CRDR function

Calculate the correlated response to selection

Calculate the correlated response to selection (CRDR) based on the fitted model. The CRDR is calculated as described by Atlin et al. E.g. for a model with trials nested within scenarios, which has a random part that looks like this: genotype + genotype:scenario + genotype:scenario:trial the CRDR is calculated as:

[REMOVE_ME]$H1 = \sigma_G^2 / (\sigma_G^2 + \sigma_S^2 / s + \sigma_{ST}^2 / st +\sigma_E^2 / str) [REMOVE_ME_2]$

[REMOVE_ME]$H2 = (\sigma_G^2 + \sigma_S^2) / (\sigma_G^2 + \sigma_S^2 +\sigma_{ST}^2 / st + \sigma_E^2 / str) [REMOVE_ME_2]$

[REMOVE_ME]$CRDR = (\sigma_G^2 / (\sigma_G^2 + \sigma_S^2)) * sqrt(H1 / H2) [REMOVE_ME_2]$

In these formulas the $\sigma$ terms stand for the standard deviations of the respective model terms, and the lower case letters for the number of levels for the respective model terms. So $\sigma_S$ is the standard deviation for the scenario term in the model and $s$ is the number of scenarios. $\sigma_E$ corresponds to the residual standard deviation and $r$ to the number of replicates.

CRDR(varComp)

Arguments

• varComp: An object of class varComp.

Description

Calculate the correlated response to selection (CRDR) based on the fitted model. The CRDR is calculated as described by Atlin et al. E.g. for a model with trials nested within scenarios, which has a random part that looks like this: genotype + genotype:scenario + genotype:scenario:trial the CRDR is calculated as:

In these formulas the $\sigma$ terms stand for the standard deviations of the respective model terms, and the lower case letters for the number of levels for the respective model terms. So $\sigma_S$ is the standard deviation for the scenario term in the model and $s$ is the number of scenarios. $\sigma_E$ corresponds to the residual standard deviation and $r$ to the number of replicates.

References

Atlin, G. N., Baker, R. J., McRae, K. B., & Lu, X. (2000). Selection response in subdivided target regions. Crop Science, 40(1), 7–13. tools:::Rd_expr_doi("10.2135/cropsci2000.4017")

See Also

Other Mixed model analysis: correlations(), diagnostics(), gxeVarComp(), herit(), plot.varComp(), predict.varComp(), vc()