repeatability {heritability}

ANOVA-based estimates of repeatability

Description

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.

Usage

repeatability(data.vector, geno.vector, line.repeatability = FALSE,
              covariates.frame = data.frame())

Arguments

data.vector

A vector of phenotypic observations. Needs to be of type numeric. May contain missing values.

geno.vector

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.

line.repeatability

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).

covariates.frame

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.

Value

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)

Author(s)

Willem Kruijer [e-mail]

References

• 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.

Examples

repeatability(data.vector=rep(rnorm(26),each=5) + rnorm(5*26),
              geno.vector=rep(letters,each=5))