Given a population where each genotype is phenotyped for a number of genetically identical replicates (either individual plants or plots in a field trial), the repeatability or intra-class correlation can be estimated by \(V_g / (V_g + V_e)\), where \(V_g = (MS(G) - MS(E)) / r\) and \(V_e = MS(E)\). In these expressions, \(r\) is the number of replicates per genotype, and \(MS(G)\) and \(MS(E)\) are the mean sums of squares for genotype and residual error obtained from analysis of variance. In case \(MS(G) < MS(E)\), \(V_g\) is set to zero. See Singh et al. (1993) or Lynch and Walsh (1998), p.563. When the genotypes have differing numbers of replicates, \(r\) is replaced by \(\bar r = (n-1)^{-1} (R_1 - R_2 / R_1)\), where \(R_1 = \sum r_i\) and \(R_2 = \sum r_i^2\). Under the assumption that all differences between genotypes are genetic, repeatability equals broad-sense heritability; otherwise it only provides an upper-bound for broad-sense heritability.
repeatability(data.vector, geno.vector, line.repeatability = FALSE,
covariates.frame = data.frame())A list with the following components:
repeatability: the estimated repeatability.
gen.variance: the estimated genetic variance.
res.variance: the estimated residual variance.
line.repeatability: whether repeatability was estimated at the
individual plant or plot level (the default), or at the level of
genotypic means (in the latter case, line.repeatability=TRUE)
average.number.of.replicates: The average number of replicates. See the description above.
conf.int: Confidence interval for repeatability. See Singh et al. (1993) or Lynch and Walsh (1998)
A vector of phenotypic observations. Needs to be of type numeric. May contain missing values.
A vector of genotype labels, either a factor or character. This vector should
correspond to data.vector, and hence needs to be of the same length.
If TRUE, the line-repeatability or
line-heritability \(\sigma_G^2 / (\sigma_G^2 + \sigma_E^2 / r)\) is estimated,
otherwise (the default) the repeatability at plot- or plant level, which is \(\sigma_G^2 / (\sigma_G^2 + \sigma_E^2)\).
A data-frame with additional covariates, the rows corresponding to
geno.vector and the phenotypic observations in data.vector.
May contain missing values. Each column can be numeric or a factors.
Willem Kruijer willem.kruijer@wur.nl
Kruijer, W. et al. (2015) Marker-based estimation of heritability in immortal populations. Genetics, Vol. 199(2), p. 1-20.
Lynch, M., and B. Walsh (1998) Genetics and Analysis of Quantitative Traits. Sinauer As- sociates, 1st edition.
Singh, M., S. Ceccarelli, and J. Hamblin (1993) Estimation of heritability from varietal trials data. Theoretical and Applied Genetics 86: 437-441.
repeatability(data.vector=rep(rnorm(26),each=5) + rnorm(5*26),
geno.vector=rep(letters,each=5))
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