Fruit yield is a function of numbers of fruit per acre and the size of those fruit. To accurately predict yield, one must have an accurate estimate of the average number of fruit per acre and average fruit size. If one would like to predict fruit packout, then an estimate of the distribution of fruit size is also needed. Obtaining accurate estimates of fruit numbers and fruit size requires appropriate sampling schemes.
Estimating Number of Fruit per Tree
If we have a good estimate of the average number of fruit per tree, then we can estimate the number of fruit per acre by simply multiplying fruit per tree by trees per acre. Unfortunately, I am not aware of methods for estimating numbers of fruit per tree or per acre. For fruit thinning experiments, researchers often use data from one to three limbs per tree to express crop density (fruit/cm2 branch cross-sectional area). My experience is that this does not provide a very good estimate of either the number of fruit or average fruit size for the entire tree. There is quite a bit of variation from one limb to another and sampling just three limbs is usually inadequate to estimate the entire tree. Currently many orchards attempt to estimate crop load by looking at trees. Experienced estimators usually provide fairly accurate estimates, but every few years the estimates are inaccurate. I think the problem is that the tree is 3-dimensional and we can only see two dimensions and we need to be able to see the fruit in the interior of the tree. So one area where we need additional research is to develop a method for accurately estimating number of fruit per tree. This chore will be easiest for high-density plantings with narrow canopies because we can see into the middle of the tree.
Estimating Fruit Size
When I was a graduate student, I helped collect data from Vermont 'McIntosh' orchards for Drs. Forshey and Elving at Cornell University (Forshey and Elvfing, 1977). They published a paper with data from 3 orchards where they thinned trees with different chemical thinners to obtain a range of fruit set. They reported that yield (lbs/tree) increased linearly with increasing numbers of fruit per tree and average fruit size declined linearly with increasing numbers of fruit per tree. In one orchard the fruit from 2 scaffold limbs from 12 trees were sampled for individual fruit weight to estimate fruit size distribution. They concluded that for yield prediction, the emphasis should be placed on estimating fruit numbers rather than fruit size. Dr. Forshey also published a bulletin in 1971 where he collected data from 4 trees from each of 6 Hudson Valley orchards for 6 years. Twenty fruits per tree were tagged and measured at 10-day intervals beginning 1 July until 1 September (3 weeks before harvest). Mid-season fruit measurements were correlated with average fruit size at harvest and predicted harvest sizes were compared with actual harvest sizes. He found that fruit size at harvest correlated well with fruit size on all sampling dates, but as expected, the correlation improved for the later sampling dates. So it seems that it should be possible to predict harvest fruit size from mid-season fruit size measurements.
Researchers must also be able to accurately estimate average fruit size to evaluate the effect of various treatments on fruit size. The best way to estimate average fruit size at harvest is to divide total yield per tree by the number of fruit on the tree, but harvesting, counting and weighing all the fruit on a tree can be time-consuming and expensive, so researchers would like to harvest a sample of fruit from which average fruit size can be estimated. In 2001, I published a paper where I compared 2 sampling methods for estimating average fruit size for 2 years (Marini, 2001). One method involved harvesting all fruit on 3 scaffold limbs per tree and the other method involved randomly harvesting 20 fruit per tree. These trees were spur 'Delicious' on M.26 rootstock trained as central leaders, so they were about 10' tall and 12' wide. Fruit from the 2 sampling methods and the entire crop were graded into 7 size categories to estimate packout. The regression technique used by Forshey has fallen out of favor and biometricians have published new statistical methods for assessing the agreement between new measurement techniques (20-fruit random sample or 3-limb sample) with the true value (average fruit size based on the entire crop). I found that average fruit size based on the 20-fruit sample differed from the true value by 13% and estimates obtained from the 3-limb sample differed by 11% to 19% depending on the year.
Packouts were used to estimate the average value of a fruit based on actual fruit prices. Fruit values estimated from the 20-fruit sample differed from the true value by 4 cents per fruit and estimates from the 3-limb sample differed from the true value by 7 cents per fruit. I don't think either of these sampling methods are adequate to accurately access fruit size for research, but they may be close enough for growers and packers. It depends on how accurate your estimates need to be. Based on my experience and a paper published by North Carolina researchers, using standard size trees (Dorsey and McMunn, 1938), I think we will have to sample about 25% of the fruit on a tree to obtain an accurate estimate of fruit size.
Quite a bit of work has been done in New Zealand to develop information for predicting fruit size of 'Gala'. A very detailed study was conducted by Austin et al. (1999) where bearing apple trees were grown in controlled environments so early season temperatures could be controlled. By repeatedly measuring fruit size they were able to develop predictive fruit growth curves. Another group (Staley et al., 2001) found that accumulated growing degree days (GDD) with a base of 10˚C (50˚C) from full bloom to 50 DAFB was correlated with final fruit weight and they could use fruit weight at 50 DAFB to predict fruit weight at harvest. Italian researchers (Costa et al., 2004) also reported that GDD at 50 DAFB and fruit size at 50 DAFB were correlated with fruit size at harvest. These studies, along with some earlier work in Washington (Batjer et al., 1957), indicate that if we account for early-season temperatures and we assume a linear fruit growth rate from 50 DAFB, harvest fruit size can be predicted fairly well. Waiting later in the season provides a more accurate estimate. The predictive equations were developed with a statistical procedure called regression to obtain a slope which describes the increase in harvest fruit size as fruit size at 50 DAFB increases. Unfortunately, a single slope value cannot be used for every year or variety because it can be influenced by a number of factors including crop load and precipitation. The models developed in New York are probably fairly robust because they were based on six years of data from six orchards, but they can only be used for 'McIntosh' and the slopes were not published. Models for other varieties have not been developed in the East. Therefore, if we want to predict harvest fruit size we will have to collect data from several orchards over several years to develop appropriate regression models for each variety.
Sampling to Obtain Accurate Estimates
The research described above was aimed at predicting harvest fruit size from fruit measured earlier in the season. However, no attempt was made to develop a sampling scheme to obtain an accurate estimate of average fruit size or to obtain an accurate estimate of fruit size distribution (packout) at sampling time. To develop a sampling scheme for an orchard, we must have good estimates of average fruit size along with estimates of fruit-to-fruit variation within a tree and tree-to-tree variation within a block, and if we want to extrapolate the scheme to other blocks or orchards we need an estimate of block-to-block variation. In general the estimates will become more accurate as the number of fruit per tree and the number of trees per block increase. To keep the costs reasonable, we would like to know the minimal number of samples needed to provide a reasonably accurate estimate of fruit size. The only paper I am aware of that addresses variation was published by Silva et al. (2000) in New Zealand. They compared the accuracy and efficiency of several sampling schemes in estimating the mean and variance of fruit size within a limb at mid-season. They found some systematic trends in FW within a tree. Generally, FW in the lower limbs increased from the base of a branch outwards, but the trend was reversed in the upper limbs. They also found that the major source of variation was between fruit within a limb. However, light conditions in the eastern U.S. are quite different than in New Zealand, so these results probably need to be verified in eastern North America. Their paper focused on fruit size variation within limbs on a tree, and they did not suggest sampling schemes to obtain good estimates for a whole tree or a block.
At a minimum, it seems that obtaining an accurate estimate of fruit size will involve measuring several fruit from the inner-, mid- and outer-section of a branch located in the top, mid-section and bottom of the canopy. While at Rutgers, I worked with a statistician to develop a sampling protocol to assess peach fruit quality (Marini and Trout, 1984) and we also found that fruit-to-fruit variation within a canopy section was greater than tree-to-tree variation. We suggested, for a given harvest date, that 6 fruit should be sampled from the upper and lower canopy on the south and north sides of each of four trees per block (24 total fruit per tree per harvest date).
So where are we in terms of being able to predict apple yield and fruit size? We still have a long way to go! We know that temperature during the first 50 days after bloom influences fruit size, so fruit size at harvest can be predicted fairly accurately from fruit size measurements made at 50 DAFB, but we need to develop regression equations for each variety and these equations may vary with different geographic locations. We know that, at least in New Zealand, mid-season fruit measurements should be made on fruit from different sections of limbs located in the top, middle and bottom of a tree to estimate fruit size distribution. However, to obtain accurate estimates of fruit size we still need to determine the appropriate number of fruit per limb section, number of limbs per tree and number of trees per block. The reason that fruit sampling schemes are still lacking is because horticulturists lack the statistical skills to do this type of work. Researchers in New Zealand have obtained assistance from statisticians and we will probably have to do the same if we want to pursue this line of research.
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