From an agronomic point of view, the growth and development of broccoli can be divided into two stages [1,8]. The first one, starting from the transplanting to the onset of the head’s formation, includes the meristem differentiation from vegetative to reproductive, given that the appropriate stimulus has been induced [9], and the second one lasts from the onset of the head’s formation to its harvest.

The main head is formed at the apex of the central shoot, while secondary heads are formed on lateral shoots that develop from the buds in the leaf axils [10]. A lateral shoot formation and development is not always a desirable trait, thus most of the modern F1 hybrids typically exhibit a strong tip dominance and a limited lateral shoot development [2] until the main head is harvested [11]. Potential transcription factors involved in the lateral eye growth’s arrest and restriction have been recognized and identified. However, a strong variability in the lateral shoot’s development occurs between genotypes, particularly under stressful environmental conditions [12]. It has been reported that 6.3 and 16.0 lateral shoots/plants have been developed in the commercial varieties of Coastal and Gem, respectively, in the range of 17–22 °C, when only a unique head was formed, while many lateral shoots developed in the range of 17–27 °C, but without simultaneously forming a head [10].

Head initiation requires the development of a certain minimum number of leaves [1,8,13,14,15], half of which are visible to the naked eye at this stage [1,15]. Counting the visible leaves is an easy and non-destructive way to assess the plant growth stage [1,15], given that the total number of leaves is linearly related to the number of visible leaves [15]. It has been reported that 13–31 leaves are required for the head’s initiation [13,15,16] depending on the genotype, with the lowest number being required in the early stage and the highest number being required in the late stage.

Therefore, the required number of leaves is primarily related to the genotype [8,13,15,17], while secondarily and partially, it is modified by the temperature in the plant growth environment [1,13,14,15,18,19,20,21].

High temperatures increase the required minimum number of leaves and delay the time of the head’s initiation [1,13,15,18,19,20,21]. Indicatively, it is reported that the number of leaves visible under the microscope before the formation of the head increased from 16.7 to 26.6, with an increase in the temperature from 13 to 30 °C [21], and from 18 to 24 with an increasing temperature from 12 to 27 °C, while a strong interaction between the temperature and genotype was exhibited [10]. In addition, high temperatures also increased the plant height. Indicatively, it is reported that the plant height increased from 7.5 to 29.9 cm while the temperature increased in the region from 13 to 30 °C [21]. However, it is worth mentioning that a negative correlation between the final number of leaves and the size of the head has been reported by Lindemann-Zutz et al. [22].

The reports on the effect of the day length (photoperiod) and the intensity of the solar radiation on the plant’s growth and development as well as the head’s formation are not only limited but are also often contradictory. According to some of these reports, neither the photoperiod [23,24] nor the light intensity and quality [25] had an obvious effect on the head’s initiation. In addition, no apparent effect on the time of the head’s emergence was observed after reducing the intensity of the solar radiation by 25 or 38%, although the number of leaves was increased by 1–3 [16]. Moreover, under conditions of a different intensity of solar radiation levels up to 70%, the number of leaves did not differ, although the duration of the crop was prolonged [26]. In contrast, according to Gauss and Taylor [21], in plants grown under controlled conditions, the time required from sowing to the head’s initiation decreased from 86 to 64 days, while the photoperiod was increased from 8 to 24 h and the light energy consequently increased from 2.4 to 7.25 × 10⁷ erg/s/cm², although the number of leaves that had developed before the head initiation was not affected by the photoperiod. Finally, according to Fujime et al. [27], the synergistic effect of the day length with the temperature was observed, but only in some of the commercial varieties. In that case, the longer the day, the higher is the temperature range in which the head’s formation is possible.

In order to calculate the required time until the beginning of the head’s formation, several thermal time models (accumulated temperature values) have been used, which are based on three basic temperatures: a minimum (base), below which the plant does not grow, an optimum, at which the growth rate is a maximum and a maximum (upper limit), above which the growth rate is zero, although there is no consensus on the proposed values. Values range from 0 to 9.9 °C for basal temperatures, from 10 to 21 °C for optimum temperatures and from 18 to 35 °C for maximum temperatures [8,14,17,20,24,28,29,30,31,32,33].

For the rate of leaf emergence, a base temperature of 2–6 °C has been proposed, depending on the genotype, while for the optimum temperature there are indications that the value is around 20 °C [9,30]. The rate of the leaf’s emergence at 15 °C ranges from 0.2 to 0.4 leaves/day for plants with 4 and 14 visible leaves, respectively [30].

Opinions vary regarding broccoli’s requirement to be exposed to low temperatures for the induction of the head’s initiation [1,18,21,23,27,33,34,35,36]. Indicatively and not exhaustively, it is mentioned that Gauss and Taylor [21], Mourão and Brito [35] and Okazaki et al. [36] consider that broccoli does not require an exposure to low temperatures for the head’s initiation. In contrast, Wiebe [23] suggests 0 °C as an inductive temperature and 20 °C as a non-inductive one, with 5 °C being more effective, combined with an exposure time of 2–4 weeks and a minimum number of 4 leaves, in order to accelerate the head’s initiation. Hadley and Pearson [9] indicated 14–16 °C as the most effective temperature and Wurr et al. [14] indicated 15.8 °C as the most effective one with 23.6 °C as a maximum, while Grevsen [37] indicated 16.3 °C as the optimum with a base temperature of 2.9 °C and a maximum of 29.7 °C. According to Fellows et al. [20] no head formation was observed at the constant temperatures of 0, 30 and 35 °C, while 96, 51, 36 and 64 days were required for the head’s initiation at 5, 10, 15 and 20 °C, respectively. According to Uptmoor et al. [33] an exposure to low temperatures for the head’s initiation is required in some genotypes. Finally, according to Fujime and Hirose [18] and Fujime et al. [27], various combinations of the day (10, 15, 20, 25 and 30 °C) and night (10, 15, 20, 25 and 30 °C) temperature or the day length (8 and 16 h) and temperature (17 and 23 °C) prevented, allowed, or accelerated the head’s formation.

This discrepancy is apparently due to the different genotypes that have been used, the difficulty in determining precisely the time of the head’s initiation, given that there are no known distinct phenological or biochemical changes that can signal this time [30] in the requirement or not for an exposure to low temperatures [33], in possible sensitivity to a specific (but indeterminate) developmental stage [36,37], as well as in the different experimental approaches applied, in terms of the growth conditions (controlled in growth chambers or diverse in the field). Presumably, an exposure to low temperatures is a facultative requirement [32], meaning that if not essential in all genotypes [36], in some it accelerates the head’s initiation [13,27] and clearly these temperatures are higher than those required for vernalization in cabbage [36].

Nevertheless, it is apparent that for the initiation of the head in broccoli, an exposure to temperatures below a maximum non-inductive temperature is required, which has not been precisely determined and apparently varies between genotypes. By some researchers [14,25,38], it is considered that no head formation is observed at temperatures > 23–24 °C and by others [39,40] that at temperatures > 30 °C (almost the optimal temperature for vegetative growth), many problems are caused in the head’s formation. According to Grevsen [15] and Wurr et al. [14], at mean daily temperatures > 20 °C, late and abnormal head development was observed in the commercial cultivar Shogun, but not in the commercial cultivars Caravel and Emperor. At higher than the optimum temperatures, depending on the value and duration, plant growth stage and genotype, even if the head is formed, characteristic lesions appear on the subsequent head [39]. The stage immediately after the differentiation of the meristem from vegetative to floral and up to the head size of 5–10 mm is considered to be the most sensitive [39,40]. This sensitive stage can be accurately identified microscopically [40], however empirically, it is placed at about 3 weeks before the head is harvested [39].

FLOWERING LOCUS C (FLC) homologues in Brassica species are considered responsible for controlling the requirement for an exposure to low temperatures (vernalization) [41,42]. Although five of them have been cloned and partially or fully characterized in Brassica oleracea species (Brassica oleracea FLOWERING LOCUS C, BoFLC1, BoFLC2, BoFLC3, BoFLC4 and BoFLC5) [36,41,42,43], it is not ascertained which one or which of them are decisive [36]. However, a sensitivity to high temperatures during the initiation stage of the broccoli’s head formation is thought not to be associated with genes controlling the vegetative-to-floral meristem differentiation [40], but with one or more genes controlling the growth processes of the floral buds that make up the head [40,44,45,46]. Given that at this stage the genes BoiAP3 (Brassica oleracea itaIica APETALA3) and BoiCAL (Brassica oleracea itaIica CAULIFLOWER) are expressed [3], it is possible [40] that their weak or delayed expression at high temperatures is related to the head characteristics due to heat stress that degrades its quality. Recently, the BoFLC3 (Brassica oleracea FLOWERING LOCUS C3) gene has also been proposed [47] as a candidate for the control of the head’s initiation under subtropical conditions (high temperature and short-day length). Finally, studies on gene expression in genotypes, that are capable of forming the head under heat stress conditions, suggest the possible involvement of compounds and hormones (such as thioglycosides and jasmonic acid as well as auxin, cytokinin and abscisic acid) in the head’s formation under high temperature conditions [47].

The first stage of the growth and development (from the transplantation to the head’s initiation) and up to a head growth of 0.6 mm in diameter is the most unpredictable period [8,37], which suggests the involvement of other factors besides temperature [8,33]. The time required for this stage varies more than the time for the second stage (from the head’s initiation to the harvest) in early genotypes, while the reversed is observed in the late ones [13]. The rate of the leaf’s emergence is mainly a plant developmental process, while the head’s initiation is mainly a meristem differentiation process [30], and these two have different optimum temperature regimes. The observations under the field conditions [22,48] demonstrated a strong variability in the time of the onset of the head’s formation in the plants of a broccoli cultivar. This is the reason for the great variability in the time of the harvesting of the heads as well, with the consequence that a considerable period of time elapses from the start of the harvest in a crop and up to its completion. The reason for this variability remains unknown. In this direction, no effect of the size of the seedling at the establishment of the culture was found on the time of the head’s initiation nor the growth rate of the head and the final size of the plant [22].

Many mathematical models have been proposed to determine the starting time of the head’s formation, among which the following are only indicative and not exhaustive.

According to Mourão and Brito [35], the required thermal time (θ, degree days) for the head’s initiation is calculated from the equation:

According to Grevsen [37], the effective sum of the temperature required for the head’s initiation in the commercial cultivars Emperor, Caravel and Shogun is estimated to be 132 degree days. This means that, theoretically, at the optimum temperature, the plants will reach this stage in about 15–18 days from transplanting the seedlings with 3–4 true leaves.

According to Uptmoor et al. [33], the time until the head’s formation is divided into the juvenile phase, the vernalization phase and the vegetative-to-reproductive transition phase. The juvenile phase is considered to be independent of the genotype and is completed at a temperature sum of 456 degree days when the plants have approximately four true leaves. Commercial broccoli cultivars are believed to be insensitive to temperature before this stage [23], in contrast to the vernalization phase [32] in which high temperatures increase the time required for the head’s formation. The thermal time required for the head’s formation was described separately for each genotype using linear regressions with a base temperature of 6 °C and a constant, which has been derived from experiments in growth chambers at 6, 12 and 18 °C [32,33].

To determine the time required from the crop’s establishment to the beginning of the head’s formation (1/f, days) in relation to the average daily air temperature (T, °C), the following linear regression has been proposed:

Fujime and Okuda [34], after 7 years of experimentation in field conditions, propose the following mathematical equations to determine the required time (days) for the head initiation in the commercial variety Wase-midori:

X₁ = the average temperature of the period of 10 days from planting;

X₂ = the maximum temperature of the period of 20 days from planting;

X₃ = the maximum temperature of the period of 30 days from planting;

X₄ = the average temperature of the period of 30 days from planting;

X₅ = the maximum temperature of the period of 40 days from planting.

Based on this relationship, the time required during ten crops in different years or periods of the year was calculated to be 29–39 days from planting, these values being in line with the actual ones. In contrast, Gauss and Taylor [21] observed that the time required from the sowing to the head’s initiation in plants grown under controlled conditions at a constant temperature of 13 or 29 °C did not differ and were 75 and 74 days, respectively.

Finally, according to Uptmoor et al. [33], the time required from the establishment of the crop of a particular commercial variety to the onset of the head’s formation can be easily and accurately determined, while the genotype × environment interaction is also predictable to some extent, using a specific mathematical model only when the conditions are favorable for the formation of the head. On the contrary, the accuracy of the determination is significantly reduced when high temperatures prevail.

Failure to form a head has been reported in cases where there is a failure of apical meristem development (blindness). This is believed [49,50] to be related to either the cessation of the leaf’s formation from the apical meristem or a failure to differentiate the vegetative to the reproductive meristem and is caused by unspecified soil-climatic factors, while a significant variation between the genotypes has also been reported.

During the second stage (from the head’s formation to the harvest), the head’s growth and development is primarily affected by the temperature, as well as the solar radiation, particularly at high plant densities [15]. Thus, simple linear or complex mathematical models have been proposed to determine the head growth rate based on the temperature alone [1,10,13,14,15,34,35,37,51,52,53,54] or solar radiation as well [1,15,21,48,51,52,54].

These mathematical simulation relationships make it possible to predict the required time from the transplanting to the harvest, based on the climatic conditions of an area, in order to schedule the crop planning. In addition, some of them are able to estimate the time of the initiation of the head’s formation in order to detect early enough any possible problems in the growth and development of the head, under the prevailing environmental conditions upon the establishment of a crop.

Regarding the temperature levels and, in particular, the minimum and maximum, the sum of the temperatures, the sum of the degree days or active degree days, with or without a base and upper limit temperatures, has been used. As a base temperature, below which the growth and development stop, temperatures of 0, 0.6 and 7 °C have been suggested for various commercial varieties [13,15,37,51] and as an upper limit temperature, that of 17 °C [15,37]. Fujime and Okuda [34], after 7 years of experimentation in field conditions, proposed a mathematical relationship to determine the required time (days) to harvest that is proportional to the time required to the head’s initiation, based on the mean and maximum air temperature of various periods since planting. Based on this equation, the time required during ten crop cycles of a genotype in different years or periods of the year was calculated to be 44–71 days from planting, these values being in accordance with the actual ones. According to Grevsen [15], the total temperature requirement of the commercial cultivar Shogun to reach harvest (12 cm head diameter) is 600 degree days.

Regarding solar radiation, the cumulative solar radiation (MJ/m²) index has been used [15].

Therefore, the two stages of the growth and development of broccoli in the field are strongly dependent on the environmental conditions, but each responds differently to them, which in turn makes it difficult to predict the effects of environmental variation [9,37].

Changes in the environmental conditions (temperature, solar radiation, relative humidity, etc.) during cultivation significantly affect both the growth and development stage of broccoli and therefore the quality and yield, while they are often causing difficulties in the production, which differs between genotypes. Indicatively, it has been reported that high temperatures (daily mean > 20 °C) caused a late and abnormal head development in the commercial cultivar Shogun, while the growth of the commercial cultivars Caravel and Emperor was not affected [15]. Additionally, in an experiment under controlled environmental conditions, temperatures > 20 °C during the first month after transplanting inhibited or greatly delayed the head initiation in the commercial cultivar Shogun [14].

However, little information is available on the effect of environmental conditions on the plant’s growth and development under field conditions, given that most of the available information comes from an experimentation under controlled conditions and the application of models derived from these conditions. This issue is also complicated by the fact that plants are at different stages of growth at the time of transplanting, and other, as yet undetermined, factors are likely to be involved [30].