Plant development.

To predict plant development as a universal function of temperature, Monteith (1977) introduced the concept of thermal time, which is the summation of temperatures above a threshold called base temperature (Ferreira et al., 1997). Perry et al. (1997), for instance, used this concept to predict tomato harvest in the southeastern United States. However, reported base temperatures values for tomato ranged from 4 to 10 °C (Calado and Portas, 1987; Folker, 1979; Scholberg et al., 1997; Warnock and Isaacs, 1969). Warnock (1973), in Davis, CA, used a base temperature of 6 °C to calculate the degree-days accumulated from seeding to ripe fruit. The inconsistencies in the base temperature values may have several explanations, but one possible reason is that the base temperature is not identical for all crop development stages. Therefore, responses to temperature during the seedling phase, for example, may differ from responses during fruit setting or fruit ripening. However, one common base temperature is often considered for all stages of the crop. Another possibility is that cultivars may vary in cardinal temperatures. Another cause could be related to the methods and data sets for deriving the cardinal temperatures, as exemplified by reported base temperatures of 6, 8, and 10 °C obtained by Calado and Portas (1987) when estimated for three locations differing from warm early spring to a cool early spring in Portugal. They computed the base temperature with the intercept method. The hypothesis in crop modeling is that cardinal temperatures for a given species and cultivar should hold constant across weather and sites. The failure to do so may be evidence of incorrect cardinal temperatures and temperature response equations. Another aspect to be considered is the type of function that a crop growth model uses to account for the temperature dependence of processes. The CROPGRO model computes hourly temperatures from the maximum and minimum temperature data using a sinusoidal function during the day plus a decay function at night that was shown to predict hourly temperature accurately (Parton and Logan, 1981). Although the development rate may have linear interpolation between cardinal temperatures, the daily rate is averaged over 24 h of simulated air temperatures moving smoothly throughout the day.

Vegetative development and early reproductive phase to anthesis.

According to Van der Ploeg and Heuvelink (2005), the optimum temperature for early vegetative growth of tomato plants is 25 °C. Tomato vegetative development can be considered as the leaf appearance rate and it is also related to the truss appearance rate because the species is a sympodic with approximately one inflorescence every three leaves (Heuvelink, 2005). De Koning (1994) showed a linear increase of leaf appearance rate with increase in average air temperature, increasing from 0.2 leaf/d at 12 °C to a maximum of 0.5 leaf/d at 28 °C and decreasing thereafter until reaching zero at 48 °C. According to Adams et al. (2001), vegetative development in tomato has an optimum temperature between 22 °C (Topt₁) and 26 °C (Topt₂). The base temperature for this phase according to their calculation is 7 °C.

A linear relation between flowering and air temperature has also been observed by Abreu et al. (2000). Truss appearance rate increased linearly from 0.11 to 0.17 truss/d when average temperature was raised from 17 to 23 °C (De Koning, 1994). According to De Koning (1993), the number of trusses per week is enhanced by temperature with 0.05 truss/week/°C. Adams et al. (2001) found the cardinal temperature values for the early reproductive phase (progression to anthesis) to be similar to that for vegetative development with a base temperature of 7.2 °C. They had no data to set Tmax. From all these sources and considering Adams et al. (2001) as the most carefully studied, we adopted 7, 22, 28, and 48 °C for T_b, Topt₁, Topt₂, and Tmax, respectively, as cardinal temperatures for vegetative and early reproductive development in the modified CROPGRO-Tomato model parameter input file (Table 1).

Late reproductive phase, anthesis to maturity, and fruit growth duration.

A critical temperature sum needs to be reached over an individual fruit growth period for fruits to achieve maturity (Heuvelink, 2005). For indeterminate greenhouse tomato cultivars, this fruit growth duration value corresponds to that for individual fruits from anthesis to hand-harvest ripe maturity for that specific cohort. For indeterminate greenhouse cultivars, flower clusters continue to be formed and mature for many months after the first fruits are being harvested. However, for semideterminate field-grown cultivars that are harvested within a period of 1 to 2 weeks, the individual fruit growth period from anthesis to maturity (green-breaker) for the first larger fruits corresponds within a few days to the whole crop period from first fruit set to total crop maturity. For this late reproductive phase (fruit development rate and progression to maturity), Adams et al. (2001) found values of 5.7 °C for base and 22 °C for Topt1. De Koning (1994) proposed 4 °C for base temperature, ≈21 °C for optimum, and presented no data for Topt₂ or the maximum value. Aikman (1996) proposed that the time from anthesis to maturity for tomato is 806 degree-days using a base temperature equal to 4.75 °C. Using the 4 °C of De Koning (1994), this time translates to 940 degree-days, whereas Scholberg et al. (1997) calculated 722 degree-days using a base temperature equal to 10 °C. Beyond these differences in computing thermal units, it is also likely the cultivars may differ in the duration from anthesis to harvest maturity.

According to De Koning (2000), temperature appears to be a principal factor determining the duration of the tomato fruit growth period. His results showed this period to be 73 d at 17 °C and 42 d at 26 °C. Similar results were found by Rylsky (1979). Verkerk (1955) found that the time interval from anthesis to harvest was 90 d at 13 °C, 53 d at 19 °C, and 40 d at 26 °C. In his experiment, De Koning divided the growth period into five phases and found different responses to temperature depending on fruit age. High temperature shortened the growth period during two phases, first during the young developmental phrase and again close to maturity when temperature had a great impact on days to harvest. The middle phase of fruit growth was less sensitive to temperature. Adams et al. (2001) and Adams and Valdez (2002) found that when tomato plants were grown at 14, 18, 22, and 26 °C, fruits ripened after 95, 65, 46, and 42 d, respectively. They found that fruits were more sensitive to elevated temperature in their later stages of maturation. Their results showed a reduction in days to harvest of 8.7 to 11.2 d when temperatures were increased from 18 to 25 °C for a 3-week period.

In summary, for rate of development from anthesis to maturity and rate of fruit development/maturation, we used cardinal temperature values of 5.2, 26, 28, and 48 °C for base, Topt₁, Topt₂, and Tmax, respectively (Table 1). In absence of data to support the Tmax value, we used a high value of 48 °C to ensure rapid progression at high temperature.

Fruit set and pollination.

The temperature range for fruit setting in tomato is narrow and especially the night temperature is critical. The optimal range reported for fruit setting in tomato is reported to be 15 to 20 °C (Went, 1945) and 18 to 20 °C (De Koning, 1994). Fruit set is low at both low and excessively high temperatures. Hot conditions may result in cone splitting, stigma exertion, and pollen sterility, and maximal day temperature in excess of 32 °C and/or minimal night temperature above 21 °C will greatly reduce fruit set (Benedictos and Yavari, 2000; Moore and Thomas, 1952). These authors did not find cultivar differences in the tomato species they evaluated with respect to flower abortion at high temperatures (37/21 °C day/night). However, differences may occur between heat-sensitive and heat-tolerant tomato cultivars (Lohar and Peat, 1998). Because flower fertility is greatly decreased by these excessively high temperatures, the result will be fewer fruits set and reduced yield. The simulation of this effect by tomato models has been poor in general as also noted by Marcelis et al. (2009). The CROPGRO-Tomato species file includes a temperature function for fruit addition (rate) that mimics elevated temperature effects on flower fertility. The cardinal temperatures of 7 °C (Tb), 22 °C (Topt₁), and 26 °C (Topt₂) proposed by Adams et al. (2001) for progression to anthesis appear to also be valid for fruit addition and pollination except their experiments did not explore values for ceiling failure temperature. For fruit pollination, the value for ceiling failure temperature is critical because the fertility of tomato flowers is compromised at high temperature. According to Benedictos and Yavari (2000) and Moore and Thomas (1952), fruit set and pollination will fail at daytime temperatures above 32 °C or at night temperatures above 21 °C. Heuvelink (2005) reported that flower fertilization in tomatoes is greatly reduced at temperatures outside the 5 to 37 °C range and that the growth rate of pollen tube is adequate within this temperature range. According to Atherton and Harris (1986), fruit pollination will fail above 40 °C and the most critical stage appears to be meiosis, which occurs ≈9 d before anthesis. The optimal temperature for pollination according to those authors is between 17 and 24 °C. They proposed a base temperature of 5 °C. However, because the Adams et al. (2001) experiments were carried out in controlled temperature environments, we will adopt values from Adams et al. for Tb, Topt₁, and Topt₂ with slight modifications slanted toward information provided by other authors with the inclusion of ceiling temperature effects on fruit set. Therefore, we propose cardinal temperature values of 6, 21, 26, and 33 °C for base, Topt₁, Topt₂, and Tmax, respectively, for fruit set in the modified CROPGRO-tomato input file (Table 1). In addition, the CROPGRO-Tomato species file includes a function that reduces the partitioning limit to fruit growth (XFRT) if temperature is too high (partitioning to fruit is reduced above 28 °C and falls to zero at 34 °C) and this function is an additional contributor to elevated temperature effects on fruit addition in the model (Boote and Scholberg, 2006).

Linking flowering, fruit set, and fruit growth with individual fruit cohorts in CROPGRO.

Flowering, fruit set, and fruit addition in the CROPGRO model are processes based on a cohort structure, whereby successive flowers are added daily, which after a very short lag become fertilized fruits that grow slowly at first and then begin a phase of rapid growth (see Boote et al., 1998, for more detail on this). The addition of successive flowers, addition of successive fruits (translation from flower to fruit), and the growth of individual fruits depend on daily assimilate supply as well as these cardinal temperatures affecting fruit set and fruit growth rate. Thus, non-optimum temperatures, beyond those affecting photosynthesis, will reduce fruit set and individual fruit growth on each day. Fruit growth has first priority for assimilate up to the genetic partitioning limit of XFRUIT; thus, a carrying capacity of numbers of fruits or “fruit load” will be reached. Moreover, this partitioning limit to fruit is reduced by heat stress as indicated previously. First-set fruits will be larger than later ones, but after this carrying capacity is reached and numbers are “set,” all fruits share equally if assimilate is limiting.

Fruit growth rate.

Temperature is the climatic factor that most affects fruit rate growth in tomato (Pearce et al., 1993; Walker and Ho, 1977). Hurd and Graves (1984) suggested a Q₁₀ value of 1.7 for tomato fruit growth and Q₁₀ of 2.0 for fruit maturation (Hurd and Graves, 1984). For fruit growth rate (DM and water accumulation), Rylsky (1979) found an optimum equal to 26 °C, whereas Adams et al. (2001) found a regimen of 25/25 °C (day/night) to be optimum for fruit growth rate. De Koning (1994) proposed 10 °C for base temperature. No authors reported on the ceiling temperature for the fruit growth rate because such values are difficult to obtain. In the absence of data on ceiling temperature effects on fruit growth, the Tmax (32 °C) for fruit growth rate was assumed close to that of fruit set (33 °C). In addition, we selected a T_b of 6 °C to be consistent within 1 °C of the T_b values used for vegetative, reproductive, and fruit set processes. From all these sources, we adopted 6, 22, 25, and 32 °C for T_b, Topt₁, Topt₂, and Tmax, respectively, as cardinal temperatures for fruit (and seed) growth rate for the modified CROPGRO tomato input file (Table 1). Individual fruits grow at a daily rate that depends on the growth temperature as well as assimilate supply, and individual fruit growth is independent of whole plant developmental stages.

Photosynthesis response to temperature.

Many plants show an optimum temperature for photosynthesis close to their normal growth temperature (Lambers et al., 1998). The optimum temperature for tomato plant growth ranges between 22 and 30 °C (Ogweno et al., 2009). According to Heuvelink and Dorais (2005), tomato single-leaf photosynthesis has an optimum temperature between 20 and 30 °C at ambient CO₂ and between 25 and 30 °C when CO₂ concentration is high. In an experiment conducted by Xu et al. (1999) net photosynthesis increased steadily as the leaf temperature increased from 18 to 23 °C and then decreased steadily from 23 to 38 °C. Dark respiration increased in an exponential manner (by a factor of 10) as the leaf temperature increased from 18 to 38 °C. In a study conducted by Ogweno et al. (2009), detached tomato leaves were exposed to 15, 25, and 35 °C for 5 d. Leaves at 15 °C exhibited similar photosynthetic rate as those at 25 °C, whereas leaves at 35 °C had significantly lower net CO₂ assimilation rates (similar to reports of De Koning, 1994). Hu et al. (2006) demonstrated that the decreased photosynthetic rate at 35 °C was not related to stomata function but was related to impaired photosynthetic apparatus. Optimal temperature for photosynthesis of tomato at 350 ppm CO₂ was reportedly 22 °C (Acock, 1991; Cannell and Thornley, 1998) and 30 °C (Heuvelink and Dorais, 2005). Low temperatures of 4 and 6 °C were found to dramatically reduce photosynthesis of tomato plants (Byrd et al., 1995), whereas at 1 °C, photosynthesis of tomato leaves ceased (Martin et al., 1981). The T_b, Topt₁, Topt₂, and Tmax, respectively, for light-saturated, CO₂-saturated leaf photosynthesis were changed from 5, 26.5, 34, and 48 °C for the default leaf level (L version) to 6, 28, 34, and 48 °C in the modified model, in part from field calibration but considering these somewhat variable reports.

There is also a minimum night temperature effect in the model that reduces the next day’s leaf photosynthesis, which concurs with reported reductions in photosynthesis of tomato when the minimum temperature (Tmin; night temperature) is below 10 °C (Byrd et al., 1995). For the modified model, an asymptotic function reduces photosynthesis beginning at Tmin of 15 °C, going to zero rate at Tmin of –2 °C. The respective values for the default version were 5 and 0 °C with no justification. The justifications for modifying these two functions are the literature values reported previously along with calibration to field growth analyses. In particular, an increase in T_b from 5 to 6 °C and increase in Topt₁ to 28 °C were found necessary for accurately predicting biomass accumulation in the contrasting cooler seasons or times of year (Bradenton) vs. the warmer seasons in Quincy and Gainesville. Likewise, the greater reduction caused by the new Tmin values was needed for the same reason to reduce DM accumulation in the cooler time of year, especially at Bradenton, and to be consistent with literature confirming a night temperature effect on photosynthesis.

Stem and leaf growth.

The internode length growth shows a marked linear response to temperature, according to Langton and Cockshull (1997) who exposed tomato plants in growth chambers to 24 factorial combinations of day (DT) and night (NT) temperatures ranging from 12 to 32 °C. Their experimental data for tomato growing over a 10-d period at 16, 20, 24, and 28 °C average (over NT and DT) air temperatures showed that the corresponding lengths reached by the internodes were 12, 18, 27, and 30 mm, respectively. Their experiments showed increased extension growth with increase in DT and indicated that the optimum DT for extension growth is close to 28 °C. In the CROPGRO model (default and modified input parameter files), the Topt₁ for stem elongation and leaf expansion (specific leaf area) is 26 °C (close to Langton and Cockshull, 1997). There is no true T_b in the model for this, but the relative expansion declines to 0.4 at 11 °C and does not appear to go below 0.4.

With the goal of improving temperature-dependent parameters in the CROPGRO-Tomato model and after a literature search of cardinal temperatures for the species, the values published by Adams et al. (2001) were considered the most valuable and most reliable and were used because their study was carried out under precisely controlled temperature environments. Therefore, the adaptation of temperature-specific input parameters that are used for model simulation described in the next section are based mainly on the data reported by Adams et al. (2001), although the work of other authors is also considered for particular values or as substantiating information.

Model description.

The CROPGRO model used in this study is part of the DSSAT V4.0 software. A more complete model description can be found in the software documentation as well as in articles published by Boote et al. (1998) and Jones et al. (2003). The CROPGRO model simulates development based on multiple phases from emergence to harvest. Phenological development and growth processes such as leaf expansion and fruit growth depend on cardinal temperatures (Boote et al., 1998). Leaf area expansion depends on the new leaf mass produced and specific leaf area, which is influenced by light, temperature, root N uptake, and plant water status. The photosynthesis input to carbon balance begins as a function of light intercepted by the hedgerow canopy with leaf photosynthesis scaled up to canopy assimilation (Boote and Pickering, 1994). The daily growth of tissues results from the gain of photoassimilates through photosynthesis minus growth and maintenance respiration losses. The allocation of assimilates among vegetative organs is driven by partitioning coefficients, but fruits, once added, are explicit sinks that have first priority for using photoassimilates for new growth. Although considered semideterminate, the fresh-market tomato cultivars grown under field conditions exhibit low partitioning to vegetative sinks after the fruits begin their rapid growth phase. Thus, semideterminacy is simulated because the partitioning of assimilates to the reproductive sinks during the reproductive phase effectively causes leaf, stem, and root growth to end to the limits of (1-XFRUIT), where XFRUIT is a parameter that determines the fraction of the available dry matter allocated to fruits (Boote and Scholberg, 2006). Submodels for N and water balance as well as pest damage coupling simulations are also available and can be switched on or off according to specific applications. The model requires three types of genetics-related files: species, ecotype, and cultivar files. The species file accounts for the sensitivity of crop processes to environmental factors such as temperature, solar radiation, CO₂, and photoperiod. The cultivar parameters define the durations of life phases for each cultivar, and coefficients in the ecotype file represent traits that are common to groups of similar cultivars within species (Boote and Scholberg, 2006).

Model implementation and adaptation.

During Scholberg et al.’s (1997) adaptation of the generic crop model for field-grown tomato, relatively little information was available on temperature-based response for tomato. However, based on more recent studies (e.g., Adams et al., 2001; Heuvelink, 2005), it appears that the cardinal temperatures affecting phenology and plant processes are different from the values used by Scholberg et al. (1997), which are used in the CROPGRO-Tomato model (Version 4.0). Therefore, temperature-based functions were modified as discussed previously and the model was recalibrated, leading to a comparison of model performance of both the original and modified model versions.

Coefficients for life cycle were adjusted to account for effects of the new cardinal temperature parameters by comparison with the dates for the occurrence of first flowering, first fruit, and maturity observed during experiments carried out in Florida in 2006 and 2007. An additional objective in our calibration process was to preserve the same calendar day occurrences of phenological events as the prior experiments (1991 to 1996), because although phenology data were not available for those experiments, the model had been calibrated by Scholberg et al. (1997) with field data on DM production and yield under optimum irrigation, fertilization, and pest management so we assumed that prior phase durations were close to correct values. Genetic coefficients (EM-FL, FL-SH, FL-SD, SD-PM, FL-LF, XFRUIT, SFDUR, SDPDV, and PODUR) shown in Table 3 were calibrated for each of four different fresh-market tomato cultivars, although differences among cultivars were relatively few and small.

Parameters affecting leaf growth, DM production, and DM partitioning from transplanting to harvest were then calibrated against the observed data. Quality of dynamic simulation of leaf area index, aboveground biomass, fruit yield, and fruit number was evaluated by comparing the RMSE and the Willmott d index statistics for simulations using default vs. modified genetic parameters.

Field data used for model evaluation.

The growth data for evaluation consisted of a series of 10 experiments conducted between 1991 and 2007 at three locations in Florida: Bradenton, Gainesville, and Quincy. Two experiments in Bradenton were conducted by Brian McNeal (University of Florida, Soil and Water Science Department) from 1991 to 1992 and are described in Scholberg et al. (1997, 2000a, 2000b). The treatments selected for evaluation were well-irrigated and well-fertilized, and, therefore, no water or N stress was present. The soil at Bradenton was Eaugallie fine sand. The data sets for Bradenton 1994 and 1995, Gainesville 1996, and Quincy 1995 were derived from field experiments conducted by Scholberg using irrigated tomatoes. Excluding the Quincy studies, all experiments were carried out during the spring season. For Quincy, one data set corresponded to the spring season and the other to the fall season. The Gainesville 2006 and 2007 data set was obtained from a well-fertilized and well-irrigated tomato crop grown in the field under plastic mulch in the spring of both years (Rybak, 2009). For Gainesville in 1996, the soil was a fine sandy soil of the Millhopper series. For Gainesville in 2006 and 2007, the soil is classified as Candler fine sand (Buster, 1979). The Quincy soils belonged to the Orangeburg series. The treatment was drip-irrigated, and the N application rate was 330 kg·ha⁻¹ at Gainesville, 180 kg·ha⁻¹ at Quincy (spring), and 200 kg·ha⁻¹ at Quincy (fall). For the simulations, the irrigation and N rates were not used as model inputs because the N and water balance were turned off for all simulations so potential growth was simulated.

The cultivars were Sunny (Asgrow, Kalamazoo, MI) for Bradenton, Agriset 761 (Petoseed, Ventura, CA) for Spring 1995 in Quincy and Spring 1996 in Gainesville, Solarset (Univ. of Florida, Gainesville, FL) for Fall 1995 in Quincy, and Florida 47 (Seminis-Monsanto, St. Louis, MO) for Gainesville in 2006 and 2007. Therefore, a different set of genetic parameters was calibrated for each cultivar but only where necessary to differentiate among cultivars. Differences were relatively few because Florida’s fresh-market types are generally similar, except for ‘Solarset’.

Life cycle phase durations.

Decreasing the base temperature from 10 to 7 °C (Table 1), without changing the cultivar growth stage durations, accelerated the plant development rate and considerably shortened the life phase durations as expected (data not shown). Because of lower T_b, the cultivar phase durations were recalibrated to larger values to attain the same phenology dates simulated with the higher T_b of Scholberg et al. (1997). In addition, the age of the plants at the time of transplanting was adjusted for each experiment (Table 2). The simulation control file requires a transplant age. For the modified model, the plants were generally 1 to 3 d younger at the time of transplanting than used in the default version, again caused by the new base temperatures. The actual age of plants for those experiments was not available and therefore the criterion for this adjustment was a better phase duration adjustment when cardinal temperatures were modified considering that plant age at transplanting usually ranges between 3 and 4 weeks in Florida production systems.

Table 2.

Tomato plant age at transplanting in CROPGRO default Version 4.0 and calibrated values in the experimental file.

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Cultivar coefficient calibration was performed to adjust the life cycle after entering the new cardinal temperatures in the species file (Table 1) and results are shown in Table 3. The main changes in the cultivar file were the coefficients that determine the phase durations. First, the timing of flower and fruit appearance was adjusted. The cultivar coefficient EM-FL (days between plant emergence and flowering) was calibrated to a larger value to predict the anthesis date. The calibration of time from flowering to first fruit, FL-SH, required a new approach that is described in the following paragraph. The next sequential phase in the life cycle, the cultivar coefficient FL-SD (time from flower to first seed), was increased by ≈2 thermal days for cultivars Sunny and Agriset 761, by 1 thermal day for cultivar Florida 47, and by 4 thermal days in case of the cultivar Solarset. To improve the growth of fruits and seeds, the coefficients PODUR (duration of pod addition) and SFDUR (duration of seed filling) required calibration. Averaging over cultivars, the PODUR was increased ≈8 thermal days, and SFDUR was increased ≈1 thermal day. The phase duration coefficients described so far represent the phase durations that would occur under optimum temperature conditions (between Topt₁ and Topt₂), but actual calendar days for a phrase could be longer at non-optimum temperature. In addition, to give more priority to shell (fruit) growth over seed growth, the threshing percentage was slightly decreased from 9.2 to 8.5. The coefficient SLAVAR (specific leaf area under standard growing conditions) was decreased from 350 to 300 cm²·g⁻¹ for all cultivars.

Table 3.

Cultivar coefficients for CROPGRO-Tomato model, default, and calibrated values for cultivars Sunny, Agriset 761, Florida-47, and Solarset after updating the cardinal temperatures in SPE file.

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Individual tomato fruit ovules (small fruits) are already present at the time the subtending flower opens; thus, there is already a fruit present at flowering (thus the requirement for a very short thermal time for FL-SH, reduced from 8 to values ranging from 2.2 to 4.6 thermal days depending on the cultivar). More importantly, individual fruit growth after flower opening has an initial period of very slow growth, which lasts ≈2 weeks after anthesis (Bohner and Bangerth, 1988; Gillaspy et al., 1993; Heuvelink, 2005; Mapelli et al., 1978; Varga and Bruinsma, 1986). This lag in fruit growth was not considered in the default version. For the modified model, we set a shorter lag (FL-SH) as well as a slow initial growth phase based on data on individual fruit growth (Rybak, 2009). For CROPGRO (already used for the peanut model), there is a PM06 coefficient that represents the fraction of time between beginning fruit growth to beginning seed growth during which the fruit grows at a slower rate (defined by SHLAG). For tomato, the coefficient PM06 was increased from 0.0 to 0.55, creating a phase of slow growth continuing from 0% to 55% of the way from beginning fruit to beginning seed during which time the fruit is growing at 0.10 of the rapid rate (Table 4), which is followed by phase of rapid fruit growth for a duration defined by LNGSH. The SHLAG is the fruit growth rate in the slow phase as a fraction of the rapid fruit growth rate (SHLAG for tomato was set to 0.10). For tomato, that means that single tomato fruit growth after anthesis occurs at a rate that is 10% of the rate occurring during the rapid growth phase, which agrees with Dorais et al. (2001). Table 4 lists these ecotype parameters for PM06, SHLAG, and LNGSH.

Table 4.

Modified parameters in ecotype file, default Version 4.0 values, and calibrated values.

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For tomato, the parameter PMO6 was set to 0.55 (Rybak, 2009). This modification was needed to appropriately simulate the development and growth over time of three fruit cohorts whose development and growth began at different dates (separated by 1 week) based on the flower tagging dates (Rybak, 2009). Our experiments during 2007 indicated that first fruit (with small open flower) were set 28 d after transplanting. Therefore, our calibration process, in addition to the changes in cardinal temperatures, had to account for these observed fruit setting dates. Fruit set (small but slow-growing fruits) occurs within a few days (FL-SH ≈3) after flowering. The ability of the model to correctly predict the time for first fruit is important for our purposes of improving the model as described in this article as well as to mimic the fundamentals of individual fruit growth for tagged cohorts that will be explained in a future article.

Changing the cardinal temperatures also required recalibration of other parameters in the ecotype file (Table 4), primarily associated with an increase in the required thermal time to complete vegetative phases in the crop life cycle according to our observations. Furthermore, the maximum rate of leaf/truss appearance was slightly reduced from 0.52 in the default version to 0.45.

After calibration, model-predicted dates for anthesis, first fruit, and physiological maturity more closely matched field observations. This also agrees with reports in the literature that indicated that first anthesis occurs 3 to 4 weeks after transplanting and that the whole life cycle from transplanting to harvest takes ≈90 d under moderately warm temperature. In addition, individual cohorts tagged at different dates during 2006 and 2007 seasons were adequately tracked by the model, which was useful for later single fruit growth studies that we performed with the model.

Aboveground biomass and fruit yield.

The total aboveground biomass and fruit DM accumulation over time were well simulated using the modified parameters for all the experiments (Figs. 1A–B to 10A–B). On average, simulations using the modified parameters produced RMSE values that were 36% lower for both total biomass and fruit dry matter observations over time as compared with the default version (Table 5). Because the comparisons were made using time-series data, the Willmott d index provided a better indication of model performance and/or improvement. Overall, the d index was higher for total dry weight and fruit dry weight using modified parameters. On average, this index for the modified version was 0.99 and 0.97 for total above biomass and fruit dry weight, respectively. The default version produced an average d value equal to 0.97 for total above biomass and 0.93 for total fruit weight.

Table 5.

Root mean square error (RMSE) and Willmott d index for time-series simulations using default (D) as compared with modified (M) genetic parameter values.

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Simulated (−) and observed (■) data of ‘Sunny’ tomato grown at Bradenton, FL, during spring of 1991. (A) Total top dry weight, (B) total fruit dry weight, (C) leaf area index, and (D) fruit number per m².

Citation: HortScience horts 47, 8; 10.21273/HORTSCI.47.8.1038

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Simulated (−) and observed (■) data of ‘Sunny’ tomato grown at Bradenton, FL, during spring of 1991. (A) Total top dry weight, (B) total fruit dry weight, (C) leaf area index, and (D) fruit number per m².

Citation: HortScience horts 47, 8; 10.21273/HORTSCI.47.8.1038

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Simulated (−) and observed (■) data of ‘Sunny’ tomato grown at Bradenton, FL, during spring of 1991. (A) Total top dry weight, (B) total fruit dry weight, (C) leaf area index, and (D) fruit number per m².

Citation: HortScience horts 47, 8; 10.21273/HORTSCI.47.8.1038

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Simulated (−) and observed (■) data of ‘Sunny’ tomato grown at Bradenton, FL, during spring of 1992. (A) Total top dry weight, (B) Total fruit dry weight, (C) leaf area index, and (D) fruit number per m².

Citation: HortScience horts 47, 8; 10.21273/HORTSCI.47.8.1038

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Simulated (−) and observed (■) data of ‘Sunny’ tomato grown at Bradenton, FL, during spring of 1992. (A) Total top dry weight, (B) Total fruit dry weight, (C) leaf area index, and (D) fruit number per m².

Citation: HortScience horts 47, 8; 10.21273/HORTSCI.47.8.1038

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Simulated (−) and observed (■) data of ‘Sunny’ tomato grown at Bradenton, FL, during spring of 1992. (A) Total top dry weight, (B) Total fruit dry weight, (C) leaf area index, and (D) fruit number per m².

Citation: HortScience horts 47, 8; 10.21273/HORTSCI.47.8.1038

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Simulated (−) and observed (■) data of ‘Sunny’ tomato grown at Bradenton, FL, during spring of 1994. (A) Total top dry weight, (B) total fruit dry weight, (C) leaf area index, and (D) fruit number per m² .

Citation: HortScience horts 47, 8; 10.21273/HORTSCI.47.8.1038

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Simulated (−) and observed (■) data of ‘Sunny’ tomato grown at Bradenton, FL, during spring of 1994. (A) Total top dry weight, (B) total fruit dry weight, (C) leaf area index, and (D) fruit number per m² .

Citation: HortScience horts 47, 8; 10.21273/HORTSCI.47.8.1038

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Simulated (−) and observed (■) data of ‘Sunny’ tomato grown at Bradenton, FL, during spring of 1994. (A) Total top dry weight, (B) total fruit dry weight, (C) leaf area index, and (D) fruit number per m² .

Citation: HortScience horts 47, 8; 10.21273/HORTSCI.47.8.1038

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Simulated (−) and observed (■) data of ‘Sunny’ tomato grown at Bradenton, FL, during spring of 1995. (A) Total top dry weight, (B) total fruit dry weight, and (C) leaf area index.

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Simulated (−) and observed (■) data of ‘Sunny’ tomato grown at Bradenton, FL, during spring of 1995. (A) Total top dry weight, (B) total fruit dry weight, and (C) leaf area index.

Citation: HortScience horts 47, 8; 10.21273/HORTSCI.47.8.1038

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Simulated (−) and observed (■) data of ‘Sunny’ tomato grown at Bradenton, FL, during spring of 1995. (A) Total top dry weight, (B) total fruit dry weight, and (C) leaf area index.

Citation: HortScience horts 47, 8; 10.21273/HORTSCI.47.8.1038

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Simulated (−) and observed (■) data of ‘Agriset 761’ tomato grown at Quincy, FL, during spring of 1995. (A) Total top dry weight, (B) total fruit dry weight, and (C) leaf area index.

Citation: HortScience horts 47, 8; 10.21273/HORTSCI.47.8.1038

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Simulated (−) and observed (■) data of ‘Agriset 761’ tomato grown at Quincy, FL, during spring of 1995. (A) Total top dry weight, (B) total fruit dry weight, and (C) leaf area index.

Citation: HortScience horts 47, 8; 10.21273/HORTSCI.47.8.1038

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Simulated (−) and observed (■) data of ‘Agriset 761’ tomato grown at Quincy, FL, during spring of 1995. (A) Total top dry weight, (B) total fruit dry weight, and (C) leaf area index.

Citation: HortScience horts 47, 8; 10.21273/HORTSCI.47.8.1038

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Simulated (−) and observed (■) data of ‘Solarset’ tomato grown at Quincy, FL, during fall of 1995. (A) Total top dry weight, (B) total fruit dry weight, and (C) leaf area index.

Citation: HortScience horts 47, 8; 10.21273/HORTSCI.47.8.1038

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Simulated (−) and observed (■) data of ‘Solarset’ tomato grown at Quincy, FL, during fall of 1995. (A) Total top dry weight, (B) total fruit dry weight, and (C) leaf area index.

Citation: HortScience horts 47, 8; 10.21273/HORTSCI.47.8.1038

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Simulated (−) and observed (■) data of ‘Solarset’ tomato grown at Quincy, FL, during fall of 1995. (A) Total top dry weight, (B) total fruit dry weight, and (C) leaf area index.

Citation: HortScience horts 47, 8; 10.21273/HORTSCI.47.8.1038

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Simulated (−) and observed (■) data of ‘Agriset 761’ tomato grown at Gainesville, FL, during 1996. (A) Total top dry weight, (B) Total fruit dry weight, (C) Leaf Area Index, and (D) Fruit number per m²

Citation: HortScience horts 47, 8; 10.21273/HORTSCI.47.8.1038

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Simulated (−) and observed (■) data of ‘Agriset 761’ tomato grown at Gainesville, FL, during 1996. (A) Total top dry weight, (B) Total fruit dry weight, (C) Leaf Area Index, and (D) Fruit number per m²

Citation: HortScience horts 47, 8; 10.21273/HORTSCI.47.8.1038

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Simulated (−) and observed (■) data of ‘Agriset 761’ tomato grown at Gainesville, FL, during 1996. (A) Total top dry weight, (B) Total fruit dry weight, (C) Leaf Area Index, and (D) Fruit number per m²

Citation: HortScience horts 47, 8; 10.21273/HORTSCI.47.8.1038

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Simulated (−) and observed (■) data of ‘Agriset 761’ tomato grown at Gainesville, FL, during 1996. (A) Total top dry weight, (B) total fruit dry weight, (C) leaf area index, and (D) fruit number per m².

Citation: HortScience horts 47, 8; 10.21273/HORTSCI.47.8.1038

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Simulated (−) and observed (■) data of ‘Agriset 761’ tomato grown at Gainesville, FL, during 1996. (A) Total top dry weight, (B) total fruit dry weight, (C) leaf area index, and (D) fruit number per m².

Citation: HortScience horts 47, 8; 10.21273/HORTSCI.47.8.1038

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Simulated (−) and observed (■) data of ‘Agriset 761’ tomato grown at Gainesville, FL, during 1996. (A) Total top dry weight, (B) total fruit dry weight, (C) leaf area index, and (D) fruit number per m².

Citation: HortScience horts 47, 8; 10.21273/HORTSCI.47.8.1038

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Simulated (−) and observed (■) data of ‘Florida 47’ tomato grown at Gainesville, FL, during 2006. (A) Total top dry weight, (B) total fruit dry weight, and (C) leaf area index.

Citation: HortScience horts 47, 8; 10.21273/HORTSCI.47.8.1038

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Simulated (−) and observed (■) data of ‘Florida 47’ tomato grown at Gainesville, FL, during 2006. (A) Total top dry weight, (B) total fruit dry weight, and (C) leaf area index.

Citation: HortScience horts 47, 8; 10.21273/HORTSCI.47.8.1038

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Simulated (−) and observed (■) data of ‘Florida 47’ tomato grown at Gainesville, FL, during 2006. (A) Total top dry weight, (B) total fruit dry weight, and (C) leaf area index.

Citation: HortScience horts 47, 8; 10.21273/HORTSCI.47.8.1038

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Simulated (−) and observed (■) data of ‘Florida 47’ tomato grown at Gainesville, FL, during 2007. (A) Total top dry weight, (B) total fruit dry weight, and (C) leaf area index.

Citation: HortScience horts 47, 8; 10.21273/HORTSCI.47.8.1038

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Simulated (−) and observed (■) data of ‘Florida 47’ tomato grown at Gainesville, FL, during 2007. (A) Total top dry weight, (B) total fruit dry weight, and (C) leaf area index.

Citation: HortScience horts 47, 8; 10.21273/HORTSCI.47.8.1038

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Simulated (−) and observed (■) data of ‘Florida 47’ tomato grown at Gainesville, FL, during 2007. (A) Total top dry weight, (B) total fruit dry weight, and (C) leaf area index.

Citation: HortScience horts 47, 8; 10.21273/HORTSCI.47.8.1038

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Leaf area index.

For most of the experiments, the progression of leaf growth was well simulated by the modified model (Figs. 1C to 10C). In general, the modified parameters demonstrated better performance for simulating leaf area index (LAI) compared with the default version (statistics of time series data are shown in Table 5). Using the modified parameters the average RMSE for LAI over all the experiments was 44% lower than using default values. The Willmott d index was higher using modified parameters than using the default ones. Nevertheless, there were some weaknesses in LAI prediction: in several experiments, the maximum LAI was overestimated, and in other experiments, the LAI was underestimated. Because of these differences, it is difficult to obtain LAI simulations that satisfy the observations for all the experiments. Later in the season, the model was not able to reproduce accurately the decline in LAI associated with senescence and N remobilization, which appeared in some but not all seasons. This may be partially solved by “turning on” the N balance of the model as well as by adjusting remobilization functions in the model such as the maximum rate of remobilization of protein (NMOBMX) from vegetative to reproductive tissues, which interacts with N nutrition, which we have assumed as unlimiting in these simulations. The N nutrition may not be unlimiting in reality, so we declined to try such modifications.

Simulations of stem and leaf weight were improved using the modified parameters for all cultivars, years, and sites (data not shown). The specific leaf area (SLA) was not well simulated by the model, regardless of the version used. In addition, the Willmott d values for SLA were low, indicating that the variability in the mean SLA throughout the season was not well captured by the model. Two possible explanations exist: 1) observed SLA can vary depending on inclusion or exclusion of midrib (because we do not know how data before 2006 were collected); and 2) the model SLA depends basically on radiation and temperature, but modeled SLA may fail to account sufficiently for ontogenetic changes and changes associated with N nutrition.

Fruit number.

The fruit number over time was well simulated by the model when modified parameters were used (Figs. 1D to 8D). The default version produced poor simulation of fruit number, always overestimating this variable with an average error equal to 38 fruits per square meter and a d value equal to 0.78 (Table 5). The error averaged over all experiments using the modified values was equal to 11 fruits per square meter and the average d value was 0.95 (Table 5). Averaged over all experiments, the RMSE was 71% lower using the modified values comparing with the default version. The reason for the large PODUR (pod addition duration) value is that the model computes this based on seed growth rate (demand) relative to assimilate supply. This constructed feature is unrealistic for crops with low THRESH (ratio of seed to fruit plus seed), but this was not modified as we wished to stay with the standard coding of the CROPGRO model.

Sensitivity analyses of CROPGRO-Tomato to temperature.

It is important to evaluate model sensitivity to temperature after inputting these new literature values for cardinal temperatures and to evaluate for reasonable behavior of predicted life cycle, biomass accumulation, and fruit yield as affected by temperature. To implement this sensitivity analyses, we started with the reference climate from the Bradenton, FL, experiments (where the mean temperature over four growing seasons was 29/19 °C and the solar radiation was 21 MJ·d⁻¹). By comparison, the coolest environment of the 10 experimental seasons averaged 28/15 °C (Tmax and Tmin) and the warmest (fall) environment averaged 32/21 °C. We then simulated a range of temperatures by steps of 3 °C using fixed temperature regimes of 20/10, 23/13, 26/16, 29/19, 32/22, 35/25, and 38/28 °C Tmax and Tmin, maintaining the Tmax and Tmin differentials. Crop life cycle to maturity was shortest at the 29/19 and 32/22 °C, being particularly longer at the coolest temperatures (Fig. 11), which is consistent with literature (Adams et al., 2001; Adams and Valdez, 2002; Bertin, 2005). Both fruit yield and biomass declined with rising temperature (Fig. 11), but the fruit yield declined more rapidly, reaching zero at the 38/28 °C regime where biomass was only reduced 45% from the coolest to the warmest temperature. A long growth period was a significant contributor to greater fruit yield and higher biomass that occurred at cooler temperature, although photosynthetic reduction at warmer temperatures contributed to reduced biomass above 27 °C. Above 29/19 °C, poor fruit set contributed to lower fruit yield, as observed by progressively lower fruit harvest index above that temperature (data not shown). Simulated fruit size (average at maturity) was largest at coolest temperature (15 °C) and was reduced progressively as temperature increased (Fig. 11C). This is consistent with reports in the literature. Adams et al. (2001) found that fruit size was largest at 18 °C and declined as temperature increased, because the effect of shorter fruit growth duration dominated the effect of a higher optimum temperature for fruit growth rate. De Koning (1996), likewise, found largest fruits at 17 °C, decreasing to 23 °C.

Response of tomato development and yield to mean temperature. (A) Days to anthesis and maturity; (B) total crop mass and fruit dry matter yield; and (C) fruit size (g dry weight per fruit) for simulations with modified model parameters vs. default model parameters. Simulations performed at constant solar radiation of 21 MJ·m⁻²·d⁻¹ and constant day/night temperature regimes of: 20/10, 23/13, 26/16, 29/19, 32/22, 35/25, and 38/28 °C (graphed against mean temperature).

Citation: HortScience horts 47, 8; 10.21273/HORTSCI.47.8.1038

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Response of tomato development and yield to mean temperature. (A) Days to anthesis and maturity; (B) total crop mass and fruit dry matter yield; and (C) fruit size (g dry weight per fruit) for simulations with modified model parameters vs. default model parameters. Simulations performed at constant solar radiation of 21 MJ·m⁻²·d⁻¹ and constant day/night temperature regimes of: 20/10, 23/13, 26/16, 29/19, 32/22, 35/25, and 38/28 °C (graphed against mean temperature).

Citation: HortScience horts 47, 8; 10.21273/HORTSCI.47.8.1038

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Response of tomato development and yield to mean temperature. (A) Days to anthesis and maturity; (B) total crop mass and fruit dry matter yield; and (C) fruit size (g dry weight per fruit) for simulations with modified model parameters vs. default model parameters. Simulations performed at constant solar radiation of 21 MJ·m⁻²·d⁻¹ and constant day/night temperature regimes of: 20/10, 23/13, 26/16, 29/19, 32/22, 35/25, and 38/28 °C (graphed against mean temperature).

Citation: HortScience horts 47, 8; 10.21273/HORTSCI.47.8.1038

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In a comparison of modified to default parameters (Fig. 11), the life cycle simulated with the default model parameters appeared much too long at the cooler temperatures because the Scholberg et al. (1997) T_b of 10 °C was too high. With default parameters, the unrealistically long life cycle also led to unrealistically high total biomass and fruit yield at the coolest temperature (Fig. 11), whereas the fruit yield was not reduced enough at high temperatures. The photosynthesis parameters for the default version are partly responsible for very high biomass and yield at cool temperature. So we conclude that the modified parameters are a major improvement over the default parameters for predicting biomass and fruit yield sensitivity to temperature. The new parameters caused a smoother, more desirable progression in fruit size simulations vs. temperature.

Time course simulations of total crop mass and cumulative fruit yield at different temperatures for the modified model illustrate the lags in biomass and total fruit growth that occur with either too cool or too warm temperature as well as the higher yield potential associated with longer life cycle at moderately cool temperature (Fig. 12A–B). Total fruit fresh weight prediction over time is a new output from this model (Fig. 12C) as well as fruit size of successive fruit cohorts over time. Fruit fresh weight prediction is based on the approach proposed by Boote and Scholberg (2006), in which percent DM concentration is predicted for individual fruits as a function of individual fruit thermal age and used to convert individual fruit dry weight to fresh weight and aggregated over all fruits. The average fresh weight per fruit over time is shown in Figure 12D, but this does not adequately show that simulated early fruits are approximately twice as large as late-set fruits.

Response of tomato yield variables over time at different day/night temperature average. (A) Total biomass; (B) total fruit dry weight; (C) total fruit fresh yield; and (D) single fruit average fresh weight for simulations with modified (M) model parameters. Simulations performed at constant solar radiation of 21 MJ·m⁻²·d⁻¹ and constant day/night temperature regimes of: 20/10, 23/13, 26/16, 29/19, 32/22, 35/25, and 38/28 °C (graphed against mean temperature).

Citation: HortScience horts 47, 8; 10.21273/HORTSCI.47.8.1038

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Response of tomato yield variables over time at different day/night temperature average. (A) Total biomass; (B) total fruit dry weight; (C) total fruit fresh yield; and (D) single fruit average fresh weight for simulations with modified (M) model parameters. Simulations performed at constant solar radiation of 21 MJ·m⁻²·d⁻¹ and constant day/night temperature regimes of: 20/10, 23/13, 26/16, 29/19, 32/22, 35/25, and 38/28 °C (graphed against mean temperature).

Citation: HortScience horts 47, 8; 10.21273/HORTSCI.47.8.1038

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Response of tomato yield variables over time at different day/night temperature average. (A) Total biomass; (B) total fruit dry weight; (C) total fruit fresh yield; and (D) single fruit average fresh weight for simulations with modified (M) model parameters. Simulations performed at constant solar radiation of 21 MJ·m⁻²·d⁻¹ and constant day/night temperature regimes of: 20/10, 23/13, 26/16, 29/19, 32/22, 35/25, and 38/28 °C (graphed against mean temperature).

Citation: HortScience horts 47, 8; 10.21273/HORTSCI.47.8.1038

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