SIGNIFICANCE TESTING OF ALTERNATE BEARING IN 'GRANNY SMITH' APPLE

Alternate bearing pattern, the idea that fruit crop has an "on" year of high yields followed by an "off" year of low yields, has long been suggested and observed by horticulturists. Currently the most popular statistic to quantify this pattern is the alternative bearing index (ABI), which uses a bootstrap method for inference. However, it has been suggested, this statistic may not be optimal for a short time period. We conducted a simulation study and compared ABI to moderated t-statistic (used extensively in genomic studies) and pooled t-statistic in terms of Type I error rate and statistical power. Results suggest that moderated t was overall statistically more powerful than the other two approaches. All three approaches control type I error rate at 5% nominal value, but the moderated t-test offers a higher power. ABI provides a power advantage over the pooled t-test only for small sample size (e.g., n <= 6). As n increases, ABI is shown to be inferior to the other two techniques. Finally we apply the methods using data from 'Granny Smith' apples (Malus x domestica Borkh.) collected for 5 years and show that 21% of the trees do show alternate bearing pattern.