Characteristics of orchards

The research started in February 2014 in two commercial ‘Méndez’ avocado orchards managed with Fertigation, Feozem haplic soil and subhumid sub-humid climate [AC(w)] (^{García, 1998}) from the southern state of Jalisco. The “Colorín 1” and “Ocote cuate 2” orchards are at distances of 7×3.5 and 5×5 m, are four and six years old and are located at 1 556 and 1 428 m altitude, respectively. In each orchard, 10 trees were selected and 30 sprout of each vegetative flow (winter or summer) occurred in each of them in 2014 and 2015.

Ringing and defoliation of sprout

Treatments were carried out in 2014 and 2015 at monthly intervals and began in march and october for outbreaks of vegetative flows of winter and summer, respectively. For each year and orchard, at each treatment date (five and six dates for the summer and winter flows, respectively), one outbreak per tree was banned and defoliated, out of a total of 10 trees per orchard. The defoliation consisted in the manual removal of all leaves from the last two vegetative growth streams. For the ringing, a full strip of bark 2 cm wide was removed in the basal part of the penultimate growth. Treatments were discontinued when shoot apical buds reached developmental stage E-6 according to the visual scale of ^{Salazar et al. (1998)}. For each year, orchard and vegetative flow were considered 25 control sprouts, which were not altered.

Floral development status

At each treatment date an apical bud per tree was collected from each of the vegetative flows. The buds were fixed in FAA (formaldehyde: acetic acid: ethanol, 5:5:90, v:v:v) and then introduced into a vacuum hood (Nalgene 8040317, Nalgen Company) at 30 KPa for 5 h. Later they were classified under a stereomicroscopic microscope (Zeiss Stereomikroskop Mod. Stemi 2000-C, Carl Zeiss, Göttingen, Germany), with the states (E) of visual scale development of ^{Salazar-García et al. (1998)} which comprises from E-1 (vegetative bud) to E-11 (anthesis). In total, for each year, 60 and 50 buds of the winter and summer flows, respectively, were collected for all treatment dates.

Once the DIF date was identified, the anatomical characterization of the buds that reached this stage of development was performed. The buds were extracted from the FAA and washed with tap water and then dehydrated with alcohol and xylene. Subsequently, they were included in paraffin (^{Ruzin, 1999}). Longitudinal anatomical sections were obtained with a rotating microtome (HM 350S, Walldorf, Germany) and 8 µm thick, mounted on slides and stained with safranin and fixed green (^{Ruzin, 1999}). At the end they were applied balm from Canada and were protected with coverslips. The sections were photographed with a digital camera (Canon Power Shot G11, NY, USA) mounted on an optical microscope (Zeiss HBO 50/AC, Carl Zeiss, Göttingen, Germany).

Type of growth produced

The type of growth (floral, vegetative or inactive sprout) produced by the apical buds of both treated and control sprout was quantified at the end of each flowering period. For the vegetative flows of winter and summer 2014 the evaluations were in October 2014 and March 2015, respectively. In the case of outbreaks of winter and summer flows 2015, the evaluation was carried out in November 2015 and April 2016, respectively.

Calculation of cold hours (HF)

In each orchard the air temperature was recorded every hour. Automated HOBO H8 (Onset Computer, Witzprod, Englewood Cliffs, NJ, USA) battery operated registers were used. Independently for outbreaks of vegetative flows of winter and summer, the occurrence of minimum temperatures, from 8 to 20 °C, was quantified in increments of 1 °C that could be associated with the date of DIF. The formula: HF = (Tmin ≤T,1,0); where: Tmin= minimum temperature recorded every hour; T= critical temperature, 8 to 20 °C. If the temperature condition is met, then the value of HF is 1, otherwise it is 0. Using the Microsoft Access Version 14 database manager, the hourly temperature records organized from 8 to 20 °C were added in increments of 1 °C. The values of HF8 to HF20, were accumulated for each period of defoliation and ringing.

These values were called accumulated cold hours (HFA). For vegetative flows of winter and summer it was considered as day zero when the apical buds were in E-1 (vegetative stage), which occurred in February and August, respectively.

Identification of temperature associated with DIF

HFA were used as independent variables and the floral development of apical buds in buds of each flow as a dependent variable. Subsequently, the Stepwise SAS/STAT procedure (^{SAS Institute Inc., 9.2.}) was used to select the best response order model (second through fifth order) for each critical temperature (from ≤ 8 °C to ≤ 20 °C, in 1 °C intervals). The criteria for choosing the best models were: 1) R2 value; 2) the smallest mean error square (CME); and 3) the value of Cp, suggested by Mellows (^{Draper and Smith, 1981}).

Obtaining the values of the mathematical coefficients.

Once the best models were identified, their mathematical coefficients (B₀,......., Bn) were calculated by the REG procedure using the HFA, from ≤8 °C to ≤20 °C, at intervals of 1 °C.

Validation of prediction models

For the outbreaks of each vegetative flow the ability to predict the DIF of the best prediction models obtained in year 1 against the same vegetative flow in year was evaluated, and vice versa. The predicted floral development values were analyzed by a regression against the observed values of the floral development of the year and corresponding vegetative flow using the program Excel (2010). The criteria for determining whether the two-year values belonged to a single population were: 1) that the ordinate at the origin of the regression was closest to one (B0= 1); 2), that the slope is the closest to one (B1= 1); and 3) the highest value of the adjusted model coefficient (R2). This procedure served to debug models and find the best.

Generation of a unique model to predict DIF in each vegetative flow

After the verification of the non-difference between years, a regression model was obtained integrating the information of the two years into a single data set, for each vegetative flow.

Analysis of the information

For the type of growth produced by the outbreaks, a completely randomized design with different treatments (dates of defoliation and ringing) and 10 replicates (sprout) was used. For winter buds, statistical analysis was made as a factorial of the form 2×2×7 (years × orchards × treatments) and for the summer sprout a factorial 2 × 2 × 6 (years × orchards × treatments) was used. Previous to their analysis, the values expressed as a percentage were transformed using the arcosene √X+ 0.5 ^{Steel and Torrie, 1984}), although the results show the actual values. The comparison of means was done with the multiple comparison testWaller-Duncan, p≤ 0.05.

Type of growth produced in response to treatments Winter Sprouts

Microscopic characteristics of the apical buds irreversibly determined to flowering

The buds collected from ‘Méndez’ for both vegetative flows macroscopically appeared more developed than the ‘Hass’ described for California (^{Salazar et al., 1998}) and Nayarit (^{Salazar et al., 2007}), so that they appeared E-4. However, microscopically, it was confirmed that they corresponded to E-3, whose characteristics are: meristem of the primary axis in convex form, presence of meristems of secondary axes of the inflorescence and of the scales that cover the yolk (Figure 1). Accordingly, the buds initially classified as E-4 were reclassified to E-3. Developmental status E-3 has already been associated with DIF in ‘Hass’ avocado (^{Salazar et al., 1999}).

Figure 1 Mean longitudinal section of apical bud of ‘Méndez’ avocado in E-3. es= yolk scale; p= meristem of the primary axis of the inflorescence; and s= meristem of the secondary axis of the inflorescence. 

Effect of the ambient temperature on the DIF

From all evaluated basal temperatures (≤8° C to ≤20° C), temperatures ≤18 and ≤20 °C were the best associated with DIF buds in outbreaks of summer and winter vegetative flows, respectively (Table 7). The result found for winter flow buds (≤ 20 °C) differs from that reported by ^{Salazar et al. (1999)} where young ‘Hass’ trees kept at constant temperature of 25/20 °C (day/night) in growth chambers did not flower. Environmental temperatures of 25/20 °C do not occur commercially as there are fluctuations in both directions that allow the successful cultivation of Hass in different producing regions (^{Salazar et al., 2013}).

As the DIF of the population of sprout sampled in the experimental trees was reached when the buds were between E-3 and E-4, for statistical purposes E-4 was considered as the state where DIF had occurred. In winter flow outbreaks from E-1 (February) to E-4 (26 June) 1480 HF accumulated (average of two years) with temperatures ≤20 °C. For summer outbreaks from E-1 (August) to E-4 (26 November) accumulated (average of two years) 1 266 HF with temperatures ≤18 ° C.

The difference in critical temperature and HF requirements to reach DIF between outbreaks of both vegetative flows may be due to the fact that winter buds developed under warm spring temperatures; the opposite occurred for summer outbreaks, which experienced a drop in typical summer-autumn temperature in the region where the study was conducted. The results confirm that the decrease in temperatures, rather than a specific value of the same, is what stimulated the transition of buds to the reproductive phase at the expense of vegetative growth.

In a growth chamber study young ‘Hass’ avocado trees were subjected to four weeks at 10/7 °C (day/night) plus four weeks at 20/15 °C. The DIF that resulted in intense flowering was reached with 1344 HF (^{Salazar et al., 1999}). These HF are very close to what was recorded in field conditions in the present study, 1 480 HF and 1 239.5 HF in winter and summer sprout, respectively.

Verification of the non-difference between data from year 1 (2014) vs. year 2 (2015)

For winter outbreaks, the HFA model ≤20 °C of year 2 showed a high predictive capacity of DIF for year 1 (R2= 0.98, Figure 2A). The same thing happened when using the model year 1 vs year 2 (R2= 0.98, Figure 2B). This test was also applied in summer sprout with the HFA model ≤18 °C and resulted in R2= 0.96 (year 2 vs. year 1) and R2= 0.98 (year 2 vs. year 1) (Figures 2C and 2D).

Figure 2 Adjustment of values between the state of floral development observed in year 1 (2014) vs. the predicted floral development obtained for year 2 (2015) and vice versa in winter flow outbreaks with HFA models ≤20 (a and b) and summer ≤18 °C (c and d). 

New models generated using data from two years

Given the non-difference between years of the predictive capacity of the models for outbreaks of winter or summer flows, data from the two years were fused and a new prediction model was obtained for each type of outbreak (Table 8). The unique models for winter outbreaks HFA ≤20 °C and summer HFA ≤18 °C were tested against the actual floral development data obtained in 2014 and 2015 and their R2 was higher than 0.98 (Figure 3) .

Figure 3 Adjustment of values between the state of floral development observed in year 1 (2014) and year 2 (2015). the predicted floral development obtained with the data set from the years 2014-2015 in winter flow outbreaks with HFA models ≤20 (a and b) and summer ≤18 °C (c and d). 

These models can be used to develop an application on the Internet that shows when the outbreaks of each vegetative flow will reach the DIF and safely program some activities in the orchard that usually inhibit or decrease the intensity of flowering, such as pruning, nitrogen fertilization and application of vegetable bioregulators, among others, which have shown to be effective to control the size of the tree, to reduce fruit drop, to accelerate physiological maturity and to increase fruit production and size.