Early Fruit Size Prediction Model Using Cubic Smoothing Splines for ‘Washington Navel’ (Citrus Sinensis L. Osbeck) Oranges in Australia

Abstract

Citrus growers need to be able to determine the expected fruit size and the proportion of export-quality fruit at harvest relatively early in the growing season. Early fruit size prediction would also help in planning harvest operations and administering marketing strategies well in advance. This will also enable growers to remove small fruits that would not attain the desired export size. Fruit diameter growth of ‘Washington Navel’ oranges was measured over three consecutive growing seasons during the Stage II (cell enlargement) period between January and July. Fruit were randomly selected from around the tree canopy and tagged to measure the fruit diameter at fortnightly intervals until harvest. The data were used to develop a fruit size prediction model using cubic smoothing splines. The model was able to predict the final fruit size and the final percent size distribution at early stages of fruit development in January/February in Australia. Results indicated that under the growth patterns shown by navel oranges, accurate predictions of the final fruit size and fruit size distribution were possible during early Stage II fruit development phase 5–6 months ahead of the final harvest.

KEYWORDS:

• Citrus sinensis
• ‘Washington Navel’
• fruit modeling
• size prediction
• fruit growth curves
• smoothing splines
• size distribution
• ASREML

INTRODUCTION

Fruit size is becoming increasingly important in fresh orange production to maximize monetary returns in domestic and export markets. It is desirable to be able to predict the final fruit size at an early stage in the growing season. The early indications of potential fruit size problems would enable growers to remove smaller fruit early in the season or use other methods to enhance the growth rate of those fruit which otherwise will not attain desirable fruit size at harvest. The timely removal of small fruit to decrease crop load would allow greater partitioning of reserves into the remaining fruits with possible gains in fruit size (Goldschmidt et al., 1992). Early predictions of expected fruit size distribution at harvest are also required by industry to assist with planning marketing programs.

In Australia, industry predictions of navel orange fruit size have been traditionally based on crop forecasting data collected during the period March to May. Although initial forecasts of fruit size made in March are generally satisfactory for marketing purposes, it is too late in the fruit growth cycle for management decisions to influence fruit size. A practice of hand thinning to manipulate fruit size in an on-year crop is generally carried out prior to March. However, the fruit removal after March will have little or no affect on fruit size.

Three growth stages have been identified in the growth of citrus fruit: Stage I (cell division), Stage II (cell enlargement), and Stage III (maturation) (Bain, 1958). In ‘Navel’ oranges, the transition from Stage I to Stage II has been reported to occur around mid to late December in the inland growing areas of south-eastern Australia (Storey and Treeby, 1999). Fruit size is mainly determined by the genetic make-up of the cultivar, but can be affected by cultural practices such as tree and climatic factors. Final fruit size is a function of the accumulative fruit development during each growth stage (Zhang et al., 1994). Accurate predictions of fruit size during the Stage I cell division growth period in citrus are difficult due to ongoing adjustment of crop loads throughout the period of natural fruit drop (Bevington et al., 1995). In heavy crop years, this process is more or less continuous from petal fall to late December/early January. Fruit drop is also strongly influenced by climatic conditions, and brief periods of hot weather can have a large effect on final crop size (Ben Mechlia and Carroll, 1989; Du Plessis, 1983). During early Stage II fruit growth (January–February) short-term fluctuations in fruit growth rates can also occur due to high temperatures and/or due to the occurrence of significant rainfall events (>25 mm). Fruit shrinkages in response to water stress have been reported in grapefruit in South Africa (Goell and Cohen, 1989) and in ‘Zhuju’ tangerine in China (Hui-Bai and Fie-Fie, 2000). Generally, the growth rate stabilizes after the complete fruitlet-drop period, and from there onward, growth stability improves with the passage of time. Therefore, it was assumed that the accurate fruit size prediction would be possible after the completion of Stage I fruit growth stage.

Previously, models have been developed for early fruit size prediction in Valencia oranges (Ben Mechlia and Carroll, 1989; Franco and Gravina, 2000) and for ‘Clementine’ and ‘Satsuma’ mandarin (Koch et al., 1999). However, to our knowledge, there is no fruit size prediction model available for navel oranges. The aim of this investigation was to develop a model for more timely prediction of navel fruit size and fruit distribution at harvest.

MATERIALS AND METHODS

Experimental Site

The experimental site used for data collection was a commercial grower's property at Dareton, New South Wales (lat. 34°1′S, long. 141°9′E), located in the Sunraysia growing area in south-eastern Australia. The soil is deep loam sand from 0–80 cm over loamy sand/clay sand from 80–140 cm. The root zone is approximately 80–100 cm deep, and electric conductivity ranged between 0–0.40 ds/m. The soil pH was between 8 and 9. General climatic conditions for Dareton indicates maximum temperature ranges of 30 to 32°C during December to February and 16 to 17°C during June to August and an average rainfall of 200 mm. Total accumulated heat units per year averages around 1,880 (Khurshid and Hutton, 2005). The typical dry semi-arid climate of south-eastern Australia necessitated irrigation for crop production, and the trees were irrigated (ca. 10 ML/ha/season) with low level sprinklers. The trees were 37-year-old ‘Washington navel’ (Citrus sinensis L. Osbeck) on sweet orange rootstock planted at a spacing of 6.7 × 3.6 m. The average tree height was 3 m. During the course of the study, the trees received routine orchard management according to the standard district practice.

Fruit growth was recorded over three consecutive growing seasons 2000, 2001, and 2002. These growing seasons varied widely in climatic conditions and crop loads carried by the trees (Table 3 below). In each growing season, a total of 300 fruit (60 fruit per tree) were randomly selected from around the tree canopy and tagged. Fruit diameter measurements were carried out at 2-week intervals with digital callipers. Measurements were recorded on 14 different occasions between January and July in each year. Experimental data collected during the course of this project were utilized to model fruit growth of navel oranges and to establish growth curves throughout Stage II growth during the period from January to July for each growing season.

TABLE 3 Final Fruit Size Distribution Predicted at Early Dates During Active Growth Period January/March for Five Different Size Classes for Three Growing Seasons in ‘Washington Navel’ Oranges

Season	Size class (mm)	Observed % fruit number at harvest	Predicted % final fruit number at early dates
		July 6	January 1	January 15	February 1	February 15	March 1
2000	<65	15	13	14	15	15	—
	65–69	18	18	19	17	18	—
	69–75	30	39	35	34	36	—
	75–77	21	18	23	23	21	—
	>77	16	12	10	11	10	—
	P value ^z	—	0.39	0.29	0.64	0.29	—
2001	<65	11	11	9	10	10	—
	65–69	12	12	14	11	11	—
	69–75	39	41	40	41	39	—
	75–77	17	22	20	20	21	—
	>77	21	14	18	18	19	—
	P value ^z	—	0.37	0.72	0.85	0.83	—
2002	<65	47	29	38	40	43	47
	65–69	18	31	26	24	26	22
	69–75	21	34	31	28	24	24
	75–77	9	5	4	6	6	5
	>77	5	1	1	2	1	2
	P value ^z	—	2.9E–08	4.2E–05	4.7E–05	0.03	0.08
^z P values are used to compare observed versus predicted values by Chi-squared test. A P value >0.05 is not significant and <0.05 is a significant difference. The nonsignificance difference between observed and predicted values shows a strong correlation.

Model Development

The development of the fruit size model was based on the following considerations.

1. The use of appropriate statistical techniques to explain the maximum variability in the growth curve established from the fruit diameter measurements recorded during the growing season. These techniques should be able to account for other sources of variations involved in the experiment.

2. The prediction of the final growth at an early date or a time interval from the established growth curve and to predict the proportion of fruit for different size classes used for the export markets.

3. To determine the required size at early stages of development to meet the export-size classes at harvest.

Statistical Analyses

To develop a standard growth curve, fruit growth data were analyzed by fitting cubic smoothing spline models using the software package ASREML (Gilmour et al., 1999). The predicted fruit growth was compared with the observed fruit growth by regression analysis; while predicted and observed fruit size distribution across the different size classes were compared using the Chi-squared goodness-of-fit test using the statistical software package GenStat (2008).

RESULTS AND DISCUSSIONS

Cubic Smoothing Splines

The data, in which all treatments were applied at the same time or all experimental units are measured at the same sampling, arises from repeated measurements. The univariate approach as separate ANOVA of each sampling data were considered inappropriate because they fail to model plot-level covariate structure inherent in the data. The univariate split-plot ANOVA, split for time as a factor, assume homogeneity of the covariate structure of the repeated measures. Time can also not be randomly allocated.

Smoothing splines are functions constructed from segments of cubic polynomials between the distinct values of the variates and constructed to be smooth at the junctions. Models that contain such functions are no longer linear but are described as additive models because the effects of separate explanatory variates are still combined additively (Verbyla et al., 1999). This presents a modern method for the analysis of longitudinal data using a cubic smoothing spline that permits the inclusion of random coefficients, covariance modeling, and estimation of nonsmoothed deviations at the various levels of the designs, such as deviation in growth rates due to changes in temperature or rainfall (Orchard et al., 2000). Fruit shrinkages during fruit growth can occur during stress conditions, and cubic smoothing functions can accommodate this with accuracy. Cubic smoothing splines have been used to model growth curves (Tapio and Koskela, 2008). The commonly used exponential models that were used to model fruit growth rates across time fail to allow for these components. The linear mixed model was the basis of all analyses for the cubic smoothing methods of Verbyla et al. (1999) and estimation was via residual maximum likelihood (REML).

Fruit Growth Curves

Fruit growth curves from the fruit diameter measurements data were constructed, and cubic smoothing splines models were fitted to the data to predict the fruit size at each measurement date. Predicted mean fruit diameter growth for the entire growth period was calculated from the spline analysis for three different seasons.

ASREML analysis indicated that the predicted splines for years 2000 and 2001 were significantly different from year 2003. However, this difference was due to the initial fruit size and not to the rate of growth (slope) throughout the growing period (Figure 1). This is consistent with the fruit growth data collected for ‘Clementine’ and ‘Satsuma’ mandarins by Koch et al. (1999), who also indicated that fruit size at the time of measurement is usually is the most important factor in predicting eventual fruit size and not minor differences in growth rates. This agrees with previous studies carried out at Dareton on ‘Imperial’ mandarins (Bevington et al., 1998). Fruit growth on a normal well-irrigated tree is nonlinear with time, exhibiting rapid growth from December through the end of January, followed by a decreasing rate of expansion until harvest in June/July for navel oranges. In our study, there were no differences in fruit growth rates for the same measurement dates across the three growing seasons.

FIGURE 1 Smoothed splines obtained from ASREML analysis. Data were recorded at 14 occasions (2-week intervals) during the growth period for three growing seasons 2000, 2001, and 2002 in ‘Washington navel’ (Citrus sinensis L. Osbeck) oranges.

Prediction of Fruit Growth and Final Fruit Size Distribution Using the Model

Fruit growth was predicted by adding the average predicted growth to the observed fruit growth at the early stages of fruit development during the 2000, 2001, and 2002 growing seasons.

Final fruit size was predicted by using the following equation:

• subscript x = predicted final fruit diameter (mm) at harvest (e.g., July 6),

• subscript y = observed fruit diameter (mm) at an early stage (obtained from the actual fruit size measurements), and

• subscript z = mean predicted growth over measurement period (obtained from the spline analysis; see Table 1).

  TABLE 1 Predicted Growth Increments and Relationship Between Observed Final Fruit Size and Predicted Final Fruit Size for ‘Washington Navel’ Oranges for Three Growing Seasons

  ^z Early dates	1999/2000		2000/2001		2001/2002
  	^y Predicted growth (mm)	^x R^2 values	^y Predicted growth (mm)	^x R^2 values	^y Predicted growth (mm)	^x R^2 values
  January 1	29.4	0.58	30.6	0.69	33.3	0.49
  January 15	25.5	0.67	27.4	0.72	28.2	0.62
  February 1	21.1	0.77	20.8	0.83	22.8	0.75
  February 15	18.0	0.83	17.2	0.85	18.9	0.81
  ^zEarly dates used for the prediction of final fruit size at harvest.
  ^yPredicted growth from an early stage of measurement was obtained for the entire growing season using spline models.
  ^xCoefficients of determination for the observed and predicted fruit size obtained by spline models. The results are based on the entire data points. All results were statistically significant at 0.001.

In each year, final fruit size was predicted at four early times in January/February. This period was chosen well after the complete fruitlet drop and was assumed to be early enough to make any adjustment to the fruit load if it was required. Average growth curves were established from the fruit size measurements, and splines were fitted to the data for each year (Figure 1). The analysis indicated that the differences between years related mainly to differences in initial fruit size at the beginning of January. There were no significant differences in the initial fruit size of years 2000 and 2001; however, both of these years were different from year 2002 for initial fruit size.

Once the final fruit size prediction was determined using the smoothing spline model, the numbers of fruits were counted and percentages calculated. Fruits were allocated into following size classes: <65 mm, 65–69 mm, 69–75 mm, 75–77 mm, and >77. Predicted fruit size distribution was then compared with the observed data.

The Effect of Crop Load and Climatic Conditions on Fruit Growth Predictions

The effect of crop load and climatic conditions during three growing seasons has been considered and discussed below.

Year 1 (2000)

Fruit growth was predicted on January 1 (day 1, 90 days after full bloom), January 15 (day 15), February 1 (day 32), and February 15 (day 46). Predicted final fruit growth was very similar to the observed values when predicted at four early dates (Table 1). There was a significant relationship (R² = 0.58) between the predicted and observed fruit growth at an early date of 1 Jan.; however, this relation improved over time and was best predicted on February 15 (R² = 0.83). The prediction of fruit size distribution in various size glasses was possible as early as January 1 with a P value of 0.39 with Chi-squared goodness-of-fit test (Table 2); however, the relation between predicted and observed final fruit size improved over time. Predicted percentage of fruit size distribution in the larger classes (69–75 mm, 75–77 mm, and >77mm) was 68% for the predicted dates as compared to the observed value of 67%. In the 2000 growing season, the trees carried a moderate–heavy crop load of 953 fruit per tree (Table 3). Despite the moderate–heavy crop load, fruit size at harvest was large due to the initial large size at the beginning of Stage II growth. Our experience suggests that larger initial fruit size ends up in a larger-size fruit. Initial fruit size produced larger fruit at harvest in ‘Satsuma’ mandarins (Koch et al., 1999). In addition to that, the year was also characterized by significant rainfall, with falls >40 mm in February and April, and therefore, the favorable condition of above average temperature and rainfall would have contributed to the large fruit size at harvest. These results also suggested that the crop of around 900 fruit per tree can be predicted more accurately.

TABLE 2 Final Fruit Size Distribution Predicted at Early Dates During Active Growth Period January/March for Five Different Size Classes for Three Growing Seasons in ‘Washington Navel’ Oranges

Season	Size class (mm)	Observed % fruit number at harvest	Predicted % final fruit number at early dates
		July 6	January 1	January 15	February 1	February 15	March 1
2000	<65	15	13	14	15	15	—
	65–69	18	18	19	17	18	—
	69–75	30	39	35	34	36	—
	75–77	21	18	23	23	21	—
	>77	16	12	10	11	10	—
	P value ^z	—	0.39	0.29	0.64	0.29	—
2001	<65	11	11	9	10	10	—
	65–69	12	12	14	11	11	—
	69–75	39	41	40	41	39	—
	75–77	17	22	20	20	21	—
	>77	21	14	18	18	19	—
	P value ^z	—	0.37	0.72	0.85	0.83	—
2002	<65	47	29	38	40	43	47
	65–69	18	31	26	24	26	22
	69–75	21	34	31	28	24	24
	75–77	9	5	4	6	6	5
	>77	5	1	1	2	1	2
	P value ^z	—	2.9E–08	4.2E–05	4.7E–05	0.03	0.08
^z P values are used to compare observed versus predicted values by Chi-squared test. A P value > 0.05 is not significant and <0.05 is a significant difference. The nonsignificance difference between observed and predicted values shows a strong correlation.

Year 2 (2001)

Final fruit size was predicted on January 1 (day 1, 83 days after full bloom), January 15 (day 15), February 1 (day 31), and February 15 (day 45). Predicted final fruit growth was very similar to the observed values when predicted at four early dates (Table 1). There was a significant relationship (R² = 0.69) between the predicted and observed fruit growth at an early date of January 1, and the relation improved over time and was best predicted on February 15 (R² = 0.85). These results were very similar to the year 2000. The prediction of fruit size distribution in various size classes was possible as early as January 1 with a P value of 0.37 with the Chi-squared goodness-of-fit test (Table 2), and the relation between predicted and observed final fruit size improved over time with a P value of 0.83 on February 15. Predicted percent fruit size distribution in the larger classes (69–75 mm, 75–77 mm, and >77mm) was 78% for the predicted dates as compared to the observed value of 77%. Seasonal conditions in 2001 were very different from the previous season, with a higher number of days where maximum temperatures exceeded 38°C and a much lower accumulated rainfall (Table 3). Generally, longer periods of air temperatures above 38°C depresses fruit growth in sweet oranges during the on-year (Hilgeman et al., 1959), but in our situation, fruit trees were in the off-year production cycle. However, trees carried a very light crop load of 351 fruit per tree, and fruit size at harvest was large. The large fruit at the beginning of Stage II due to the lighter crop had 7% more fruit in the large size class compared to the year 2000. Large fruit size with lower crop load has been previously reported in navel oranges (Treeby et al., 2007), and it is also common in other cultivars of sweet oranges.

Year 3 (2002)

Final fruit size was predicted on January 1 (day 1, 86 days after full bloom), January 15 (day 15), February 1 (day 31), and February 15 (day 45). Predicted final fruit size was very similar to the observed values when predicted at four early dates (Table 1). There was a significant relationship (R² = 0.49) between the predicted and observed fruit growth at an early date of January 1, and the relation between actual and predicted fruit size improved over time and was best predicted on February 15 (R² = 0.81). However, the R² values were slightly lower compared to the previous 2 years. The prediction of fruit size distribution in various size classes was attempted at four early dates, which resulted in a poor prediction of the fruit size distribution (Table 2). In size class <65 mm, there was an underestimation of fruit percentage; while in fruit ranging from 65–75 mm, there was an overestimation of fruit percentage compared to the observed percentages at harvest. Therefore, it was attempted to extend the prediction date to March 1 (Table 2). This date revealed better prediction than the four early dates. In this year, the crop load was very heavy compared to the last year, and initial fruit size was much smaller at Stage II. Lower crop load one year can contribute to larger size crop in next year and has been reported to reduce the fruit size in navel oranges (Khurshid and Hutton, 2005). This season was also characterized by very dry weather conditions and milder temperatures than the previous seasons (Table 1). Therefore, heavy crop load in the previous year and adverse climatic conditions contributed to the smaller fruit size; however, fruit size prediction was still possible at a later date. These results suggest that in a heavy crop year, fruit thinning should be carried out before using the prediction model. Accurate fruit size predictions will only be possible after fruit crop has been adjusted on the tree.

Size Requirements to Achieve Final Outcomes

Based on predicted growth from the model, the required minimum sizes for ‘Washington Navel’ oranges during January and February for fruit to attain particular size ranges at harvest are shown in Table 4. Fruit would need to be at least 40 mm in diameter at the beginning of January and 50 mm in diameter at the beginning of February to attain a size of 75 mm at harvest. In its present form, the model can be used to predict navel orange fruit diameter growth for any nominated time interval throughout Stage II fruit development to harvest. Predicted fruit diameter growth increments based on fruit growth derived from the fitted spline curves for four early dates are summarized in Table 1. It is recommended that fruit that are below 40 mm in diameter at the beginning of January need to be thinned, as they will not attain the required fruit size at harvest.

TABLE 4 Predicted Minimum Fruit Diameter (mm) Required During January and February for ‘Washington navel’ Oranges to Attain 69–75 mm, 75–77 mm, and >77 mm Size Ranges at Harvest

Early dates	Fruit size range
	69–75 mm	75–77 mm	>77 mm
January 1	41	44	47
January 15	44	46	50
February 1	50	54	56
February 15	53	57	60

Validation of the Model

To validate the current model, in 2003, fruit diameter on 50 fruit per tree was recorded on January 15 from ten randomly selected trees from an orchard block, which was originally used to collect the data for the model development in the previous years. Fruit size distribution was predicted using Table 4. Ten trees were fully harvested on July 1, 2003, and their fruit size distribution was determined by using a commercial fruit grader (Colour Vision Systems Pty Ltd., Australia (MAF Rodd Group)) to compare it to the predicted fruit size distribution. The average crop load of the harvested trees was 750 fruit per tree. The results in Table 5 indicate a strong relationship between the predicted and observed fruit size distribution. This test proved to be very useful for the validity of the model.

TABLE 5 Comparison of Predicted Average Fruit Size Distribution to Observed Fruit Size Distribution in 2003 for ‘Washington Navel’ Oranges

Size class	^z Predicted in January 2003	^y Observed inJuly 2003
69–	15	14
75 mm	31	28
75–77 mm	51	57
>77 mm
^x P value
^zFruit diameters were randomly recorded on ten trees (50 fruit/tree) on January 15, and final fruit size distribution was predicted using Table 5.
^yFull tree harvest was carried out on July 1, 2003, and fruit size distribution was determined on ten trees.
^x P values are used to compare predicted versus observed values by Chi-squared test. A P value > 0.05 is not significant and <0.05 is a significant difference. The nonsignificance difference between observed and predicted values shows a strong correlation.

CONCLUSIONS

Despite wide seasonal differences in climatic conditions and crop load carried by the trees during previous three years, the predicted growth increments were stable, especially after mid-January. This model is likely to be fairly robust and will be easily used by citrus growers for ‘Washington navel’ oranges. The fruit growth model is based on 3 years of data collected in the Sunraysia district of south-eastern Australia. Therefore, the model will be most accurate when used in this area. However, for other regions or citrus cultivars, the model would need further testing and refinement. Further data sets are needed from other growing areas to determine how widely the model can be applied, and sampling protocols need to be established for whole tree estimation of size distribution.

Our results indicate that under the growth patterns shown by navel oranges, accurate predictions of fruit size distribution were possible during early Stage II fruit development 5–6 months prior to harvest. Predictions of the expected fruit size at harvest in late January and February would still be early enough to make adjustments to the management programs. Currently, an experimental program for early, mid, late, and very late maturing commercial navel cultivars is underway at Dareton. Fruit diameter, crop load, climatic data, and detailed phenological data is being recorded to be utilized in the further development and refinement of fruit size prediction models for a range of navel cultivars.

ACKNOWLEDGMENTS

This research was supported by Horticulture Australia Limited. The authors are indebted Dr. Michael Treeby (Senior Research Scientist—NSW DPI, Dareton) for his critical comments during the preparation of this manuscript.