Characteristics of the gardens

The research was carried out during two production cycles (2014-2015 and 2015-2016) in two commercial avocado orchards ‛Mendez’ grafted on Creole rootstocks of the company Agro González, SPR of RL, with fertigation, Feozem haplico soil and semi-warm climate subhumid [AC(w)] (^{García-Amaro, 1998}) from the south of the state of Jalisco. The garden “Colorin 1” is located in Atequizayan, Municipality of Zapotlan el Grande and the garden “Ocote cuate 2” is in Zapotiltic, Municipality of Zapotiltic. For these orchards, the altitude is 1 556 m and 1 428 m, the distance between trees 7x 3.5 m and 5x5 m, the age at the beginning of the study of 4 and 6 years, respectively. The orchards received the standard handling of the producer.

Sampling and processing of yolks

In each orchard, 10 trees were selected without cross-linking and with a production history of at least 50 kg tree^-1. Each tree was marked 30 shoots at the beginning of each vegetative flow of winter (February 2014 and 2015) and summer (August 2014 and 2015). From each marked tree an apical bud was collected at monthly or biweekly intervals as the anthesis approached. For the vegetative flow of winter (both years) the samplings were carried out from February to October and for summer from August to March of the following year.

The buds were fixed in FAA (formaldehyde:acetic, acid: ethanol, 5:5:90, v:v:v) and then placed in a vacuum hood (Nalgene 8040317, Nalgen Company) at 30 KPa for 5 h. Subsequently, they were classified under a stereoscopic microscope (Zeiss Stereomikroskop Mod. Stemi 2000-C, Carl Zeiss, Göttingen, Germany), with the visual scale of ^{Salazar-García et al. (1998)} which comprises from E-1 (vegetative bud) to E-11 (anthesis).

Calculation of cold days (DF)

In each orchard, the air temperature was recorded every 15 min with automated recorders HOBO H8 (Onset Computer, Witzprod, Englewood Cliffs, NJ, USA) operated with batteries. Independently for outbreaks of winter and summer vegetative flows, the occurrence of minimum temperatures from 8 to 20 °C was measured in increments of 1 °C. The formula was used: DF= (Tmin ≤ T, 1.0); where: Tmin= minimum registered temperature; T= critical temperature, from 8 to 20 °C. If the temperature condition is met, then the value of DF is 1, otherwise it is 0. Using the Excel program (2010). The values of DF₈ to DF₂₀ were accumulated for each period of sampling of apical buds. These values were called accumulated cold days (DFA). As zero day was considered when the apical buds were in E-1 (vegetative stage), which occurred in February (winter shoots) and August (summer shoots).

Identification of the temperature associated with floral development

The DFA were used as independent variables and the state of floral development of the apical buds in shoots of each flow as a dependent variable. The Stepwise SAS/STAT procedure (^{SAS, 2011}) was used to select the best model in order of response (second to fifth order) for each selected temperature (from ≤ 8 °C to ≤ 20 ^oC, in 1 °C intervals). ). The criteria for choosing the best prediction models were: 1) higher value of R²; 2) lower mean square error (CME); 3) the value of Cp (^{Draper and Smith, 1981}).

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

Test of the best prediction models

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

After verification of the no difference between years, a regression model was obtained for each vegetative flow integrating the information of the two years into a single data set.

Floral development

The state of floral development of apical shoot buds of vegetative flows of winter and summer, were used to generate the models of floral development prediction (Tables 1 and 2). On average, floral development (vegetative yolk to anthesis) in outbreaks of winter and summer vegetative flow took 216 and 187 days, respectively. The shorter time required for the ‛Mendez’ summer buds to complete their floral development could be due to the fact that when they emerged (August-September) the environmental temperature had already started its descent (average of 18 °C), suppressing the vegetative growth and stimulating floral development.

Effect of environmental temperature on floral development

Of all the minimum temperatures used ( ≤ 8 °C to ≤ 20 °C), ≤ 17 and ≤ 15 °C were the best associated with floral development in outbreaks of winter and summer vegetative flows (two years in each case), respectively (Tables 3 and 4). ^{Buttrose and Alexander (1978)} and ^{Salazar-García et al. (1999)} found in young trees of ‛Fuerte’ and ‛Hass’, respectively, that under controlled conditions constant temperatures >20 °C did not promote flowering.

Later, in a field study with ‛Hass’ avocado in Nayarit, Mexico, ^{Salazar-García et al. (2007)} associated the temperatures ≤ 21 °C with the floral development of outbreaks of winter flow and ≤ 19 and ≤ 20 °C with that of summer shoots. In an investigation carried out in Michoacán (subhumid semi-warm climate) it was found that temperatures of ≤ 19 to ≤ 21 °C were related to the floral development process in outbreaks of winter and summer flows of cv. Hass (^{Salazar-García et al., 2009}).

In the present study, the floral development process from buds in state E-1 (term of vegetative shoot lengthening) to anthesis (E-11) in winter buds for 2014 and 2015 accumulated 111 and 140 DFA ( ≤ 17 °C), respectively. In summer outbreaks 133 DFA (2014) and 143 DFA (2015) were accumulated at temperatures ≤ 15 °C. In the two years of the study, an average of 126 and 138 days were accumulated with temperatures ≤ 17 and ≤ 15 °C for winter and summer outbreaks, respectively.

The amount of cold accumulated by the apical buds of the shoots of both vegetative flows was lower than that found for ‛Hass’ in the semi-warm subhumid climate of Nayarit for winter shoots (179 DFA with temperatures ≤ 21 °C) and summer (183 and 201 DFA with temperatures ≤ 19 and ≤ 20 °C, respectively) (^{Salazar-García et al., 2007}). In Michoacán, for this same cultivar and type of climate, 375 (winter) and 198 (summer) DFA were required with temperatures ≤ 19 and ≤ 21 °C (^{Salazar-García et al., 2009}). The differences described show the genetic plasticity of the avocado to different environments in which it is grown and the apparent irrelevance of establishing a unique or critical value of temperature associated with floral development since the “cold” necessary to initiate and complete a development cycle floral depends on the temperatures that occur in each producing region.

Verification of the no difference between year 1 (2014) vs year 2 (2015)

The verification of the floral development prediction models (adjustment of observed vs. predicted values) was performed reciprocally (year 1 vs year 2 and vice versa), to determine if the data for the two years were statistically equal (Figures 1A -D). For winter outbreaks the DFA model ≤ 17 °C of year 2 showed a high predictive capacity of floral development for year 1 (R²= 0.99) (Figure 1A). Something similar was obtained when using the model of year 1 to predict floral development in year 2 (R²= 0.99) (Figure 1B). For summer outbreaks the DFA model ≤ 15 °C of year 2 was tested, which showed a good predictive capacity of floral development for year 1 (R²= 0.99) (Figure 1C). Something similar was obtained when using the model of year 1 to predict the floral development in year 2 (R²= 0.97) (Figure 1D).

Figure 1 Adjustment of values between the state of floral development observed in year 1 (2014) vs. the floral development predicted obtained for the year 2 (2015) and vice versa in outbreaks of the winter flow with the models DFA ≤ 17 (A and B) and summer DFA ≤ 15 °C (C and D). 

New models generated with two-year data

The prediction models for outbreaks of the winter and summer flow of year 1 were able to predict the floral development of year 2 and vice versa. Before this, a single data set was integrated with information of two years for each type of outbreak, obtaining two new prediction models: winter ≤ 17 °C and summer ≤ 15 °C (Table 5). These models were incorporated into an application (www.cesix.inifap.gob.mx/frutalestropicales/desarrollofloralmendezjalisco.php) which shows the floral development of each vegetative flow of the 'Mendez' avocado. In this way, it is possible to use this information for the best programming of the garden management activities that could inhibit or diminish the intensity of flowering, or plan the introduction to the orchard of pollinating insects. Another use of floral development prediction models is to support students, technicians and researchers involved in the cultivation of ‛Mendez’ avocado.

Temperature record. During the study period, the lowest minimum temperatures occurred in the first quarter of 2016 (Figure 2). In week six and 11, 6 and 5 °C were registered, respectively. On the other hand, in 2014 between week 25 and 29 (last of June and July, respectively) the minimum temperatures reached on average 21.8 °C.

Figure 2 Maximum and minimum air temperatures recorded February 2014 to August 2016. Weekly average of data of the “Colorín 1” and “Ocote cuate 2” orchards.