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Optimal Replication on the Basis of the Multi-Year, Multi-Location Test
This protocol is extracted from research article:
Estimation of the Optimal Number of Replicates in Crop Variety Trials
Front Plant Sci, Jan 13, 2021;

Procedure

The discussion above can be extended to multi-year, multi-location tests. The heritability under the multi-year, multi-location framework, HMLY, is determined by

Where $σG,M⁢L⁢Y2$ is the genotypic variance and $σε,M⁢L⁢Y2$ the experimental error variance estimated on the multi-location, multi-year trial basis; $σG⁢Y2$ and $σG⁢L⁢Y2$ are variances for genotype by year interaction (GY) and genotype by location by year three-way interaction (GLY), respectively, and y is the number of years the test is conducted.

From Eq. 9 the number of replicates required to achieve a certain level of heritability is determined by:

where

HMMLY is the maximum possible heritability on the multi-year, multi-location basis. Equation 11 is a special case of Eq. 9, i.e., the cross location and year heritability, assuming 0 experimental error variance or infinite number of replicates. If the target heritability is set to HMLY=0.75HMMLY, then the number of replicates for optimal replication can be determined by

The implications discussed above regarding Eq. 7 can also be extended to Eq. 12. Furthermore, the definition of heritability in Eq. 9 is for variety trial systems in which a single crop is grown each year and is under a single management. Factors such as season and management should be added when multiple crops are grown in the same year (e.g., Swallow and Wehner, 1989) or in agronomic experiments in which multiple managements are involved.

Note that the definition of the heritability at various levels is consistent with the concept of mixed effect models (DeLacy et al., 1996). The genotypic main effect (G), the genotype by environment effects (GL, GY, GLY), and the experimental errors (ε) are treated as random effects as they appear in the formulas of heritability (Eqs 1, 4, and 9). Effects not included in the heritability formulas, such as the main effects of block, location, and year, are treated as fixed effects.

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