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 eciency 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 aected by the shoot type, the spur fruit being signi®cantly 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 ecient estimator of mean FW compared with random or strati®ed sampling. Monte Carlo re-sampling provided standard error estimates that were about 10 % lower for systematic sampling. Both the systematic and strati®ed 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.

In relation to horticultural crops, for purposes of predicting mean plant attributes, there has recently been an interest in using model based approaches such as kriging that account for spatial dependencies within a plant. These models assume stationarity, i.e. observed values for two fruit on a plant depend only on their physical separation and not on their location. However, in most situations systematic trends exist within a plant, and these need to be included in formulating the spatial models for studying within-plant variation patterns. We propose the use of mixed models which can simultaneously model fixed and random effects as well as the underlying covariance structure on the residual variation. The method is illustrated by analysis of two data sets of kiwifruit fruit sizes. The results indicate systematic trends in fruit size within a vine, due to the position of cane along the cordon and the shoot position along the cane. There is also evidence of a positive correlated response ( ρ l 0n49) of fruit within a shoot, and to a lesser extent between fruit borne on different shoots within a cane. Once the within-plant variation patterns are described we propose several sampling strategies aimed at estimating the vine mean fruit weight. We compare, by simulation, the performance of different sampling strategies by estimating the bias and variance of each estimator. Based on simulation results we recommend modifications to the existing systematic sampling plan that should result in an efficient and unbiased estimator of vine mean fruit weight.# 1997 Annals of Botany Company