respond to selection more strongly than the form of the plant and its inflorescences.[25] Such estimates include dominance and epistatic variance, whereas the breeder's equation uses the additive part alone.[1]
See also
References
- ↑ 1.00 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 Beavis, W.; Lamkey, K.; Mahama, A.A.; Suza, W. (2023). "Selection response". In Suza, W.P.; Lamkey, K.R. (eds.). Quantitative genetics for plant breeding. Iowa State University Digital Press. doi:10.31274/isdup.2023.146.
- ↑ 2.0 2.1 2.2 2.3 2.4 Hennink, S. (1994). "Optimisation of breeding for agronomic traits in fibre hemp (Cannabis sativa L.) by study of parent-offspring relationships". Euphytica. 78 (1–2): 69–76. doi:10.1007/BF00021399.
- ↑ 3.0 3.1 3.2 Міщенко, С.В. (2020). "Фенотиповий прояв ознак наявності та вмісту канабіноїдів у процесі самозапилення однодомної коноплі та спрямованого добору" [Phenotypic manifestation of the traits of presence and content of cannabinoids in the process of self-pollination in monoecious hemp and selection]. Plant Breeding and Seed Production (in українська) (118): 58–73. doi:10.30835/2413-7510.2020.222333.
- ↑ 4.0 4.1 Mishchenko, S.; Laiko, I.; Kyrychenko, H. (2021). "Breeding of industrial hemp with a high content of cannabigerol by the case of 'Vik 2020' cultivar". Plant Varieties Studying and Protection. 17 (2): 105–112. doi:10.21498/2518-1017.17.2.2021.236514.
- ↑ 5.0 5.1 Felsenstein, J. (December 2019). Theoretical evolutionary genetics. Seattle: Department of Genome Sciences, University of Washington. pp. 443–444.
- ↑ Felsenstein, J. (December 2019). Theoretical evolutionary genetics. Seattle: Department of Genome Sciences, University of Washington. p. 450.
- ↑ 7.0 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 Hill, W.G. (2014). "Applications of population genetics to animal breeding, from Wright, Fisher and Lush to genomic prediction". Genetics. 196 (1): 1–16. doi:10.1534/genetics.112.147850.
- ↑ 8.0 8.1 8.2 Felsenstein, J. (December 2019). Theoretical evolutionary genetics. Seattle: Department of Genome Sciences, University of Washington. pp. 444–447.
- ↑ 9.0 9.1 9.2 9.3 Cobb, J.N.; Juma, R.U.; Biswas, P.S.; Arbelaez, J.D.; Rutkoski, J.; et al. (2019). "Enhancing the rate of genetic gain in public-sector plant breeding programs: lessons from the breeder's equation". Theoretical and Applied Genetics. 132 (3): 627–645. doi:10.1007/s00122-019-03317-0.
- ↑ 10.0 10.1 10.2 10.3 Felsenstein, J. (December 2019). Theoretical evolutionary genetics. Seattle: Department of Genome Sciences, University of Washington. pp. 447–450.
- ↑ Clarke, Robert C.; Merlin, Mark D. (2016). "Cannabis domestication, breeding history, present-day genetic diversity, and future prospects". Critical Reviews in Plant Sciences. 35 (5–6): 293–327. doi:10.1080/07352689.2016.1267498.
- ↑ 12.0 12.1 Bredemann, G.; Schwanitz, Fr.; von Sengbusch, R. (1956). "Problems of modern hemp breeding, with particular reference to the breeding of varieties of hemp containing little or no hashish". Bulletin on Narcotics (3). United Nations: 31–35.
- ↑ Schilling, S.; Melzer, R.; Dowling, C.A.; Shi, J.; Muldoon, S.; McCabe, P.F. (2023). "A protocol for rapid generation cycling (speed breeding) of hemp (Cannabis sativa) for research and agriculture". The Plant Journal. 113 (3): 437–445. doi:10.1111/tpj.16051.
- ↑ Yoosefzadeh Najafabadi, M.; Torkamaneh, D. (2024). "Machine learning-enhanced multi-trait genomic prediction for optimizing cannabinoid profiles in cannabis". The Plant Journal. 121 (1) e17164. doi:10.1111/tpj.17164. PMC 11711876.
- ↑ Moose, S.P.; Dudley, J.W.; Rocheford, T.R. (2004). "Maize selection passes the century mark: a unique resource for 21st century genomics". Trends in Plant Science. 9 (7): 358–364. doi:10.1016/j.tplants.2004.05.005.
- ↑ Laurie, C.C.; Chasalow, S.D.; LeDeaux, J.R.; McCarroll, R.; Bush, D.; Hauge, B.; et al. (2004). "The genetic architecture of response to long-term artificial selection for oil concentration in the maize kernel". Genetics. 168 (4): 2141–2155. doi:10.1534/genetics.104.029686.
- ↑ Cooper, M.; Powell, O.; Gho, C.; Tang, T.; Messina, C. (2023). "Extending the breeder's equation to take aim at the target population of environments". Frontiers in Plant Science. 14 1129591. doi:10.3389/fpls.2023.1129591.
- ↑ Petit, J.; Salentijn, E.M.J.; Paulo, M.-J.; Thouminot, C.; van Dinter, B.J.; et al. (2020). "Genetic variability of morphological, flowering, and biomass quality traits in hemp (Cannabis sativa L.)". Frontiers in Plant Science. 11 102. doi:10.3389/fpls.2020.00102.
- ↑ Morrissey, M.B.; Kruuk, L.E.B.; Wilson, A.J. (2010). "The danger of applying the breeder's equation in observational studies of natural populations". Journal of Evolutionary Biology. 23 (11): 2277–2288. doi:10.1111/j.1420-9101.2010.02084.x.
- ↑ Morrissey, M.B.; Parker, D.J.; Korsten, P.; Pemberton, J.M.; Kruuk, L.E.B.; Wilson, A.J. (2012). "The prediction of adaptive evolution: empirical application of the secondary theorem of selection and comparison to the breeder's equation". Evolution. 66 (8): 2399–2410. doi:10.1111/j.1558-5646.2012.01632.x.
- ↑ Pujol, B.; Blanchet, S.; Charmantier, A.; Danchin, E.; Facon, B.; et al. (2018). "The missing response to selection in the wild". Trends in Ecology & Evolution. 33 (5): 337–346. doi:10.1016/j.tree.2018.02.007.
- ↑ Baluch, S. (2026). "Advances in hemp breeding". Achieving sustainable cultivation of hemp. Burleigh Dodds Science Publishing. pp. 49–70. doi:10.19103/as.2025.0161.04.
- ↑ de Meijer, E. (1994). Diversity in Cannabis (PhD thesis). Wageningen: Landbouwuniversiteit Wageningen. p. 115. doi:10.18174/207065. ISBN 90-5485-338-7.
- ↑ de Meijer, E. (1994). Diversity in Cannabis (PhD thesis). Wageningen: Landbouwuniversiteit Wageningen. pp. 46–47. doi:10.18174/207065. ISBN 90-5485-338-7.
- ↑ Naim-Feil, E.; Elkins, A.C.; Malmberg, M.M.; Ram, D.; Tran, J.; et al. (2023). "The cannabis plant as a complex system: interrelationships between cannabinoid compositions, morphological, physiological and phenological traits". Plants. 12 (3) 493. doi:10.3390/plants12030493.