Developing a predictive model with data from 2018 plus 2019.

There were 20 potential regressor variables: SL, N, P, K, Ca, Mg, S, Mn, Fe, B, Cu, Al, Zn, Na, N/Ca, K/Ca, Mg/Ca, (Mg + K)/Ca, (Mg + K + N)/Ca {[(Mg + K)/Ca + (N/Ca)] − 38 (referred to as the accumulated ratio)}. Relationships among the regressor variables were evaluated graphically as scatter plots with SAS PROC GPLOT, PROC SGSCATTER, and PROC G3D. PROC CORR (Freund and Littell, 2000) was used to generate a correlation matrix to evaluate the linear relationships between the response variable (percentage of fruit with bitter pit symptoms after storage) as well as the 20 potential regressor variables The accumulated ratio was included as a variable because it is used by Washington packers to segregate fruit by storage potential (developed by Harold Ostenson; Hanson, 2012). Based on the correlation and scatter plot matrices, six variables (S, Mn, Fe, Cu, Al, and Na) were discarded as nonimportant explanatory variables. The accumulated ratio was also discarded because it correlated perfectly (r = 1.0) with the less complicated variable (N + K + Mg)/Ca.

Candidate multiple regression models to predict bitter pit were identified using four options with SAS PROC REG (FORWARD selection, BACKWARD elimination, STEPWISE selection, and MAXR maximum R-square improvement) by including the regressor variables N, P, K, Ca, Mg, B, and SL. The five ratios of cations [N/Ca, K/Ca, Mg/Ca, (K + Mg)/Ca and (N + K + Mg)/Ca] were not included because they were highly correlated (r > 0.87) (Table 2). Although these model selection methods are easily performed and usually identify good models based on the selection criteria, they rarely identify the best model (Myers, 1990) because they ignore potential collinearity problems and fail to include variables involved in interactions. A plot of Mallow’s C_p indicated that a model with five or fewer regressor variables would prevent overfitting the model. The model with all six individual elements plus SL had an R² = 0.78. The RSQUARE option was included in the model statement to generate all possible one-variable, two-variable, three-variable, and so on up to 12-variable models that included the six individual elements plus SL and five cation ratios. Criteria considered for model selection included the coefficient of determination (R²), adjusted R², Mallow’s C_p, mean square error, Akaike information criterion, Bayesian information criterion, and predicted sum of squares. A manual backward selection technique was used as a final method of developing a model. A multiple regression model was fit with all 12 predictor variables (six individual elements, SL, and five ratios). The variable with the largest P value was deleted and the reduced model was fit. This process continued until only significant variables (P < 0.05) remained. Then, the INFLUENCE option in PROC REG was included in the model statement to generate variance inflation factors, tolerance indices, eigenvalues, condition indices, and proportion of variance values to identify and delete variables that were collinear.

Table 2.The best one-, two-, three-, and four-variable multiple regression models for predicting the percentage of ‘Honeycrisp’ apples that will develop bitter pit after storage based on shoot length (SL; cm) and peel nutritional concentrations (%) sampled 3 weeks before harvest. Models were developed with the trial 1 data set (2015, 2016, and 2017; Baugher et al., 2017), with the trial 2 data set (2018 plus 2019), and with the combined data sets (2015–19). All R² values were significant (P < 0.0001). Except for phosphorus (P) and boron (B) in the data set for 2018 plus 2019, all regression coefficients were significant (P < 0.05).

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Developing a model with the pooled data set for 5 years.

Data used to develop the previously published model using data from 2015 to 2017 (Baugher et al., 2017) plus data from 2018 and 2019 were pooled (n = 178), and the same process that was previously descried was used to develop a new model. After the final model was selected, two influential observations, based on DFFITS and Cook’s D statistic, were deleted from the data set and the final model was developed using the data set with 176 observations.

Using data from nine individual trees at six orchards for 3 years, we previously identified the best two-, three- and four-variable models for predicting bitter pit (Baugher et al., 2017). This original 3-year data set (n = 161) is referred to here as trial 1. The data collected in 2018 and 2019 are referred to here as trial 2. One method of cross-validation to graphically evaluate the predictive ability of a model is determining how well the bitter pit models from trial 1 estimate bitter pit for trial 2. The OUTEST option in PROC REG was used to produce the parameter estimates for the best one-, two-, and three-variable models using data from trial 1, and PROC SCORE was used to calculate the estimated responses for trial 2 data.

Verification of published models.

The regression models for trial 2 containing one, two, three, or four variables had similar R² values compared with the corresponding models developed with trial 1 data, and the regression coefficients were only slightly different (Table 2). The se of the estimates were larger for models developed with trial 2 data, likely because there were only ≈10% as many observations for trial 2. Values of bitter pit incidence predicted with the two-, three-, and four-variable models were linearly related to observed values (Fig. 1). However, all three models were biased and underpredicted bitter pit, especially at the higher levels of observed bitter pit. A perfect relationship between predicted and observed bitter pit would have a slope of 1.0 and an R² = 1.0. Slopes and R² values were 0.55 and 0.52, 0.63 and 0.57, and 0.59 and 0.54, respectively, for the two-, three-, and four-variable models. These results support our results from trial 1 using PROC SCORE, in which bitter pit values were underpredicted for trees with high levels of observed bitter pit (Baugher et al., 2017). Predictions were slightly better for the three- and four-variable models, but they still underpredicted the bitter pit incidence for 15 of the 17 orchards in trial 2. At low levels of bitter pit, the predicted values were only ≈5% too low; however, when observed bitter pit was ≈70%, the predicted values were only 37% of the observed values. Al Shoffe et al. (2019) recently published a bitter pit prediction model based on a “passive method” reported by England and Larson (1973). The method involved sampling fruit 3 weeks before the anticipated harvest and holding the fruit at 20 °C to allow bitter pit to develop. The model based on the passive method also underpredicted bitter pit for ‘Honeycrisp’ fruit.

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Developing a model with trial 2 data (2018 and 2019).

For apples collected in 2018 and 2019, bitter pit incidence was positively and linearly related to P and all six cation ratios, and it was negatively related to Ca (Table 3). Ca and P were the only individual elements significantly correlated with bitter pit (r > 0.48); however, bitter pit was better correlated with all cation ratios (r > 0.77). The six cation ratios were also highly correlated with each other (Table 3). Scatter plots of raw data and residuals provided no evidence that the relationships between bitter pit and the predictor variables were curvilinear. SL was not correlated with any of the other 12 variables. N was positively correlated with Mg and Ca. K was correlated with Mg, P, and B. Mg was correlated with N/Ca, and Ca was correlated with all the ratios except N/Ca. Three of the ratios, (K + Mg)/Ca, (N + K + Mg)/Ca, and the accumulated ratio, were nearly perfectly correlated (r ≥ 0.99). The best model with all significant (P < 0.05) variables and no collinear terms was BP (%) = −45.19 + 1.07*B + 18.89*(Mg/Ca), with R² = 0.84 and adjusted R² = 0.81. This model contains different regressor terms than the best models developed with data from 2015, 2016, or 2017 data sets and from the pooled (2015–17) data set. The results support our previous results (Baugher et al., 2017) indicating that the best predictive models for bitter pit incidence contained different predictor variables each year. When data from trial 1 were fit with the best model from trial 2, R² = 0.49 and bitter pit was underpredicted at low levels of observed bitter pit and overpredicted at high levels of observed bitter pit (data not shown).

Table 3.Matrix of correlation coefficients to evaluate the linear relationships between bitter pit (%) after storage and various concentrations (%) of ‘Honeycrisp’ fruit peel elements measured 3 weeks before harvest in 2018 and 2019 (r values > 0.48 and 0.61 are significant at the 5% and 1% levels, respectively; n = 17).

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Revising the model with 5 years of data.

A three-dimensional plot for the 5-year data set showed that bitter pit incidence was low when shoots were short and when the N/Ca ratio was low, but there was quite a bit of variation in the data (Fig. 2). When the SL × (N/Ca) interaction term was included in the model, it was not significant (P = 0.21) and it did not improve the predictive ability of the model.

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Data from the two trials were combined and all possible regression models were requested with the RSQUARE option in PROC REG (Table 4). The same variables that were selected using data from trial 1 (Baugher et al., 2017) were again selected: the best one-variable model contained N/Ca, the best two-variable model contained N/Ca and SL, the best three-variable model contained N/Ca, SL, and P, and the best four-variable model contained N/Ca, SL, P, and B (Fig. 1). Residual plots for trial 1 and the pooled data set looked similar and no patterns were noticeable (data not shown). The reason why the same predictor variables were selected for both data sets is likely that 161 of the 178 observations (90%) in the combined data set were from trial 1.

Table 4.The best four multiple regression models for one to four regressor variables along with fit statistics using data from single trees at six orchards for 3 years (2015–17; n = 161) plus data from blocks of 20 trees in 2018 and 2019 (n = 17). The pooled data set (trials 1 and 2) had 175 observations.

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In an attempt to identify a model that was less biased, various models were developed with trial 1 data and used to predict bitter pit incidence for trial 2 data. Models that were evaluated included models with one variable [SL, K, Ca, Mg, N/Ca, (N + K + Mg)/Ca, and accumulated ratio], and models with two variables {[(N+K+Mg)/Ca + SL] and [accumulated ratio + SL]}. In all cases, the models developed from trial 1 data underpredicted the bitter pit incidence at higher levels of observed bitter pit. Nitrogen is expensive to analyze; therefore, a model that does not include nitrogen would be desirable. The best model without nitrogen [SL + (K + Mg)/Ca] explained 55% of the variation in bitter pit incidence compared with 64% for the best model (SL + N/Ca). The model without nitrogen not only explained less variation but also was more biased and overpredicted all observations, with bitter pit incidence greater than 45%.

The fact that our best models and those previously published explain less than 70% of the variation in bitter pit incidence suggests that one or more important variables are missing from the models. Bitter pit is a complex disorder, and some important contributing factors may not have been identified yet. There may be several reasons why our best model explained only 67% of the variation in bitter pit incidence. It is possible that a single peel sample at 3 weeks before harvest does not fully represent the nutritional status of the fruit, and additional sampling times may be beneficial. Preliminary work showed that bitter pit could be predicted reasonably well from peel samples at 3 weeks before harvest. Additional sampling dates may improve the prediction, but it would also increase the expense. Taking samples later than 3 weeks before harvest may not allow enough time to obtain results for making marketing decisions.

In this study, fruit maturity was not assessed; however, for most cultivars, bitter pit is most severe in early picked fruit (Perring, 1986). We found this to be the case for ‘Honeycrisp’ in a preliminary experiment. Al Shoffe et al. (2016, 2020) recently discussed the development of bitter pit and soft scald during storage for conditioned and unconditioned fruit in relation to mineral contents and harvest indices. For unconditioned fruit sampled at the start of commercial harvest, bitter pit incidence was least severe for fruit with high internal ethylene concentration, low starch values, and high Ca concentrations in peel tissue. Bitter pit was most severe for fruit with green skin color (I_AD) and high peel tissue P, K, Mg, and cation ratios. ‘Honeycrisp’ is usually harvested based on ground color. However, ground color may not always be a good indicator of fruit maturity. Giacomo et al. (2017) recently evaluated the delta absorbance meter as a nondestructive method of predicting the ripening stage of ‘Delicious’ and ‘Golden Delicious’ apples. They harvested fruit at commercial maturity and recorded changes in commonly used indices of maturity (soluble solids concentration, flesh firmness, internal ethylene concentrations, and titratable acids) over a 4-week postharvest period at 20 °C. The index of absorbance difference (I_AD) that measures ground color was significantly and linearly associated with all four indices, but R² values ranged only from 0.22 to 0.72. Based on the ratio performance deviation obtained by cross-validation, I_AD values can be used to discriminate low values from high values of maturity indices, but course quantitative predictions were not possible. Prance et al. (2011) showed that bitter pit severity declined as ‘Honeycrisp’ apples became more mature, and few incidents bitter pit developed when fruit were harvested with a starch index of ≈5.4 and internal ethylene concentration of 2.9 μL·L⁻¹. In a preliminary experiment with a sample of 20 ‘Honeycrisp’ apples from each of three orchards, we found that I_AD did not correlate well with the starch index because the relationship between I_AD and starch varied with the orchard. Even within an orchard, individual fruits with I_AD values of 0.66 could have starch index values of 1 to 7 (Marini, unpublished data). Ground color and starch index are unreliable as standalone indices of maturity, but they are the maturity indices most used by mid-Atlantic growers of ‘Honeycrisp’. Currently, there is no reliable nondestructive measure of ‘Honeycrisp’ maturity, but inclusion of a such a variable in the model would likely enhance bitter pit prediction.

Fruit harvested from different canopy positions may vary in susceptibility to bitter pit. Calcium moves in the transpiration stream of trees; therefore, fruit developing in shade or parts of the canopy with low transpiration rates may have low calcium levels and a high incidence of bitter pit. Unexpectedly, concentrations of Ca and K in ‘Cox’s Orange Pippin’ fruit in New Zealand were lower in fruit harvested from the upper parts of the tree than in fruit from the lower canopy, and the incidence of bitter pit increased from 12% in the lower parts to 24% in the upper parts of the canopy (Ferguson and Triggs, 1990). However, in a study using high-density orchards in Washington, Kalcsits et al. (2019) reported that ‘Honeycrisp’ apples from the upper canopy had higher concentrations of Ca and lower internal ethylene than fruit from the lower canopy. The K concentrations were similar regardless of canopy position. Only 14% of the fruit in the upper part of the canopy developed bitter pit compared with 31% in the lower canopy. Another factor that may influence bitter pit is crop load; Ferguson and Watkins (1992) found that fruit harvested from light-cropped trees had lower Ca and higher K concentrations as well as a higher incidence of bitter pit. They suggested that the ability to predict bitter pit from fruit Ca concentrations may be influenced by crop load. Fruit exposed to wind may have less bitter pit because high Ca concentrations of apple fruit and low levels of bitter pit were associated with increased wind speed (Lewis et al., 1977). The effect of canopy position may vary with environmental factors or orchard system because preliminary data from Pennsylvania suggest that the influence of canopy position on bitter pit severity may vary with orchard and year (unpublished data). Rootstocks influence vegetative vigor and nutrient uptake (Fazio et al., 2015). In the current study, trees on the more vigorous rootstocks (M.26 and M.7) had the highest incidence of bitter pit (Table 1). A group of researchers evaluating rootstocks in an NC-140 ‘Honeycrisp’ trial are evaluating the influence of rootstock on fruit mineral concentrations and bitter pit, but unpublished preliminary results were inconsistent across locations and years within locations. As new models are developed to predict bitter pit, some of these variables should be considered.

Critical concentrations of various elements in apple fruit flesh have been related to bitter pit for several apple cultivars. Models for predicting bitter pit have been published for several apple cultivars based on Ca alone, or combinations of Ca plus Mg, B, K, and/or N, and R² values were typically less than 0.70 (Al Shoffe et al., 2019; Perring, 1986; Torres et al., 2017). The model based on the passive method (R² = 0.68) also underpredicted bitter pit (Al Shoffe et al., 2019). To our knowledge, the current study is the first attempt to verify a bitter pit prediction model. Our best models explained less than 70% of the variation in bitter pit incidence and were biased, suggesting that models based on elemental levels in peel tissue, fruit weight, SL, and crop density will not accurately predict the incidence of bitter pit after storage. However, the model based on the passive method (Al Shoffe et al., 2019) and our model based on fruit peel analysis plus SL can be used to identify orchards with a relatively low risk (<15%) of developing bitter pit after cold storage.