Genotype-by-environment interaction
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Genotype-by-environment interaction (G×E, also written GEI) is the dependence of the differences among genotypes on the environment in which they grow. Where it is present, the gap between two genotypes in a measured trait changes from one site, season or treatment to another. The better genotype in one place may be the poorer one in the next.[1] It is estimated by growing the same set of genotypes in several environments and dividing the variation in the trait among genotype, environment and their interaction.[2]
In Cannabis the interaction has been measured mostly in hemp cultivars and accessions at field sites in Europe and North America. Its share of the variation differs by trait and by trial. In one season in Colorado it was the largest component of the variation in grain yield, at 35 per cent. For total THC and CBD it was about 2 per cent.[3] In a European panel of 123 accessions, flowering, bast fibre content and most cell wall components had large genetic components and small interactions. Pectin-related sugars and most agronomic traits had small genetic components and varied mostly with the site.[4]
Forms of the interaction
The model for a quantitative trait adds an interaction term to the effects of genotype and environment: Pij = μ + Gi + Ej + GEij, where Pij is the phenotype of genotype i in environment j.[2] The performance of one genotype plotted across environments is its norm of reaction. Where genotype and environment act additively, the norms of different genotypes are parallel.[1] R.W. Allard and A.D. Bradshaw set out the possible patterns for two genotypes in two environments in 1964. In their first two types both genotypes respond to the environment and the difference between them stays the same, so there is no interaction.[2]
Norms that are not parallel spread apart (divergence), draw together (convergence) or cross (a crossover interaction, in which the genotypes change rank). Crossovers matter most to breeders, because the choice of the best genotype then depends on the environment.[1] One extreme crossover has been called a "racehorse" response: one genotype takes full advantage of a favourable environment and fails in a stressful one, while the other is steadier.[2]
The interaction variance has two components: the heterogeneity of genetic variance among environments and the lack of correlation between the performance of genotypes in different environments. A method published by Muir and colleagues in 1992 separates the two; in one worked data set they accounted for 18 and 82 per cent of the interaction.[2] Better environments usually show more genetic variance, though poorer ones sometimes do. Similar environments give strong genetic correlations and dissimilar ones weak correlations.[1] Interaction that comes from a lack of correlation can matter even without crossovers among the entries of a trial, once its results are extended to a wider target region.[5]
Phenotypic plasticity is the response of one genotype to different environments, while the interaction is a difference among genotypes in that response. A large interaction variance points to a range of plasticity within the population.[3] In a model that adds genotype and environment together, the interaction is a source of variation that cannot easily be attributed to either. Feldman and Lewontin argued on these grounds in 1975 against the use of heritability where such interactions are present.[6]
In a yield trial an environment is usually one location in one year, with its climate, soil, pests, diseases and management. A "genotype" is a cultivar, which may be a uniform line or clone or a heterogeneous open-pollinated population.[5] The interaction can therefore be divided further, as genotype by location, genotype by year or genotype by a treatment such as irrigation or nitrogen rate.[5][3][7]
Measuring and partitioning
Analysis of variance
The standard analysis is an analysis of variance of a multi-environment trial, in which every genotype is replicated in every environment. The analysis gives mean squares for genotype, environment and interaction. The variance components follow from the expected mean squares. These calculations hold for balanced data; with unbalanced data the estimates come from restricted maximum likelihood in a mixed model.[2] Results appear as percentages of the total sum of squares,[3] as percentages of the total variance or as the ratio of the interaction variance to the genetic variance. A ratio near zero means that the accessions keep their order from site to site.[4] On an entry-mean basis the interaction variance is divided by the number of environments, which is how it enters many field estimates of heritability.[2]
The size of the interaction depends on which environments are sampled. Some of the interaction variance measured over a broad population of environments becomes genotypic variance when the same genotypes are judged within a narrower, more uniform subset. Narrowing the set raises the genotypic variance and lowers the interaction variance. Widening it does the reverse.[2]
Models of the interaction
Models of multi-environment data start from a two-way table of genotype-by-environment means and differ in what they use to describe the environment.[1]
| Model | How it describes the interaction | Information about the environment |
|---|---|---|
| Regression on the mean (Finlay and Wilkinson, 1963) | A separate regression slope for each genotype on the quality of the environment, a slope being a sensitivity to improvement of the environment | The mean of all genotypes in that environment[1] |
| AMMI (additive main effects and multiplicative interaction) | Several products of a genotypic score and an environmental score, from a principal component analysis of the interaction, drawn as a biplot | Hypothetical scores with no measured meaning of their own[1] |
| GGE biplot | As AMMI, with the genotype main effect included with the interaction, so that a projection shows overall performance | Hypothetical scores[1] |
| Cluster analysis | Groups of environments, or of genotypes, chosen to have little interaction within a group | Dissimilarity between the responses of the genotypes[2] |
| Factorial regression | Genotypic sensitivity to named factors, such as temperature or water availability | Measured covariables[1] |
| QTL-by-environment models | Marker information as predictors, testing whether the effect of a quantitative trait locus changes with the environment | Environments, or measured covariables[1] |
Stability has two contrasting meanings in this work. A genotype with static stability keeps a constant yield across environments. A genotype with dynamic stability responds in parallel with the mean of the genotypes tested, which is zero interaction, so its measure depends on which genotypes were tested.[5] The WAAS index (weighted average of absolute scores), proposed by Olivoto and colleagues, takes its lowest value in the genotype that deviates least from average performance across environments. It is plotted against yield so that the two can be read together.[8]
Consequences for selection
A large interaction weakens any prediction of how genotypes will perform elsewhere from how they performed in one environment.[1] Petit and colleagues warned that selecting on a trait with a large interaction can bias decisions, since the effects in untested environments are unknown.[4] In 1985 Sara Via and Russell Lande modelled a character expressed in two environments as two genetically correlated states of that character. In their model a genetic correlation between the states constrains the response to selection much as a correlation between two characters does. Very high positive or negative correlations can slow evolution substantially. Evolution towards the optimum in a rare environment is much slower than in a common one.[9]
Breeding for wide adaptation aims at a variety that performs well in nearly all environments. Breeding for specific adaptation aims at one that performs well in a defined subset of a target region.[5] Dividing a target region among several specific targets replaces one breeding programme with several.[2] In the second half of the 20th century it was commonly believed that selection in favourable areas would also raise yields in less favourable ones. Theory and trials under drought and low nutrients challenged that belief. Optimal management on research stations can itself create interaction with neighbouring farmers' fields. ICARDA selected barley under conditions like those of the target environment, while CIMMYT alternated selection between stressed and irrigated sites to obtain widely adapted material.[5]
On one view only genotype-by-location effects can be exploited through specific adaptation, because the climate of future years cannot be foreseen. Year effects bear on stability instead. A farmer's location does not change, so for the farmer consistency over time is what counts.[5]
Göte Turesson's work of the 1920s, which introduced the term ecotype, showed specific adaptation to particular areas. In less favourable areas local germplasm is often preferred to improved varieties for its tolerance of severe stresses.[5] In Via and Lande's subdivided-population model, restricted migration can facilitate local adaptation.[9]
Measured in cannabis
| Study | Entries | Environments |
|---|---|---|
| Petit and colleagues (2020) | 123 accessions, mainly for fibre, with some landraces and wild material | Three sites at 45, 48 and 53°N in Italy, France and the Netherlands, in 2013[4] |
| Campbell and colleagues (2019) | 13 cultivars from Europe and Asia | Two sites in Colorado, one with two irrigation treatments, 2016[3] |
| Ferfuia and colleagues (2021) | Five monoecious cultivars | Six combinations of site, year and sowing date in north-eastern Italy, 2018–2019[8] |
| Beleggia and colleagues (2023) | Six monoecious and dioecious genotypes of chemotypes III and IV | One site at Rovigo, Italy, in 2018, 2019 and 2020[10] |
| Mahdi and colleagues (2026) | 32 fibre and dual-purpose cultivars | Three regions of Missouri, 2021–2023[11] |
| Nain and colleagues (2026) | Varieties for biomass and grain | Sites across Missouri, 2023–2025[12] |
| Yazıcı and colleagues (2026) | 16 genotypes | Four growing seasons, 2022–2025[13] |
| Trait | Study | Genotype | Environment | Interaction |
|---|---|---|---|---|
| Grain or seed yield | Campbell | 28.4 | 24.8 | 34.6 |
| Seed yield | Ferfuia | 4 | 82 | 12 |
| Above-ground biomass | Campbell | 11.5 | 61.5 | 12.9 |
| Above-ground biomass | Ferfuia | 15 | 60 | 20 |
| Plant height | Campbell | 35.9 | 37.8 | 9.0 |
| Plant height | Ferfuia | 40 | 47 | 12 |
| Stem height | Petit | 6.84 | 81.81 | 2.31 |
| Beginning of flowering | Petit | 74.43 | 9.06 | 8.97 |
| Full flowering | Petit | 78.86 | 4.62 | 14.66 |
| Emergence to full flowering | Ferfuia | 61 | 27 | 12 |
| Days to maturity (Fort Collins treatments only) | Campbell | 97.3 | 0.0 | 1.0 |
| Emergence to seed maturity | Ferfuia | 11 | 59 | 30 |
| Seed oil content | Ferfuia | 7 | 77 | 13 |
| Bast fibre content after decortication | Petit | 66.79 | 16.66 | 5.36 |
| Total THC (Fort Collins treatments only) | Campbell | 80.4 | 1.7 | 2.1 |
| Total CBD (Fort Collins treatments only) | Campbell | 82.7 | 6.0 | 1.7 |
| Cannabinoids as a class (three years at one site) | Beleggia | 34.0 | 36.5 | 21.4 |
The percentages rest on different calculations, shares of the total sum of squares in Campbell and variance components in Petit, so the columns are not strictly comparable. The interaction terms for THC and CBD in Campbell are not significant.[3][4] The environment column means year in Beleggia and a combination of site, year and sowing date in Ferfuia.[8][10]
Yield and biomass
The Colorado trial had two sites, Fort Collins with limited and full irrigation and Yellow Jacket with full irrigation. Mean grain yield of the cultivars ran from 27 to 2,366 kg per hectare. Every cultivar yielded more with more water, but not equally. Félina 32 gave the most grain under both treatments at Fort Collins, 611 kg per hectare with limited irrigation and 2,337 kg with full irrigation, the largest response of any cultivar. Of 13 cultivars, Bialobrzeskie stood 12th and 11th in stand establishment in the two Fort Collins treatments and first at Yellow Jacket. Rankings for yield and biomass were closer between the two Fort Collins treatments than between either and Yellow Jacket, from which the authors concluded that the interaction has causes beyond soil moisture.[3]
In the Italian trial, sowing in June raised seed yield in Ferimon, Fedora and Felina, whereas Zenit and Futura fell in rank. High temperature early in grain filling lowered seed yield in the medium and early cultivars. The authors held that this explains at least part of the environmental and interaction effects.[8] Among 14 cultivars at four European sites, the cultivar effect on stem and seed yield came mainly from the genetic variation in flowering time. Only the early cultivars Fedora 17 and Markant set seed at the most northern site, in Latvia.[14]
An AMMI analysis across sites in Missouri found strong interactions for biomass and grain yield. Saturated soils caused crop failure at some of those sites in each of three years.[12] In another Missouri trial Jinma gave the highest fibre yield at two of three sites, while MS 77 and Puma were comparatively high at the third.[11] Genotype-by-year effects were significant for every agronomic trait examined in 16 genotypes over four seasons.[13] In a trial of two cultivars under irrigation in a high-elevation semi-arid climate, Altair yielded 28.5 per cent more stem than Hliana at 160 kg of nitrogen per hectare. At 80 kg the two yielded alike.[7]
Flowering and maturity
Flowering traits in the European panel had large genetic components and interaction ratios of 0.12 to 0.19, across sites that differed mostly in photoperiod, temperature and water.[4] Days to maturity in Colorado were almost wholly genetic, though some cultivars took longer to mature under full irrigation and others less long, a small crossover. The authors added that wider differences in latitude may strengthen the environmental effect on phenology.[3] In Italy the period from emergence to full flowering was mainly genetic, while the period from emergence to seed maturity was mainly environmental, with 30 per cent of its variation in the interaction.[8]
Cannabinoids and terpenes
Total THC and total CBD were measured at one Colorado site under two irrigation treatments. Both were largely genetic and neither showed a significant interaction. Cannabichromene differed, with 16.8 per cent of its variation in the interaction and no detectable effect of the environment. One cultivar, Tiborszállási, tested above the 0.3 per cent THC limit. The authors cautioned that their sample does not allow a precise estimate of the variance components and that environmental factors other than soil moisture may affect THC.[3]
Over three years at Rovigo the cannabinoids were divided almost evenly among genotype, year and their interaction. The share of genotype was highest for CBD and cannabigerol, at 44.6 and 46.2 per cent.[10] THC stayed below the legal limit in the Missouri trials, apart from small increases in Jinma and Puma at certain site-years in one of them.[12][11] Medicinal cannabis genotypes were also grown as clones in one controlled-environment facility. The percentage difference between clones of a genotype was 25 to 43 for THC and 11 to 36 for CBD, and the ratios between cannabinoids stayed fairly stable. With one facility there is no second environment from which to estimate an interaction.[15]
Of 23 terpenes measured in Colorado, two showed a significant interaction, α-pinene and β-pinene, each with 12 per cent of its variation in the interaction.[3] The interaction with year accounted for 13.3 to 21.8 per cent of the variation in the terpene classes other than triterpenes at Rovigo, where year was the largest source.[10]
Fibre quality and water use
In the European panel the contents of glucose, xylose, mannose and lignin kept the accessions in nearly the same order at the three sites. The dry weight fraction, arabinose content, average stem weight and the decortication index had interaction ratios of 1.42 to 5.41. The order of the accessions changed from site to site. Fibre weight had higher ratios still, 8.43 and 30.70, on genetic components below 3 per cent. Petit and colleagues judged the traits with large interactions unsuitable as breeding targets and as candidates for mapping and proposed crop management for the poorly heritable ones.[4] In Colorado 29 per cent of the variation in the carbon isotope ratio, a proxy for water use efficiency, lay in the interaction. Some cultivars used water more conservatively under full irrigation and others less so.[3]
Genetic basis
A genome-wide association study of the 123 accessions of the European panel found eight QTLs common to more than one site, six for flowering time and two for sex determination. Markers for sex from all three sites formed one cluster, which the authors read as a common genetic regulation across the sites. For the beginning of flowering they found a partly common regulation.[16] Petit and colleagues had earlier proposed "plastic genetic systems", in which certain genes are expressed in combination with particular conditions, as the likely control of the interaction variation.[4]
Halpin-McCormick and colleagues related public whole-genome data from 149 samples, 111 of them georeferenced, to the climate at the sampling locations. Their genomic estimates of adaptive value are predictions from those data, with no trial across environments.[17]
Scope of the measurements
The figures describe the entries and environments of each trial. Campbell and colleagues wrote that one season of data is not enough for general conclusions about a trait such as yield.[3] Ferfuia and colleagues called for more cultivars in more environments.[8] Variance components in the European panel were estimated over the whole panel, for one season.[4]
See also
References
- ↑ 1.00 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.10 Malosetti, M.; Ribaut, J.-M.; van Eeuwijk, F.A. (2013). "The statistical analysis of multi-environment data: modeling genotype-by-environment interaction and its genetic basis". Frontiers in Physiology. 4 44. doi:10.3389/fphys.2013.00044. PMC 3594989.
- ↑ 2.00 2.01 2.02 2.03 2.04 2.05 2.06 2.07 2.08 2.09 Beavis, W.; Lamkey, K.; Espinosa, K.; Mahama, A.A.; Suza, W. (2023). "G x E". In Suza, W.; Lamkey, K. (eds.). Quantitative Genetics for Plant Breeding. Iowa State University Digital Press. doi:10.31274/isdup.2023.146.
- ↑ 3.00 3.01 3.02 3.03 3.04 3.05 3.06 3.07 3.08 3.09 3.10 3.11 Campbell, B.J.; Berrada, A.F.; Hudalla, C.; Amaducci, S.; McKay, J.K. (2019). "Genotype × environment interactions of industrial hemp cultivars highlight diverse responses to environmental factors". Agrosystems, Geosciences & Environment. 2 (1): 1–11. doi:10.2134/age2018.11.0057.
- ↑ 4.0 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 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.
- ↑ 5.0 5.1 5.2 5.3 5.4 5.5 5.6 5.7 Annicchiarico, P. (2002). Genotype × environment interactions: challenges and opportunities for plant breeding and cultivar recommendations. FAO Plant Production and Protection Paper. Vol. 174. Rome: Food and Agriculture Organization of the United Nations. ISBN 92-5-104870-3.
- ↑ Felsenstein, J. (December 2019). Theoretical evolutionary genetics. Seattle: Department of Genome Sciences, University of Washington. pp. 435–438.
- ↑ 7.0 7.1 Solomon, J.K.Q.; Opoku, A.; Ogunleye, A.M. (2026). "Genotype-specific nitrogen requirements overpower seeding density effects for irrigated fiber hemp in a high-elevation semi-arid climate". Industrial Crops and Products. 249 123693. doi:10.1016/j.indcrop.2026.123693.
- ↑ 8.0 8.1 8.2 8.3 8.4 8.5 Ferfuia, C.; Zuliani, F.; Danuso, F.; Piani, B.; Cattivello, C.; et al. (2021). "Performance and stability of different monoecious hemp cultivars in a multi-environments trial in north-eastern Italy". Agronomy. 11 (7) 1424. doi:10.3390/agronomy11071424.
- ↑ 9.0 9.1 Via, S.; Lande, R. (1985). "Genotype-environment interaction and the evolution of phenotypic plasticity". Evolution. 39 (3): 505–522. doi:10.1111/j.1558-5646.1985.tb00391.x.
- ↑ 10.0 10.1 10.2 10.3 Beleggia, R.; Menga, V.; Fulvio, F.; Fares, C.; Trono, D. (2023). "Effect of genotype, year, and their interaction on the accumulation of bioactive compounds and the antioxidant activity in industrial hemp (Cannabis sativa L.) inflorescences". International Journal of Molecular Sciences. 24 (10) 8969. doi:10.3390/ijms24108969.
- ↑ 11.0 11.1 11.2 Mahdi, S.H.; Asiamah, J.Y.; Tamang, K.R.; Koirala, P.; Akotsen-Mensah, C.; et al. (2026). "Performance of industrial hemp cultivars across U.S. Midwestern environments: evidence from multi-location trials in Missouri". Frontiers in Agronomy. 8 1745927. doi:10.3389/fagro.2026.1745927.
- ↑ 12.0 12.1 12.2 Nain, A.; Kaur, G.; Nelson, K.A.; Bish, M.; Calhoun, J.; et al. (2026). "Effect of different environmental conditions on growth, biomass, and grain yield of industrial hemp varieties". Industrial Crops and Products. 250 123890. doi:10.1016/j.indcrop.2026.123890.
- ↑ 13.0 13.1 Yazici, L.; Yılmaz, G.; Yıldırım, C.; Akdaş, O.; Erol, O.; et al. (2026). "Multi-year and multi-trait evaluation of hemp (Cannabis sativa L.) genotypes using AMMI, GGE, WAASB, and MGIDI". Crop Science. 66 (6) e70391. doi:10.1002/csc2.70391.
- ↑ Tang, K.; Struik, P.C.; Yin, X.; Thouminot, C.; Bjelková, M.; et al. (2016). "Comparing hemp (Cannabis sativa L.) cultivars for dual-purpose production under contrasting environments". Industrial Crops and Products. 87: 33–44. doi:10.1016/j.indcrop.2016.04.026.
- ↑ 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.
- ↑ Petit, J.; Salentijn, E.M.J.; Paulo, M.-J.; Denneboom, C.; Trindade, L.M. (2020). "Genetic architecture of flowering time and sex determination in hemp (Cannabis sativa L.): a genome-wide association study". Frontiers in Plant Science. 11 569958. doi:10.3389/fpls.2020.569958.
- ↑ Halpin-McCormick, A.; Thomson, R.; Clarke, R.C.; Neyhart, J.; Kantar, M.B. (2026). "Dissecting genotype-environment relationships with functional implications for parental selection in Cannabis breeding". Journal of Heredity. 117 (1): 24–38. doi:10.1093/jhered/esaf048.