Epistasis
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Epistasis is an interaction between genes at different loci, in which the effect of an allele at one locus depends on the genotype at another.[1] The word has two established senses. In a dihybrid cross it means that a genotype at one locus masks the effect of another, which shows in the Mendelian ratios of the offspring. In quantitative genetics it means any statistical departure from adding up the effects of the two loci.[1]
Interaction between genes and interaction variance in a population are separate quantities. Pathways and networks imply that genes interact, while most measured genetic variance is additive.[2] In one cross of Cannabis hemp cultivars, the interaction between two genomic regions explained between 3.89 and 15.11 per cent of the variance in each of eight traits.[3] The two regions correspond to the chemotype loci B and O.[4]
Masking in a cross
William Bateson used the word in 1909 for dihybrid crosses in which some expected classes of offspring did not appear or some combinations gave new phenotypes. An allele that stopped the effect of another locus was epistatic to it. The allele it stopped was hypostatic.[5] Two loci that assort independently and show complete dominance give four classes in the F2, in the ratio 9:3:3:1. Epistasis merges some of these classes.[6]
| Ratio | Material | Reading |
|---|---|---|
| 9:3:3:1 | Cannabis plants homozygous for the CBD allele at locus B, scored for the share of propyl cannabinoids | Two independent loci, no epistasis in the model[6] |
| 9:7 | Flower colour in sweet pea, from a cross of two white-flowered plants | Two complementary genes in the anthocyanin pathway; a mutation in either disrupts colour[5] |
| 9:4:3 | Coat colour in mice, agouti and extension | Recessive epistasis, which places extension downstream of agouti[5] |
| 7:6:3 | Cannabis plants homozygous for the THC allele at locus B, scored for the share of propyl cannabinoids | Dominance at one gene pair, partial dominance at the second, the first epistatic to the second when homozygous recessive[6] |
A ratio of this kind says something about function, since the phenotype depends on a combination of alleles. George Beadle, Edward Tatum and their students used crosses of separate knockouts to put the steps of a pathway in order. In the nematode C. elegans, the order of genes for sex determination and other traits was worked out in this way before the genes were characterised.[5]
Epistasis belongs to particular alleles and not to a locus in general. Forest and beach mice differ at agouti and at extension (now called Mc1r). In nature the pattern between the two loci runs the opposite way from the laboratory cross, presumably because the beach-mouse Mc1r allele keeps partial function.[5]
Departure from additivity
In 1918 R.A. Fisher coined "epistacy" for any departure from adding up the effects of two loci on a trait.[5][7] Fisher's concept spread under Bateson's word.[7] Patrick Phillips separates three uses. Functional epistasis is a molecular interaction between proteins. Compositional epistasis is the effect of substituting alleles against one fixed genetic background. It takes in the older masking sense. Statistical epistasis is the same substitution averaged over the backgrounds present in a population.[5] A result in one sense does not carry over: a clear interaction in a cross can be absent from the statistical measures of a population.[5]
With two diploid loci there are nine genotypes, and an interaction shows when their values are plotted. Without epistasis, the effects at one locus stay the same whatever the genotype at the other. With it, the other locus can enhance or suppress those effects or reverse their direction.[1] Where a pair of mutations each lower fitness alone and raise it together, the sign of the interaction differs from the signs of the single effects. This is called sign epistasis. It leaves a valley between two adaptive states.[5]
The result also depends on the scale of measurement. Fisher used an additive scale and expected that some transformation of the phenotype would usually make effects additive.[5] From the late 1960s population geneticists often measured departure from a multiplicative model of fitness, because loci with multiplicative fitnesses evolve independently.[5] Where the logarithm of fitness is a curved function of a trait with additive loci, fitness shows epistasis while the trait shows none.[8]
Epistatic variance
The genotypic variance among plants is divided into additive, dominance and epistatic parts.[9] These parts depend on allele frequencies. An interaction between the values of individual genotypes does not. Epistatic variance is largest when both loci sit at intermediate frequencies. Interacting loci also add to additive variance through their main effects over much of the range of allele frequencies.[1]
Additive variance usually makes up more than half of the genetic variance and often close to all of it in estimates for many traits and species. On a neutral model most alleles are rare, which yields mostly additive variance even for loci with marked dominance or epistasis.[2] Models with many loci give the same result: interaction terms feed into the average effect of each locus, so they raise additive variance more than epistatic variance.[10] Direct estimates are scarce because the epistatic parts contribute little to the resemblance of relatives and are confounded with the environment that full sibs share.[2]
Trudy Mackay draws a different conclusion from the same pattern: additive variance may be real or may be an apparent product of epistatic gene action at many loci. On that account the difference does not affect heritability or the prediction of short-term response. It does affect long-term response, the consequences of drift and inbreeding and the tracing of genes and networks.[1] The broad-sense heritability of fully inbred lines holds additive and additive-by-additive variance, so it can exceed what additive variance alone would give.[1]
Finding interacting loci
Interaction between quantitative trait loci is tested by fitting a model with the main effect of each locus and an interaction term.[1] Crosses between inbred lines give the most power because every allele has a frequency of 0.5. Two limits apply. Few plants fall into the rarer double-homozygous classes of a small population. The number of pairs to test grows with the square of the number of loci: 190 pairs for 20 genes, over 18 million for the yeast genome.[1][5] Most mapping studies therefore estimate additive effects only.[1]
Large panels measure the share directly. In 4,390 segregants of one yeast cross, pairwise interactions between loci explained 9 per cent of phenotypic variance on average across 20 traits and additive loci 43 per cent.[11] In Drosophila, none of the loci found for three traits in a panel of inbred lines were found again in an outbred population made from them, and 50–60 per cent of the loci took part in at least one interaction.[1][12]
Selection and crop breeding
Selection acts on the additive variance and on the part of the epistatic variance built from additive components, usually a small part. On this ground James Crow held that breeders are right to leave epistasis out of their prediction equations for quantitative traits.[7] In chicken lines selected for about 40 generations for high and low body weight, mapping found one locus with a weak effect of its own and further regions that showed effects only on its high-growth background. These loci together accounted for 45 per cent of the difference between the lines.[5] Their interactions gave a considerably larger response to selection than a single-locus model predicts.[13]
Genetic background changes the effect of an allele in these plant cases:
- Two loci that separate maize from teosinte interact epistatically. The effect of teosinte branched1 on plant and inflorescence architecture is strong in a teosinte background and reduced in a maize background.[14]
- In tomato, one mutation gave larger leaf-like organs on the fruit and another gave jointless fruit stems. Each was selected separately. Combined, they caused unwanted branching and sterility, which breeders overcame with suppressors.[15]
- In Arabidopsis, two haplogroups of the gene FLC differ in flowering time under field conditions only with a putatively functional FRI allele. Their distribution with latitude also depends on the FRI genotype.[16]
Genomic prediction can include epistasis through a marker-based relationship matrix. On wheat and maize data, this can improve accuracy in selfing species and may not in outcrossing species.[17]
Hybrids and divergence
Epistasis affects hybrid performance over a range from heterosis to sterility or lethality.[18] Outbreeding depression is the lowered performance of some crosses between populations. In the Dobzhansky–Muller model, alleles that are harmless in their own lineages harm a hybrid that combines them.[18] Hybrid necrosis in Arabidopsis is an example: about 2 per cent of 861 F1 combinations were affected, through at least five independent systems of two to four loci. In one case, a disease-resistance gene homologue of the NB-LRR class from one parent and an allele at a single locus from the other were enough to cause necrosis.[18]
In cannabis
| Study | Material | Trait | Result |
|---|---|---|---|
| Woods and colleagues (2021) | F2 of the hemp cultivars Carmagnola × USO31, in the field in Colorado | 8 agronomic and 17 biochemical traits | Region LG6.35 × region LG9.40 significant for 8 biochemical traits, 3.89–15.11 per cent of variance. One interaction among the agronomic traits (stem diameter, 4.38 per cent)[3] |
| Welling and colleagues (2019) | 210 F2 plants of a cross between THCV-rich and CBDA-rich parents | Share of propyl cannabinoids | 7:6:3 accepted in plants homozygous for the THC allele at locus B (50 plants; χ² = 1.20, critical value 5.99); 9:3:3:1 in plants homozygous for the CBD allele (44 plants; χ² = 2.71, critical value 7.82)[6] |
| Campbell and colleagues (2020) | Line means from two published crosses (2003 and 2014) | THC, CBD and CBC concentration; chemotype | Additive-by-additive effects among the second-best models for THC in the 2014 cross; a small contribution, more minor in the 2003 cross[19] |
In the Carmagnola × USO31 cross, one pair of regions interacted for three cannabinoids and five terpenes. For CBDA concentration the interaction explained 9.59 per cent of variance, against 28.21 and 44.79 per cent for the two regions alone. For THCA the interaction explained 8.36 per cent, against 24.54 and 32.10.[3] Woods and colleagues proposed olivetol synthase as the gene behind LG9.40 and found nine amino acid differences in it between the parents. No candidate was named for LG6.35, and the design had limited power to find further loci of small effect.[3]
Stack and colleagues (2023) later matched these regions to chemotype loci. LG6.35 corresponds to locus B, which holds the synthase genes that determine the dominant cannabinoid. Plants segregating at LG9.40 match locus O, where o/o plants have under 0.05 per cent total cannabinoids. Stack and colleagues call B and O "two epistatic Mendelian loci", with O acting biochemically upstream of B.[4] In the model of de Meijer and colleagues (2009), o is a recessive factor that segregates independently of the other chemotype loci, with a low-content heterozygote and an F2 ratio of 1:2:1.[20]
The cross of Welling and colleagues concerns the length of the cannabinoid side chain. Their suggestion, which they call speculative, is that the two gene pairs of the 7:6:3 model encode sequential steps in forming the fatty-acid starter unit of propyl cannabinoids.[6] The parents were not fully inbred, which may have contributed to the unusual ratios, and the authors raise linkage between these loci and locus B.[6] De Meijer and Hammond (2016) proposed a different model for the same trait from inbred lines of six progenitors, with several loci whose alleles are partly different, complementary and additive.[21]
Carlson and colleagues (2021) attribute complex interactions among flowering genes in hemp to latitudinal adaptation and recent admixture, and call the early-flowering ratios of their hybrids possible evidence of epistasis.[22] An F1 between the day-neutral grain hemp Picolo and an Autoflower1 line flowered under long days, which left open whether one gene lies behind both. Inbred progeny of plants heterozygous at the flowering-time loci Autoflower1 and Early1 would form nine genotypic groups, which could test for epistasis between them.[23]
See also
References
- ↑ 1.00 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 Mackay, T.F.C. (2014). "Epistasis and quantitative traits: using model organisms to study gene–gene interactions". Nature Reviews Genetics. 15 (1): 22–33. doi:10.1038/nrg3627.
- ↑ 2.0 2.1 2.2 Hill, W.G.; Goddard, M.E.; Visscher, P.M. (2008). "Data and theory point to mainly additive genetic variance for complex traits". PLOS Genetics. 4 (2) e1000008. doi:10.1371/journal.pgen.1000008.
- ↑ 3.0 3.1 3.2 3.3 Woods, P.; Campbell, B.J.; Nicodemus, T.J.; Cahoon, E.B.; Mullen, J.L.; McKay, J.K. (2021). "Quantitative trait loci controlling agronomic and biochemical traits in Cannabis sativa". Genetics. 219 (2) iyab099. doi:10.1093/genetics/iyab099.
- ↑ 4.0 4.1 Stack, G.M.; Snyder, S.I.; Toth, J.A.; Quade, M.A.; Crawford, J.L.; et al. (2023). "Cannabinoids function in defense against chewing herbivores in Cannabis sativa L." Horticulture Research. 10 (11) uhad207. doi:10.1093/hr/uhad207.
- ↑ 5.00 5.01 5.02 5.03 5.04 5.05 5.06 5.07 5.08 5.09 5.10 5.11 5.12 Phillips, P.C. (2008). "Epistasis: the essential role of gene interactions in the structure and evolution of genetic systems". Nature Reviews Genetics. 9 (11): 855–867. doi:10.1038/nrg2452.
- ↑ 6.0 6.1 6.2 6.3 6.4 6.5 Welling, M.T.; Liu, L.; Raymond, C.A.; Kretzschmar, T.; Ansari, O.; King, G.J. (2019). "Complex patterns of cannabinoid alkyl side-chain inheritance in Cannabis". Scientific Reports. 9 (1) 11421. doi:10.1038/s41598-019-47812-2.
- ↑ 7.0 7.1 7.2 Crow, J.F. (2010). "On epistasis: why it is unimportant in polygenic directional selection". Philosophical Transactions of the Royal Society B. 365 (1544): 1241–1244. doi:10.1098/rstb.2009.0275.
- ↑ Felsenstein, J. (December 2019). Theoretical evolutionary genetics. Seattle: Department of Genome Sciences, University of Washington. pp. 363–364.
- ↑ Beavis, W.; Lamkey, K.; Espinosa, K.; Mahama, A.A.; Suza, W. (2023). "Components of Variance". In Suza, W.; Lamkey, K. (eds.). Quantitative Genetics for Plant Breeding. Iowa State University Digital Press. doi:10.31274/isdup.2023.146.
- ↑ Mäki-Tanila, A.; Hill, W.G. (2014). "Influence of gene interaction on complex trait variation with multilocus models". Genetics. 198 (1): 355–367. doi:10.1534/genetics.114.165282.
- ↑ Bloom, J.S.; Kotenko, I.; Sadhu, M.J.; Treusch, S.; Albert, F.W.; Kruglyak, L. (2015). "Genetic interactions contribute less than additive effects to quantitative trait variation in yeast". Nature Communications. 6 (1) 8712. doi:10.1038/ncomms9712.
- ↑ Huang, W.; Richards, S.; Carbone, M.A.; Zhu, D.; Anholt, R.R.H.; et al. (2012). "Epistasis dominates the genetic architecture of Drosophila quantitative traits". Proceedings of the National Academy of Sciences. 109 (39): 15553–15559. doi:10.1073/pnas.1213423109.
- ↑ Carlborg, Ö.; Jacobsson, L.; Åhgren, P.; Siegel, P.; Andersson, L. (2006). "Epistasis and the release of genetic variation during long-term selection". Nature Genetics. 38 (4): 418–420. doi:10.1038/ng1761.
- ↑ Doebley, J.; Stec, A.; Gustus, C. (1995). "teosinte branched1 and the origin of maize: evidence for epistasis and the evolution of dominance". Genetics. 141 (1): 333–346. doi:10.1093/genetics/141.1.333.
- ↑ Soyk, S.; Lemmon, Z.H.; Oved, M.; Fisher, J.; Liberatore, K.L.; et al. (2017). "Bypassing negative epistasis on yield in tomato imposed by a domestication gene". Cell. 169 (6): 1142–1155.e12. doi:10.1016/j.cell.2017.04.032.
- ↑ Caicedo, A.L.; Stinchcombe, J.R.; Olsen, K.M.; Schmitt, J.; Purugganan, M.D. (2004). "Epistatic interaction between Arabidopsis FRI and FLC flowering time genes generates a latitudinal cline in a life history trait". Proceedings of the National Academy of Sciences. 101 (44): 15670–15675. doi:10.1073/pnas.0406232101.
- ↑ Jiang, Y.; Reif, J.C. (2015). "Modeling epistasis in genomic selection". Genetics. 201 (2): 759–768. doi:10.1534/genetics.115.177907.
- ↑ 18.0 18.1 18.2 Bomblies, K.; Lempe, J.; Epple, P.; Warthmann, N.; Lanz, C.; Dangl, J.L.; Weigel, D. (2007). "Autoimmune response as a mechanism for a Dobzhansky–Muller-type incompatibility syndrome in plants". PLOS Biology. 5 (9): e236. doi:10.1371/journal.pbio.0050236.
- ↑ Campbell, L.G.; Dufresne, J.; Sabatinos, S.A. (2020). "Cannabinoid inheritance relies on complex genetic architecture". Cannabis and Cannabinoid Research. 5 (1): 105–116. doi:10.1089/can.2018.0015.
- ↑ de Meijer, E.P.M.; Hammond, K.M.; Sutton, A. (2009). "The inheritance of chemical phenotype in Cannabis sativa L. (IV): cannabinoid-free plants". Euphytica. 168 (1): 95–112. doi:10.1007/s10681-009-9894-7.
- ↑ de Meijer, E.P.M.; Hammond, K.M. (2016). "The inheritance of chemical phenotype in Cannabis sativa L. (V): regulation of the propyl-/pentyl cannabinoid ratio, completion of a genetic model". Euphytica. 210 (2): 291–307. doi:10.1007/s10681-016-1721-3.
- ↑ Carlson, C.H.; Stack, G.M.; Jiang, Y.; Taşkıran, B.; Cala, A.R.; et al. (2021). "Morphometric relationships and their contribution to biomass and cannabinoid yield in hybrids of hemp (Cannabis sativa)". Journal of Experimental Botany. 72 (22): 7694–7709. doi:10.1093/jxb/erab346.
- ↑ Toth, J.A.; Stack, G.M.; Carlson, C.H.; Smart, L.B. (2022). "Identification and mapping of major-effect flowering time loci Autoflower1 and Early1 in Cannabis sativa L." Frontiers in Plant Science. 13 991680. doi:10.3389/fpls.2022.991680.