Inbreeding
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Inbreeding is mating between relatives, in which the chance that two individuals mate depends on how closely they are related.[1] Relatives share ancestors, so an inbred plant can carry at a locus two copies of one ancestral gene. The probability of this is the plant's inbreeding coefficient, f. Heterozygotes are fewer in inbred plants by the factor 1 − f, while allele frequencies stay the same on average.[2][3] In self-fertilisation, or selfing, one plant is both parents of its offspring.[4] A small population becomes inbred even when it mates at random, because its members come to share ancestors.[5]
Cannabis is mostly dioecious and pollinated by the wind, so its plants ordinarily mate with other plants.[6] Selfing occurs in monoecious hemp, on plants that bear flowers of both sexes and on plants treated to form flowers of the other sex.[6][7] Marker surveys have found fewer heterozygotes than random mating predicts in hemp varieties and about the predicted number in feral plants of the United States.[8][9] The loss of fitness that can follow is inbreeding depression. Lines bred by repeated inbreeding are inbred lines.
Identity by descent
Two gene copies are identical by descent when both were copied from one gene copy in an ancestor. The reckoning starts from a base population, whose gene copies are all taken to be unrelated. Traced back far enough, any two copies would otherwise share an origin.[2]
At a locus with alleles A and a at frequencies p and 1 − p, a plant whose inbreeding coefficient is f has these genotype probabilities:[2]
| Genotype | Probability |
|---|---|
| AA | p2(1 − f) + pf |
| Aa | 2p(1 − p)(1 − f) |
| aa | (1 − p)2(1 − f) + (1 − p)f |
The frequency of A among such plants is still p.[3] At f = 0 these are the Hardy–Weinberg proportions. A recessive allele at a frequency of 0.1 occurs in homozygotes at 0.01 when f is 0 and at 0.1 when f is 1, a tenfold rise. The rarer the allele, the greater the rise.[10]
The coefficient can be worked out from a pedigree. For the offspring of two half-siblings, three independent events must all happen: the first half-sibling passes on a gene copy from the shared parent, the second does the same and both copies come from the same one of that parent's two. Each has a probability of 1/2, so f = 1/8.[11] Sewall Wright developed the method in papers of 1921 and 1922. Gustave Malécot restated it in terms of probabilities in 1948.[2][11] The coefficient of kinship of two plants is the probability that a gene copy drawn at random from each is identical by descent. It equals the inbreeding coefficient that an offspring of the two would have, whether or not they ever mate.[12]
An XY plant has one copy of each gene found only on the X chromosome, so the coefficient for such a locus applies to XX plants alone. In a given pedigree it is often, though not always, higher than the coefficient for a locus on the other chromosomes. In one worked pedigree the X-linked value is 0.3125 and the other 0.21875.[13]
Templeton and Read separated three uses of the word: shared ancestry in the two lineages of one individual, drift in a finite population and the system of mating in a reproducing population. They warned that confusing them can lead to wrong management of small populations.[14] A small population that mates at random is inbred in the sense of drift and not in the sense of the mating system.[15]
Systems of mating
Under a system of mating one pattern is repeated in every generation, so the inbreeding coefficient follows a fixed course.[4]
| System | Generation 1 | 2 | 3 | 5 | 10 | Heterozygosity kept per generation in the long run |
|---|---|---|---|---|---|---|
| Selfing | 0.50 | 0.75 | 0.875 | 0.969 | 0.999 | 0.5[4] |
| Full siblings | 0 | 0.25 | 0.375 | 0.594 | 0.859 | 0.809[16] |
| Double first cousins | 0 | 0 | 0.125 | 0.25 | 0.508 | 0.920[17] |
| Random mating, 100 plants | 0.005 | 0.010 | 0.015 | 0.025 | 0.049 | 0.995[15] |
| Random mating, 10 plants | 0.050 | 0.098 | 0.143 | 0.226 | 0.401 | 0.95[15] |
A line kept by selfing loses half of its remaining heterozygosity each generation. A line kept by mating full siblings comes to lose nearly a fifth and one kept by mating double first cousins about 8 per cent.[4][16][17] Wright analysed full-sib mating and nine other simple systems in 1921.[16] These figures assume no mutation and no selection at the locus or at any locus linked to it.[11]
The two rows for random mating come from a model of plants that release gametes into a common pool, with selfing allowed by chance. Such a population loses on average a fraction 1/(2N) of its heterozygosity per generation, while any one population wanders from that average.[15] The random change in allele frequency called genetic drift and the rise in identity by descent are one process.[5] In plants with separate sexes the rate depends on the effective population size, which comes close to four times the number of the scarcer sex when one sex is scarce.[18]
For a fixed number of plants, regular systems approach homozygosity more slowly in the long run the more closely related the mates are. Among systems for a population of fixed size, separate lines that each become fixed lose the fewest alleles.[10]
Selfing and related matings in plants
Charles Darwin reported eleven years of comparisons of crossed and self-fertilised seedlings in 1876. He concluded "that cross-fertilisation is generally beneficial, and self-fertilisation injurious".[19] In dioecious plants, he wrote, cross-fertilisation is "assured". He expected wind-pollinated monoecious plants to be largely "dioecious in function", with some seed self-fertilised.[19]
A plant population may mix selfing with outcrossing. Where a fraction s of seed comes from selfing, FIS, the shortfall of heterozygotes against Hardy–Weinberg proportions, settles at s/(2 − s). Half selfing therefore gives one third.[20] Early models treated predominant outcrossing and predominant selfing as alternative stable states. Outcrossing rates among animal-pollinated species have not shown the two peaks those models expected. Igic and Kohn found that published studies hold far fewer obligate outcrossers than expected and judged conclusions about the shape of the distribution premature.[21]
Mating between relatives other than selfing is called biparental inbreeding. It raises homozygosity much as selfing does, but a selfing estimate from several loci falls as loci are added, which gives one way of telling them apart.[22] Limited movement of seed and pollen leaves relatives growing near one another. Among 47 plant species, this fine-scale structure was stronger in selfing species, in herbs and at low density.[23]
Where a share of matings is by selfing and family sizes are Poisson distributed, the effective population size is about N/(1 + FIS).[24][25] The same form holds for a fixed system of partial inbreeding repeated each generation, on Caballero and Hill's correction of earlier equations for partial sib mating.[25] Two loci that are tightly linked become identical by descent together, while unlinked loci do so independently within a known pedigree.[26] Linkage disequilibrium is predicted to extend further in selfing species. Some forms of inbreeding bring it with them, and not only at closely linked loci.[27][28]
Reading inbreeding from markers
The f of a pedigree is an expected value. The share of the genome actually identical by descent varies around it, because recombination differs from one offspring to another.[29] In human progeny of first cousins it averages 6.25 per cent with a standard deviation of 2.4 per cent. The spread is widest in species with few chromosomes and short maps.[29][30] In simulations by Kardos and colleagues, measures from 35,000 or more SNPs generally explained over 90 per cent of the variation in that share among individuals. The pedigree coefficient explained under 80 per cent on average, even with 20 generations of pedigree.[30] In simulations by Wang, 10,000 SNPs also outperformed pedigrees, which remain useful for coefficients involving more than two individuals or more than one locus.[31]
FIS compares the heterozygotes in a sample with the number its allele frequencies predict. Another measure counts one plant's excess of homozygous sites over that prediction. A third, FROH, is the share of the genome inside runs of homozygosity, long stretches where a plant received identical sequence from both parents.[30][32] Such runs are common in human genomes, even in people described as outbred.[32]
Null alleles and partial dominance of markers lower the count of heterozygotes without any selfing. In two of four data sets, David and colleagues obtained a selfing rate of zero from the pattern across loci despite a positive FIS.[20] In the freshwater snail Radix balthica, 1,034 embryos from 60 families included no selfed embryo, while selfing rates based on FIS were positive in all six population samples.[33] A sample that pools several populations also falls short of heterozygotes, the Wahlund effect.
Inbreeding in cannabis
Where it arises
Natural populations and those kept by mass selection are mostly made up of heterozygous plants sharing a gene pool, which reproduce in nature by wind-borne outcrossing.[6] Plants that bear hermaphroditic flowers can pollinate themselves, and without males nearby most of their seed is likely to be selfed.[7] The methods of inducing flowers of the other sex and of feminised seed are described under outcrossing.
Monoecious hemp descends largely from monoecious plants of a Central Russian landrace, taken into R. von Sengbusch's breeding programme in the 1930s. These plants were inbred and used as the pollen donor of Fibrimon and related European fibre varieties.[34] The monoecious cultivar USO-31 had the lowest heterozygosity of four genomes sequenced in 2011, which the authors presumed to come from self-pollination.[35] A selfed XX plant gives only XX offspring, while a line selfed through an XY plant keeps both the X and the Y.[34]
Marker surveys
| Plants | Markers | FIS | The authors' reading |
|---|---|---|---|
| 104 plants of 11 hemp varieties | 20 microsatellites | 0.41 (mean over loci) | Null alleles, or selection and repeated crosses of related plants[36] |
| 83 plants, hemp and drug type | 10 microsatellites | 0.417 | Non-random mating or inbreeding within breeding programmes[37] |
| 24 hemp varieties | 13 microsatellites | 0.19 (mean over varieties) | Bottlenecks in current breeding[8] |
| Several drug-type breeds, some of them clones | 13 microsatellites | Reaching −1 | Clonal propagation of hybrids of two parental strains[8] |
| 346 feral plants, United States | 21,037 SNPs | −0.03 (clusters −0.08 to 0.06) | Random mating; small size and isolation for the lowest heterozygosity, in New York[9] |
Borin and colleagues could not estimate null alleles in their varieties, whose groups held 3 to 13 plants and lay outside Hardy–Weinberg proportions. Their second explanation is selection and inbreeding.[36] In the study by Boutsika and colleagues the groups compared were hemp and drug type, each holding many accessions.[37] Sawler and colleagues found lower heterozygosity in drug-type plants than in hemp and suggested a narrower genetic base, more breeding among close relatives or both.[38] A 2023 review proposes inbreeding and bottlenecks in illegal production and calls for studies of a broader set of genotypes.[39]
Homozygosity in inbred plants
The halving of heterozygosity under selfing is an average over many lines.[4] Mansueto and colleagues followed a small set of lines from the F1 to the F4 on a marker panel, where heterozygous sites fell from about 30 per cent to under 10 per cent.[40] García-de Heer and colleagues measured starting values of 0.17 to 0.35 at 1,500 SNPs and highly variable changes from one generation to the next.[41] One round of selfing of hermaphroditic drug-type plants left seedlings as varied at markers as seedlings from crossed seed.[7] A 2023 review suggests that somatic mutation in plants long kept as cuttings may add to that variation.[39]
Among 50 phased assemblies, some have no aligned run of homozygosity longer than 20 million bases and others have up to half of the genome in runs of 30 million or more. The inbred line FL 58, made by several generations of self-pollination, has such runs along almost all of chromosomes 2, 3, 4, 7, 8 and X. A plant from a small feral population isolated in New York, inbred further, has them across chromosomes 6, 7 and 9. Stack and colleagues take these assemblies to show that much of the genome can be homozygous in a viable plant.[42] The plant numbers that limit drift and inbreeding when accessions are regrown are described under effective population size.
See also
References
- ↑ Felsenstein, J. (December 2019). Theoretical evolutionary genetics. Seattle: Department of Genome Sciences, University of Washington. p. 217.
- ↑ 2.0 2.1 2.2 2.3 Felsenstein, J. (December 2019). Theoretical evolutionary genetics. Seattle: Department of Genome Sciences, University of Washington. p. 219.
- ↑ 3.0 3.1 Felsenstein, J. (December 2019). Theoretical evolutionary genetics. Seattle: Department of Genome Sciences, University of Washington. p. 220.
- ↑ 4.0 4.1 4.2 4.3 4.4 Felsenstein, J. (December 2019). Theoretical evolutionary genetics. Seattle: Department of Genome Sciences, University of Washington. pp. 231–233.
- ↑ 5.0 5.1 Felsenstein, J. (December 2019). Theoretical evolutionary genetics. Seattle: Department of Genome Sciences, University of Washington. pp. 251–252.
- ↑ 6.0 6.1 6.2 Barcaccia, G.; Palumbo, F.; Scariolo, F.; Vannozzi, A.; Borin, M.; Bona, S. (2020). "Potentials and challenges of genomics for breeding cannabis cultivars". Frontiers in Plant Science. 11 573299. doi:10.3389/fpls.2020.573299.
- ↑ 7.0 7.1 7.2 Punja, Z.K.; Holmes, J.E. (2020). "Hermaphroditism in marijuana (Cannabis sativa L.) inflorescences – impact on floral morphology, seed formation, progeny sex ratios, and genetic variation". Frontiers in Plant Science. 11 718. doi:10.3389/fpls.2020.00718.
- ↑ 8.0 8.1 8.2 Dufresnes, C.; Jan, C.; Bienert, F.; Goudet, J.; Fumagalli, L. (2017). "Broad-scale genetic diversity of Cannabis for forensic applications". PLoS ONE. 12 (1) e0170522. doi:10.1371/journal.pone.0170522.
- ↑ 9.0 9.1 Aina, Ademola; Wenger, Jonathan P.; Stanton, Eliot; Majumdar, Chandrani Gon; ElSohly, Mahmoud; Weiblen, George D.; Ellison, Shelby (1 July 2025). "Genetic diversity, population structure, and cannabinoid variation in feral Cannabis sativa germplasm from the United States". Scientific Reports. 15 (1) 20423. doi:10.1038/s41598-025-07912-8. PMC 12215616.
- ↑ 10.0 10.1 Felsenstein, J. (December 2019). Theoretical evolutionary genetics. Seattle: Department of Genome Sciences, University of Washington. pp. 242–244.
- ↑ 11.0 11.1 11.2 Felsenstein, J. (December 2019). Theoretical evolutionary genetics. Seattle: Department of Genome Sciences, University of Washington. pp. 221–222.
- ↑ Felsenstein, J. (December 2019). Theoretical evolutionary genetics. Seattle: Department of Genome Sciences, University of Washington. pp. 226–227.
- ↑ Felsenstein, J. (December 2019). Theoretical evolutionary genetics. Seattle: Department of Genome Sciences, University of Washington. pp. 225–226.
- ↑ Templeton, A.R.; Read, B. (1994). "Inbreeding: one word, several meanings, much confusion". In Loeschcke, V.; Jain, S.K.; Tomiuk, J. (eds.). Conservation Genetics. Basel: Birkhäuser. pp. 91–105. doi:10.1007/978-3-0348-8510-2_9.
- ↑ 15.0 15.1 15.2 15.3 Felsenstein, J. (December 2019). Theoretical evolutionary genetics. Seattle: Department of Genome Sciences, University of Washington. pp. 254–256.
- ↑ 16.0 16.1 16.2 Felsenstein, J. (December 2019). Theoretical evolutionary genetics. Seattle: Department of Genome Sciences, University of Washington. p. 237.
- ↑ 17.0 17.1 Felsenstein, J. (December 2019). Theoretical evolutionary genetics. Seattle: Department of Genome Sciences, University of Washington. pp. 240–242.
- ↑ Felsenstein, J. (December 2019). Theoretical evolutionary genetics. Seattle: Department of Genome Sciences, University of Washington. pp. 266–268.
- ↑ 19.0 19.1 Darwin, C. (1876). The effects of cross and self fertilisation in the vegetable kingdom. London: John Murray. pp. 10, 413–414, 436 – via Darwin Online.
- ↑ 20.0 20.1 David, P.; Pujol, B.; Viard, F.; Castella, V.; Goudet, J. (2007). "Reliable selfing rate estimates from imperfect population genetic data". Molecular Ecology. 16 (12): 2474–2487. doi:10.1111/j.1365-294x.2007.03330.x.
- ↑ Igic, B.; Kohn, J.R. (2006). "The distribution of plant mating systems: study bias against obligately outcrossing species". Evolution. 60 (5): 1098–1103. doi:10.1111/j.0014-3820.2006.tb01186.x.
- ↑ Ritland, K. (2002). "Extensions of models for the estimation of mating systems using n independent loci". Heredity. 88 (4): 221–228. doi:10.1038/sj.hdy.6800029.
- ↑ Vekemans, X.; Hardy, O.J. (2004). "New insights from fine-scale spatial genetic structure analyses in plant populations". Molecular Ecology. 13 (4): 921–935. doi:10.1046/j.1365-294x.2004.02076.x.
- ↑ Pollak, E. (1987). "On the theory of partially inbreeding finite populations. I. Partial selfing". Genetics. 117 (2): 353–360. doi:10.1093/genetics/117.2.353.
- ↑ 25.0 25.1 Caballero, A.; Hill, W.G. (1992). "Effective size of nonrandom mating populations". Genetics. 130 (4): 909–916. doi:10.1093/genetics/130.4.909.
- ↑ Felsenstein, J. (December 2019). Theoretical evolutionary genetics. Seattle: Department of Genome Sciences, University of Washington. pp. 228–230.
- ↑ Nordborg, M. (2000). "Linkage disequilibrium, gene trees and selfing: an ancestral recombination graph with partial self-fertilization". Genetics. 154 (2): 923–929. doi:10.1093/genetics/154.2.923.
- ↑ Szulkin, M.; Bierne, N.; David, P. (2010). "Heterozygosity-fitness correlations: a time for reappraisal". Evolution. doi:10.1111/j.1558-5646.2010.00966.x.
- ↑ 29.0 29.1 Keller, M.C.; Visscher, P.M.; Goddard, M.E. (2011). "Quantification of inbreeding due to distant ancestors and its detection using dense single nucleotide polymorphism data". Genetics. 189 (1): 237–249. doi:10.1534/genetics.111.130922.
- ↑ 30.0 30.1 30.2 Kardos, M.; Luikart, G.; Allendorf, F.W. (2015). "Measuring individual inbreeding in the age of genomics: marker-based measures are better than pedigrees". Heredity. 115 (1): 63–72. doi:10.1038/hdy.2015.17.
- ↑ Wang, J. (2016). "Pedigrees or markers: which are better in estimating relatedness and inbreeding coefficient?". Theoretical Population Biology. 107: 4–13. doi:10.1016/j.tpb.2015.08.006.
- ↑ 32.0 32.1 Ceballos, F.C.; Joshi, P.K.; Clark, D.W.; Ramsay, M.; Wilson, J.F. (2018). "Runs of homozygosity: windows into population history and trait architecture". Nature Reviews Genetics. 19 (4): 220–234. doi:10.1038/nrg.2017.109.
- ↑ Bürkli, A.; Sieber, N.; Seppälä, K.; Jokela, J. (2017). "Comparing direct and indirect selfing rate estimates: when are population-structure estimates reliable?". Heredity. 118 (6): 525–533. doi:10.1038/hdy.2017.1.
- ↑ 34.0 34.1 Garcia-de Heer, L.; Mieog, J.; Burn, A.; Kretzschmar, T. (2024). "Why not XY? Male monoecious sexual phenotypes challenge the female monoecious paradigm in Cannabis sativa L." Frontiers in Plant Science. 15 1412079. doi:10.3389/fpls.2024.1412079.
- ↑ van Bakel, H.; Stout, J.M.; Cote, A.G.; Tallon, C.M.; Sharpe, A.G.; Hughes, T.R.; Page, J.E. (2011). "The draft genome and transcriptome of Cannabis sativa". Genome Biology. 12 (10) R102. doi:10.1186/gb-2011-12-10-r102.
- ↑ 36.0 36.1 Borin, M.; Palumbo, F.; Vannozzi, A.; Scariolo, F.; Sacilotto, G.B.; Gazzola, M.; Barcaccia, G. (2021). "Developing and testing molecular markers in Cannabis sativa (hemp) for their use in variety and dioecy assessments". Plants. 10 (10) 2174. doi:10.3390/plants10102174.
- ↑ 37.0 37.1 Boutsika, A.; Deligiannidou, E.; Moysiadis, T.; Tourvas, N.; Karnoutsos, P.; et al. (2025). "Molecular profiling and sex determination of Cannabis sativa germplasm collection: exploring microsatellite markers and high-resolution melting (HRM) analysis". PeerJ. 13 e19770. doi:10.7717/peerj.19770.
- ↑ Sawler, Jason; Stout, Jake M.; Gardner, Kyle M.; Hudson, Darryl; Vidmar, John; Butler, Laura; Page, Jonathan E.; Myles, Sean (2015). "The genetic structure of marijuana and hemp". PLOS ONE. 10 (8) e0133292. doi:10.1371/journal.pone.0133292.
- ↑ 39.0 39.1 Ingvardsen, C.R.; Brinch-Pedersen, H. (2023). "Challenges and potentials of new breeding techniques in Cannabis sativa". Frontiers in Plant Science. 14 1154332. doi:10.3389/fpls.2023.1154332.
- ↑ Mansueto, L.; Tandayu, E.; Mieog, J.; Garcia-de Heer, L.; Das, R.; Burn, A.; Mauleon, R.; Kretzschmar, T. (2024). "HASCH: a high-throughput amplicon-based SNP-platform for medicinal cannabis and industrial hemp genotyping applications". BMC Genomics. 25 (1) 818. doi:10.1186/s12864-024-10734-z.
- ↑ Garcia-de Heer, L.; Mieog, J.; Burn, A.; Nolan, M.; Liu, L.; et al. (2026). "Weeding out variability: a proof-of-concept for producing uniform F1 hybrid Cannabis sativa L. using single-seed descent". Horticulture Research. 13 (5) uhag038. doi:10.1093/hr/uhag038. PMC 13188225.
- ↑ Stack, G.M.; Quade, M.A.; Wilkerson, D.G.; Monserrate, L.A.; Bentz, P.C.; et al. (2025). "Comparison of recombination rate, reference bias, and unique pangenomic haplotypes in Cannabis sativa using seven de novo genome assemblies". International Journal of Molecular Sciences. 26 (3) 1165. doi:10.3390/ijms26031165. PMC 11818205.