Calculate average heritability of differences between genotypes from model object

Instead of computing heritability on a "entry-mean" basis, this method calculates heritability using "entry-differences". Entry here is referring to the genotype, line or variety of interest. See reference for origin and interpretation of H2_Delta and it's variants

Usage

H2_Delta(model,
         target,
         type = c("BLUP", "BLUE"),
         aggregate = c("arithmetic", "harmonic"),
         options
         )

Arguments

model: Model object of class lmerMod/merMod or asreml
target: The name of the random effect for which heritability is to be calculated.
type: character, whether heritability is calculated using BLUEs or BLUPs
aggregate: character, when taking means in the calculation, should harmonic or arithmetic mean be used?
options: NULL by default, for internal checking of model object before calculations

Value

Numeric

Details

The heritability of differences between genotypes is given by:

$$H^2_{\Delta ..} = 1 - \frac{PEV^{BLUP}_{\overline\Delta ..}}{2\sigma^2_g}$$

where:

$PEV^{BLUP}_{\overline\Delta ..}$ is the mean of the prediction error variance matrix for the pairwise differences among BLUPs (BLUEs if method = "BLUE") across all genotypes
$\sigma^2$ is the variance attributed to differences between genotype

See reference page 995 - 997 for full derivation of this heritability measure and related variants

References

Schmidt, P., Hartung, J., Rath, J., & Piepho, H.-P. (2019). Estimating Broad-Sense Heritability with Unbalanced Data from Agricultural Cultivar Trials. Crop Science, 59(2), 525–536. https://doi.org/10.2135/cropsci2018.06.0376

Examples

# lme4 model
lettuce_subset <- lettuce_phenotypes |> subset(loc == "L2")
lettuce_lme4 <- lme4::lmer(y ~ rep + (1 | gen), data = lettuce_subset)
H2_Delta(lettuce_lme4, target = "gen", type = "BLUP")
#> [1] 0.8294971

# asreml model (Requires license)
if (FALSE) { # \dontrun{
lettuce_asreml <- asreml::asreml(fixed = y ~ rep,
                                 random = ~ gen,
                                 data = lettuce_subset,
                                 trace = FALSE
                                 )

H2_Delta(lettuce_asreml, target = "gen", type = "BLUP")
} # }