Materials and Methods

Sweet pepper [cultivar Artega (Enza Zadan, Enkhuizen, the Netherlands)] plants were grown hydroponically in a rockwool system in a greenhouse (width, 9 m; length, 18 m; gutter height, 4.75 m) at Tsukuba, Japan (lat. 36°26′N, long. 140°10′E). Seeds were sown in seed trays on 4 June 2019 and incubated in a germination chamber under dark conditions for 3 d at 28 °C. After germination, the seed trays were placed in a seedling growth chamber (Nae-Terrace; Mitsubishi Chemical Agri Dream, Tokyo, Japan) and raised for 3 weeks. In the growing chamber, the seedlings were illuminated with fluorescent lamps at a photosynthetic photon flux density (PPFD) of 400 μmol⋅m⁻²⋅s⁻¹ with a 16-h day (25 °C)/8-h night (20 °C) cycle at 1000 μmol⋅mol⁻¹ CO₂. The seedlings were fertilized every day with a commercial nutrient solution (High-Tempo; Sumitomo Chemicals, Tokyo, Japan) adjusted to an EC of 1.8 dS⋅m⁻¹. According to manufacturer’s instructions, this solution consisted of 10.07 mmol nitrogen (consisting of NO₃⁻ and NH₄⁺; ratio of total nitrates to NH₄⁺ = 0.09), 3.07 mmol phosphorus, 5.61 mmol potassium, 4.96 mmol calcium, 1.67 mmol magnesium, 0.34 mg⋅L⁻¹ manganese, 0.23 mg⋅L⁻¹ boron, 3.39 mg⋅L⁻¹ iron (Fe-EDTA), 0.13 mg⋅L⁻¹ zinc (Zn-EDTA), 0.04 mg⋅L⁻¹ copper (Cu-EDTA), and 0.06 mg⋅L⁻¹ molybdenum [(NH₄)₆Mo₇O₂₄⋅4H₂O].

After the seedling period, plants in their seed trays were moved to the greenhouse as a secondary nursery until the transplanting date. On 10 July 2019, the plants were transplanted onto rockwool slab (Grotop Expert; Grodan, Roermond, the Netherlands) in the greenhouse. The greenhouse was divided into six rows. The interrow width was ≈1.6 m. The plants were transplanted in the six rows. However, the plants in the outside rows were excluded from our measurements because the plants in outside rows received more light than those in the central four rows. Plants were planted with 96 plants in each row (3.75 plants/m²). The six plants at the north and south ends were excluded from measurements. Plants were trained with two main stems per plant. All flowers were removed at nodes 0 to 2 of the main stem. On each main stem with dichotomous branching, the weaker lateral stem was pruned just above the second leaf at 0 to 36 d after transplanting (DAT), and just above the first leaf at 37 to 246 DAT. The experiment ended at 246 DAT.

We supplied plants with a commercial nutrient solution (OAT-SA; OAT Agrio, Tokyo, Japan) adjusted to EC of 1.5 dS⋅m⁻¹ at 0 to 47 DAT, 2.0 dS⋅m⁻¹ at 48 to 70 DAT, and 2.5 dS⋅m⁻¹ at 71 to 246 DAT. The OAT-SA solution adjusted to an EC of 2.6 dS⋅m⁻¹ (including clear water with an EC of 0.3 dS⋅m⁻¹), which is the value recorded for a standard solution made in accordance with the manufacturer’s instructions, consisted of 21.5 mmol nitrogen (consisting of NO₃⁻ and NH₄⁺; ratio of total nitrates to NH₄⁺ = 0.02), 4.4 mmol phosphorus (P₂O₅), 10.2 mmol K (K₂O), 4.1 mmol calcium [CaO and Ca(NO₃)₂], 1.5 mmol magnesium (MgO), 2.75 mg⋅L⁻¹ manganese (MnO), 3.05 mg⋅L⁻¹ boron (B₂O₃), 7.95 mg⋅L⁻¹ iron (Fe-EDTA), 0.07 mg⋅L⁻¹ copper (Cu-EDTA), 0.17 mg⋅L⁻¹ zinc (Zn-EDTA), and 0.07 mg⋅L⁻¹ molybdenum [(NH₄)₆Mo₇O₂₄⋅4H₂O]. A drainage rate (drainage volume/volume of nutrient solution supplied) of ≈30% to 40% per day was maintained. Fertigation was performed every 30 min during the day (0700–1700 hr) from 0 to 52 DAT, and from sunrise to 1 h before sunset from 53 to 246 DAT; during the latter period, the frequency of application was determined by the amount of solar radiation.

Operating setpoints of the ventilation windows, heat pump, CO₂ gas regulator, and shade curtain are shown to Table 1. Setpoints of ventilation windows were mainly determined based on the periods of highly concentrated CO₂ application in the greenhouse. During the daytime at 85 to 246 DAT, the concentration of CO₂ gas was supplied from a liquid CO₂ source, and it was controlled when the ventilation windows were closed. A heat pump (Green Package; Nepon, Tokyo, Japan) was turned on for cooling during the early growing period (0–71 DAT). A shade screen (SLS50 Harmony; Svensson, Kinna, Sweden) was extended across the whole roof of the greenhouse during daytime when the outside solar radiation reached the setpoints (Table 1). To maintain a daily average temperature of 20 °C, a heater (House Kaonki; Nepon) was set to turn on at 104 to 246 DAT when the air temperature decreased 18 °C at night (1600–0800 hr) and 23 °C during the daytime (0800–1600 hr). From 0 to 246 DAT, a fogging system was operated during the daytime when the humidity deficit exceeded 8.0 g⋅m⁻³.

Table 1.Operating setpoints of ventilation windows, heat pump, CO₂ gas regulator, and shade curtain in the greenhouse for growing and examining sweet pepper ‘Artega’ from 0 to 246 d after transplanting.

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Air temperature, humidity deficit, solar radiation, and CO₂ concentration in the greenhouse were recorded every 1 min by a Ubiquitous Environmental Control System (YoshiMax; SANKI KEISO, Tokyo, Japan). Drainage and the amount of nutrient solution supplied were also recorded every 1 min by the system. We plotted the daily average air temperature (°C) and daytime and nighttime average air temperatures (°C) in the greenhouse during the whole experimental period (Fig. 1).

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During this experiment, the anthesis date was defined as the date when the petals had completely opened and pollen was considered to be produced (Wubs et al., 2011). Anthesis dates at each node of the main stem were investigated two or three times per week from 42 to 83 DAT. Flowers were selected randomly from plants in each row. To plot a fruit growth curve, 33 fruit were harvested at 78 DAT, 25 fruit were harvested at 84 DAT, 22 fruit were harvested at 90 DAT, and 34 fruit were harvested at 97 DAT from any plants in each row; 1 fruit was harvested between the age of 0 to 9 d after anthesis (DAA), 15 fruit were harvested between the age of 10 to 19 DAA, 36 fruit were harvested between the age of 20 to 29 DAA, 26 fruit were harvested between the age of 30 to 39 DAA, 34 fruit were harvested between the age of 40 to 49 DAA, and 2 fruit were harvested between the age of more than 50 DAA. Fresh fruit were assessed for fresh weight (grams per fruit) and dry matter weight (grams per fruit). Fruit were dried for at least 72 h at 105 °C before dry matter weight was measured (large forced ventilation drier; Maruto Testing Machine; Tokyo, Japan).

For three randomly selected plants in each row (a total of 12 plants), the anthesis and abortion dates at each node on the main stem at 0 to 246 DAT were recorded twice per week. At the time of each measurement, if the flowers had fallen, then the abortion date of each node was recorded. Anthesis and abortion dates of all flowers on the 12 plants were recorded, and all fruit were harvested at the fully mature stage.

Each main stem had 40 to 50 nodes (80–100 flowers per plant) at the end of the experiment. Twenty-nine flowers dropped before anthesis from 12 plants; therefore, we excluded them from the analyses. A total of 1035 data points were recorded for the anthesis and abortion dates from 12 plants. Flowers observed at 233 to 246 DAT were excluded from our analyses because it was possible that they would abort after the end of the experiment. Hence, the anthesis and abortion dates of 952 flowers at 0 to 232 DAT were used for the statistical analyses.

Daily total dry matter (TDM) production per unit area (grams per m²) was defined as the source strength that day. TDM_m at m DAT was estimated based on Eqs. [1] to [3] using the calculations presented by Higashide (2018) and Watabe et al. (2021): $${\text{TDM}}_{\text{m}}={\text{LUE}}_{\text{m}}\times {\text{IL}}_{\text{m}}$$[1] $${\text{LUE}}_{\text{m}}=\text{a}\times \text{ln}\left({\text{CO}}_{2\text{m}}\right)+\text{o}$$[2] $${\text{IL}}_{\text{m}}=\left(1-{\text{e}}^{-\text{k}\times {\text{LAI}}_{\text{m}}}\right)\times {\text{T}}_{\text{g}}\times {\text{R}}_{\text{p}}\times {\text{Sr}}_{\text{m}}$$[3] where LUE_m (grams per megajoule) is the light use efficiency at m DAT (Table 2). LUE_m is a function of daytime mean CO₂ concentration in the greenhouse. IL_m (megajoules per m²) is the cumulative amount of light intercepted by the plant at m DAT; this amount is a function of outside solar radiation at m DAT (Sr_m; megajoules per m²), light transmissivity of the greenhouse (T_g = 0.65 MJ⋅MJ⁻¹) (Watabe et al. 2021), ratio of photosynthetically active radiation (PAR) to outside solar radiation (R_p = 0.5 MJ⋅MJ⁻¹) (Ohtani 1997), leaf area index at m DAT (LAI_m; m² per m²), and light extinction coefficient (k) (Monsi and Saeki, 2005; Watabe et al., 2021). Coefficients for estimating LUE_m and light extinction coefficients were cited by Watabe et al. (2021). Details of the methodology for estimating light extinction coefficients were reported by Monsi and Saeki (2005) and Watabe et al. (2021). During this experiment, PPFD and LAI in each plant were measured at 196 and 198 DAT and at 210 or 211 and 212 DAT, respectively. During the PPFD measurements at 196 and 210 or 211 DAT, the plant canopy was segmentalized into four and five layers, respectively, and the PPFD in each layer was measured by using a line quantum sensor (LI-191R; LI-COR, Lincoln, NE) and light meter (LI-250A; LI-COR). Each leaf area in each layer was measured individually to estimate the LAI. During the destructive measurement, the leaf area was measured using an automatic leaf area meter (AAC-400; Hayashi Denko, Tokyo, Japan). The daily LAI was obtained by linear interpolation of the averaged data of destructively measured plants. Eight plants were measured destructively at 0, 15, 30, 49, 84, 118, 160, 184, 198, and 212 DAT. Approximately two leaves grew in each node, and the node numbers eventually reached 37 to 42 at 212 DAT. Therefore, ≈74 to 84 leaves per stem were measured at 212 DAT.

Table 2.All abbreviations and units considered in the model used for estimating the effects of source and sink strength on the fruit set ratio of sweet pepper ‘Artega’ from different days before and after the anthesis date.

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The daily total dry matter production per stem (TDM_{m_st}; grams per stem) was obtained using Eq. [4] by dividing the TDM_m by the stem density: $${\text{TDM}}_{\text{m}\_\text{st}}=\frac{{\text{TDM}}_{\text{m}}}{\text{STD}}$$[4] where STD is the stem density in this experiment (7.5 stems/m²) and st is the number of stems per plant.

We used the Gompertz function in Eq. [5] based on the method of Wubs et al. (2012), to express the relationship between the cumulative temperature after anthesis and dry matter weight per fruit (DWF): $$\text{DWF}=\text{K}\times {\text{b}}^{{\text{e}}^{-\text{c}\times \text{x}}}$$[5] where DWF is the dry matter weight per fruit (grams per fruit) at time x (cumulative temperature from 0 DAA; °C⋅d⁻¹), K is the asymptote line, b is the intercept of the function, and c is a constant determining the curvature.

Fruit sink strength per fruit (SSF_{m_n}; grams per fruit) at m DAT was calculated using Eq. [6] according to Wubs (2010) and Wubs et al. (2012). Eq. [6] is a derivative of Eq. [5]: $${\text{SSF}}_{\text{m}\_\text{n}}=-{[\left(\text{K}\times {\text{b}}^{{\text{e}}^{-\text{c}\times \text{x}}}\right)\times \ln \left(\text{b}\right)\times \left(\text{c}\times {\text{e}}^{-\text{c}\times \text{x}}\right)]}_{\text{m}}$$[6] where n is the number of fruit per stem at m DAT. The explanatory variable x and the coefficients (K, c, and b) are the same as those in Eq. [5]. By accumulating SSF_{m_n} (grams per fruit) for each fruit at m DAT, the daily fruit sink strength per stem (SST_{m_st}; grams per stem) can be estimated using Eq. [7]. The source-to-sink ratio (SSR_{m_st}; grams per gram) per stem at m DAT was calculated using Eq. [8]: $${\text{SST}}_{\text{m}\_\text{st}}={\displaystyle {\mathrm{\Sigma }}_0^{\text{n}}\left({\text{SSF}}_{\text{m}\_\text{n}}\right)}$$[7] $${\text{SSR}}_{\text{m}\_\text{st}}=\frac{{\text{TDM}}_{\text{m}\_\text{st}}}{{\text{SST}}_{\text{m}\_\text{st}}}$$[8]

Wubs et al. (2007, 2009a, 2011) reported that flowers were most susceptible to abortion just before anthesis and at 0 to 14 DAA. During this experiment, we investigated the anthesis and abortion dates of 952 flowers at 0 to 232 DAT. An abortion rate of 78.1% occurred between 0 and 7 DAA, and a rate of 91.4% occurred between 0 and 14 DAA. Therefore, by using the method of Higashide (2009), we investigated the average TDM_{m_st}, SST_{m_st}, SSR_{m_st}, and fruit number (FRN_{m_st}; fruit per stem) at m DAT at different periods before and after anthesis. Then, we determined Pearson’s correlation coefficients (r) of TDM_{m_st}, SST_{m_st}, SSR_{m_st}, and FRN_{m_st} with the fruit set ratio (FSR) every 7 d from 25 to 232 DAT to determine the period with the highest correlation with the FSR. During the calculation of FSR, data from 0 to 24 DAT were excluded because we could not measure the first flower of 12 investigated plants until 24 DAT. The FSR_m at m DAT was defined using Eq. [9]: $${\text{FSR}}_{\text{m}}=\frac{{\text{BFL}}_{\text{m}}-{\text{AFL}}_{\text{m}}}{{\text{BFL}}_{\text{m}}}$$[9] where BFL_m is the number of flowers at m DAT and AFL_m is the number of aborted flowers at m DAT. We counted BFL_m and AFL_m once to twice per week in the greenhouse.

After identifying the factors affecting FSR_m and the effective period for FSR_m, we analyzed the quantitative effects of these factors within an effective period on FSR_m by applying a regression analysis. We used statistical software (R version 3.6.3; R Foundation for Statistical Computing, Vienna, Austria) for all analyses.

Results

The observed DWF (grams per fruit) increased gradually with the cumulative temperature after anthesis (Fig. 2). The Gompertz function was applied to estimate the relationship between cumulative temperature after anthesis and DWF. We plotted the estimated DWF values (solid line in Fig. 2). We chose the Gompertz function for expressing fruit growth based on previous studies (Adams et al., 2001; Wubs, et al., 2012). All estimated parameters (K, b, c) of the Gompertz function were statistically significant (P < 0.001); therefore, this function could describe fruit growth with statistical validity during this experiment. We also plotted a differential curve of the Gompertz function (dashed line in Fig. 2) and treated it as the SSF_{m_n}. The estimated DWF values (solid line in Fig. 2) showed increasing cumulative fruit weight corresponding to the cumulative temperature. The differential curve of the Gompertz function (dashed line in Fig. 2) showed the instantaneous fruit weight increase with each cumulative temperature. SSF_{m_n} increased rapidly from anthesis (0 °C⋅d⁻¹) to the vertex of the regression curve (at a cumulative temperature of ≈622 °C⋅d⁻¹); then, it decreased gradually from the vertex to the harvestable period (1200 °C⋅d⁻¹ to 1400 °C⋅d⁻¹). In other words, the fruit growth rate reaches its maximum at 622 °C⋅d⁻¹, which indicates a half time x temperature period for the fruit to reach its final size. At this point, the fruit has not started to change its color.

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The estimated TDM_{m_st} fluctuated from 0.2 to 3.1 g/stem per day with the changes in solar radiation and daily CO₂ concentration in the greenhouse (Fig. 3A and B). Estimated and observed cumulative TDM_{m_st} are shown in Fig. 3C. We examined the SST_{m_st} and SSR_{m_st} of weekly moving averages from 0 to 232 DAT (Fig. 4A). The daily SST_{m_st} had an inverse relationship with SSR_{m_st}; a high SST_{m_st} with a low SSR_{m_st} alternated with a low SST_{m_st} with a high SSR_{m_st}. The daily SST_{m_st} at 73 to 94 DAT, 135 to 150 DAT, and 207 to 234 DAT exceeded 0.7 g/stem. We plotted the change in the mean FSR_m of 10-d moving averages from 0 to 232 DAT (Fig. 4B). High values (>0.50) were observed at ≈20, 60, 120, and 180 DAT (Fig. 4B). The values fluctuated cyclically; the mean FSR_m over the whole period was ≈0.37 (Fig. 4B). SSR_{m_st} at 0 to 26 DAT, 110 to 123 DAT, and 170 to 192 DAT exceeded 3.0; these periods corresponded to periods of high FSR_m (exceeding 0.50) (Fig. 4A and B). High SST_{m_st} periods corresponded to periods of low FSR_m (<0.20) (Fig. 4A and B). Additionally, SST_{m_st} increased and FSR_m decreased ≈30 d (≈622 °C⋅d⁻¹ from anthesis) after each flush period.

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Harvested fruit fresh yields of 10-d moving averages fluctuated cyclically through cultivation (Fig. 4C). Before ≈2 months from harvest, FSR_m also fluctuated with the same tendency (Fig. 4B and C). From 25 to 232 DAT, the average daily TDM_{m_st} was 1.16 g/stem, the average daily SST_{m_st} was 0.59 g/stem, and the average daily SSR_{m_st} was 2.18 g⋅g⁻¹ (data not shown).

Table 3 shows Pearson’s correlation coefficients (r) of the FSR_m and weekly average TDM_{m_st}, SST_{m_st}, SSR_{m_st}, and FRN_{m_st} during different 7-d periods before and after anthesis during the period from 25 to 232 DAT. FSR_m was correlated positively and significantly with TDM_{m_st} and SSR_{m_st}, except during the periods from 9 DBA to 5 DAA and from 9 DBA to 1 DBA, respectively. FSR_m was correlated negatively and significantly with SST_{m_st} and FRN_{m_st}, except during the period from 5 DBA to 13 DAA for FRN_{m_st} (Table 3). The r values in the case of SST_{m_st} during the period 3 DBA to 5 DAA were more than 0.60; in the case of SSR_{m_st}, the r values during the period 1 DBA to 13 DAA were also more than 0.60 (Table 3).

Table 3.Pearson’s correlation coefficients (r) of the relationships between weekly average fruit set ratio (FSR_m) and daily average total dry matter production per stem (TDM_{m_st}), fruit sink strength per stem (SST_{m_st}), source-to-sink ratio per stem (SSR_{m_st}), and fruit number per stem (FRN_{m_st}) of sweet pepper ‘Artega’ grown in the greenhouse from 25 to 232 d after transplanting. Weekly average FSR_m for 7-d periods (n = 30) were calculated using 909 flower samples from 12 plants, and the corresponding TDM_{m_st}, SST_{m_st}, SSR_{m_st}, and FRN_{m_st} were calculated for 7-d periods from 9 d before anthesis (DBA) to 13 d after anthesis (DAA).

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We examined the relationships between FSR_m calculated using 30-sample moving averages and the average TDM_{m_st} (Fig. 5A), SST_{m_st} (Fig. 5B), SSR_{m_st} (Fig. 5C), and FRN_{m_st} (Fig. 5D) of these samples. Explanatory factors were sorted in ascending order and averaged during the period 1 to 7 DAA. This period was chosen because the r value for the correlation between FSR_m and SSR_{m_st} was highest (Table 3), and the relationships between FSR_m and TDM_{m_st}, SST_{m_st}, and SSR_{m_st} during this period were all statistically significant. The R² value of the regression curves for the correlation of FSR_m with TDM_{m_st} was 0.41 (Fig. 5A). The R² value of the regression curves for the correlation of FSR_m with SST_{m_st} was 0.80 (Fig. 5B). The R² value of the regression curves for the correlation of FSR_m with SSR_{m_st} was 0.81 (Fig. 5C). The R² value of the regression curves for the correlation of FSR_m with FRN_{m_st} was 0.14 (Fig. 5D). FSR_m increased as TDM_{m_st} increased within the range of 0.5 to 2.0 g/stem per day (Fig. 5A). FSR_m decreased as SST_{m_st} increased; then, it tended toward saturation at values ≥0.1 (Fig. 5B). FSR_m increased when SSR_{m_st} was within the range of 1.0 to 4.0; then, it tended toward saturation at values ≤1.0 (Fig. 5C).

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Discussion

We defined fruit sink strength based on fruit growth (Eqs. [5] and [6]) according to the method of Wubs (2010) and Wubs et al. (2012). During some studies, fruit sink strength was calculated on a daily basis (Kleijbeuker and Lee, 2019; Wubs et al., 2009b). However, fruit growth is closely related to the daily mean temperature (de Koning, 1994). For example, the growth rate of tomato (Solanum lycopersicum) fruit grown in high temperatures was significantly increased compared to tomato fruit grown in low temperatures (Adams et al., 2001). Therefore, we calculated the fruit sink strength based on the cumulative temperature (Fig. 2). Adams et al. (2001) indicated that the tomato fruit weight decreased when grown under high temperatures. This implies that the fruit sink strength of each fruit also fluctuates during the seasons. During this experiment, the monthly averaged fruit fresh weight throughout cultivation also slightly fluctuated (P < 0.05), but all values were within the sd (Fig. 6). Therefore, during this experiment, we could calculate the fruit sink strength without considering the seasonal variation of the fruit weight.

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Crop parameters for estimating TDM_{m_st} [IL_m (k), LUE_m (a and o)] have statistical validity according to Watabe et al. (2021). During this study, we used TDM_{m_st} calculated using these crop parameters, but there were differences between the observed and calculated TDM_{m_st} at 84 and 118 DAT (observed TDM_{m_st} > calculated TDM_{m_st}); these differences decreased after 118 DAT (Fig. 3C). During our experiment, we enhanced the EC of the nutrient solution from 2.0 to 2.5 dS⋅m⁻¹ at 71 DAT. Yasuor et al. (2013) reported that the EC of the nutrient solution was closely related to the photosynthesis ability of sweet peppers. The enhancement of the EC of the nutrient solution at 71 DAT might improve photosynthesis and TDM_{m_st}.

By using models of dry matter production (Higashide, 2018, 2022; Watabe et al., 2021) and fruit growth based on Eqs. [5] and [6], we investigated the quantitative conditions associated with fruit set and abortion. As a result, the fruit set ratio was significantly and positively correlated with the total dry matter production and negatively correlated with the fruit sink strength (Table 3, Figs. 4 and 5). We represented the source-to-sink ratio using Eq. [8] as a function of total dry matter production and fruit sink strength. The fruit set ratio was also significantly and positively correlated with the source-to-sink ratio (Table 3, Fig. 5C). Based on these results, we propose that yield fluctuation of sweet pepper could be closely related to source-to-sink ratio fluctuation, which was determined by the change in total dry matter production and fruit sink strength. In other words, yield fluctuations are caused by both weather conditions and the quantity of fruit the plant is producing at the moment and the growth phase of those fruit.

Rapid increases in the source-to-sink ratio throughout the experimental period (Fig. 4A) were closely related to the occurrence of flushing, as reported previously (Heuvelink et al., 2004; Kleijbeuker and Lee, 2019; Wubs et al., 2009a, 2009b). Several studies have already presented models of the source-to-sink ratio and have evaluated its effects on the fruit set (Kleijbeuker and Lee, 2019; Wubs et al., 2009b, 2011). Our results showed that the fruit set ratio was significantly correlated with the source-to-sink ratio (Fig. 5C) when considering both the source-to-sink ratio and the most critical period for the fruit set (Table 3). From 1 DBA to 7 DAA, positive correlations between the source-to-sink ratio and fruit set ratio were observed (Table 3). Our results show an obvious relationship between flowering/pollination and fruit set. This period comprised anthesis to 156 ± 15 °C⋅d⁻¹ and represented the cumulative temperature. That is, the source-to-sink ratio from anthesis to ≈156 °C⋅d⁻¹ was most closely related to the fruit set ratio results reported by Wubs et al. (2011). Because there was no difference between the source-to-sink ratio from anthesis to ≈156 °C⋅d⁻¹ and the source-to-sink ratio from 1 DBA to 7 DAA during our experiments, we described the source-to-sink ratio on a daily basis during this study.

The fruit set ratio increased when the source-to-sink ratio at 1 to 7 DAA (from anthesis to 156 °C⋅d⁻¹) was within the range of ≈1.0 to 4.0; the increment in the fruit set ratio decreased when the source-to-sink ratio increased to more than ≈4.0 (Fig. 5C). The fruit set ratio was ≈0.5 when the source-to-sink ratio was within the range of 3.0 to 4.0. In other words, it will be possible for growers to harvest constant fruit quantities by supplying three- to four-times the surplus photosynthates compared with that of fruit growth. Therefore, controlling and maintaining the source-to-sink ratio within this range might mitigate yield fluctuations. However, source and fruit sink manipulation may affect the dry matter distribution to each organ; therefore, further experimental studies are needed. Also, we investigated the relationship between the fruit set ratio and the source-to-sink ratio within the following environments: daily average temperature, ≈20 to 27 °C (Fig. 1); daytime CO₂ concentration in the greenhouse, ≈400 to 1600 μmol⋅μmol⁻¹ (Fig. 3); and daily drainage rate, 30% to 40%. However, not only the source-to-sink conditions within plants but also the high and low temperatures (<16 or <32 °C) (Bosland and Votava, 2012), lack of fertigation (positive correlation between irrigation level and fresh yields) (de Souza et al., 2019), and CO₂ application during the winter season (Nederhoff and van Uffelen, 1988) considerably change the amount of fruit set as well. Therefore, we consider that our presented hypothesis has validity within the range of the environments used during this experiment. Overall, based on the relationship between the fruit set ratio and source-to-sink ratio at 1 to 7 DAA, it would be possible to predict the fruit set ratio. Prediction of the fruit set will help to moderate flushing and promises to help growers and retailers of sweet peppers.

In conclusion, we revealed the quantitative effects of the source-to-sink ratio and its critical period on the fruit set ratio. The fruit set ratio was positively correlated with SSR_{m_st} (R² = 0.81) from 1 to 7 DAA (from anthesis to 156 °C⋅d⁻¹). Therefore, the change in the source-to-sink ratio is similar to the fluctuation of the fruit set ratio, and the yield fluctuation occurred because the quantity of harvestable fruit could be determined by the fruit set ratio. Hence, the yield fluctuation of sweet pepper could be partly explained by this relationship. Knowledge of this relationship should be helpful for managing sweet pepper production and planning the harvest and labor distribution.