Experimental Designs and Statistical Analyses for Rootstock Trials

Abstract

Modern agricultural research, including fruit tree rootstock evaluations, began in England. In the mid-1800s, field plots were established at the Rothamsted Research Station to evaluate cultivars and fertilizer treatments for annual crops. By the early 1900s, farmers questioned the value of field experimentation because the results were not always valid due to inadequate randomization and replication and poor data summarization. During the first half of the 20th century, Rothamsted statisticians transformed field plot experimentation. Field trials were tremendously improved by incorporating new experimental concepts, such as randomization rather than systematically arranging treatments, the factorial arrangement of treatments to simultaneously test multiple hypotheses, and consideration of experimental error. Following the classification of clonal apple rootstocks at the East Malling Research Station in the 1920s, the first rootstock trials were established to compare rootstocks and evaluate rootstock performance on different soil types and with different scion cultivars. Although most of the statistical methods were developed for annual crops and perennial crops are more variable and difficult to work with, rootstock researchers were early adopters of these concepts because the East Malling staff included both pomologists and statisticians. Many of the new statistical concepts were incorporated into on-farm demonstration plots to promote early farmer adoption of new practices. Recent enhancements in computing power have led to the rapid expansion of statistical theory, the development of new statistical methods, and new statistical programming environments, such as R. Over the past century, in many regions of the world, the adoption of new statistical methods has lagged their development. This review is intended to summarize the adoption of error-controlling experimental designs by rootstock researchers, to describe statistical methods used to summarize the resulting data, and to provide suggestions for designing and analyzing future trials.

1. Introduction

Tree fruit rootstock research began with the classification of nine clonally propagated dwarfing apple rootstocks (M.1–M.9) by Ronald Hatton around 1920 at the East Malling Experiment Station in Kent, England [1]. Previously, commercial fruit growers obtained trees on seedling rootstocks from nurseries. Soon after rootstock classification, experiments were established to evaluate rootstock performance with different cultivars and on different soil types. Data from early tree fruit experiments involving trees on seedling rootstocks were so variable that pomologists had difficulty interpreting their results [2]. Much of the variation was due to seedling rootstocks. About 130 km northwest of Kent, the Rothamsted Experimental Station was founded in 1843 to investigate the impact of inorganic and organic fertilizers on annual crop yields [3]. In 1919, Ronald Fisher was hired to investigate the possibility of analyzing and interpreting the large amount of data from the field trials [4]. Between 1912 and 1930, Fisher developed the theory of experimental design along with most of the statistical tests used by agricultural researchers today, and beginning in 1926, the techniques devised by Fisher were adopted for all the annual experiments at Rothamsted [5]. T. N. Hoblyn studied with Fisher [6] and was hired as a statistician at East Malling, and he introduced statistical methods to enhance the quality of research with perennial crops [7]. The close association between statisticians and pomologists at East Malling led to refinements in the design and interpretation of laboratory and field experiments with tree fruits. During the first half of the 20th century, the statistical methods developed in England, such as the t-test, analysis of variance, and analysis of covariance, were gradually adopted by pomologists around the world. Rootstock trials are more complicated than many experiments involving both annual and perennial crops [8]. Multiple sources of variation can influence results from rootstock trials, including variation due to tree quality at planting, tree-to-tree variation, year-to-year variation, correlations between years, and the relatively large land area required for trees, which causes variation in soil and topography [9]. To address these problems, rootstock researchers adopted the statistical methods as they were developed, but adoption lagged by more than a decade. Examples of techniques that were slowly adopted include multiple comparisons that consider experiment-wise error rate [10,11,12], slicing without separating the data to compare levels of one factor within levels of another factor in factorial experiments [13,14], and the use of linear mixed models and generalized linear mixed models for data analysis. Over the past several decades, keeping abreast of the rapid developments in statistical theory and methodologies that are useful for rootstock research has become difficult. The goals of this review are (1) to summarize the history of rootstock research and statistical methods used by rootstock researchers; (2) to describe the experimental designs and statistical methods previously and currently used for rootstock evaluations; and (3) to critically evaluate the methods currently used to analyze commonly reported response variables and, where appropriate, suggest alternatives for experimental designs and statistical analyses.

2. Development of Modern Statistical Methods for Agricultural Research

2.1. Early Estimates of Variation

Statistics is a relatively new science and agricultural field researchers were among the first to use statistics to enhance the quality and validity of their research [15]. In the early part of the 20th century, many new and important ideas in statistical methodology were developed, including the distribution theory of small samples from a normal distribution, which was the basis of the Student’s t-test [16]. During much of the 19th century, probable error was commonly used as a measure of variation around a mean [17] and was used as a measure of reliability of the average [18]. Probable error was a term coined by Bessel in 1815, and C.F. Gauss and F.W. Bessel published formulae for its calculation. By 1832, it was commonly used and designated as r.

Probable error is a statistic to measure precision among replicates. The probable error of a single plot is calculated as two-thirds of the standard deviation and indicates the limits within which there is an even chance a particular observation will fall. If the mean yield of several plots is 149 kg and the probable error is 9.2 kg, there is an even chance that the yield of any given plot is more than 139.8 kg and less than 158.3 kg, or 6.2% of the mean [19]. In the early 1900s, researchers were interested in determining the optimum number of replicates and the size of plots that were needed to generate reliable data. Using data from the Rothamsted plots, Mercer and Hall [19] showed that the probable error associated with a single plot was about ±10%. They estimated variation by varying plot size and number of plots per treatment. Error was reduced a little with more than five plots and with plots that were larger than 100 m². Anthony and Waring [20] were probably the first American pomologists to use probable error to compare fertilizer treatments for apple trees. Other tree fruit researchers also reported probable error, but it was soon replaced by Fisher’s techniques. Most of the common experimental designs and analyses used by modern agricultural researchers were developed by the late 1930s.

2.2. Annual Crops

Agricultural field experimentation began in 1843 with the Rothamsted classical field experiments, where trials were established to evaluate fertilizers on annual field crops [21]. Sir Ronald Fisher was appointed as a statistician at the Rothamsted Experiment Station in 1919 to investigate the possibility of summarizing, analyzing, and interpreting the accumulated 75 years of data. During the 1800s, field experiments were rarely replicated but were repeated over the years. By the end of the 19th century, the advantages of replication to avoid bias were generally recognized, but replicates were usually arranged systematically [21,22]. Fisher described the analysis of variance (ANOVA) and showed that estimates of treatment means and experimental errors from systematically arranged experiments were often not valid [23]. Fisher used these data to develop the basic concepts of experimental design and data analysis [21]. By the mid-1930s, Fisher obtained exact distributions for correlation coefficients and the F-statistic; he introduced the concept of degrees of freedom; he developed the methodology for testing goodness of fit of a regression function and for testing significance of individual coefficients; he introduced the maximum likelihood theory; and he introduced the field of experimental design [24]. In 1935, Fisher published “The Design of Experiments” where he discussed the importance of randomization to obtain nonbiased data [25]. By the early 1930s, treatments were usually compared with multiple t-tests, and Fisher also introduced the post-ANOVA Least Significant Difference (LSD), using the pooled standard error, for the pairwise comparison of means [25]. He discussed p-values and suggested the p-value of 0.05 as a limit for significance [23]. He also introduced the analysis of covariance (ANCOVA) and multiple regression. In another paper, Fisher [22] described the principles of his experimental designs, including replication, randomization, and blocking to avoid biased estimates of error. To obtain valid estimates of error, he stressed the importance of randomizing treatments, subject to appropriate restrictions such as blocks or in the rows and columns of a Latin square. To improve the efficiency of experiments, he also described factorial experiments to evaluate more than one factor simultaneously [25]. Some of these designs were later extended by Frank Yates, who joined Fisher’s Statistics Section in 1931.

2.3. Fruit Trees

Most of the statistical methods commonly used today were developed between 1920 and 1935 to interpret data from fertilizer and cultivar trials with annual crops [23]. Experiments involving perennial crops, especially tree fruit, are more complicated and have additional sources of variation that must be considered [26,27]. Fortunately for pomologists, Thomas Noel Hoblyn, a pioneer of agricultural statistical methods, worked closely with Hatton, a pomologist, at the East Malling Research Station to develop methods to minimize variation in experiments involving fruit trees and berry crops. Hoblyn was a field recorder at East Malling and was frustrated by the large variation between fruit trees. He was sent to study with Fisher before being hired to head the Statistics Section at East Malling [6,7]. In addition to being a competent statistician, Hoblyn also understood tree growth and the difficulties associated with field experimentation and data collection. The first major statistical publication on horticulture was probably Hoblyn’s “Field Experiments in Horticulture” [26]. S.C. Pearce joined Hoblyn’s Statistics Section in 1938 and in collaboration with Fisher, new tree experiments were established using Fisher’s methods [26]. In 1959, G.F. Freeman joined the Section for several years before moving to Africa at the Cocoa Research Institute of Nigeria. While at East Malling, Freeman published a paper describing the computation of ANOVA, estimating treatment means and estimating particular effects [27]. Based on two decades of work with fruit trees, Pearce published an updated and expanded version of Hoblyn’s publication called “Field Experiments with Fruit Trees and Other Perennial Plants” [28]. Later in his career, after 26 years of consulting with agricultural researchers, Pearce felt that statisticians and biologists often did not understand each other because they used different terminology. In 1965, he published “Biological Statistics: An Introduction”, which describes most of the important concepts of experimental design and methods for data analysis with a minimum of math and many examples from tree fruit experiments [29]. This book would be a valuable addition to the library of any pomologist.

Variation in trials with trees is usually greater than for agronomic crops. For fertilizer experiments involving tree fruits, differences between trees within a treatment were often greater than differences between treatments [20,30]. A single plot (the experimental unit) of an annual crop contains many plants, which minimizes plant-to-plant variation. Plots of annual crops are usually relatively small, which also minimizes soil and environmental variation. Research at Rothamsted showed that yields of nearby agronomic plots were frequently correlated due to variations in soil and topography [22]. Experiments with annual plants can often be repeated in subsequent years. Since it is more difficult to repeat experiments with perennial plants, the experiments usually require more replication than for annual crops [31]. For fruit trees, especially those on seedling rootstocks, variation due to location was less important than tree-to-tree variation [32]. Additional sources of variation for perennial crops include the cumulative effects of treatments on soils and trees over time, seasonal differences, seedling rootstocks, and correlations between observations in succeeding years [32]. When fruit quality or shoot length was evaluated, an additional source of variation was the fruit-to-fruit or shoot-to-shoot variation in samples within the tree [33,34].

Tree fruit researchers were often frustrated by unacceptably high variation in apple fertilizer trials using trees on seedling rootstocks [20,35]. Treatment differences that were considered economically important were not statistically significant. Some of the earliest uses of statistical methods by tree fruit researchers involved understanding the nature of variation. Parker and Batchelor [32] were among the first to systematically study orchard variation and used data from several large long-term tree trials with ‘Washington Navel’ orange trees on sweet orange seedling rootstock. Systematic soil characterization, including soil moisture, nitrates, and nematodes, showed that soil factors were not the primary cause of yield variation as in trials with annual crops. The average coefficient of variation (CV) for yield of individual orange trees was 25.4% [32]. The CV is the ratio of the standard deviation to the mean and is a relative measure of the dispersion of data from the mean value. Other pomologists reported that CVs of individual trees were usually between 19.7% for ‘Jonathan’ apple trees [36] and 89.6% for ‘Ben Davis’ apple trees [37,38]. They also learned that yields of individual orange trees for a given year were usually normally distributed, yields of adjacent trees within a plot were correlated (r = 0.132 to 0.537), and the yield of trees in one year was positively correlated with yields in the following years; the correlations decreased as more remote years were compared [32]. Using data from Batchelor and Reed [30], Harris [39] reported that correlation coefficients between yields of adjacent trees were 0.306 for ‘Valencia’ orange, 0.375 for ‘Navel’ orange at Antelope Heights, 0.517 for ‘Navel’ orange at Arlington, 0.448 for ‘Eureka’ lemons, 0.214 for ‘Jonathan’ apple, and 0.232 for seedling walnut trees, which are similar to the correlations reported for several agronomic crops including potato, alfalfa, wheat, rice, corn, and timothy [39]. In orchards, soil water, nitrate, and carbon content were positively correlated with soil depth (r = 0.32 to 0.70) [32] and heterogeneity was greatest at 1.3 m. The surface layer appeared uniform, but the soil was less uniform at 1.0m and this may explain the correlation between the yields of adjacent trees in orchards planted in apparently uniform fields [32].

Batcher and Reed [30] also studied data from orange, lemon, walnut, and apple orchards on seedling rootstocks and reported standard deviations and coefficients of variation to estimate variation. CVs declined at a decreasing rate as trees/plots increased, but there was little improvement with more than eight trees/plot. For cultural experiments, they suggested four replicates of 8 to 10 trees and for rootstock experiments, they suggested eight replicates with 4 to 5 trees. Using probable error, Pickering [37] recommended 6 to 12 apple trees/plot. With a similar approach, Parker and Batchelor [32] later made several suggestions to consider when designing new experiments involving fruit trees. They suggested that cumulative yield data from several pretreatment years could be used as a blocking factor when selecting trees for new experiments to evaluate fertilizers or pruning treatments. Although this is not possible for rootstock trials, yield data from different sections of an orchard used for previous trials might be considered when blocking. Single-tree plots were highly variable and combining adjacent trees to increase the area reduced the variation. But, the reduction in variation was small due to the correlation between adjacent trees. They felt that a better approach to reduce variation was to replicate plots. Using the t-test, they found that with four replicates per treatment, yield differences of 16.7% between the two treatments would be significant.

Hoblyn et al. [26] discussed additional factors that fruit tree researchers should consider when designing experiments. They suggested that researchers should consider the history of the tree before it is planted. Differences in treatment in the nursery, during transplanting and in early tree training, may contribute to tree quality and, therefore, tree-to-tree variation in rootstock trials. They described “the device of calibration”, previously suggested by Pearce and Taylor [40], where some characteristics of the tree, such as initial tree size can be used as a covariate to correct the performance of individual trees, and this may reduce experimental error by as much as one-third. They also explained how trees from a trial can be used for new experiments upon termination of the first trial and proposed possible designs for subsequent trials where the initial design was a randomized block.

2.4. Common Experimental Designs

Experiments can be designed to identify and isolate the effects of natural variation and determine whether the differences between treatments are real within certain limits of probability. Fruit tree researchers usually rely on one of three experimental designs: completely randomized design (CRD) [41,42], randomized complete block design (RCBD) [43,44], and split-plot design (SPD) [45,46]. Occasionally, Latin square designs (LSD) are used, but the primary disadvantage is that they require the same number of rows and columns [47]. The choice of experimental design depends on the hypotheses being tested and the expected sources and magnitudes of variation associated with the experimental factors.

In his bulletin, “Field Experiments with Fruit Trees and Other Perennial Plants”, Pearce [28] stated that with multiple-tree plots, field position was the major source of variation, but with single-tree plots, tree-to-tree variation was usually more important. Summarized below are his descriptions of the experimental designs most often used to study fruit trees, along with their advantages and disadvantages. Most experimental design textbooks describe these designs in detail [48,49].

The CRD is the simplest and assumes no positional effects. For CRDs, each experimental unit (EU) is assigned randomly to a position within the experimental site. An EU is the smallest unit of experimental material to which a treatment is assigned. If there are positional effects (variations in soil, environment, topography, training systems, or tree growth habits), the error variation is large, but positional effects are usually more important with annual crops. Less positional variation is expected in small trials covering small areas. The linear model for a CRD usually does not have random effects and data can be analyzed with a least squares approach [47].

For the typical RCBD in the experimental site is divided into blocks and there are as many plots per block as there are treatments. One plot of each treatment (the experimental unit) is randomly assigned to each block. Blocks do not need to be contiguous. There are advantages of the RCBD for perennial plants.

1. The design is orthogonal. This simplifies the statistical analysis and the significant differences between treatment means will be a minimum for the degree of replication used;

2. The design is robust. In cases where trees die over time, whole blocks and whole treatments may be omitted from the analysis without disturbing the basic design, which remains orthogonal, but the sensitivity of the trial is somewhat diminished;

3. The RCBD is flexible and with some planning, the same trees can be used for future experiments.

The RCBD is the most popular of all of the designs, but for rootstock trials, there may be times when a modification of the RCBD is preferred. The RCBD effectively reduces residual error when the variation between blocks is greater than within blocks. For trials comparing many rootstocks, the blocks become large, and the within-block variation increases. Although positional effects are usually not very important for perennial crops, large blocks containing more than 10 or 12 plots should be avoided because they lose efficiency as they fail to adequately minimize the effect of soil heterogeneity [50].

To avoid large blocks for experiments with more than about 10 or 12 treatments, incomplete block designs (IBD) may be preferable [51]. For complete block designs, all blocks contain all treatments, while some but not all treatments are found in incomplete blocks. Yates [52] first introduced the IBD and suggested the name “quasi-factorial”. The analysis is less complicated when the block size remains constant compared to when blocks are of unequal size. IBDs reduce within-block heterogeneity but sacrifice all or part of the information on certain treatment contrasts, which are confounded with blocks [52]. The analyses are more complicated, but where soil heterogeneity or other positional characteristics are expected to be large, the experiments are more efficient than RCBD [50]. There are many modifications of the IBD, which are beyond the scope of this review.

To avoid all plots or trees of one treatment being located near each other as might occur in a CRD, while also conserving error DF, Pearce [28] suggested a compromise by including more than one EU per treatment per block. Thus, each block contains 2 or more plots of each treatment randomly assigned to positions within the blocks. This increases the error DF because there are fewer blocks than there are replicates. Pearce [28] did not name this modification of a RCBD, but it is probably what we now call the generalized randomized block design (GRBD) [53]. The GRBD is a modification that is often not discussed in experimental design texts or courses. The GRBD may have advantages in rootstock trials and was recommended by Addelman [54]. The RCBD requires that the number of blocks be equal to the number of replicates of each treatment, whether the experimental units divide naturally into that many blocks of homogeneous units. In GRBDs, two or more trees or multi-tree plots on each rootstock are randomly planted in each block [52,55]. This method of more than one plot per treatment per block has the advantage of allowing a formal test for the rootstock × block interaction. If the interaction is not significant, it can be pooled into the error term. Compared to experiments with multiple-tree plots or experiments with more blocks of single-tree plots, the GRBD has more degrees of freedom in the error term for a given number of trees per treatment and minimizes complications caused by open cells if trees die [47].

Rootstock trials are often continued for at least 10 years and some trees may die before the trial is terminated. In other cases, there may be inadequate trees of all rootstocks to appear in every block, resulting in an incomplete block design [55]. Although incomplete block designs provide some information for each rootstock–block combination, inter-block information often cannot be recovered, and Pearce [56] described a method for adjusting treatment means to account for intra-block information. Each missing value destroys the balance feature of the RCBD, and some treatment contrasts will be contaminated with block effects [56]. When there are missing values, some statistical software packages do not properly adjust the means or standard errors for the effect of incomplete blocks and the estimated means may be incorrect [57]. To increase the likelihood that the trial remains balanced with all rootstocks appearing in all blocks, multiple-tree plots are often used [58,59,60,61,62,63]. Therefore, the multiple-tree plot is the experimental unit, and the trees are samples or observational units. Some researchers using multiple-tree plots use the samples to calculate the plot means and perform ANOVA on these mean values. Such an approach is appropriate when all EUs have the same number of trees. However, when the sample size is unequal, the amount of information per plot mean also varies and affects the robustness of the assumptions of normality [64] and equal variance [65]. Therefore, rather than having a single value for each rootstock–block combination, it is preferable that the dataset should include a value for each tree in the trial, and the correct error term for testing rootstock effects is the block × rootstock interaction.

2.5. Using Additional Information

The analysis of covariance (ANCOVA) was developed in the early 1920s and was first discussed in Statistical Methods for Researcher Workers [23]. Pearce [29] discussed ANCOVA in a way that is easily understood by researchers. ANCOVA is an extension of ANOVA and combines regression and ANOVA. If an experiment has one or more qualitative factors (such as treatments or indicator factors) and one or more measurable quantitative factors (covariates) that may influence the response variable, the variation due to regression can be removed before comparing the treatments. In this way, the means can be compared after correcting or adjusting them for the covariate(s) [57].

Rootstock researchers sometimes used ANCOVA to adjust the means for a covariate [41,42,43,44,45,46]. Least square means or adjusted means obtained with ANCOVA are treatment means estimated at the mean value of the covariate [57]. Results from ANOVA are reliable when the errors are independent, with the same normal distributions. However, ANCOVA requires three additional assumptions: the response variable is linearly related to the covariate; the estimated regression lines are parallel; and the range of the covariate(s) is similar for all treatments [57,64]. The assumption of homogeneous slopes can be evaluated by testing the treatment × covariate interaction. If the interaction is significant, then the slopes are not equal and a normal ANCOVA may lead to erroneous conclusions [46,65]. When slopes differ, the slopes can be compared, or the means can be compared at a minimum of three levels of the covariate [57]. Pearce [40] provided an example of ANCOVA, where apple yield variability was reduced by using tree size at the beginning of the experiment, and the amount of crop a tree had already produced was used as a covariate to study the effects of treatments on bearing-age trees.

To reduce variation, some researchers block on factors that can be quantified, such as initial tree size or crop load. Considering the factor as a quantitative factor rather than a block has two advantages. (1) There are more degrees of freedom in the error term. The penalty for including the factor as a block is the number of treatments minus one degree of freedom, but the penalty for considering it as a covariate is only one degree of freedom for the linear effect of the covariate. (2) ANCOVA provides more information than ANOVA. When the slopes are heterogeneous, the interpretation is that the treatment response depends on the level of the covariate, so treatments may differ at some levels of the covariate, but not at other levels. Pearce and Moore [66] obtained data from apple and peach experiments to compare blocking vs. covariance, using neighboring plots to reduce experimental error. The variation removed by blocks was correlated to that removed by covariance, and adjustment by neighboring plots can be very effective, especially on irregular land.

2.6. Advances in Statistical Software and Data Analysis

2.6.1. Statistical Models Commonly Used in Agricultural Research

The term “general linear model” typically refers to simple linear regression models that are used to model the relationship between two variables: the continuous response variable and the quantitative predictor variable. The error term in the model is a random variable. Ordinary least squares (OLS) are used to estimate the parameters and require some assumptions about the error term; the residuals are normally distributed, with constant variance, and have a zero mean [47,53]. Multiple linear models involve more than one predictor variable. Analysis of variance (ANOVA) and analysis of covariance (ANCOVA) models are special cases of regression models and include qualitative predictors [67].

The term “generalized linear model” (GLM) refers to a larger class of models [67,68,69], where the response variable is assumed to follow an exponential family of distributions. Fisher [70] realized that several commonly used distributions were members of one family and called them the “exponential family”. In 1972, Nelder and Wedderburn [71] developed a class of generalized linear models (GLMs) that extended standard linear regression to incorporate a variety of responses including count, binary, proportions, and continuous distributions, using maximum likelihood estimates [72]. Maximum likelihood estimation is an alternative to OLS that attempts to find the model parameters that maximize the likelihood of the model. The GLM is an extension of OLS that allows for different error distributions and has transformation functions, called link functions. These include logistic regression, probit regression, Poisson regression, and log-linear models. GLM methodology can be used for various linear regression techniques, including ANOVA, MANOVA, t-tests, and ANCOVA, which involve categorical predictors.

2.6.2. Statistical Software Development

Before the availability of statistical software packages, data were analyzed by hand or business machines. Fisher bought the first Millionaire calculating machine for Rothamsted’s statistics department in the early 1920s. In the 940s and 1950s, electro-mechanical desk calculators were used to calculate the sum of squares [73]. The first commercial computers became available in the early 1950s [74]. The first statistical program was BMDP (bio-medical data package), developed in 1957 for IBM mainframes at the UCLA Health Computing facility, which consisted of several subroutines to perform parametric and nonparametric analyses and was released to the public in 1962 [74]. Rothamstead’s research began programming on an Elliot 401 in 1954. Some early programs were developed at Rothamsted and by 1962, programs were available for several types of analyses including multiple regression, probit analysis, and analysis of designed experiments, such as factorial designs, split plots, and ANCOVA [75]. By 1960, the first unified programs started to replace individual programs. Over the past 60 years, several statistical software packages have been released. An examination of the 62 articles published in the Journal of the American Society for Horticultural Science in 2014 indicated that 89% used one of the following five software packages for data analysis [76]: SAS, which was developed in 1966; JMP, which was added in 1989 for Mac, with a point-and-click interface added in 2004; SPSS in 1968; Minitab in 1972; R, which is a free open-source software environment for statistical computing and graphics and the R Core team released R to the public in 2000 [77]; or Genstat (General Statistics), which was developed in 1968 by the Rothamsted Research in the UK and is distributed by VSN International [75]. SAS 9.4 and Genstat 23 are probably the most used statistical software packages for agricultural research worldwide. Since SAS was used for 56% of the papers published in the Journal of ASHS in 2014 [76], SAS products will be used as an example to explain how software packages have evolved to incorporate advances in model theory.

In the mid-1970s, PROC ANOVA, PROC REG, and PROC GLM used the method of least squares to fit general linear models. These procedures could perform regression, ANOVA, ANCOVA, MANOVA, and partial correlation for fixed-effect models. Valid analyses required the assumptions of normally distributed residuals, homogeneous variances, and independent residuals. PROC GLM, but not PROC ANOVA, could accommodate unbalanced experiments. Repeated measures analysis could be performed using a multivariate approach. Because there were no alternatives, these packages were widely used to analyze models with random effects, such as blocks and subsamples, but the standard errors for estimates and means based on the fixed-effects model may be smaller than those based on a true random-effects model. Some functions were not estimable at all under the fixed effects model [78,79,80].

The first SAS procedure to use GLMs was PROC GENMOD in 1993 [81] and in some common analyses, it was used for included logistic regression, probit models for binary, and log-linear models for multinomial data.

In 1996, SAS introduced PROC MIXED to fit linear mixed models (LMM) [78]. LMMs are more general and flexible than models relying on least squares and offer a variety of covariance structures. Mixed models use an estimation method similar to maximum likelihood called restricted maximum likelihood (REML). Data obtained from RCBDs and SPDs should be analyzed with a mixed model approach because a block is usually a random factor. LMM can model random and mixed effect data, repeated measures, spatial data, data with heterogeneous variances, and autocorrelated observations.

In 2005, SAS introduced the GLIMMIX procedure for generalized linear mixed models (GLMM) [79]. GLMMs extend mixed models to non-normal data and often have options not available in LMM software, especially the ability to perform multiple comparisons within each level of a factor without physically slicing interactions in experiments with factorial structure.

Since the RCBD is the most common experimental design for rootstock trials, data should be analyzed with packages that offer LMM or GLMM. This is especially true for unbalanced experiments, where for whatever reason, there is unequal replication. These packages can also be used to correctly perform regression analyses in RCBDs [79].

3. Rootstock Classification, Introduction, and Evaluation

Due to the large volume of information published on tree fruit rootstocks, this section provides only a limited summary and emphasizes experimental designs and data analyses commonly utilized for rootstock trials. Fruit trees have been cultivated for nearly 3000 years [82]. Clonal propagation was needed to maintain the genetic identity of tree fruit genotypes with valuable traits, and grafting techniques were discussed more than 2000 years ago [83]. European commercial apple growers started replacing trees on seedling rootstocks with trees on clonal rootstocks in the 1940s, whereas North America lagged by about 20 years [84]. Trees on seedling rootstocks were relatively inexpensive, easy to produce, and performed adequately with varying training systems and on a wide range of soils in most environments. However, seedling rootstocks were relatively non-precocious, produced large trees that were difficult to manage and were variable. Trees on seedling rootstocks were not well suited for research due to great variability. With changing orchard economics during the 20th century, commercial orchardists and researchers preferred smaller precocious more uniform trees [85].

3.1. Apple Rootstock Classification at East Malling

Self-rooting dwarfing apple rootstocks have been available in Europe for more than 2000 years. Two types of dwarf rootstocks were available in the 1800s. “Paradise” was dwarfing and precocious. “Doucin” or “English Dwarfing Stock” was described in France as slightly dwarfing and no more precocious than seedling [86]. In the early 20th century, seedling rootstocks were known as “Crab” regardless of origin. Variable performance of trees on seedling rootstocks frustrated commercial fruit growers and researchers, so clonally propagated rootstocks were desired [86]. By the late 1800s, there was confusion about the identity and nomenclature of different forms of Paradise rootstocks. While trying to trace the history of Paradise rootstock, Bunyard [87] felt there were several dwarfing rootstocks and he divided them into two groups that he called “French Paradise” and ‘Broad-Leaf Paradise”. In 1912, R. Wellington and R.G. Hatton obtained Paradise rootstocks from nurseries in Europe and planted them for evaluation at the East Malling Research Station, in Kent. Based on vegetative and fruit characteristics, Paradise was a collection of nine rootstocks with a wide range of vigor and were designated as Types I to IX [88]. Later, the designation was changed to (East Malling) EM 1–EM IX, and in the 1970s, the nomenclature changed to M.1–M.9. Known viruses were eliminated from Malling rootstocks and the designation changed to East Malling-Long Ashton (EMLA). The virus-free M.9 is now known as M.9 EMLA. A group of Crabs was designated as Crab A, B, C, etc. [89].

3.2. Development of Malling Merton Rootstocks

Another program at the Long Ashton Station classified French Crab and “free” stocks (seedlings of commercial cultivars, mostly cider cultivars) into 10 groups, designated A–J. Following the classification of known rootstocks, M.B., Crane of the John Innes Horticultural Institute at Merton, and H.M., Tydeman at East Malling, initiated a breeding program to develop new rootstocks resistant to wooly apple aphid (Eriosoma lanigerum), which was a serious problem in New Zealand [90]. Of 35,000 seedlings, 15 were selected and numbered Malling-Merton 101–115 and later renamed MM.101–115 and they were described by Preston [91] and Tydeman [92]. Additional rootstocks were produced for cider cultivars at the Long Ashton Research Center. Although little information is available for these rootstocks, three were evaluated by American researchers [93].

3.3. Error-Controlling Designs for European Rootstock Trials

The first apple rootstock trial was established in 1919 at East Malling to evaluate the growth and productivity of ‘Lane’s Prince Albert’ on 16 clonal rootstocks. In 1920, new trials were established on four different soil types [2]. The East Malling Annual Report mentioned 17 trial acres (6.9 ha) of apple trees with 11 cultivars on various rootstocks. Over 15 years, Hatton [2,94] summarized the results of these trials. The initial plantings had inadequate trees for randomization and replication. One early trial had 10 trees/rootstock planted in two groups of five trees and one group was pruned [2].

Early rootstock plantings were not described in detail. Hatton [91] realized that the lack of replication did not allow accurate comparisons. He stated, “Horticultural science is in its infancy, and its investigators are as yet out to measure fairly large differences; but the time is not far off when they will want to discover smaller differences, and the more highly controlled this material, the more likely will be their experiments to yield significant results”. He used his data with a “rather high estimation of the standard deviation” to estimate the number of trees needed under similar conditions to show certain degrees of differences for total wood growth per tree. A table showed the differences between two means of 1, 10, 25, and 50%, and the number of trees required to detect differences were 8520, 85, 14, and 3, respectively [2]. In general, he felt that with 20 trees/rootstock, he could detect differences of 20 to 25% [2], but he did not mention that restrictions on randomization, such as blocking or multiple-tree plots, might influence experimental error. The 1920 trials had 20 trees with five trees/rootstock in each of four blocks to account for soil variability. In another trial, 5 to 10 trees were planted on four different soils, but there was no mention of replication or randomization. A third trial involved four cultivars on 16 rootstocks, but again, replication and randomization were not mentioned. Early results were reported as means plus standard errors of the mean for tree height and spread, number of blossoms and fruit per tree, and yield [2].

Although some early rootstock trials established before 1930 were not replicated, researchers used adjacent trees to estimate variation [95]. Pickering [94] calculated the probable error for the yield of six adjacent 18-year-old apple trees on Paradise as ±7.1%. From studies with apples and pears, he concluded that experimental plots should include 6 to 12 trees. Hatton [8] compared the yields of a row of Crab seedlings to a row of Paradise and the CVs were 57.1 for trees on Crabs and only 36.5 for trees on Paradise. To evaluate variation, 8 trees on Paradise No. I were grown in widely separated locations. With the probable error of ±4.6% for yield, it was possible to detect yield differences of 21% between the two means. Hoblyn [9] used data from a pruning experiment with 14-year-old ‘Early Victoria’ apple trees on seedling or Paradise rootstocks to demonstrate the need for adequate replication. Trees were similar in size at planting, but trees on seedlings yielded 66 to 651 kg, and the range for trees on Paradise was only 79 to 308. So, tree-to-tree variation was reduced by using clonal rootstocks for experiments. A second source of variation was soil. For ‘Prince Albert’ apple trees in one location, the average yield was 29 kg vs. 41 kg for trees 50 m away and the difference was significant. Taken together, these data plus data from several other trials confirmed that trees on clonal rootstocks were less variable than on seedlings [96].

In early trials, each plot was typically divided into two replicates to account for soil variation. In 1918, Hatton [2] planted 10 apple trees per rootstock with two replicates of five trees. Based on the means and standard errors, he suggested that variability can be reduced by planting uniform trees and the largest sources of variation were soil and biennial bearing. In 1919, he planted 20 trees per rootstock with four replicates of 5 trees. By the late 1920s, most rootstock trials at East Malling had several replicates of multiple-tree plots. A plum rootstock trial consisted of at least two replicates of 6- to 12-tree plots [96]. Four clones of Paradise were compared with ‘Prince Albert’ using four replicates of single trees, and data were reported as mean yield and growth plus standard errors and there were large differences between rootstocks [8].

During the late 1920s and early 1930s, there was a transition toward using error-controlling experimental designs. As statisticians started collaborating with pomologists, researchers realized that replication was needed to estimate experimental error. However, they were slower to adopt randomization [97]. Fisher [9] was a strong advocate for randomization to reduce bias and to permit valid tests of significance. He also introduced the concept of randomized blocks to obtain a valid and usually smaller error [25]. In the absence of replication, experiments with annual crops could be repeated for several years, but interpreting results with perennial crops was more complicated because the response to a treatment may be related to the previous history of the plant. Early rootstock trials at East Malling were not randomized [1], but they were repeated many times on different soils and rootstock differences were often large [2]. However, smaller differences that were economically important required more refined techniques [2]. The first trial at East Malling using the methods developed by Fisher was an RCBD for a raspberry manurial trial in 1927 [97]. Hatton [98] was the first to report pair-wise comparisons of rootstock means. Means were reported with brackets to indicate non-significant differences, where pairs of means differing by more than twice the standard error of their difference were considered different at the 5% level. This is an approximate t-test for two means.

Hoblyn [9] explained that for the RCBD, SPD, and LSD, there are two sources of variation: position in the field and inherent variability of plants. Using data from a pruning experiment with 14-year-old ‘Early Victoria’ apple trees on seedling or Paradise rootstocks, he demonstrated the need for adequate replication. Trees were similar in size at planting, and tree-to-tree variation for yield was reduced by using clonal rootstocks for experiments. A second source of variation was soil. For ‘Prince Albert’ apple trees in one location, the average yield was 29 kg vs. 41 kg for trees 50 m apart and the difference was significant [91]. Hoblyn [9] explained that statisticians can estimate variability and calculate the chances of repeating a result under certain conditions, but to use the formulae legitimately, certain rules must be followed. First, an adequate number of samples to calculate variability was needed and the number of samples needed to increase as variability increased. Second, for a valid estimate of variability, samples should be selected at random.

Pearce [28] used data from three experiments to study sources and magnitudes of variation. He noted that young apple trees tended to be more variable than trees more than 6 years old and coefficients of variation (CV) decreased until trees were 10 years old. He encouraged researchers to continue experiments long enough for the manifestation of treatment effects. He suggested using small blocks to reduce intra-block variation. He also recommended using initial TCSA as a covariate when analyzing yield data.

From the mid-1930s to the present, most rootstock trials in England and other countries were RCBD, often with three or four blocks with three- to six-tree plots [96,97,98,99,100,101,102,103,104,105,106]. Some trials had single-tree plots with 5 to 10 replicates in an RCBD [107,108,109]. Fewer rootstock trials were designed as CRD with 4 replicates of three-tree plots [110] or 10 single-tree reps [111]. For some experiments involving container-grown trees, the experimental designs and statistical analyses were not described but p-values were sometimes reported in the text [112].

Results from ANOVA and regression may be incorrect if the data seriously violate the assumptions of independence, normality, and common variance. Testing the assumptions for valid parametric tests was rarely mentioned in early reports, but some researchers took precautions to ensure that data adequately satisfied the assumptions for ANOVA. Since treatment effects with small samples often depart from normal, and treatment variances are often heterogeneous, Pearce [28,29] described three transformations that often stabilize variances and improve normality. He suggested the log transformation when standard deviations were proportional to the square of the mean, and the square root transformation when standard deviations were proportional to the mean. The angular, or arcsine, transformation can be used for proportion data when values fall outside the range of 0.15 and 0.85 [28,29]. Count data could be transformed to the square root of (n + 1/2) [113]. Tubbs [112] transformed data and reported back-transformed values.

Hoblyn [9] explained the difference between experimental and demonstration plantings because some research plots were intended as demonstrations for fruit growers. Hoblyn explained that a good demonstration plot was of no experimental value and a sound experiment very seldom made a good demonstration. Experimental plots are designed to generate new information or to test hypotheses based on previous information. Demonstration plots are designed to demonstrate results that were already observed in research trials.

3.4. Experimental Designs in North America

Americans have been mildly interested in dwarfing apple rootstocks since the mid-1800s. Increased interest in dwarf apple trees in the early 1900s led to the evaluation of dwarfing rootstocks in New York and Virginia, followed by Massachusetts, New Jersey, and Connecticut [114]. But due to their small canopies and tendency to fall over unless supported, trees on dwarf rootstocks were no more productive than those on seedling rootstocks, and dwarf trees were recommended only for home gardens. As in England, American fruit growers and researchers were frustrated by the variable growth and productivity of trees on seedling rootstocks [20]. Based on favorable results with the Malling rootstocks in England, clonal apple rootstocks were obtained from East Malling by Anthony in Pennsylvania in 1920 and 1922, Shaw in Massachusetts in 1922, Tukey in New York in 1928, and by the Ontario Agricultural Experiment Station before 1929 [114]. When the U.S. government prohibited the importation of plant material from Europe in 1930, Tukey and Brase, at Cornell University, propagated and disseminated Malling rootstocks and budded trees for interested nursery growers, experiment stations, and growers [114].

The earliest American rootstock trials were established in the 1920s. In 1924, three Malling rootstocks were compared to seedling and own-rooted trees in Massachusetts [115]. The evaluation of Malling rootstocks began in Pennsylvania in 1929 with ‘Stayman’ trees on six Malling stocks [116]. In 1937, rootstock material was disseminated by the New York Station at Geneva to 13 states for testing [114]. Reports on the early trials often lacked information concerning randomization and the number of trees per rootstock.

Based on early comparisons, the primary advantage of clonal rootstocks was improved uniformity, but dwarfing rootstocks were not considered superior to seedlings [116]. From the early 1920s to the 1940s, pomologists vegetatively propagated cherry and apple cultivars and their seedlings [117,118]. Trials in several states compared apple trees budded to Malling rootstocks, clonal rootstocks from the USDA program, and seedlings of commercial cultivars. Some trials included non-budded trees of self-rooted commercial cultivars as another source of clonal material. In general, trees on clonal rootstocks from the USDA program, which were not selected for dwarfism, had a similar size and productivity as trees on seedling rootstocks, and based on CVs and standard deviations, yield and trunk circumference of clonal rootstocks were less variable [115,119]. The purpose of some of these early trials was to screen large numbers of rootstocks, often with more than one cultivar to determine which had the potential for further testing; means ± SE for trunk circumference and yield were often reported [119,120,121]. These trials were not described in detail, but the number of trees per cultivar/rootstock combination varied greatly, and there was no mention of randomization or replication [120,121,122].

One of the first designed rootstock trials was established in 1940 to compare three apple cultivars on eight rootstocks [123]. There were 10 blocks of three rows and each cultivar was assigned randomly to a row within each block. Pairs of two trees per rootstock were randomly assigned to a location in each row. Although the experimental design was not mentioned, it was apparently a SPD with 10 blocks of 2-tree plots, where cultivar was the whole plot and rootstock was the sub-plot.

Although statistics courses were taught at some universities as early as 1915 [124], the first statistics department in the U.S. was established at Iowa State University in 1947, so until the 1950s, most pomologists had little formal statistical training [125]. During the 1930s and 40s, some pomologists began using experimental designs and data analyses recently developed in England [115,117,122]. In the 1950s, as pomologists hired after World War I retired, many new pomologists were hired in North America. During the quarter century following World War II, higher education in the U.S. expanded rapidly, as did the field of statistics [125]. At about the same time, many Colleges of Agriculture hired consulting statisticians to teach and to work with researchers [126]. Sometimes, consulting statisticians coauthored research papers with pomologists [13,33,127]. From the 1950s until the mid-1970s, pomologists usually reported randomization schemes and the number of replications and sometimes named the experimental design, but methods for data analysis were often not reported [128,129]. Data were usually reported as means followed by letters from a multiple comparison. The LSD [128,129,130,131,132] was commonly used until the 1960s when some researchers used Tukey’s HSD [132,133,134,135] or Duncan’s multiple range test [136,137,138].

Until the 1960s, most commercial apple trees were propagated on ‘Delicious’ seedlings from Western processing plants or on several semi-dwarfing rootstocks, primarily MM.111, MM.106, and M.7 [139]. The International Fruit Tree Association (IFTA), formerly the International Dwarf Fruit Tree Association, was founded in 1958 and sponsored annual meetings to keep fruit growers informed on the latest research information [140]. In addition to research reports, conference programs included orchard tours and presentations by progressive growers. Members of IFTA were very interested in dwarf rootstocks and intensive planting systems. Pomologists in many states were evaluating apple rootstocks, but results from different states were difficult to compare due to differences in sources of trees, nursery tree quality, scion cultivars, experimental designs, numbers of replications, tree spacing, methods of data collection and analysis, management practices, soils, and climate [141]. In 1976, a group of pomologists from the midwestern states organized and established the North Central Project 140 (NC-140) [142]. The first multi-state rootstock trial was planted in 1976 with ‘Delicious’ and ‘Empire’ budded to M.9 inter-stems on three vigorous rootstocks [142]. The second trial was established in 1980–1981 with ‘Delicious’ at 26 locations on nine rootstocks ranging in vigor from seedling to M.27 [143] and a third trial with ‘Delicious’ on 19 rootstocks at 27 locations in the U.S., 4 in Canada and 1 in Mexico was planted in 1984 [143]. Also in 1984, the first multi-location peach trial was planted with ‘Redhaven’ on 9 rootstocks at 16 locations [144]. By the early 2000s, the NC-140 had established more than 30 trials, most with 15 to 24 cooperators in the U.S., Canada, and Mexico, involving apple, peach, plum, pear, and sweet and sour cherry [142]. All trials were replicated RCBDs with 8 to 10 single-tree replicates at each location. Based on discussions with charter members, the choice of experimental design and replication was based on past experiences. For most of the trials, initial tree size based on TCSA was considered a blocking factor along with location in the field, so the two factors were confounded.

By the early 2000s, additional experimental designs were used. One trial involved six-tree plots of eight apple rootstocks in four blocks at six locations [145]. For the 2003 trial, two trees were randomly assigned to each of the four blocks in a generalized randomized block design to avoid open cells and to allow TCSA to be used as a covariate [54]. The primary purpose of these trials was to determine tree survival and to classify rootstock vigor, for which the single-tree reps worked well. There was an apple tree training/orchard systems trial with four five-tree plots and data were collected from the middle three trees [146]. For new trials, recently planted or that will be planted soon, the objective has changed to evaluate the potential of new rootstocks at close spacings. Based on discussions with NC-140 members, these trials have four or five replicates of five-tree plots in a replicated RCBD. Unfortunately, in some cases, the rootstock vigor was greater than expected and was not suited for the close spacing. A new approach involving two phases is being considered. A preliminary trial with only four or five single-tree replicates lasting about five years will evaluate rootstock vigor and early yield. Promising rootstocks with appropriate vigor will then be evaluated for 8 to 10 years with four replicates of five-tree plots.

3.5. Factorial Experiments

Factorial experiments were used to evaluate rootstocks at different spacings [147], with different crop loads [148], with different cultivars [149,150,151] at different locations [141,143,144,145]. Two approaches were used to evaluate the performance of different cultivars on various rootstocks. In most cases, the experimental site was divided into blocks and cultivars were randomly assigned to plots in the blocks; the plots were divided into sub-plots and rootstocks were randomly assigned to locations within each sub-plot. Data were analyzed as an SPD to evaluate the main effects and rootstock × cultivar interaction [151,152,153]. Sometimes, cultivars were considered separate experiments and data were analyzed by cultivars [151] or location [153] as RCBDs.

Schneider et al. [147] used a split-split-plot design, with two-tree plots to study the effects of apple rootstocks, tree spacing, and cultivar on tree size and yield. Data analyses were not described. The significance of the rootstock × scion interaction, but not the rootstock × spacing, scion × spacing, or rootstock × scion × spacing, were included in tables. Regardless of the significance of the interaction, marginal means were compared with Duncan’s multiple range test, and cell means were not reported.

4. Analysis of Fruit and Tree Measurements

Although there are exceptions, rootstock researchers typically record tree mortality, TCSA, tree height, and spread, number of fruit harvested/tree, and yield (kg fruit/tree). These data can be used to estimate several additional variables, including mean fruit weight (FW = yield/number of fruit), crop density (CD = number of fruit/cm² TCSA), yield efficiency (YE = yield/cm² TCSA), and biennial bearing index (BBI). Rootsuckers and burrknots are often counted either annually or periodically during the study. Sometimes, various aspects of fruit quality are recorded, such as red surface color, flesh firmness, starch index, titratable acidity, internal ethylene concentration, and soluble solids concentration. Occasionally, fruit size is sorted by commercial grades. Some researchers also report concentrations of inorganic elements from leaf tissue analysis [46]. Below is a critical evaluation of how these variables are measured and how the resulting data are typically analyzed, along with suggestions for future rootstock trials.

4.1. Field Measurements

Tree Survival

Tree survival is one of the most important rootstock characteristics and tree survival is usually recorded annually. Sometimes, tree survival was not reported [41,151,152,153,154,155], but tree survival was often reported after 5 or 10 years or when the trial was terminated [143,144,145,146]. Although tree survival has a major economic impact in commercial orchards, tree survival is often not considered when reporting other response variables. Some reports clearly explain that average cumulative yield was based on the trees surviving until the study was terminated or it was based on the number of planted trees [141,143,144,145,146], but yield was usually based on data from only trees surviving until the end of the trial [141,143,144,145,146], obscuring the impact of tree loss on cumulative yield per ha.

Trees that die in the early years have a greater negative economic impact than trees that die later. To account for tree mortality in a 10-year multi-location apple rootstock trial, tree survival after 10 years, the average life span of the trees, and cumulative yield per surviving tree, along with cumulative yield per planted tree, were reported [55]. Therefore, if a tree produced fruit in years 3 and 4 of the study before dying, the cumulative yield for that tree was based on data for years 3 and 4, and zero yield was recorded for the remainder of the trial. Accounting for tree longevity drastically influenced the results. Data for ‘Golden Delicious’ trees on 11 rootstocks growing at two locations are presented in

Table 1. Cumulative yield data for ‘Golden Delicious’ trees on 11 rootstocks at IA and KY after 10 years. Data are for yield per tree surviving after 10 years and yield per planted tree.

	Iowa				Kentucky
Rootstock	Survival at 10 Yrs.	Cum. Yld. (kg/Surviving Tree)	Avg. Life Span (Yrs)	Cum. Yld. (kg/Tree Planted)	Survival at 10 Yrs.	Cum. Yld. (kg/Surviving Tree)	Avg. Life Span (Yrs)	Cum. Yld. (kg/Tree Planted)
B.9	100	74 ab z	10	74 ab	50 b	87 a	6.9 a	43 a
G.41	100	133 b	10	133 b	88 a	307 bcd	9.0 b	266 c
G.16	100	119 b	10	119 b	50 b	298 bcd	6.0 a	150 b
M.9 T337	100	115 b	10	115 b	75 a	295 bc	8.8 b	243 c
B.10	100	107 b	10	107 b	100 a	310 bcd	10.0 b	310 cd
G.935	100	149 b	10	149 b	25 c	296 bc	5.4 a	133 b
M.9 pajam 2	100	117 b	10	117 b	88 a	347 d	9.5 b	310 d
J-TE-H	100	123 b	10	123 b	100 a	333 cd	10.0 b	333 d
M.26	100	117 b	10	117 b	75 a	287 b	8.6 b	228 c
PiAu 51-4	100	94 ab	10	94 ab	100 a	441 e	10.0 b	440 e
PiAu 56-83	100	61 a	10	61 a	100 a	425 e	10.0 b	425 e

^z Least squares means within columns were compared within a location with the slicediff option of SAS’s GLIMMIX Procedure, where values within columns followed by common letters do not differ at the 5% level of significance.

. After 10 years, all trees survived in Iowa, but in Kentucky, tree survival ranged from 25% for G.935 to 100% for trees on B.10, J-TE-H, PiAu 51-4, and PiAU 56-83. For Iowa, the cumulative yield per surviving tree was the same as the cumulative yield per planted tree, where the highest yields were for trees on G.935, G.41, and J-TE-H, whereas trees on B.9, PiAu 51-4, and PiAu 56-83 had the lowest yields. In Kentucky, the cumulative yield was influenced by tree longevity. When the cumulative yield for the surviving tree was ranked from high to low, G.935 ranked eighth with 296kg/tree and did not differ statistically from M.9 T337 with 295 kg/tree. However, the average lifespan of trees on G.935 was 5.4 years and it was 8.8 years for trees on M.9 T337. When cumulative yield per planted tree was considered, trees on G.935 ranked 10th with 133 kg/planted tree, which was significantly lower than trees on M.9 T337 with 243 kg/planted tree.

Rootstock trials often continue for 10 or more years, and tree mortality due to biotic or abiotic factors is common. Causes of tree mortality were rarely reported but are important for making commercial recommendations. Some researchers recently reported the causes of tree death. For peach trees, tree mortality was related to bacterial canker (Pseudomonas syringae) [156], calcareous soil [157] water logging [158], and wind damage [156], and calcareous soil [159] and for unknown causes. For apple trees, the most common reasons for tree mortality were graft union breakage and fireblight [160,161,162,163,164] Determining the cause of tree death is often difficult but should be reported when possible. Growers can adopt practices that may minimize some causes of tree death, such as enhanced tree support to prevent graft union breakage or soil drainage to prevent water logging.

The number of trees that died during the trial was sometimes reported [106]. For some trials, such as NC-140 multi-location rootstock trials, tree survival was reported as 1 = live and 0 = dead; data were analyzed by ANOVA and reported as percentages. Although ANOVA is quite robust for non-normal data, tree survival data are binomial and the probability of incorrectly rejecting the null hypothesis (all rootstocks are equal) may increase. Until the advent of GLMM software, a binomial distribution for tree survival in block designs could not be properly analyzed. However, data with a binomial distribution from block designs can now be analyzed by ANOVA with GLMM software [79].

Survival data were sometimes analyzed for each year of a rootstock trial, ignoring the correlations between years. GLMMs can be used to perform a repeated measures analysis while requesting a binomial distribution [79]. Logistic regression offers another approach that provides useful information and can be used to estimate the probability of a tree surviving at different times. When tart cherry trees were planted in 1998, 100% of trees on Edabriz and Gi.5 survived until the trial was terminated in 2006. However, for trees on W.53, the probability of survival was only 85% in 2000, and survival declined curvilinearly until 2006 when the probability of survival was only 20% (Figure 1).

4.2. Tree Size: Most Researchers Record Tree Height and Spread Each Year

Data for these variables are typically reported after 5 or 10 years or at the termination of the trial. Tree size for a given species can be influenced by many factors including scion/rootstock combination, soil conditions, climate, water availability, and orchard management. Both tree height and spread may be greatly influenced by pruning to maintain trees in their allotted space. These variables are good indicators of tree vigor until trees attain the desired height and have filled their space. Thereafter, canopy size is controlled with pruning and the rootstock effect may be misleading. To avoid violating the assumption of independence, when canopy size is recorded annually, it should be analyzed with repeated measures rather than analyzing data by year. Since TCSA, tree height, and tree spread are not independent, a multivariate approach (MANOVA) may be preferable to analyzing each variable separately. Pászti et al. [166] used a MANOVA to analyze the three non-independent variables of canopy diameter, tree height, and tree volume. LMM software is preferable to GLM software for MANOVA because random factors are treated appropriately and can use observations with incomplete responses [167].

4.3. Trunk Cross-Sectional Area (TCSA)

TCSA was often reported after 5 or 10 years or when the trial was terminated [106]. TCSA is probably a better indication of tree vigor than canopy size because it is less influenced by pruning, but it can be influenced by cropping [148,168]. TCSA is easily calculated from trunk diameter or circumference measurements. Westward and Roberts [169] found a linear relationship between TCSA and the above-ground fresh weight of several apple cultivars growing on various rootstocks and the correlation coefficients ranged from 0.960 to 0.997. This relationship was confirmed by Strong and Azarenko [170] with 10-year-old ‘Delicious’ trees on rootstocks providing a wide range of tree vigor. There was a strong linear relationship between TCSA and the fresh weight of the above-ground portion of the tree (R² = 0.95). Treatment variances from rootstock trials are often unequal for TCSA. Data should be transformed to stabilize the variances [171] or data should be analyzed with LMM or GLMM software that can fit unequal variance models.

4.3.1. Accounting for Initial Tree Size

Trunk growth may be related to initial trunk size. Therefore, in addition to reporting TCSA, some researchers reported an increase in TCSA [159]. Vivyan [172,173] studied the influence of rootstock on the growth of young apple trees by measuring the fresh and dry weights of the trees. Since there was a linear relationship between initial fresh weight and fresh weight at harvest, initial fresh weight was used as a covariate in an ANCOVA to adjust the values for the initial fresh weight as suggested by Pearce [174]. ANCOVA greatly reduced the standard errors but often changed the mean values little.

Data for New York in the NC-140 2003 dwarf apple rootstock trial were used to compare three methods of reporting TCSA for 11 rootstocks after five seasons of growth (

Table 2. Trunk cross-sectional area (cm²) of ‘Golden Delicious’ apple trees as influenced by 11 rootstocks in New York after five growing seasons. Trees were planted in spring 2003 and TCSA was measured in fall 2003 and fall 2008.

Stock	TCSA 2003	TCSA 2008	Increase 2003–2008	ANCOVA
P I 514	4.19 a z	56.32 a	52.1 a	48.6 a y
P I 5683	3.45 ab	52.53 a	49.1 a	48.4 a
J THE	3.08 bc	29.20 b	26.1 b	26.8 b
B. 62396	2.74 bcd	26.9 bc	19.9 b	21.9 b
G.935	2.56 cde	21.48 bc	18.9 b	21.6 b
G.16	2.61 cde	19.49 bcd	16.8 bc	18.9 b
M.9 P2	2.88 bcd	25.69 bc	22.8 b	24.3 b
g.41	2.22 de	18.60 cd	16.4 bc	20.3 b
M.26	1.84 ef	23.61 bc	21.8 b	27.2 b
T337	1.84 ef	18.77 cd	16.9 bc	22.3 b
B.9	1.10 f	11.0 d	9.9 c	18.1 b
p-values from ANCOVA
Rootstock	0.0001	0.0001	0.0001	0.0001
Covariate	- - -	- - -	- - -	0.0015
Rootstock × covariate	- - -	- - -	- - -	0.8564

^z Data were analyzed by ANOVA and values followed by common letters do not differ at the 5% level of significance, by Tukey’s HSD. ^y Data were analyzed by analysis of covariance, where TCSA in fall 2003 was the covariate. Values are means adjusted for the covariate.

). Initial TCSA was not recorded, but after the first season (fall 2003), TCSA ranged from 1.1 cm² for B.9 to 4.19 cm² for PiAu 5-14. At that time, rootstocks differed at the 0.0001 level of significance, and Tukey’s test divided the rootstocks into six groups. After five years (fall 2008), TCSA ranged from 11.0 cm² for B.9 to 56.3 cm² for PiAu 5-14. The ANOVA for 2008 had a p-value for rootstock of 0.0001 and there were four groups. Trees with the greatest TCSA in 2003 tended to increase the most over the five-year period, and the five-year increase in TCSA ranged from 9.9 cm² for B.9 to 52.1 cm² for PiAu 5-14. When the increase in TCSA from 2003 to 2008 was analyzed by ANOVA, the p-value was 0.0001 and Tukey’s test divided rootstocks into three groups. When TCSA in 2003 was included in the model as a covariate, p-values from ANCOVA were 0.0001 for rootstock, 0.0015 for the covariate (TCSA in 2003), and 0.856 for the rootstock × covariate interaction. The TCSA in 2008, adjusted for TCSA in 2003, was 18.1 cm² for B.9 and 48.6 cm² for PiAu 5-14, and based on Tukey’s test, there were only two groups of rootstocks. ANCOVA adjusted the values down for the more vigorous rootstocks and it adjusted the values up for the less vigorous rootstocks. Although analyzing TCSA with an ANOVA may seem preferable because the rootstocks were separated into more categories, the differences in 2008 were due to initial differences rather than the increase in TCSA after planting. Variation in TCSA at planting may be due to different rootstock vigor, but not always. Due to inadequate numbers of trees for some rootstocks, researchers may be forced to include trees that are smaller than desired. This is especially true for multilocation trials where more than 400 trees per rootstock are needed. The nonsignificant rootstock × covariate interaction indicates that the slopes between initial and final measurements were similar and a normal ANCOVA was appropriate. If the rootstock × covariate interaction had been significant, then rootstock means adjusted for a minimum of three levels of the covariate would be the appropriate approach. Using initial trunk size as a covariate to adjust means is preferable to analyzing the increase in trunk size because the rootstock × covariate interaction can be tested [173].

The early NC-140 trials used RCBDs, where the experimental site was divided into blocks, and trees were also assigned to blocks based on initial TCSA, so the largest trees for each rootstock were assigned to the first block, and the smallest tree for each rootstock was assigned to the last block [143,144,145,156,161,162,163,164,165]. Therefore, TCSA was confounded in the block and could not be used as a covariate. In future rootstock trials, initial tree size should not be considered as a blocking factor, but initial tree size should be used as a covariate. There are two advantages to using initial tree size as a covariate. (1) An assumption for blocked experiments is that rootstock will have the same effect in every block, so there is no interaction between rootstock and block. But, the assumption may not always be valid [174] and when trees are blocked on initial size, the assumption cannot be tested. (2) More degrees of freedom are lost for blocked designs. For a trial with 10 blocks where trees are blocked on initial size, the penalty is 10 − 1 = 9 degrees of freedom, but the penalty for a covariate is only 1 degree of freedom for the linear effect of the covariate.

4.3.2. Accounting for Cropping

Rootstocks influenced both trunk growth and cropping [161,175,176,177], but most rootstock trials were not designed to account for cropping while evaluating the influence of rootstock on trunk growth. The NC-140 2003 multilocation trial was designed to study the individual and combined effects of rootstock, CD (number of fruit/cm² TCSA), and locations over five consecutive years on tree growth and cropping of ‘Golden Delicious’ apple trees [175]. Each year, trial cooperators at 11 locations hand-thinned two trees on each of three dwarfing rootstocks to target CDs of 3, 5, 8, 11, or 14 fruit per cm² TCSA. In 42 of the 55 location-year combinations, rootstock influenced trunk growth after adjusting the means for CD with ANCOVA. The influence of rootstock and CD on trunk growth was usually additive because the interaction was significant in only five situations. Because rootstocks often influence CD and YE, which suppress trunk growth, rootstock researchers should consider using ANCOVA to adjust TCSA for CD or YE.

4.3.3. Accounting for Correlated Errors

TCSA was sometimes reported for each year of the trial [43,159] and sometimes, ANOVAs were performed by year [43,104,130,131]. Because the assumption of independent errors is usually violated when data collected annually are analyzed by year, a repeated measures approach should be considered. To take advantage of all the replication in the trial, a GLMM approach could be used to compare means within each year without physically slicing the data [14].

4.3.4. Yield and Fruit Weight

Yield is one of the most important characteristics of a rootstock. Although annual yield or cumulative annual yields were sometimes reported [154,159], mean cumulative yields were usually reported for the first several years and at the end of the trial [141,145,161,162,163,164,165]. Yield was usually determined by weighing all the fruit on a tree. However, yield was sometimes estimated by counting the number of fruits per tree during the growing season and multiplying the number of fruits counted by the average weight of a sample of fruit obtained at harvest (B.H. Barritt, personal communication). This method of estimating yield may not be very accurate because it is difficult to accurately count fruit on a tree [178] and also requires an accurate estimate of the average FW, which requires sampling about 25% of the fruit on a tree [179,180,181,182].

FW was usually calculated by dividing the total weight of the crop by the number of fruits per tree [141,145,161,162,163,164,165] or estimated from samples collected from each EU [42,146,150]. For large trees or multiple-tree plots, counting all the fruits may be costly and some researchers have inadequate labor to count all fruits for every EU. Estimating FW from subsamples is an alternative, but it is probably impossible to obtain fruit samples that are truly random. Two factors must be considered for accurate FW estimates from a sample. First, possible variation in FW associated with canopy position must be accounted for, and secondly, the sample size must be adequate to accurately represent the population of fruits on the tree. Pearce [180] evaluated several sampling schemes to estimate apple FW. To account for the canopy position, he used trees with 3 to 6 bushels per tree (50 to 100 kg/tree). He sampled equal numbers of fruit from the top layer of fruit in every third box to obtain about 14 kg of fruit per tree. This method tended to over-estimate the true FW because large fruit contributed more than small fruit and all fruit from a layer in the box were obtained from the same part of the canopy. Sampling vertically in the box was better. To determine sample size, he used trees from two plantings with average yields of 67 and 100 kg, respectively. In the first case, a sample of 10% of the crop had an error of 6.4% and a sample consisting of 20% of the crop had an error of 5.1%. In the second case, a sample representing 7% of the crop had an error of 9.0% and a sample representing 15% of the crop had an error of 5.3%. He concluded that although a sample size of less than 20% of the crop does not accurately estimate the average FW, it is probably adequate for identifying treatment differences. Dorsey and McMunn [182] found that a sample representing about 25% of the crop provided estimates of mean FW within about 10% of the true mean for large trees with yields of about 91.0 kg/tree. For trials with multiple-tree plots, sampling about 25% of the fruit from every two or three boxes of fruit may provide an adequate estimate of mean FW.

Many rootstock trials use single-tree plots and trees are small with an average yield of less than 20 kg. Marini [179] used semi-dwarf trees with about 400 fruits per tree to compare two sampling methods to estimate the average FW. A random sample of fruit representing about 5% of the crop provided an estimate that differed from the true mean by about 13%, and sampling 17% of the crop obtained by harvesting all fruits on three limbs per tree provided estimates differing from the true mean by 11% to 19%. In another report, dwarf trees with about 100 fruit per tree were used to evaluate sampling methods to estimate average FW and fruit size distribution [180]. Counting and weighing all fruit from a vertical wedge from a tree representing about 25% of the canopy provided estimates of average FW within 7% of the true mean and the distribution of fruit size did not statistically differ from the distribution for the whole tree.

4.3.5. Yield Efficiency and Crop Density

YE and CD are widely used to quantify the amount of photosynthate partitioned to fruit vs. wood for individual trees. These variables seem appropriate for trials involving trees planted at wide spacings. In general, dwarfing rootstocks tend to have higher YE than more vigorous rootstocks for apple [141,143,146], but not necessarily for sour cherry [165] or peach [183].

Canopy volume increases annually until trees fill their space when it is maintained by pruning, but TCSA continues to increase as trees age [161,162,163,164]. Therefore, annual YE will only increase as long as tree volume increases. Barden and Marini [184] compared eight rootstocks, where the experimental unit was three-tree plots and tree spacing varied depending on the anticipated rootstock vigor. Over the 18-year experimental period, TCSA increased linearly, but the estimated cumulative yield/ha increased curvilinearly. YE provides information about photosynthate partitioning, but for rootstock trials where trees are intentionally planted close enough to fill their space, yield/ha may be a more important expression of efficiency, as reported by Reig et al. [185].

The concept of harvest index (weight of economic product/above-ground plant dry weight) is used in field crop research. Pruning time and weight of wood removed by pruning increased linearly with increasing TCSA and slopes for two strains of two cultivars were similar [184]. Averaged over rootstocks, the ratio of cumulative crop to scion weight (weight of prunings plus above-ground tree) varied from 9.1 to 11.1, depending on cultivar/strain, and was nearly twice as great for dwarfing than vigorous rootstocks. The cumulative yield increased at a decreasing rate as scion weight increased and as TCSA increased. DeJong et al. [186] compared two peach cultivars on six rootstocks in two training systems and reported the calculated mean modified harvest increments (kg fruit dry weight/kg pruning weight) for four consecutive years. The relative efficiency varied depending on the combination of cultivar, rootstock, training system, and year, but trees on the size-controlling rootstocks were more efficient in portioning dry matter to crop than trees on the vigorous Nemaguard rootstock. Barden and Marini [187] suggested that tree weights should be recorded when rootstock trials are terminated to calculate the harvest index.

4.3.6. Root Suckers and Burrknots

Root suckers are shoots arising from the rootstock shank and roots. These shoots are undesirable because they may interfere with weed management, they can absorb translocatable herbicides, and they can be infected by fireblight in apples (Erwinia amylovora Burrill), leading to the death of the root system [188]. Suckering was also negatively related to the growth and yield of apple interstem trees [189,190]. The physiology of sucker initiation is poorly understood [191], but in most rootstock trials, the number of rootsuckers per tree was positively related to rootstock vigor for apples [162,163], but not for peaches [167].

Burrknots are areas of partially developed adventitious root initials originating in apple tree stem tissue [192]. Burrknots form on the above-ground portion of many apple rootstocks, and on some scion cultivars, such as ‘Gala’ and ‘Empire’. Burrknots are undesirable because they can interfere with vascular transport and stunt the tree [193]. Burrknots may also be sites for oviposition of dogwood borer (Synthanthedon scitula Harris), feeding by ambrosia beetle (Xylosandrus germanus Blandford), and fire blight infection. Rootstocks vary in their propensity to produce root suckers and burrknots, but the severity of both characteristics depends on the location and some locations are more prone to root sucker production for both peach and apple [187,194,195]. Both characteristics are not always reported [131,157]. Until the factors that induce burrknots and root suckers are better understood, rootstocks should be evaluated for these disorders where these characteristics have been problematic.

In one trial, the number of burrknots in three size categories was recorded for each apple tree [194]. Additionally, the total number of burrknots per tree and the burrknot density (burrknots/cm² TCSA) were reported [195]. The rootstock variances were not equal, and data were analyzed separately for each size category by ANOVA with an unequal variance model. However, since the three size categories are not independent, in the future, such data would be better analyzed with a multivariate ANOVA (MANOVA) [195].

4.3.7. Biennial Bearing

Biennial bearing is exhibited as an alternate cropping pattern, where a heavy crop one year inhibits blossom initiation, resulting in a few blossoms the following year. Biennial bearing is usually expressed as the biennial bearing index (BBI) using the method of Hoblyn [196] and Jonkers [197], $\mathrm{b}\mathrm{i}\mathrm{e}\mathrm{n}\mathrm{n}\mathrm{i}\mathrm{a}\mathrm{l} \mathrm{b}\mathrm{e}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{i}\mathrm{n}\mathrm{d}\mathrm{e}\mathrm{x}\left(\mathrm{B}\mathrm{B}\mathrm{I}\right)={\displaystyle \frac{\sum (\frac{\mathrm{a}}{\mathrm{b}})}{\mathrm{c}}}$, where a is the difference in yield per tree between two consecutive years, b is the sum of the yield per tree in the two consecutive years, and c is the number of consecutive year pairs. In some trials, rootstocks influenced BBI [188,198,199]. In a multi-location apple rootstock trial, Cline et al. [164] reported that rootstocks influenced the BBI at three of seven locations. Assessing the influence of rootstock on BBI is complicated by crop load and environmental factors, especially spring frost. A multi-location rootstock trial was designed to evaluate the individual and interactive effects of rootstock and CD on FW, BBI, and trunk growth [200]. There were 17 combinations of year and location, and flower density (flower cluster/cm² TCSA) was negatively related to the previous season’s CD in a linear manner 43% of the time, whereas rootstock significantly affected flower density 32% of the time [200]. The interaction of the previous season’s CD × rootstock was never significant, so for ‘Golden Delicious’, the two factors affected flower density independently. Rootstock sometimes influenced flower density in seasons following both low and high crop density, but the level of flower density was not consistently associated with any rootstock [200]. To truly assess the influence of rootstock on BBI, experiments should be designed to minimize differences in CD.

4.4. Evaluating Fruit Maturity and Quality

The peach bloom date, fruit maturity, and fruit quality were often affected by rootstock [201,202,203,204]. The effect of rootstock on apple fruit maturity and quality was more variable [205,206,207,208,209,210,211]. One of the challenges associated with studying the influence of rootstock on various aspects of fruit quality is that there is often a year × rootstock interaction [44,212]. Multi-location trials are more complicated because there may be a three-way interaction of location × year × rootstock. Therefore, at least two years of data are needed to assess rootstock effects on fruit quality [205,211]. Fruit quality can also be influenced by CD [212]. Although some authors acknowledged that differences in indices of fruit quality may have been influenced by the differences in CD [159], only a few attempted to adjust the means by including yield, CD, YE, or number of fruits per tree as covariates in the linear model [213,214,215,216] he assumption for ANCOVA, namely that the rootstock × covariate interaction is not significant, was usually not tested [163,205,213]. However, when tested, the rootstock × CD interaction was usually significant [175,177,178]. Therefore, adjusting the means with a normal ANCOVA was not appropriate [68]. To properly account for the influence of CD on FW, where there is a significant rootstock × CD interaction, the average FW for a rootstock should be compared at a minimum of three values of the covariate. A strategy for determining the covariate part of an ANCOVA model for designed experiments was previously explained [217] and used to analyze subsequent rootstock trials [218].

4.5. Duration of the Trial

The optimum duration of rootstock trials depends on the tree species and the characteristics being studied. For most rootstock trials, a primary objective is to classify tree vigor, by measuring various aspects of vigor, such as TCSA, and canopy height and spread, which are easily measured. Rootstock trials comparing vigorous with non-vigorous apple rootstocks were often continued for more than 15 years because vigorous rootstocks are relatively nonprecious [90,184]. More recently, only dwarfing apple rootstocks were compared, and most trials were terminated after no more than 10 years. Carlson and Tukey [128] plotted the trunk circumference for six apple cultivars on eight rootstocks against year for seven years, and rootstocks started separating after four to seven years depending on the cultivar. Data from two multilocation rootstock trials were used to estimate the number of years required to determine the size class of a rootstock [219]. TCSA was affected by the three-way interaction of location × rootstock × year, so a repeated measures analysis was performed by location, and rootstocks were compared within each year. Depending on the trial and location, vigorous rootstocks (PiAu 56-83) could be distinguished from low-vigor rootstocks (M.9) after just four years. Detecting statistical differences between rootstocks representing the extremes within the dwarf class, such as M.26 vs. M.9 NAKBT337, required six or seven years at most locations. Rootstocks with similar vigor, such as M.9 NAKBT337, G.935, and G.16, were not significantly different after 10 years [211].

Although the vigor classification of apple rootstocks may require only seven years, other rootstock characteristics may require longer to evaluate [220]. In two 18-year apple trials, the relative ranking for tree survival changed little during the first five years, but trees on some rootstocks continued to die after 14 years [184,211]. Sometimes, tree loss may be due to fireblight or an extreme weather event, such as wind, that may occur in the later years of a trial [54,159]. For a trial involving three apple cultivars on two Malling rootstocks, tree loss was 7 to 21% after 10 years, but following two cold winters, an additional 0 to 26% of the trees were dead after 12 years [128].

For most trials, the relative ranking of rootstocks for the number of rootsuckers per tree changed little after 5 years [184,219]. Although rootstock ranking may change slightly after five years, rootstocks with a tendency to produce root suckers can usually be identified after just five years [132,163,177].

The relative ranking of rootstocks for cumulative yield per ha changed little from the 10th to the 18th year [128,211] and for an eight-year trial, the relative ranking of cumulative YE (kg/TCSA) changed little from the fifth to the eighth year [128,211].

Early results for NC-140 multi-location rootstock trials are usually published after 5 years and final results are published when the trial is terminated, usually after 10 years for apples [161,162,214] and after 6 to 9 years for peaches [144,155,183]. After coordinating several multilocation peach rootstock trials, Reighard et al. [156] concluded that in terms of productivity, the relative ranking of rootstocks changed little after three years of bearing if trees survived. However, in areas where trees may succumb to biotic and abiotic factors, trials should be continued for about 10 years to evaluate rootstock susceptibility to those factors [156].

Rootstock trials are expensive to establish and maintain. In the mid-1990s, members of the NC-140 project estimated that a 10-year multilocation trial cost about USD 1 million (about USD 2 million in 2024). Therefore, it is undesirable to maintain a trial longer than necessary to accurately evaluate rootstock performance. Although some rootstock characteristics can be evaluated in 5 to 7 years, tree survival probably requires at least 10 years.

5. Designing Future Rootstock Trials

5.1. Choice of Experimental Design: CRD vs. RCBD

Most rootstock trials are RCBDs, but blocking is beneficial only when the variation between blocks is greater than within blocks [47]. Rows of trees are often used as blocks, but soil, topography, or treatments from previous experiments may vary down a row, increasing within-row variation. Detailed knowledge of variation across an experimental site is required to appropriately divide a site into uniform blocks. Within-block variation typically increases as the number of rootstocks and the size of blocks increase. Using rows as blocks may facilitate orchard operations and data collection but may not reduce experimental error. Four possible scenarios are presented in Figure 2 for an RCBD to evaluate four apple rootstocks. Scenario 1 uses rows as blocks. Such an arrangement assumes that the site varies across rows rather than down the rows. In scenario 2, blocks run across the rows and assume that the site varies down the rows rather than across the rows. Scenario 3 assumes that the outside rows are uniform and that the two ends of the middle rows differ from each other. Scenario 4 assumes that the yellow row is uniform, and sections of the site, in green and gray, are uniform. Blocks need not be contiguous, and the two sections of the red blocks are assumed to be similar.

Data from four sites in the multilocation NC-140 1990 ‘Gala’ rootstock trial [97] were used to obtain information that would be useful while designing future rootstock trials. Data for trunk cross-sectional area (TCA) after 10 years and cumulative yield per tree and cumulative YE for the final two years of a 10-year dwarf apple rootstock experiment were obtained for each tree at four locations. The experiment was a replicated randomized complete block design with eight rootstocks, four locations, and four blocks per location, and the EUs were plots of four trees/rootstock/block (samples).

To assess the precision of an RCBD compared to a CRD for each location, the Estimated Relative Efficiency (ERE) was calculated as described by Hinkelmann and Kempthorne [53]. The ERE is often expressed as a percentage. Any value greater than 1.0 or 100% indicates that the RCBD is more efficient than a CRD. The value of ERE may be interpreted as the ratio of treatment replications needed for the two designs to give equal variances of treatment means. For example, if the value of ERE is 2.0, the CRD would require twice as many replications to achieve the same variance of a rootstock mean as the RCBD.

Based on the variance components, the percentage of total variation attributable to the block was less than 12% for all three response variables. Rootstock accounted for >50% of the variance at most sites and tree (block × rootstock) was the second most important source of variation (10 to 43% depending on site and response variable). For TCA, the EREs were 1.2, 1.1, 1.1, and 1.2, respectively, for Michigan, New York, Ontario, and Virginia. According to Hinkelmann and Kempthorne [53], ERE addresses only the question of estimation (precision of the estimate) and not the question of power (sensitivity of the experiment). For this reason, they suggest considering an RCBD with an ERE larger than 1.25 to be better than the comparable CRD. Thus, the RCBD was no better than a CRD at any of the locations for TCA. For cumulative yield, the EREs were 1.6, 1.0, 1.0, and 1.1, respectively, for Michigan, New York, Ontario, and Virginia. For detecting differences in cumulative yield, blocking was beneficial in only one of four locations (Michigan). For cumulative YE, the relative efficiencies were 2.0, 1.0, 1.2, and 1.1, respectively, for Michigan, New York, Ontario, and Virginia, again indicating that blocking was beneficial in only Michigan. Therefore, using rows as blocks without detailed knowledge of site variation was usually no better than using CRDs.

5.2. Sample Size Estimates

The number of replications per rootstock, or sample size, is important. Ideally, there should be enough replications to detect meaningful treatment differences and draw accurate conclusions (power) about the rootstocks being compared, while avoiding excessive replication that increases the cost of the trial [47]. The appropriate sample size for a given experiment depends on the response variable being considered, the magnitude of the variability inherent in the data, the p-value used to test hypotheses, and the magnitude of the rootstock differences one considers important. Without data from a similar previous experiment on a similar site from which to estimate error, the choice of sample size is subjective [40,221]. Researchers generally test hypotheses at the 0.05 level, meaning that there is a 5% chance of incorrectly rejecting the null hypothesis (all rootstocks are equal).

Data from the 1990 ‘Gala’ rootstock trial [222] were used to obtain variance components to estimate the Minimum Detectable Difference (MDD) for varying numbers of blocks and numbers of trees per block (samples) [53]. The MDD is the estimated minimum detectable difference between two rootstock means that is significant at the 5% level.

Figure 3 shows curves for the MDD for the three response variables in Michigan and Ontario. Similar to graphs for CVs published by Batchelor and Reed [30], the MDD declined at a decreasing rate as the number of blocks and trees per block increased, but the improvement was small for more than six blocks or three trees per block. The MDD was similar for 10 blocks of single trees (total trees/rootstock = 10) and four blocks of three trees (total trees/rootstock = 12).

6. Multilocation Trials

Multilocation trials provide opportunities to hasten rootstock evaluations by quickly exposing new rootstocks to a wide range of soil and environmental factors. Such trials are usually replicated RCBDs with factorial structures. A significant location × rootstock interaction indicates that rootstock performance depends on the location. For most response variables, the interaction was almost always significant because there were typically more than 1000 degrees of freedom in the error term [132,135,141,143,144,146,156,162,164,165,222,223,224,225]. Below are some examples of the approaches researchers have used to analyze factorial experiments involving rootstocks, but a detailed discussion of analyzing and interpreting experiments with factorial treatment structure was recently published [226].

6.1. Factorial Structure Ignored

Statistical analyses of factorial experiments are sometimes reported in so little detail that it is not clear if data were analyzed with a 1-way ANOVA or a multi-way ANOVA, but all treatment combinations were sometimes analyzed with a 1-way ANOVA [62,134,227]. For example, for an experiment with three apple rootstocks and four types of nursery trees, the statistical analysis was not explained in enough detail to determine if the interaction was tested, but marginal means were compared with Newman–Keuls, so data were likely analyzed with a 1-way ANOVA with 12 treatment combinations [60]. Sometimes, rootstock means were averaged over another factor, such as years, then data were analyzed with a one-way ANOVA, and rootstock marginal means (main effect means) were reported [41]. For a 3-way factorial experiment with three rootstocks, three training systems, and four tree densities, the original analysis was a 3-way ANOVA. The rootstock × tree density interaction was significant, and data were reanalyzed with a 1-way ANOVA and all 36 simple effect means (sometimes called cell means or interaction means) were compared with a single LSD [228]. For an experiment with five apple cultivars on five rootstocks, the data were analyzed with a 1-way ANOVA and the 25 simple effect means were compared with a single LSD [62]. For a split-plot experiment involving pear cultivars and rootstocks, each cultivar was analyzed separately [229]. For an experiment comparing two lemon rootstocks receiving four irrigation treatments, data were originally analyzed with a two-way ANOVA, but when the interaction was significant, the data were reanalyzed as a one-way ANOVA and the eight simple effect means were compared with Duncan’s multiple range test [227]. For an experiment involving 7 cherry rootstocks and 2 cultivars, each cultivar was analyzed separately [230]. A factorial experiment involving 2 plum rootstocks on 2 soil types for 2 years was analyzed as a factorial, and the 8 cell means were compared with a Tukey’s test [231]. In another case, a split-plot experiment involving three soil treatments and two apple cultivars on B.9 rootstock was analyzed with one-way ANOVAs for each cultivar [134]. For an experiments with 11 peach rootstocks, data were collected over seven years and the rootstock × year interaction was significant, but rootstock marginal means, averaged over years, were reported [155]. For other rootstock experiments, data were analyzed by year [43,158,202].

6.2. Physical Slicing the Data

For various reasons, data from multilocation trials were often analyzed by location or year. Data for some multilocation rootstock trials were analyzed by location because variances differed by location [153]. Using LMM [57] or GLMM software [79], unequal variance models can now be used to analyze treatments with heterogeneous variances [69]. ANOVAs were performed by year to compare apple yield data for 5 training systems were but there was no indication that the year × training system was tested [232]. In some multilocation trials, locations were considered separate experiments and data were analyzed by location [149,153]. Analyzing data by location does not allow a formal test for interaction. When the location × rootstock interaction was significant, some researchers physically sliced the dataset and analyzed each location as an RCBD, and sometimes analyzed each rootstock to compare locations within each rootstock [141,143]. Before the introduction of LMM software, this approach was common, but interpreting the analyses was not straightforward, and only a portion of the information in the dataset was used for each analysis.

6.3. Slicing without Separating the Data

For a multilocation rootstock trial, an attempt was made to compare rootstocks within each location with SAS’s Proc Mixed [233], but the software does not use the correct error terms for the multiple comparison [13]. LMM software has many advantages to GLM models; it did not support a method of performing multiple comparisons within locations when interactions were significant. SAS’s SLICE option in PROC MIXED does compare levels of one factor within each level of another factor, but it uses incorrect error terms (personal discussions with Klaus Hinkelmann and Oliver Schebenberger). To utilize available replication and to account for the unbalanced number of observations, a macro program was written in SAS [13]. The macro was written to use the individual error terms and least squares means generated with SAS’s PROC MIXED to make each individual Tukey’s multiple comparisons between rootstocks within each location [13]. Fortunately, GLMM software now offers a method to correctly compare rootstock means within each location and to compare location means within each rootstock [14] and has been used to analyze recent rootstock trials [55,177,178].

6.4. Stability Analysis

The performance of some rootstocks varies with location. A rootstock is considered stable if its performance is relatively constant across different environments and soils. Breeders of agronomic crops often perform stability analyses to evaluate the genotype × environment interaction (GEI) [234]. The first stability analysis for rootstocks was performed by Olien et al. [127], using the joint regression analysis. Over the past 60 years, new stability analyses were developed to evaluate GEI using different criteria. Data from two NC-140 rootstock trials with ‘Gala’ apples were used for six stability analyses [235]. Results for the two trials varied because the locations and rootstocks were not consistent. Results for the different stability tests also differed because they measured different aspects of stability. Olien et al. [127] reported that M.26 had above-average stability for cumulative YE. Marini et al. [235] found that in one trial M.26, B.9, and B.491 had above average stability for all response variables. In the other trial, M.9 NAKBT337 and B.62396 had above-average stability for TCSA and cumulative yield, and G.41 and G.935 had above-average stability for cumulative YE.

6.5. Genotype-Genotype × Environment Biplot (GGE Biplots)

Biplot methodology was developed for graphical analysis of genotype × environment data and displays the genotype main effect (G) and genotype × environment interaction (GE) of a genotype-by-environment dataset, where the environment main effects are removed, and the G main effect and GE are retained and combined [236,237].

Biplot analysis was used to graphically evaluate rootstock × location interaction for two NC-140 apple rootstock trials [238]. Examples of GGE biplot analyses are presented in Figure 4 and Figure 5 for cumulative yield data for ‘Gala’ apple trees on 18 rootstocks at 23 locations. Figure 4 is a GGE biplot showing the performance of each rootstock at each location. The vectors for both rootstocks and locations are drawn to evaluate the performance of rootstocks at specific locations and visualize specific interactions between a rootstock and location. The rootstocks B.9, P.2, M.27, B.491, Mark, and P.16 had lower than average yields at all locations because they have negative PC1 values. The yield for a rootstock at a location is better than average if the angle between its vector and the location vector is <90°, and it is near average if the angle is close to 90°. B.9 had a slightly above-average yield at NC (North Carolina), average yield at PARS (Pennsylvania Rock Springs), and slightly below-average yield at WI (Wisconsin). In this way, Figure 4 can be used to rank the rootstocks based on the yield of any location, and to rank locations on the relative yield of any rootstock.

The which-won-where polygon view of the biplot summarizes the GGE pattern of the data and allows one to identify mega-environments (Figure 5). The plot in Figure 4 was used to draw a polygon on rootstocks that are furthest from the biplot origin so that all other rootstocks are contained within the polygon. Then, perpendicular lines to each side of the polygon are drawn, starting from the biplot origin. Rootstocks located on the vertices of the polygon had the highest or lowest yield at one or more locations. The perpendicular lines are equality lines between adjacent rootstocks on the polygon, which facilitate visual comparison of the rootstocks. The equality lines divide the biplot into sectors, and the winning rootstocks (rootstocks with the highest yields) for each sector are those located on the respective vertex. In this example, most locations fall between the second and third equality lines, where trees on V.1 had the highest cumulative yield. IA (Iowa) and WI fall between the first and second equality lines, whereas M.9 Pajam 2 had the highest yield. This pattern suggests that there are two groups of locations and, based on cumulative yield, different rootstocks should be selected for each group.

In general, differences in rootstock vigor, based on TCSA, were more apparent at high-vigor locations than at low-vigor locations [238]. Therefore, for future rootstock trials, attempts should be made to include sites with a range of vigor, rather than sites with geographical diversity. For TCSA, cumulative yield, and cumulative YE, M.9 NAKBT337 was one of the most stable rootstocks and was less sensitive to location conditions than most other rootstocks. In general, M.26 and the Geneva rootstocks (G.16, G.41, and G.935) were less stable and responded to location conditions more than M.9 NAKBT337 and B.9 [239]. Coordinators of future multilocation trials should consider stability analyses and GGE biplots as methods to help interpret and summarize the influence of the environment on rootstock performance.

7. Final Suggestions

Experimental designs and statistical analyses of tree fruit experiments have improved over the past few decades. However, it is still difficult to critically evaluate the validity of the results and conclusions presented in some papers. Sometimes, the experimental design is not mentioned, EUs are not described, samples are confused with replicates, and factorial structure is ignored. Statistical analyses are often reported in too little detail to determine their appropriateness. Statistical analyses should be reported in enough detail that a reader can repeat the analyses if provided with the dataset. Variables in the model should be listed and designated as fixed or random effects. The statistical package should be specified as what was used along with the types of analyses that were performed and if data were analyzed with a GLM, LMM, or GLMM model. When designing rootstock trials, researchers should consider the variation in the experimental site. If the researcher can identify areas of the site that are relatively uniform and vary from other areas of the site, then an RCBD should reduce experimental error. Otherwise, a CRD may be more efficient. When it is possible to quantify factors that may influence the response variables, such as soil nutrient levels or initial TCSA, those factors can be used as covariates to reduce experimental error.

When analyzing data, the appropriate software and statistical models should be used to account for models with random factors, heterogeneous variances, non-normal distributions, and non-independent errors. For experiments with a factorial treatment structure, slicing without separating the data is the preferable method to dissect significant interactions.

With the establishment of new journals, keeping abreast of research within a scientific field is becoming increasingly difficult and there is little time for horticulturalists to learn about new statistical methods as they become available. After examining 139 articles published from January 2014 to January 2015 in the Journal of the American Society for Horticultural Science, Kramer et al. [76] reported that about half had statistical problems. Similar levels of statistical problems were previously published for plant science publications and other fields [239,240,241]. Since graduate training in statistics for plant science majors appears inadequate, they suggested that researchers seek opportunities to improve and update their statistical knowledge throughout their careers and engage statisticians as collaborators early when unfamiliar methods are needed to design or analyze research studies.