Mixed Model Analysis of Within-plant Variation of Fruit Weight with Implications for Sampling of Kiwifruit Vines

Abstract

Abstract 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=0.49) 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.