Heritability
More actions
Heritability is the share of the variation in a measured trait that is due to genetic differences among the plants of a population, grown in a given set of environments. Broad-sense heritability counts all the genetic variance. Narrow-sense heritability counts only its additive part, the share of the variation that is transmitted from parents to their offspring.[1] A heritability belongs to a population, its environments and the way the plants were measured. Plant breeders who report one are expected to name the population of genotypes, the target environments and the units on which selection is made and its response measured.[2]
Broad-sense estimates for Cannabis have come from medicinal cannabis genotypes grown as clones in a controlled environment, from hemp accessions grown at several sites and from landrace populations grown together in one greenhouse.[3][4][5] A Dutch study of fibre hemp, published in 1994, estimated heritability from 252 plants and their progenies. Its author wrote that no realised or narrow-sense estimates for hemp had been published before.[6] The authors of the clonal trials have asked for narrow-sense estimates of the traits they measured.[3][7]
Genetic and environmental variance
The model plant breeders use for a quantitative trait divides the variance among the plants of a population. If genotypes and environments are independent, the phenotypic variance (VP) is the sum of the genotypic variance (VG) and the environmental variance (VE). Where the two are correlated, twice their covariance is added.[1] Such a correlation arises, for example, when the best genotypes are grown more often in the best conditions.[8] The genotypic variance in turn has three parts: the additive variance (VA), which is the variance of breeding values; the dominance variance (VD), from interactions between the alleles at one locus; and the epistatic variance (VI), from interactions between loci.[1] The statistician Ronald Fisher defined these components in 1918 and derived from them the covariances between relatives. Sewall Wright reached the covariances independently, without the dominance term.[9]
The animal breeder Jay Lush named the ratio VG/VP heritability in the broad sense in 1937. He defined heritability in the narrow sense, h2 = VA/VP, in the same year.[1] Narrow-sense heritability is the slope of the regression of offspring on the mean of their two parents. It measures how much of the variation in a trait the phenotypes of the two parents predict. The name can mislead: h2 is not the fraction of the variation that has genetic causes, which is the broad-sense ratio.[10][11]
How heritability is estimated
The covariance between two relatives can be written in terms of the variance components, so the variance components can be estimated from the resemblance among related plants, and the heritability from them.[11] Replicates of a single genotype give the genotypic variance in the same way.[1]
From clones
Plant breeders can replicate a genotype by clonal propagation.[2] Repeated measurements of one genotype share its genotypic value. The correlation among them, the genotypic intraclass correlation, is therefore VG/VP, the broad-sense heritability. It includes the dominance and epistatic variance with the additive part.[1]
Erez Naim-Feil and colleagues grew 121 medicinal cannabis genotypes, each raised from a single seed and of high-THC or balanced THC and CBD chemotype, as cuttings in a controlled-environment facility in Australia. Before the trial they measured how much clones of one genotype differed and settled on four to five clones of each. Broad-sense heritability for nine physiological and phenological traits ranged from 0.30 to 0.53.[3] Measured each week, the heritability of plant height fell from 0.78 in the second week after planting to 0.52. The authors ascribed the fall to environmental effects that built up over the season and enlarged the phenotypic variance.[3] In 119 genotypes grown the same way, the heritability of individual cannabinoids ranged from 0.51 to 0.96. The lowest value was for cannabinol (CBN), which forms as THC degrades. The authors had expected its heritability to be lower than that of the cannabinoids the plant synthesises, because light, heat and oxygen speed its formation.[7]
From replicated field trials
Field trials grow each entry, such as an accession or a family, in replicated plots at several sites or over several years. Breeders then often report heritability on an entry-mean basis. The genotypic variance is divided by the variance of entry means: the genotypic variance, plus the genotype-by-environment interaction variance divided by the number of environments, plus the error variance divided by the number of plots per entry. The ratio resembles Lush's broad-sense heritability. It differs in that it rises as replicates and environments are added.[2] Hanson defined heritability in 1963 as "the fraction of the selection differential expected to be gained when selection is practiced on a defined reference unit".[2]
Petit and colleagues grew 123 hemp accessions at three sites in Europe and estimated entry-mean heritabilities for 28 traits, which ranged from 0.05 to 0.96. Three flowering traits, the sex of the plants and the content of bast fibre reached 0.93 to 0.96, with little interaction between accession and site.[4] In stem height the sites accounted for 82 per cent of the variation and the accessions for 7 per cent, yet the heritability was 0.81. The site effect does not enter the ratio. In stem height the interaction was also small beside the genetic variance. Petit and colleagues explained such unexpected values by this definition of the ratio.[4]
From families of seed
Narrow-sense heritability needs relatives whose resemblance comes from the genes they share. A parent and its offspring have a covariance of ½VA and half-sibs one of ¼VA. Full sibs have ½VA + ¼VD, so they resemble each other more than parent and offspring do to the extent that the trait has dominance variance.[10] Three methods are in wide use: doubling the regression of offspring on one parent; an analysis of variance of half-sib groups, whose variance component equals ¼VA; and maximum likelihood on all the data at once.[11] When the data are unbalanced, the variance components are estimated correctly only by restricted maximum likelihood.[2]
Relatives often share an environment besides their genes. Seeds from one mother plant start with similar reserves in their endosperm, so their resemblance can be mistaken for genetic resemblance. Designs for estimating heritability therefore usually compare fathers with their offspring or half-sibs that share a father. They assume that the father contributes only pollen. Allocating seeds to plots at random keeps relatives from sharing conditions more often than chance allows.[8]
Sebastiaan Hennink's study belonged to a hemp breeding programme begun at the research institute CPRO-DLO in Wageningen, in the Netherlands, in 1990 to supply fibre for paper pulp. In 1991 he scored 252 plants for bast fibre content, plant height, flowering date, stem diameter and cannabinoid content. In 1992 he grew their progenies as half-sib families, estimated heritability for each trait and tested the estimates by selection.[6] Naim-Feil and colleagues later set his narrow-sense estimate of 0.22 for stem diameter against their own broad-sense estimate of 0.53 for the same trait.[3] Selection itself gives a realised heritability: the response of the offspring divided by the selection differential applied to their parents.[2]
Among landrace populations
Mehdi Babaei and colleagues collected seed of 25 populations from traditional farmers and local markets in different regions of Iran. They grew them in randomised blocks in a greenhouse at Ferdowsi University of Mashhad and estimated broad-sense heritability across the populations, for female and male plants separately.[5] The entries compared were the populations themselves, each grown from seed. For the time to 50 per cent flowering in individual plants the estimate was 0.61 in female plants and 0.98 in male plants. For the dry weight of the flowers it was 0.33 and 0.87. Male plants had the higher estimate in every morphological trait but two.[5]
Estimates in cannabis
| Study | Material and setting | Kind of estimate | Estimates reported |
|---|---|---|---|
| Hennink (1994) | 252 fibre hemp plants and their half-sib progenies, Netherlands, 1991–1992 | Narrow-sense, from parents and offspring | High for bast fibre content;[6] 0.22 for stem diameter, as cited by Naim-Feil and colleagues (2021)[3] |
| Petit and colleagues (2020) | 123 hemp accessions at three sites in Europe | Broad-sense, entry-mean basis | 0.05 to 0.96 across 28 traits; three flowering traits, sex and bast fibre content 0.93 to 0.96; stem height 0.81[4] |
| Naim-Feil and colleagues (2021) | 121 medicinal cannabis genotypes as clones, controlled environment, Australia | Broad-sense | 0.30 to 0.53 for nine traits: plant height 0.52, days to maturation 0.49, dry weight of flower buds 0.33[3] |
| Naim-Feil and colleagues (2023) | 119 medicinal cannabis genotypes as clones, controlled environment, Australia | Broad-sense | Cannabinoids 0.51 to 0.96: CBD 0.96, THC 0.89, total cannabinoids 0.62; inflorescence traits 0.15 to 0.38[7] |
| Babaei and colleagues (2024) | 25 landrace populations of Iran, greenhouse, Mashhad | Broad-sense, among populations, each sex apart | Phenology 0.61 to 0.91 in female and 0.75 to 0.98 in male plants; morphology 0.23 to 0.95 and 0.56 to 0.99[5] |
Each figure describes the material, sites and seasons of its own study.[2] The broad-sense estimates include the dominance and epistatic variance with the additive part.[1] The estimates on an entry-mean basis depend on how many sites and plots each entry had.[2]
Interpreting an estimate
The phenotypic variance is the denominator of the ratio, so a change in the environmental variance changes the heritability. Averaging each entry over more plots raises an entry-mean estimate.[2] In the clonal trial the build-up of environmental effects over the season lowered the heritability of plant height.[3] The Iranian landrace populations gave different values for their female and male plants.[5] Small samples give large errors: in 20 pairs of relatives a correlation of 0.4 does not differ significantly from zero.[8]
Where genotypes respond differently to the same change of environment, the phenotype is no longer the sum of a genetic and an environmental part. Feldman and Lewontin argued in 1975 that heritability is then meaningless and potentially misleading.[8] In the hemp trial most agronomic traits varied more with the site than with the accession, a sensitivity its authors read as adaptation to the environment.[4] The response of one genotype to different growing conditions is the subject of phenotypic plasticity.
Measured on the same plants, the narrow-sense heritability cannot exceed the broad-sense one, since the additive variance is part of the genotypic variance.[1] Predicting the response to selection needs only the phenotypic variance and the additive variance.[11]
Heritability and selection
In the breeder's equation, R = h2S, the response to selection R is the narrow-sense heritability times the selection differential S.[2] Hennink found the heritability of bast fibre content high and mass selection for it efficient, with no unwanted effect on other characters. Mass selection also reduced THC content, though he was not certain it was the most efficient method for that purpose.[6]
Naim-Feil and colleagues judged from their estimates that cannabinoid composition would respond more strongly to selection than the morphology and phenology of the plant and its inflorescences.[7] Petit and colleagues proposed combining breeding for the traits with large genetic components with crop management, such as irrigation, for the poorly heritable ones. Their example was the pectin content of the stem.[4]
See also
References
- ↑ 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 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.
- ↑ 2.00 2.01 2.02 2.03 2.04 2.05 2.06 2.07 2.08 2.09 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.
- ↑ 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 Naim-Feil, E.; Pembleton, L.W.; Spooner, L.E.; Malthouse, A.L.; Miner, A.; et al. (2021). "The characterization of key physiological traits of medicinal cannabis (Cannabis sativa L.) as a tool for precision breeding". BMC Plant Biology. 21 (1) 294. doi:10.1186/s12870-021-03079-2.
- ↑ 4.0 4.1 4.2 4.3 4.4 4.5 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 Babaei, M.; Nemati, H.; Arouiee, H.; Torkamaneh, D. (2024). "Characterization of indigenous populations of cannabis in Iran: a morphological and phenological study". BMC Plant Biology. 24 (1) 151. doi:10.1186/s12870-024-04841-y.
- ↑ 6.0 6.1 6.2 6.3 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.
- ↑ 7.0 7.1 7.2 7.3 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.
- ↑ 8.0 8.1 8.2 8.3 Felsenstein, J. (December 2019). Theoretical evolutionary genetics. Seattle: Department of Genome Sciences, University of Washington. pp. 435–438.
- ↑ Felsenstein, J. (December 2019). Theoretical evolutionary genetics. Seattle: Department of Genome Sciences, University of Washington. p. 439.
- ↑ 10.0 10.1 Felsenstein, J. (December 2019). Theoretical evolutionary genetics. Seattle: Department of Genome Sciences, University of Washington. pp. 429–430.
- ↑ 11.0 11.1 11.2 11.3 Felsenstein, J. (December 2019). Theoretical evolutionary genetics. Seattle: Department of Genome Sciences, University of Washington. pp. 434–435.