Variation of Fruit Size and Growth within an Apple Tree and its Influence on Sampling Methods for Estimating the Parameters of Mid-season Size Distributions

This paper presents a quantitative description of variation of mid-season (62 days after bloom) fruit weight (FW) and proceeding growth rates within an apple tree. Based on this knowledge, several sampling strategies were designed and compared for their accuracy and efficiency in estimating the mean and variance of fruit size within an apple tree limb at mid-season. The analysis revealed the presence of systematic trends in FW within the canopy. Fruit weight, at the base of each limb increased from the bottom tier vertically upwards within the canopy. Generally, FW in the lower tier limbs increased from the base outwards, but this trend was reversed in the upper tier. Mid-season FW was also affected by the shoot type, the spur fruit being significantly larger than lateral or terminal fruit. We conclude that the systematic variation in FW is a result of plant factors interacting mainly with the within-canopy light environment. This study also demonstrated that the predominant source of the remaining random variation of FW within a tree is between fruit within a limb. In terms of within-limb sampling strategies, this study provides clear evidence that a systematic sample along a limb gives a more efficient estimator of mean FW compared with random or stratified sampling. Monte Carlo re-sampling provided standard error estimates that were about 10% lower for systematic sampling. Both the systematic and stratified sampling, however, may be seriously biased in their estimation of the within-limb variance. Therefore, when both the mean and variance are needed, especially for small sample sizes (say n = 5), we recommend simple random sampling. Some methods for extending the limb estimator to the whole tree level are also discussed. Keywords Malus domestica (Borkh.), Royal Gala, modelling, within-tree variation, fruit size, sampling methods