Environmental sample size estimation based on variety means estimation and means comparison for multi-environment trial

Multi-environment trial (MET) is important and necessary for breeding and insight of crop variety. How many locations should be tested at least is critical to the reliability of MET. Researchers previously put forward 200 locations basing on experiences and considering accuracy of variance evaluation for varieties, however, these approaches cannot express the sample size differences of various crops, trial regions and traits, which are important for accurate measurement of reliability and resource allocation in MET. In this paper, (1) a method of sample size estimation adapted to MET features was put forward, considering evaluation and comparison of variety mean value. (2) A measurement of test reliability was proposed. (3) Six sets of maize and wheat MET data were collected as examples to estimate sample sizes, assess reliabilities, and analyze differences and applications of various crops, traits and trial regions using new methods. The results showed: this method was suitable to estimate sample sizes and reliabilities considering differences in various crops, trial regions and traits. And it was found that, sample size required will be less with a higher representativeness (R2) of test environment to regional average, higher rate of successful tests (P), acceptable tolerance (E), and a lower standard deviation among test environments of a variety (Se). Sample sizes of maize and wheat regional trials in China were severely deficient, and test reliabilities of them were low. If taking accurate estimation of yield difference between varieties tested and the mean variety as the objective, 6 regional trials needed an average of 1-3 times increase in test locations. For corn, MET resource allocation of China could be optimized because various traits and regional trials differ in sample sizes and reliabilities. This method can help to measure the sample size and reliability of MET accurately, and improve the efficiency of resource allocation.