Forcing Temperature Effects on Plant Development for Containerized Blackberry Grown Using Long-Cane Techniques

: Dormant containerized blackberry plants grown as long canes are forced into protected environments, such as plastic tunnels or greenhouses, to schedule harvesting for important market weeks. The time needed to produce a crop is mainly a function of temperature. In this study, the objectives were to quantify the effects of temperature on plant development rates for long-cane blackberry and develop simple models predicting the time from forcing dormant plants to ﬁrst open ﬂowers and ripe fruit as a function of average daily temperature (ADT). The crop time and ADT at the ﬁrst-ﬂower and -fruit stages were measured for the cultivars ‘Loch Ness’, ‘Osage’, ‘Ponca’, and ‘Prime-Ark ® 45 (cid:48) grown as long canes during a greenhouse and high-tunnel experiment, and the days to ﬂowering and fruiting were converted to rates by calculating the reciprocal. Nonlinear models relating ﬂowering and fruiting rates to ADT were developed for each cultivar using a combination of the experimental data and base (6 ◦ C), optimum (25 ◦ C), and maximum (35 ◦ C) temperature parameters derived from a previous blackberry heat unit study. Model accuracy was evaluated by comparing the predicted to observed times to ﬁrst ﬂower and fruit per cultivar. Average daily temperature was shown to have a main inﬂuence on crop timing, as shown by a strongly positive and near 1:1 relationship between predicted and observed days to ﬂowering/fruiting. However, there was signiﬁcant variability depending on the cultivar and model accuracy within ± 7 days, ranging from 50% (‘Prime-Ark ® 45) to 90% (‘Loch Ness’) for the ﬂower models and from 60% (‘Prime-Ark ® 45) to 100% (‘Loch Ness’) for the fruit models. To the best of our knowledge, this study is the ﬁrst to characterize the relationship between temperature and crop timing for soilless long-cane blackberry, and it provides a framework for modeling temperature effects on crop timing for these systems. The authors discuss further methods to improve model accuracy and precision for commercial use. These models can also be used for general training purposes to help educate growers on how temperature inﬂuences crop scheduling during long-cane blackberry production.


Introduction
Production using soilless culture and protected environments, such as plastic tunnels and greenhouses, is an increasing trend for all berry crops [1,2].The soilless "long-cane" production of raspberry and blackberry originated decades ago in The Netherlands, the U.K., and Belgium but has since been adopted in other European countries as well as in Africa, Southeast Asia, North and South America, and Australia [3][4][5][6][7][8].The term "longcane" is derived from how these crops are grown and trellised in soilless cultivation [3][4][5].Blackberry and raspberry have a perennial root system producing biennial stems called "canes"; in the first year, these canes grow vegetatively (and are called "primocanes"), and in the second year, after dormancy, these canes (now called "floricanes") produce flowers and fruit before senescing [8].The long-cane process involves growing vegetative primocanes (~2 m height), usually outdoors during the summer of year 1, allowing the 2 of 11 plants to initiate flower bud development in the fall, followed by transferring the plants into cold storage (−1.5 to 4 • C) to satisfy chilling requirements and dormancy, and finally transferring the dormant plants into plastic tunnels or greenhouses to force flowering and fruit development in year 2, as shown in Figure 1 [9][10][11].Plants are grown completely in soilless substrates and containers with cultural practices more like those for greenhouse hydroponics than traditional field-based production [7,12].Varying the length of cold storage and the environmental conditions during forcing, particularly air temperature, can be manipulated as a strategy for scheduling crops so that they finish (i.e., harvest) during important and off-season market weeks [12][13][14][15].
Horticulturae 2023, 9, x FOR PEER REVIEW 2 of 11 primocanes (~2 m height), usually outdoors during the summer of year 1, allowing the plants to initiate flower bud development in the fall, followed by transferring the plants into cold storage (−1.5 to 4 °C) to satisfy chilling requirements and dormancy, and finally transferring the dormant plants into plastic tunnels or greenhouses to force flowering and fruit development in year 2, as shown in Figure 1 [9][10][11].Plants are grown completely in soilless substrates and containers with cultural practices more like those for greenhouse hydroponics than traditional field-based production [7,12].Varying the length of cold storage and the environmental conditions during forcing, particularly air temperature, can be manipulated as a strategy for scheduling crops so that they finish (i.e., harvest) during important and off-season market weeks [12][13][14][15].Scheduling crops requires the ability to predict the amount of time needed for production, which involves identifying how quickly plants progress (i.e., the rate of progress) towards desired stages of plant development [16,17].The time needed to reach an important developmental stage, for example, the number of days to flowering or fruiting (DTF), is converted to a rate by calculating the reciprocal of the DTF (e.g., 1/DTF).The influence of environmental factors, like temperature and light, on plant development rates can be quantified using mathematical functions [17].These types of models can be used as decision-support tools, for example, for long-cane blackberry and raspberry, allowing growers to select the date at which dormant long-canes should be forced in a greenhouse or high tunnel and manipulate the production temperatures to schedule crops' off-season harvesting.
The rate of progress towards a development event, such as flowering or fruiting, is mostly a function of average daily temperature (or ADT) [18,19], as shown in Figure 2. Plant development rates increase from zero to a maximum value when the ADT increases from a base temperature to an optimum temperature for plant growth, respectively [20- Scheduling crops requires the ability to predict the amount of time needed for production, which involves identifying how quickly plants progress (i.e., the rate of progress) towards desired stages of plant development [16,17].The time needed to reach an important developmental stage, for example, the number of days to flowering or fruiting (DTF), is converted to a rate by calculating the reciprocal of the DTF (e.g., 1/DTF).The influence of environmental factors, like temperature and light, on plant development rates can be quantified using mathematical functions [17].These types of models can be used as decision-support tools, for example, for long-cane blackberry and raspberry, allowing growers to select the date at which dormant long-canes should be forced in a greenhouse or high tunnel and manipulate the production temperatures to schedule crops' off-season harvesting.
The rate of progress towards a development event, such as flowering or fruiting, is mostly a function of average daily temperature (or ADT) [18,19], as shown in Figure 2. Plant development rates increase from zero to a maximum value when the ADT increases from a base temperature to an optimum temperature for plant growth, respectively [20][21][22].The optimum temperature is the point where the rate of plant development is the highest, after which plant development rates decrease as the ADT exceeds the optimum temperature, and the critical temperature is where plant development ceases because of heat stress.Models describing plant development rates as a function of ADT have been developed for many species grown in soilless substrates and protected environments and allow users to predict the time needed for crop production based on anticipated temperatures [16,17].Measuring ADT over time is also used to calculate the accumulation of heat units (e.g., thermal time or degree days or hours), wherein heat units are commonly used to estimate the developmental stage or forecast the date at which a plant will reach a predetermined developmental stage, for many field-grown specialty crops, including blackberry [18].Heat units, particularly degree days, are often calculated from ADT measurements; therefore, it is important to note that the effects of ADT on heat unit accumulation and the rate of plant development are interrelated, i.e., these are not separate processes.
Horticulturae 2023, 9, x FOR PEER REVIEW 3 of 11 22].The optimum temperature is the point where the rate of plant development is the highest, after which plant development rates decrease as the ADT exceeds the optimum temperature, and the critical temperature is where plant development ceases because of heat stress.Models describing plant development rates as a function of ADT have been developed for many species grown in soilless substrates and protected environments and allow users to predict the time needed for crop production based on anticipated temperatures [16,17].Measuring ADT over time is also used to calculate the accumulation of heat units (e.g., thermal time or degree days or hours), wherein heat units are commonly used to estimate the developmental stage or forecast the date at which a plant will reach a predetermined developmental stage, for many field-grown specialty crops, including blackberry [18].Heat units, particularly degree days, are often calculated from ADT measurements; therefore, it is important to note that the effects of ADT on heat unit accumulation and the rate of plant development are interrelated, i.e., these are not separate processes.There are very few published studies on modeling temperature effects on growth and plant development rates for blackberry.Black et al. [18] modeled heat unit accumulation for the purpose of predicting bloom dates in field-grown Rubus crops and reported base, optimum, and critical temperature parameters using several linear and curvilinear models.However, these authors did not include the model equations, making it difficult to reproduce or expand upon their results.To the best of our knowledge, Dickson et al. [23] was the first to attempt modeling temperature effects on plant development rates for longcane blackberry; however, this work is still in the early stages, and more investigation is needed to develop useful models for commercial practice.
Modeling the relationship between the rate of plant development and ADT would assist long-cane blackberry growers in predicting crop timing and in making scheduling decisions.In this study, the first objective was to quantify temperature effects on the rate of progress towards flowering and fruiting for four blackberry cultivars grown as longcanes.The second objective was to develop simple models predicting the time from forcing dormant plants to the appearance of the first open flowers and ripe fruit as a function of ADT.The models were developed using data from a greenhouse and high-tunnel experiment, with long-cane blackberries and temperature parameters derived from a blackberry heat unit study [18].There are very few published studies on modeling temperature effects on growth and plant development rates for blackberry.Black et al. [18] modeled heat unit accumulation for the purpose of predicting bloom dates in field-grown Rubus crops and reported base, optimum, and critical temperature parameters using several linear and curvilinear models.However, these authors did not include the model equations, making it difficult to reproduce or expand upon their results.To the best of our knowledge, Dickson et al. [23] was the first to attempt modeling temperature effects on plant development rates for long-cane blackberry; however, this work is still in the early stages, and more investigation is needed to develop useful models for commercial practice.
Modeling the relationship between the rate of plant development and ADT would assist long-cane blackberry growers in predicting crop timing and in making scheduling decisions.In this study, the first objective was to quantify temperature effects on the rate of progress towards flowering and fruiting for four blackberry cultivars grown as long-canes.The second objective was to develop simple models predicting the time from forcing dormant plants to the appearance of the first open flowers and ripe fruit as a function of ADT.The models were developed using data from a greenhouse and hightunnel experiment, with long-cane blackberries and temperature parameters derived from a blackberry heat unit study [18].

Materials and Methods
The blackberry cultivars 'Loch Ness', 'Osage', 'Ponca', and 'Prime-Ark ® 45' were grown using long-cane techniques and supplied by Nourse Farms (Whately, MA, USA).This process involved starting long-cane plants for each cultivar from tissue culture liners and growing the canes outdoors in 5 L containers with coconut coir substrate during summer and fall of 2020.In late fall, dormant plants were transferred to a −1.5 • C cold storage facility after they had been subjected to ~200 natural chilling hours and were shipped frozen to the experiment locations at the University of Arkansas in early spring of 2021.Dormant long-cane plants were shipped to a polycarbonate controlled-environment greenhouse (GH) at the University of Arkansas in Fayetteville, AR (36.100173, −94.170697), on 12 March 2021 and to an unheated plastic-covered high tunnel (HT) at the University of Arkansas Fruit Research Station in Clarksville, AR, USA (35.533430, −93.403465), on 21 January 2021.Dormant plants were immediately transplanted into 10 L containers (Plantlogic ® , Zapopan, Mexico) with a sphagnum peat-and bark-based substrate (BM7; Berger, Saint-Modeste, QC, USA).At both locations, containers were center-spaced at 70 cm in trellised rows, and rows were spaced 2 m apart.Budbreak and development of flowers and fruit occurred under natural lighting and within a natural photoperiod.
Plants were fertilized at each irrigation event using drip emitters (with 1 emitter per plant) and a commercial 15.0N-2.2P-12.5K(ICL Specialty Fertilizers, Dublin, OH, USA) water-soluble fertilizer mixed at 200 mg•L −1 N in the irrigation water.The irrigation system was manually adjusted daily to supply each plant with 1.5 to 3.0 L of fertilizer solution per day depending on root zone moisture and weather conditions and to maintain a leaching fraction of approximately 20%.Fertilizer concentration and nitrogen form were adjusted as needed to maintain a target substrate pH between 5.4 and 6.0 and electrical conductivity (EC) between 1.5 and 2.5 mS•cm −1 .
The average daily temperature (ADT), daily minimum and maximum temperatures, and daily light integral (DLI) at the GH and HT locations were measured using WatchDog 2400 Mini Stations (Spectrum Technologies, Aurora, IL, USA) placed just above the plant canopy.ADT refers to the daily 24 h temperature average, which has been shown to be highly correlated with plant development rates [16,17,20,[24][25][26][27].
For the GH location, the ADT and daily minimum and maximum temperatures over the duration of the project were (average ± standard deviation) 23.0 ± 3. For the HT location, the ADT and daily minimum and maximum temperatures over the duration of the project were 18.7 ± 6. ADT values tended to increase as ambient outdoor temperature increased over time at both GH and HT locations.Daily ADT values were averaged from the time the plants were removed from cold storage and placed in the GH or HT until the point at which the first open flower and first ripe fruit appeared for each plant to characterize the average ADT experienced by plants up until those developmental stages.Each long-cane blackberry plant was considered one observational unit, and there were four and six observational units per cultivar at the GH and HT locations (a total of ten observational units per cultivar), respectively.
Model development: Biological rate (R) responses to temperature often follow an asymmetric, peak-shaped curve [20] like that shown in Figure 1.The authors of this study mathematically described the relationship between ADT and the rate of progress towards the appearance of the first open flower and ripe fruit for long-cane blackberry following a modified version of a function from the work of Landsberg [21] and Reed et al. [22]: where and B = (T crit − T opt )/(T opt v T base ) The parameters T opt , T crit , T base , and R min have biological meaning, and the B value defines the skew.T base and T crit are the base and critical temperatures below and above T opt , respectively, where R equals zero.R min is the minimum value estimated for R above zero.It should be noted that for T < T base , R will become negative, and for T > T crit , Equation ( 1) cannot be calculated unless B is an integer [21].
Since T opt was not observed for any cultivar in the experiment, it was not possible to estimate T opt and T crit using Equation (1).Therefore, the temperature parameters (T opt T crit , and T base ) used in Equations ( 1)-( 3) were derived from a Rubus sp.heat unit modeling study conducted by Black et al. [18], where heat unit accumulation at the first-open-flower stage was measured for >100 blackberry genotypes grown over several years and at field sites in various geographical locations across the U.S. In this study, the best-fitting heat unit model (R 2 = 0.815) indicated T base and T opt values of 6 and 25 • C, respectively.The same authors estimated a T crit of 35 • C for blackberry grown in soilless container substrates based on a separate growth chamber study.
For each cultivar, separate model equations were developed to predict the rate of progress towards the appearance of the first flower and fruit based on the flowering and fruiting data collected, temperature parameter estimates from the heat unit modeling study [T base = 6 • C, T opt = 25 • C, T crit = 35 • C; reference [18]], and Equation (1).Nonlinear regression (PROC NLIN procedure in SAS 9.4, (SAS Institute, Cary, NC, USA)) was used to generate estimates for R min for each equation.The model accuracy for an Equation was evaluated by comparing the predicted to observed time (d) to first flower and fruit for each cultivar as well as by determining kurtosis and skew.Other temperature-based modeling studies have used similar forms of analysis for crops grown in soilless culture and greenhouse environments [24][25][26].

Results and Discussion
The ADTs upon the appearance of the first flower and ripe fruit were similar between cultivars but differed by location (Table 1).The average ADTs across cultivars for the GH and HT locations were 19.9 and 12.3 • C at the first-flower stage and 20.8 and 14.5 • C at the first-fruit stage, respectively.Overall, the GH provided a more protected and heated environment with warmer temperatures compared to the HT, for which the temperatures were lower (Table 1, see temperature data in the Section 2).
At both the GH and HT locations, the time to first flower tended to be earlier for 'Osage' and 'Prime-Ark ® 45 , whereas flowering occurred later for 'Loch Ness' and 'Ponca' (Table 1).Similar trends were observed between cultivars for the time to first ripe fruit (Table 1).There was an 11-and 28-day spread in time to flowering between cultivars in the GH and HT, respectively, and an 11-and 15-day spread in time to fruiting between cultivars in the GH and HT, respectively (Table 1).In other words, the difference in time to flowering/fruiting between cultivars was greater when the plants were grown at lower temperatures (in the HT), whereas the crop times between cultivars were more similar when grown at higher temperatures (in the GH).Overall, flowering and fruiting in the HT required nearly double the amount of time required in the GH, a result of lower daily air temperatures and a lower ADT in the HT.The same trends were observed for the rate of progress towards flowering and fruiting (1/d, Table 1).
Table 1.Average daily temperature (ADT, in • C) upon the appearance of the first open flower and ripe fruit and the time (in days, d) from the last day of cold storage to the appearance of the first flower and fruit for dormant blackberry cultivars forced in a controlled-environment greenhouse (Location 1) and in an unheated high tunnel (Location 2).The rates of progress towards the first-flower and -fruit stages were calculated as the reciprocal of time to flowering and fruiting, respectively ( 12) 110 ( 7) 2.25 × 10 −2 (6.09 × 10 −3 ) 9.12 × 10 −3 (5.57× 10 −4 ) Dickson et al. [23] reported results like those shown in Table 1 for the long-cane blackberry cultivars 'Natchez', 'Ouachita', 'Prime-Ark ® Freedom', and 'Prime-Ark ® Traveler' grown under different air temperature conditions.Averaged across cultivars, the plants in that study, forced at approximately 20  [23] study resulted in greater differences between cultivars in terms of time to flowering/fruiting, whereas the cultivar crop times were more similar at higher temperatures.
Table 2 shows the estimated parameters A, B, and R min for each cultivar for the firstflower and first-fruit models developed using Equation (1).All parameters are typically cultivar-specific; however, B is constant in this study since the same T base , T opt , and T crit values derived from Black et al. [18] were assumed constant across cultivars (see Section 2). Figure 3 plots the model-predicted number of days (x-axis) against the observed days to flowering and fruiting (y-axis) for individual observational units and shows an approximate goodness of fit across models developed for cultivars using Equation (1).The data in Figure 3 were also analyzed using linear regression, wherein the regression equation had an adjusted-r 2 value of 0.952 and indicated a near 1:1 positive relationship between the predicted and observed values [regression equation, observed days = predicted days × 1.02 ± 0.05 − 0.03 ± 4.19, (±95% confidence intervals)].The strong relationship in Figure 3 suggests temperature had the main influence on time to flowering/fruiting for these blackberry cultivars, Since only ADT was included in Equation ( 1) and the effects of other environmental factors (e.g., light, humidity, and carbon dioxide) were not included, the main and often dominant effects of temperature on crop timing seen in this study were consistent with those reported by Dickson et al. [23] for long-cane blackberry as well as those from previous modeling studies concerning other species [16,17,20].
The accuracy of the flowering models in describing the data sets within ±7 d ranged from 60% to 90% for the actual flowering data across cultivars, and the accuracy of the fruiting models ranged from 60% to 100% for the actual fruiting data (Table 3).The models were consistently most accurate for 'Osage', least accurate for 'Prime-Ark ® 45 , and intermediately accurate for 'Loch Ness' and 'Ponca' (Table 3).The flowering and fruiting models had average ±7 d accuracies of 70% and 83%, respectively, which were lower than the values of 80% and 85% (for ±7 d accuracy) reported by Dickson et al. [23] for 'Natchez', 'Ouachita', 'Prime-Ark ® Freedom', and 'Prime-Ark ® Traveler'.Model accuracy was also evaluated as the predicted minus the observed days to flowering and fruiting for each cultivar and observational unit, the results of which are summarized in Table 3.The average predicted minus observed days ranged from 0 d (for the fruit model for 'Prime-Ark ® 45 ) to −4 d (for the flower model for 'Loch Ness'), and overall, the models tended to slightly underestimate the crop time by 2 d (Table 3).
Overall, the data in Figure 3 and Table 3 highlight some of the variability and lack of precision for the first-flower and -ripe-fruit models developed across cultivars.The ±1 standard deviations ranged from 3 d (for the flower model, 'Osage') to 10 d (for the flower model, 'Prime-Ark ® 45 ), indicating the inconsistency across observational units.The Kurtosis and skew values in Table 3 suggest the variability in the predicted minus observed days to flowering/fruiting was not normally distributed for all cultivars.For example, only the first-flower models for 'Osage' and 'Ponca' and first-fruit model for 'Ponca' had positive kurtosis values indicating an approximately normal peak-shaped distribution (Table 3).The skew values were within the range of −0.5 to 0.5, indicating an approximately symmetrical distribution for most models (Table 3), except for the flower models for 'Osage' (−1.15) and 'Ponca' (−0.99) and the fruiting model for 'Ponca' (−1.29), wherein the negative skew values indicated these models over-predicted the time to flowering/fruiting for most observational units.Since only ADT was included in Equation ( 1) and the effects of other environmental factors (e.g., light, humidity, and carbon dioxide) were not included, the main and often dominant effects of temperature on crop timing seen in this study were consistent with those reported by Dickson et al. [23] for long-cane blackberry as well as those from previous modeling studies concerning other species [16,17,20].The accuracy of the flowering models in describing the data sets within ±7 d ranged from 60% to 90% for the actual flowering data across cultivars, and the accuracy of the fruiting models ranged from 60% to 100% for the actual fruiting data (Table 3).The models were consistently most accurate for 'Osage', least accurate for 'Prime-Ark ® 45′, and intermediately accurate for 'Loch Ness' and 'Ponca' (Table 3).The flowering and fruiting models had average ±7 d accuracies of 70% and 83%, respectively, which were lower than the values of 80% and 85% (for ±7 d accuracy) reported by Dickson et al. [23] for 'Natchez', 'Ouachita', 'Prime-Ark ® Freedom', and 'Prime-Ark ® Traveler'.Model accuracy was also evaluated as the predicted minus the observed days to flowering and fruiting for each cultivar and observational unit, the results of which are summarized in Table 3.The average predicted minus observed days ranged from 0 d (for the fruit model for 'Prime-Ark ® 45′) to −4 d (for the flower model for 'Loch Ness'), and overall, the models tended to slightly underestimate the crop time by 2 d (Table 3).The techniques used in this research to model temperature effects on crop timing serve as a good starting point; however, further improvements of the models' accuracy are needed prior to using them to make predictions in commercial blackberry long-cane pro-duction.The relatively low model accuracy observed was partially a result of the variability in the time to flowering/fruiting between plants (observational units) in both GH/HT locations (Table 1, Figure 3).The authors believe that much of this variability resulted from differences in individual plant quality, non-uniform budbreak and pollination, variations in microclimate, and other factors linked with source-sink relationships between leaves and developing fruit.These variables can be better controlled by selecting for more uniform plants meeting the commercial specifications for long-cane production, improving climate control, and measuring temperature in the microclimates around developing flowers and fruit.In addition, the T base , T opt , and T crit parameters are likely cultivar-specific but are not known for the cultivars used in this study, so they were selected from the previous blackberry heat-unit study conducted by Black et al. [18].More effort is needed to determine accurate T base , T opt , and T crit parameters for these cultivars, which would likely increase model accuracy substantially.Other factors such as photosynthetic light, which was measured in this study using daily light integral (DLI, see Section 2) values, can influence plant development rates [16], especially at sub-optimal levels.The daily DLI values tended to increase as the daily ADT values increased over time during the study, and this process occurs naturally during the transition from the late winter/early spring (when this study was initiated) to the summer.Overall, the inclusion of DLI values along with ADT may also improve model accuracy in future research.

Cultivar
In some scenarios, using ADT may over-simplify the relationship between temperature and plant development.For example, extreme heat or frost events may cause significant and lasting delays in development and may not be well-reflected by ADT, particularly if these events are infrequent, and therefore have little weight when determining the average ADT over time.The models developed in this research would be most accurate in predicting the time to first flower and fruit in environments where the ADT is relatively stable over time and where daily temperature highs and lows are mostly within the T base (6 • C) and T crit (35 • C) range used in Equation (1).These types of environments may include greenhouses and tunnels with adequate climate control and the capacity to protect crops from extreme weather events.
To improve model accuracy, future studies should focus on ensuring that long-cane plants are at a uniform stage of development at the point of forcing, increasing cultivar sample sizes and temperature levels, and ensuring that evaluated temperature levels are below and above T opt to allow for more accurate estimates of T base , T opt , T crit , and R min .Although temperature is used as the main environmental parameter in other similar modeling and crop-scheduling studies, for example, degree-day or heat-unit studies on blackberry [18], and studies concerning greenhouse container crops [24][25][26], including other parameters such as light levels may improve accuracy.In addition to modeling the time to first flower and fruit, modeling the effects of temperature and light on the time to first marketable yield, harvested yields over time, and total harvest duration would also be practical for growers and useful for planning harvest labor.
This was a first attempt at developing flowering/fruiting models for long-cane blackberry, with the intention that these models can be improved upon in later studies and incorporated into crop scheduling and decision support tools for growers.The methods used are not crop-specific and can be adapted for other berry crops grown in similar production systems.For example, growers can estimate daily or weekly air temperatures over time for their location-either via experience, measurements collected on-site, or accessing local historical climate data-and use the model equations developed to simulate the anticipated date of flowering and harvest and the effects of changing temperature over time on harvest date and compare production times between cultivars.Similar models have been developed and used in this way by commercial greenhouse growers to schedule crops [16,27].

Conclusions
This was a first attempt at developing cultivar-specific models in order to predict the amount of time from forcing dormant long-cane blackberry plants to first open flower and first ripe fruit as a function of mean daily temperature.The modeling methods used are universal and can therefore be adapted to other berry crops grown in similar production systems.To the best of our knowledge, this study is also the first to characterize the relationship between temperature and crop timing for long-cane blackberry.A strong and positive relationship between predicted and observed days to flowering and fruiting suggested that temperature had a dominant influence on crop time.However, there was considerable variability depending on the blackberry cultivar (i.e., 'Loch Ness', 'Osage', 'Ponca', and 'Prime-Ark ® 45'), and the overall accuracy of these models within ±7 days was found to be between 50% and 100% across cultivars.This variability needs to be addressed in future studies, and we have discussed methods to further improve and calibrate the models prior to commercial use.In general, these models describe the general relationship between temperature and crop timing for long-cane blackberry and may be more immediately useful for general training purposes and to educate growers on how temperature influences crop scheduling in these systems.Additionally, this study provides a framework for how to model temperature effects on crop timing for long-cane blackberry that can be expanded upon to develop more robust and accurate models.

Figure 1 .
Figure 1.Blackberry grown using soilless culture as "long-canes" during the first year of production (top) and during the forcing of flowers and fruit under a high tunnel in the second year of production (bottom).

Figure 1 .
Figure 1.Blackberry grown using soilless culture as "long-canes" during the first year of production (top) and during the forcing of flowers and fruit under a high tunnel in the second year of production (bottom).

Figure 2 .
Figure 2. Representation of temperature effects on plant development rates based on suggestions for Rubus sp. by Black et al. [18].Base, optimum, and critical temperature parameters represent temperatures where plant development is 0%, 100%, and 0%, respectively.

Figure 2 .
Figure 2. Representation of temperature effects on plant development rates based on suggestions for Rubus sp. by Black et al. [18].Base, optimum, and critical temperature parameters represent temperatures where plant development is 0%, 100%, and 0%, respectively.
8 • C, 11.6 ± 7.4 • C, and 30.1 ± 7.2 • C, respectively.Daily temperature values ranged from 2.8 to 30.0 • C for ADT, −5.0 to 24.4 • C for daily minimum temperature, and 5.0 to 43.3 • C for daily maximum temperature.Average DLI was 19.7 ± 11.4 mol•m −2 •d −1 of photosynthetically active radiation (PAR), and daily values ranged from 0.9 to 43.3 mol•m −2 •d −1 of PAR.Data collected for each long-cane plant consisted of measurements of the time (in days, d) to reach a development stage corresponding to the appearance of the first open flower and first ripe fruit from transplant (12 March 2021 and 21 January 2021 for GH and HT, respectively).The development rate was calculated as the reciprocal of days to first open flower and ripe fruit per plant (e.g., 1/d).

Table 2 .
Parameters A, B, and Rmin for modeling the amount of time (d) to the appearance of the first flower and ripe fruit per cultivar.Model parameters are used in Equations (1)-(3).

Figure 3 .
Figure 3. Predicted (x-axis) versus observed (y-axis) time to reach first open flower and first ripe fruit stages across cultivars and locations.Data represent values for individual observational units.Cultivars 'Loch Ness', 'Osage', 'Ponca', and 'Prime-Ark ® 45′ are indicated by triangular, circular, square, and diamond markers, respectively.Closed and open markers indicate the time to the appearance of the first open flower and ripe fruit, respectively, per cultivar.The dashed line represents areas where the predicted values minus the observed values equals zero.

Figure 3 .Table 3 .
Figure 3. Predicted (x-axis) versus observed (y-axis) time to reach first open flower and first ripe fruit stages across cultivars and locations.Data represent values for individual observational units.Cultivars 'Loch Ness', 'Osage', 'Ponca', and 'Prime-Ark ® 45 are indicated by triangular, circular, square, and diamond markers, respectively.Closed and open markers indicate the time to the appearance of the first open flower and ripe fruit, respectively, per cultivar.The dashed line represents areas where the predicted values minus the observed values equals zero.Table 3. Percentages of model accuracy within ±7 days and the predicted minus observed days to the appearance of the first open flower and ripe fruit, and kurtosis and skew values per cultivar data set.Data for predicted minus observed days represent least-square means of ten observational units ± 1 standard deviation.Kurtosis, skew, and model accuracy were determined from the same data (with ten observational units per cultivar).
1/d).Sample sizes (n) were four and six for Locations 1 and 2, respectively.Values in parentheses indicate ±1 standard deviation.Location 1 denotes the greenhouse, and Location 2 denotes the high tunnel.
• C and 13 • C, developed flowers in 32 d and 63 d and developed ripe fruit in 76 d and 116 d, respectively.As shown in Table 1, the forcing of long canes at lower temperatures in Dickson et al.'s

Table 2 .
Parameters A, B, and R min for modeling the amount of time (d) to the appearance of the first flower and ripe fruit per cultivar.Model parameters are used in Equations (1)-(3).