Models for Predicting Pineapple Flowering and Harvest Dates

Abstract

The growing-degree-days (GDD) model for pineapple was developed to predict flowering and harvest dates; however, it has not been adapted to the climate in Japan’s growing regions, where air temperatures fluctuate over a wide range, and the prediction accuracy is low. The present study aimed to develop models for predicting flowering and harvest dates with high accuracy by analyzing a large phenological dataset from Japan’s main (Nago) and warmer (Ishigaki) production areas. The number of days between budding and flowering decreased at air temperatures of up to approximately 25°C and remained constant above 25°C. The number of days between flowering and harvest decreased until approximately 23°C. The effect of day length on both days to flowering and harvest was small. The relationship between air temperature and the developmental rate after budding to flowering and after flowering to harvest was modeled using the GDD and exponential function models, both with upper limits. The GDD model with an upper limit temperature was more accurate at predicting flowering and harvest dates compared to the conventional GDD model. In particular, the prediction accuracy of the harvest date was dramatically improved. Because the relationship between the developmental rate until flowering and the air temperature was exponential rather than linear, the exponential function model provided a more accurate prediction of the flowering date. The root-mean-square errors of the most accurate models were 3.7–6.1 days for predicting the flowering date and 6.1–10.2 days for the harvest date. We believe that these models will be useful for planning shipments of pineapple in regions with wide temperature ranges, such as Japan, and for cultivation management in response to climate change.

Introduction

Pineapple (Ananas comosus L. Merr.) is an important tropical fruit plant, with a production of 28 Mt globally in 2019 (FAO, 2022). It is cultivated at low latitudes that experience small seasonal variations in air temperature and day length. Costa Rica and the Philippines were the top producers of pineapples in 2019 (FAO, 2022). Normal year monthly mean air temperature in Costa Rica (San José, 10.0°N, 84.2°E) ranged from 21.9°C (October) to 23.8°C (March and April), and in the Philippines (Maynila, 14.5°N, 121.0°E) from 26.1°C (October) to 29.5°C (April); the annual air temperature ranges span just a few degrees (National Astronomical Observatory of Japan, 2018). However, in Japan, which is at the northern limit of economic pineapple cultivation (Ogata et al., 2016), there is an annual air temperature range of more than 10°C, from 16.5°C (January) to 28.9°C (July) in the main production area of Okinawa Island (Nago, 26.6°N, 128.0°E), and from 18.9°C (January) to 29.6°C (July) in Ishigaki Island (Ishigaki, 24.4°N, 124.2°E), which is a lower latitude production area (Japan Meteorological Agency, 2022).

In Japan, pineapple fruits are harvested throughout the year because of ethephon application, which results in flower bud induction, and other factors (Onaha, 1984). Because pineapple development is strongly affected by air temperature (Fleisch and Bartholomew, 1987; Lechaudel et al., 2010), the developmental rate after budding varies depending on the season and year. The prediction of flowering and harvest dates of pineapple is useful for the efficient management of growing systems. Moreover, it helps in planning the shipping of fresh fruits and the supply of fruits to canneries. If the fruit development period can be predicted, the relationship between temperature and the acid and soluble solid content during the fruit growing period (Sugiura et al., 2023) can be used to estimate the fruit quality at harvest.

The growing-degree-days (GDD) model was developed to predict the flowering and harvest dates of pineapple (Fleisch and Bartholomew, 1987; Lechaudel et al., 2010). However, the GDD model has not been adapted to the climate in Japan’s growing regions, where air temperatures fluctuate over a wide range; therefore, flowering and harvest dates of pineapple have not been predicted accurately in Japan. There are few reports on the sensitivity of pineapples to a wide range of air temperatures or photoperiodism.

In the present study, we aimed to clarify the quantitative relationship between the developmental rate of pineapple and climate conditions using a large phenological dataset from Japan’s main production area (Nago), as well as a warmer production area (Ishigaki), and to develop models for predicting flowering and harvest dates adapted to regions with wide temperature ranges such as Japan.

Materials and Methods

Plant materials and field observations

Budding, flowering, and harvest dates were collected for five pineapple cultivars, ‘N67-10’, ‘Soft Touch’, ‘Bogor’, ‘Gold Barrel’, and ‘Okinou P17’, that were harvested between 1999–2019 in experimental fields at the Okinawa Prefectural Agricultural Research Center in Nago (26.6°N, 128.0°E) and Ishigaki (24.4°N, 124.2°E). Ishigaki is located approximately 450 km southwest of Nago. ‘N67-10’, ‘Bogor’, ‘Soft Touch’, and ‘Gold Barrel’ are the top four cultivars produced in Japan (Ministry of Agriculture, Forestry and Fisheries, 2022), and most of the pineapples grown in Japan are one of these cultivars. ‘N67-10’, the leading pineapple cultivar in Japan, is a vegetative selection from ‘Hawaiian Smooth Cayenne’, while the other cultivars were bred using artificial hybridization techniques (Ogata et al., 2016; Shoda et al., 2012).

Pineapples were planted between March and October, and 25 mL of a mixture of 0.1% ethephon and 4% urea was applied to the growing point of each plant between April and November of the year following planting to trigger induction of the flower bud. However, most plants planted between August and October were excluded, and the mixture was not applied to these plants. Harvesting was conducted between September one year after planting and August two years after planting.

All plants were labeled for identification purposes. Each plant was considered to be budding when the growing point opened by approximately 2.4 cm, exposing the inflorescence. Additionally, when at least one corolla was visible, the plant was considered to be flowering. The harvest date was selected based on the peel color (percentage of the peel surface that turned yellow). As the pineapple peel contains more carotenoids in winter than in summer (Joomwong and Sornsrivichai, 2006), the peel color at the time of flesh ripening varies with the season (Onaha, 1984). In accordance with the harvest criteria of the Okinawa Prefecture Fruit Tree Cultivation Guidelines (Okinawa Prefecture, 2019), the fruit of ‘N67-10’ was harvested when the peel color ranged from 20% (June to August) to 80% (December to March). In the present study, the fruit was harvested when the peel color was 20–90% for ‘Soft Touch’ and 10–80% for the other cultivars. Other cultivation conditions, which included planting methods, soil management, and disease and pest control, were as recommended by prefectural guidelines.

Climate data

The daily mean air temperatures obtained from the Agro-Meteorological Grid Square Data (Ohno et al., 2016), a climate dataset with 1 km resolution (each grid cell measures 45" longitude × 30" latitude) based on records at observatories, were used for the two experimental fields owing to the distances between them and the observatories. Daily day lengths in each field were calculated using the method described by Yoshida (1985).

Statistical analysis

Only data pertaining to the first fruit of each plant were used in our analysis. The number of data pairs for budding and flowering dates of ‘N67-10’, ‘Soft Touch’, ‘Bogor’, ‘Gold Barrel’, and ‘Okinou P17’ were 2081, 2249, 1562, 220, and 957, respectively. The number of data pairs for flowering and harvest dates were 2092, 2286, 1565, 220, and 957, respectively.

To minimize individual variations within each cultivar in each experimental field, the budding and flowering dates from plants that budded in the same month of the same year were averaged and considered as one data pair for subsequent steps in the development of models to predict flowering dates. However, when more than 30 plants budded in a given month, the month was divided into three 10-day periods, averaged, and used as a single data pair thereafter. The number of data pairs after averaging is presented according to location or budding month in Table 1. With the exception of ‘Gold Barrel’, data for budding and flowering dates were obtained throughout the year. More than 90% of the data were obtained from Nago.

Table 1

The number of data pairs (budding and flowering dates) used to develop models to predict the flowering date, shown according to location or budding month.

Similarly, the flowering and harvest dates of plants that flowered in the same month of the same year or in the same 10-day period of the same year were averaged and used in the development of models to predict the harvest dates (Table 2).

Table 2

The number of data pairs (flowering and harvest dates) used to develop models to predict the harvest date, shown according to location or flowering month.

The prediction accuracy of the model was evaluated using the root-mean-square error (RMSE) (day), which was calculated as follows:

  

$$\mathit{RMSE}=\sqrt{\sum _1^n{\left(D_e–D_m\right)}^2/n}$$(1)

where n is the number of data used in the calculation, D_e is the estimated date obtained from the model, and D_m is the observed date in the experimental field.

All calculations were performed using Excel for Microsoft 365, and coefficients for approximation by linear or exponential functions were calculated using the “Linest function” or “Logest function” in Excel.

Models to predict the flowering date

1)  Modeling developmental rate

Previously, developmental rate (DVR) models have been used to predict the development of fruit tree buds and fruits (Konno et al., 2020; Sakamoto et al., 2015; Sugiura and Honjo, 1997a, b; Sugiura et al., 1991). These studies defined DVR as the amount of development per unit of time. The developmental stage index (DVI) was expressed as the accumulated value of DVR.

In the present study, to develop a DVR model to predict the pineapple flowering date, daily DVR (DVR_d) after budding to flowering was defined as a function of daily mean air temperature:

  

$${\mathit{DVI}}_D=\sum _{d=1}^D{\mathit{DVR}}_d$$(2)

where DVI_D is the developmental stage index on D (day) after budding and DVR_d (day⁻¹) is the amount of development per day. A value of 0 and 1 was assigned to the DVI_D for the budding and flowering dates, respectively.

If flowering occurs F (day) after budding, the DVI on the flowering date is expressed using the following equation:

  

$${\mathit{DVI}}_F=\sum _{d=1}^F{\mathit{DVR}}_d=1$$(3)

If the relationship between the DVR_d and daily mean air temperature is formulated, the flowering date can be estimated from the daily mean air temperature and equation (3). In this study, three models, namely the GDD model, GDD model with an upper limit temperature, and exponential function model with an upper limit temperature, were used to formulate the relationship between DVR_d and daily mean air temperature.

2)  GDD model

Fleisch and Bartholomew (1987) used the GDD model to predict pineapple flowering and harvest dates. The GDD model corresponds to a linear approximation of the relationship between the DVR_d and daily mean air temperature (Sugiura, 1997) under a certain assumption described below. The relationship after budding to flowering was approximated with a linear function using the following method:

  

$${\mathit{DVR}}_d=p·T_d+q$$(4)

where T_d (°C) is the daily mean air temperature and p (°C⁻¹·day⁻¹) and q (day⁻¹) are the coefficients. From equations (3) and (4), the following equations are satisfied on the flowering date:

  

$$\sum _{d=1}^F(p·T_d+q)=1$$(5)

  

$$\sum _{d=1}^F{(T}_d+q/p)=1/p$$(6)

The GDD model determines the flowering date when the accumulated air temperature above the base air temperature (T_base, °C) reaches a specific value (GDD_F, °C·day). In cases where T_d is lower than T_base, 0 is normally accumulated. The GDD model can be described by the following equation:

  

$$\sum _{d=1}^F\max \left(T_d-T_{\mathit{base}},0\right)={\mathit{GDD}}_F$$(7)

where “max” is a function that returns the largest value in parentheses.

In a previous study, the T_base of a GDD model to predict pineapple flowering date was 13.5°C (Fleisch and Bartholomew, 1987). Since most of the T_d values observed in the present study were > 13.5°C, we performed subsequent analyses assuming that T_d is always larger than T_base. Then, the left side of equation (7) is the accumulated value of T_d–T_base, which is a linear expression for T_d identical to equation (6). Therefore, by comparing the coefficients of equation (7) with those of equation (6), the following equation is obtained:

  

$$\mathit{-q}/p=T_{\mathit{base}}$$(8)

  

$$1/p={\mathit{GDD}}_F$$(9)

We determined p and q in equation (6) using the data from field observations and obtained the unknown coefficients T_base and then GDD_F in equation (7) from equations (8) and (9).

3)  GDD model with the upper limit temperature

As detailed in the Results and Discussion section, the number of days after budding to flowering decreased for all cultivars as the mean air temperature increased; however, above a certain temperature (T_u, °C), the effect of air temperature decreaseed. Therefore, in this model, assuming T_u as the upper limit of air temperature, equation (4) was modified so that DVR_d above T_u is equal to that at T_u.

  

$${\mathit{DVR}}_d=p·{\min (T_u, T}_d)+q$$(10)

where “min” is a function that returns the least value in parentheses. Equation (7) was then modified as follows:

  

$$\sum _{d=1}^F\max \left[{\min (T_u,T}_d)-T_{\mathrm{base}},0\right]={\mathit{GDD}}_F$$(11)

The unknown coefficients T_u, T_base, and GDD_F in equation (11) were determined using data from field observations.

4)  Exponential function model with an upper limit temperature

Temperature treatment experiments on trees showed that the relationship between air temperature and the developmental rate of Japanese pear (Sugiura et al., 1991) and grape buds (Sugiura et al., 1995) could be approximated by an exponential function. Exponential approximations have been employed in a few statistical studies on the developmental rates of tree buds, including cherry (Aono and Moriya, 2003) and Japanese apricot (Aono and Sato, 1996). Therefore, we considered using the following equation instead of equation (10):

  

$${\mathit{DVR}}_d=b·\exp \left[a·{\min (T_u, T}_d)\right]$$(12)

where a (°C⁻¹) and b (day⁻¹) are coefficients. From equations (3) and (12), the following equation for the flowering date is satisfied:

  

$$\sum _{d=1}^{F}b·\exp \left[a·{\min (T_u, T}_d)\right]=1$$(13)

By rearranging equation (13), equation (14) can be obtained.

  

$$\sum _{d=1}^F\exp \left[a·{\min (T_u, T}_d)\right]=1/\mathrm{b}$$(14)

Once the unknown coefficients T_u, a, and b are determined, equation (14) can be used to predict the flowering date. These coefficients were determined using field observation data.

Models to predict harvest date

To predict the pineapple harvest date, the relationship between daily DVR_d after flowering to harvest and daily mean air temperature were modeled using similar equations to predict the flowering date. In equation (2), a value of 0 and 1 was assigned to the DVI_D for the flowering and harvest dates, respectively. All equations in the present study were also used substituting “budding” to “flowering” and “flowering” to “harvest.”

Results and Discussion

Days to flowering and harvest

The mean number of days between budding and flowering was 26–37 days, with a standard deviation (SD) of 11–15 days (Table 3). The number of days between budding and flowering decreased for all cultivars as the mean air temperature after budding to flowering increased (Fig. 1). However, the effect of air temperature lessened when it exceeded around 25°C. The number of days between budding and flowering was similar in both experimental fields (Nago and Ishigaki) when air temperatures were equal. Data from Nago are presented according to mean day length after budding to flowering (Fig. 1): ≥ 12 h (long day) and < 12 h (short day). The effect of day length on the relationship between air temperature and days to flowering was unclear.

Table 3

The number of days between budding and flowering and between flowering and harvest.

Fig. 1

The relationship between the number of days and the mean air temperatures after budding to flowering for (A) ‘N67-10’, (B) ‘Soft Touch’, (C) ‘Bogor’, (D) ‘Gold Barrel’, and (E) ‘Okinou P17’ in Nago and Ishigaki. Data from Nago are presented separately for long days (≥ 12 h) and short days (< 12 h).

The mean number of days between flowering and harvest was 91–133 days, with an SD of 12–25 days (Table 3). The number of days between flowering and harvest also decreased as the mean air temperature after flowering to harvest increased (Fig. 2), and the effect of air temperature lessened when air temperature exceeded around 23°C. The effect of the region or day length on the relationship between air temperature and days to harvest was not clear. As the region and day-length conditions had little effect on these periods, data from both regions and all day-length conditions were combined for further analysis.

Fig. 2

The relationship between the number of days and mean air temperatures after flowering to harvest for (A) ‘N67-10’, (B) ‘Soft Touch’, (C) ‘Bogor’, (D) ‘Gold Barrel’, and (E) ‘Okinou P17’ in Nago and Ishigaki. Data from Nago are presented separately for long days (≥ 12 h) and short days (< 12 h).

Predicting the flowering date

1)  GDD model

To predict the flowering date using equation (7), we determined the coefficients T_base and GDD_F using the mean DVR_d after budding to flowering (DVR_mean, day⁻¹). The DVR_mean was calculated using the following equation:

  

$${\mathit{DVR}}_{\mathit{mean}}=\frac{\sum _{d=1}^F{\mathit{DVR}}_d}{F}$$(15)

As equations (3) and (15) yield equation (16), the DVR_mean of each observed data pair can be calculated from the observed F.

  

$${\mathit{DVR}}_{\mathit{mean}}=1/F$$(16)

Figure 3A shows the relationship between the DVR_mean of ‘N67-10’ and the mean air temperature after budding to flowering. DVR_mean increased as air temperature increased. There was a significant correlation between DVR_mean and mean air temperature (Table 4). A similar relationship between DVR_mean and the mean air temperature was observed for all cultivars as for ‘N67-10’, with a significant correlation (Table 4).

Fig. 3

The relationship between mean developmental rate (DVR_mean) and mean air temperatures for the ‘N67-10’ pineapple cultivar in the period (A) after budding to flowering or (B) after flowering to harvest. The dashed line represents a linear approximation of all data. A linear approximation below (A) 25°C or (B) 23°C is shown as a solid line with an approximate equation. An exponential approximation below (A) 25°C or (B) 23°C is shown as a curve with an approximate equation.

Table 4

Coefficients and RMSEs of models to predict the flowering date.

The relationship between DVR_mean and the mean air temperature was approximated using a linear regression equation (the dashed line in Fig. 3A):

  

$${\mathit{DVR}}_{\mathit{mean}}=P·T_{\mathrm{mean}}+Q$$(17)

where T_mean (°C) is the mean air temperature after budding to flowering, and P (°C⁻¹·day⁻¹) and Q (day⁻¹) are coefficients. The obtained P and Q values of ‘N67-10’ are as follows:

  

$$P=0.00582$$(18)

  

$$Q=\mathrm{-0.0808}$$(19)

When T_d > T_base, in the GDD model, the relationship between DVR_d and T_d is linear (equation [4]). In such a case, the relationship between DVR_d and T_d is consistent with the relationship between DVR_mean and T_mean. Therefore, from coefficients P and Q in equation (17), the coefficients p and q in equation (4) can be obtained.

  

$$P=p$$(20)

  

$$Q=q$$(21)

The coefficients T_base = 13.9 and GDD_F = 171.9 (Table 4) were obtained from equations (8), (9), and (18–21). T_base and GDD_F of all cultivars were determined using the same calculation method (Table 4). The T_base was approximately 13°C for each cultivar. Almost all T_d observed in this study were > 13°C, thereby validating that the coefficients in equation (4) and equation (17) were consistent. The difference from T_base = 13.5°C obtained using ‘Smooth Cayenne’ (Fleisch and Bartholomew, 1987) was small.

Using these coefficient values and equation (7), the flowering date could be estimated from the observed T_d of each dataset. The RMSE of the estimated and observed flowering date was 4.3–7.9 days (Table 4). These RMSE values were less than the SD of the observed days between budding and flowering (Table 3), indicating the effectiveness of the GDD model.

2)  GDD model with an upper limit temperature

To predict the flowering date using equation (11), we determined the coefficients T_u, T_base, and GDD_F. The number of days after budding to flowering decreased in all cultivars as the mean air temperature increased, and the effect of air temperature reduced above approximately 25°C (Fig. 1). Therefore, T_u was set to 25°C.

In the previous section, the relationship between DVR_d and T_d was represented by a single straight line (equation (4)), so that coefficients p and q in equation (4) could be obtained from the regression equation (equation (17)). However, when the relationship between DVR_d and T_d is considered as two lines in the range of air temperatures obtained from field observations, the relationship between DVR_d and T_d is not consistent with the relationship between DVR_mean and T_mean. Therefore, coefficients p and q in equation (10) cannot be obtained directly using the regression equation. Thus, the unknown coefficients T_base and GDD_F in equation (11) were determined using the following methods.

A T_base value was tentatively determined from the coefficients of the regression equations for DVR_mean and T_mean at < 25°C and then this tentative value was optimized so that the RMSE becomes minimum. For example, the regression equation for ‘N67-10’ below 25°C is shown in Figure 3A. From the coefficients of this regression equation and equation (8), a tentative T_base = 14.3 was obtained.

When the T_base value is tentatively determined, the value for the left side of equation (11) (hereafter described as L₁₁) can be obtained from the T_u and observed T_d. The average of L₁₁ (L_11mean) was used as the tentative GDD_F value corresponding to the tentative T_base in this method.

When the tentative T_base is 14.3, the L_11mean obtained from the observed T_d values for all ‘N67-10’ data is 159.7. Assuming T_base = 14.3 and GDD_F = 159.7, the flowering date can be estimated using the observed T_d and equation (11). The RMSE of the estimated and observed flowering date is then 8.49 days.

If the tentative T_base is changed, the corresponding GDD_F and RMSE values also change. Figure 4A shows the RMSE value when the tentative T_base was changed by 0.1°C from 10–15°C. When T_base = 12.5, the corresponding GDD_F was 208.5, and the RMSE was a minimum of 6.95 days (Table 4).

Fig. 4

Change in RMSE of the observed and estimated flowering date for the ‘N67-10’ pineapple cultivar calculated by altering the coefficients (A) T_base or (B) a.

The T_base and GDD_F values based on the minimum RMSE of all cultivars were calculated using the same method (Table 4). The RMSE for each cultivar decreased by 0.1–1.5 days from that of the GDD model without the upper limit temperature. The T_base values were approximately 12°C for each cultivar and were slightly smaller than those obtained using the GDD model without the upper limit temperature, but there was no clear difference.

3)  Exponential function model with an upper limit temperature

To predict the flowering date using equation (14), we determined the coefficients a, b, and T_u as follows: the T_u was set to 25°C, the same as in the GDD model with the upper limit temperature.

The a value was tentatively determined using the exponential approximate equation for DVR_mean and T_mean at < 25°C. The approximate curve and equation for ‘N67-10’ at < 25°C are shown in Figure 3A. From the coefficients of this equation, the tentative a = 0.173 was obtained.

When the coefficient of a is tentatively determined, the value for the left side of equation (14) (hereafter described as L₁₄) can be obtained from the observed T_d. The average of L₁₄ (L_14mean) was calculated, and the reciprocal of L_14mean (1/L_14mean) was obtained as b corresponding to this tentative a.

For example, when the tentative a is 0.173, the L_14mean obtained from the observed T_d values of all ‘N67-10’ data is 1039, and its reciprocal is 0.00096. Assuming a = 0.173 and b = 0.00096, the flowering date can be estimated using the observed T_d and equation (14). The RMSE of the estimated and observed flowering date is then 6.18 days.

If the tentative a is changed, the corresponding b and RMSE values also change. Figure 4B shows the RMSE value when the tentative a was changed by 0.001°C from 0.15 to 0.20. When a = 0.168, the b corresponding a was 0.00107, and the RMSE was a minimum of 6.13 days (Table 4).

The a and b values based on the minimum RMSE of all cultivars were calculated using the same method and are shown in Table 4 along with RMSE values. The RMSE for each cultivar was 3.7–6.1 days. The RMSE of the model for predicting the flowering date was smaller for all cultivars using the approximation by the exponential function compared to the linear function. This may be due to the curvilinear relationship between DVR_d and T_d after budding to flowering, as suggested by the relationship between DVR_mean and T_mean (Fig. 3A). This indicates that the exponential function model with the upper limit temperature is the optimal model for predicting the flowering date in the present study.

Predicting the harvest date

1)  GDD model

Figure 3B shows the relationship between DVR_mean of ‘N67-10’ and the mean air temperature after flowering to harvest. DVR_mean increased as air temperature increased. A similar relationship between DVR_mean and mean air temperature was found for all cultivars as for ‘N67-10’, with a significant correlation (Table 5).

Table 5

Coefficients and RMSEs of models to predict the harvest date.

The coefficients p and q in equation (4) were obtained from the linear regression equation between DVR_mean and mean air temperature after flowering to harvest (the dashed line in Fig. 3B). T_base, GDD_F, and RMSE of each cultivar were determined using respective p and q (Table 5). The T_base was 0.4–4.8°C, which is lower than T_base after budding to flowering. The RMSE values were less than the SD of the observed days between flowering and harvest (Table 3).

2)  GDD model with an upper limit temperature

The number of days between flowering and harvest decreased as the mean air temperature increased; however, the effect of air temperature lessened when air temperatures exceeded around 23°C (Fig. 2). Therefore, T_u was set to 23°C. The T_base and GDD_F values based on the minimum RMSE were calculated using the same method as that of the model for predicting flowering date (Table 5).

The T_base values were 9.7–11.4°C. In a previous study, T_base of GDD models for predicting pineapple harvest date was 9.2°C for ‘Queen Victoria’ (Lechaudel et al., 2010) and 11.7°C for ‘Smooth Cayenne’ (Fleisch and Bartholomew, 1987). The T_base values of the GDD model without the upper limit were lower than T_base of the previous study; however, T_base values of the GDD model with the upper limit were close to them. These results suggest that the temperature response of DVR_d at < 23°C was similar to those of previous studies.

The RMSE decreased dramatically and was about half of the RMSE of the GDD model without the upper limit temperature. The decrease in RMSE to predict the harvest date was more than that to predict the flowering date, i.e., the effect of adopting the upper temperature limit was higher in the prediction of harvest than in the prediction of flowering.

A peak (optimum) temperature is known to exist for the DVR of many plant species (Hatfield and Prueger, 2015). At temperatures lower than the peak temperature, the DVR increases as the temperature rises; however, near the peak temperature, the rate of change in DVR with respect to temperature is smaller. Therefore, in a narrow temperature range, the relationship between DVR and air temperature can be approximated by a single straight line; however, over a wider temperature range, the RMSE is expected to be smaller when approximated by multiple straight lines. As a result, the RMSE of the GDD model with the upper limit temperature would have been smaller than that of the conventional GDD model. Since the upper temperature limit was lower in the prediction of harvest than in the prediction of flowering, the effect of adopting the upper temperature limit may have been higher in the prediction of harvest.

3)  Exponential function model with an upper limit temperature

The a and b values in equation (14) of the model for harvest date were calculated using the same method as the model for flowering date (Table 5). The RMSE values of the model for predicting the harvest date were smaller for ‘Bogor’, ‘Gold Barrel’, and ‘Okinou P17’ using the approximation generated by the exponential function than by the linear function. However, the RMSE values of ‘N67-10’ and ‘Soft Touch’ were larger than those obtained by a linear function. The small difference in RMSE between the linear and exponential functions was possibly because the curvature of the relationship between DVR_d and T_d after flowering to harvest was small, and the curve was close to a straight line, as suggested by the relationship between DVR_mean and T_mean (Fig. 3B). Although optimal models for predicting the harvest dates differed by cultivar, the smallest RMSE for each cultivar was 6.1–10.2 days.

Conclusions

The present study confirmed that the development of pineapples after budding is controlled largely by air temperature, but not clearly by day length. The GDD model with the upper limit temperature was more accurate at predicting flowering and harvest dates in Japan, which has a wide air temperature range, compared to the conventional GDD model. In particular, the prediction accuracy of harvest date was dramatically improved. Because the relationship between the developmental rate after budding to flowering and the air temperature was exponential rather than linear, the exponential function model with the upper limit temperature was shown to give a more accurate prediction of the flowering date. The RMSE values of the best model for each cultivar were 3.7–6.1 days to predict the flowering date and 6.1–10.2 days to predict the harvest date.

Our proposed models could be used to predict flowering and harvest dates in most pineapple-growing regions in Japan as they correspond to the two studied growing regions and the majority of pineapple cultivars. We anticipate that the models will be useful for planning shipments of pineapple in regions with wide temperature ranges such as Japan, and for the management of cultivation in response to climate change.

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