Materials And Methods

Site of study. Chapingo is located at 2,250 m over sea level (19º 30’ latitude north and 98º 53’ longitude west), in the State of Mexico. Its weather is Cb (Wo) with an annual average temperature of 15.2 °C and an annual rainfall of 635.5 mm (^{García, 1987}). Planting seasons in this region depend on rainfalls and last from mid-June to mid-October.

Tomato/blight pathosystem. The P. infestans-tomato pathosystem was studied under the weather conditions in Chapingo, State of Mexico during two planting cycles (2017 and 2018) in a period of five weeks, which ran between the months of August and September, using three scenarios: (1) expected, (2) observed and (3) simulated. In the experiment, we used a control (Rio grande) and six tomato lines (L-03, L-51, L-72, L-92, L-43, L-77). The expected scenario consisted in obtaining the amount of possible P. infestans infection cycles that could exist during the planting cycle. This is obtained from analyzing the association of weather variables with factors that influence the progress of P. infestans (^{Díaz et al., 2014}). The observed scenario is the progress of the real infection of P. infestans during a particular plantation cycle. This consists of the evaluation of readings of the infection of the foliage using the ^{Henfling scale to obtain the AUDPC (Henfling, 1987}). The simulated scenario consists of the prediction of the AUDPC using the “LATEBLIGH” algorithm, which is executed with the supply of data on weather parameters, resistance of the host and epidemiological variables (Díaz et al., 2014; ^{Andrade-Piedra et al., 2005b}; Andrade-Piedra et al., 2005c).

Agronomic crop management. In 2017, seeds were planted on May 23 and transplanted on June 21. On both dates, seeds were planted in styrofoam trays with 200 holes. The transplants for both dates were carried out in experimental units composed of three furrows, with an area of 12 m² in each experimental unit. The experiment was located in lot X-2 of the Xaltepa experimental field of the Autonomous University Chapingo. The auxiliary irrigations were performed using a drip tape (caliber eight thousand, with drippers every 20 cm and a flow of 1.02 L h^-1 per emitter) when required by the crop; granulated N, P, K fertilizer was applied (46-00-00; 18-46-00; 00-00-60). Foliar fertilizer of microelements was applied (Tradecorp AZ). For pest control, we applied flonicamid and cypermethrin.Weed control was performed by hand. Depending on the phenological stage of the crop, the plant was provided support with nylon raffias.

Expected scenario. Six weather variables (Table 1) on the development of late blight were analyzed by multiple linear regression (^{SAS, 2002}). The selection of the best model, with a minimum independence variability, was based on the criterion of the highest determination coefficient. The weather data were related with conditions that can impact the survival, permanence and dissemination of P. infestans (^{Andrade-Piedra et al., 2005c}; ^{Iglesias et al., 2010}; ^{Johnson et al., 2009}; ^{Morales et al., 2011}; ^{Nowicki et al., 2012}; ^{Skelsey et al., 2009}; ^{Skelsey et al., 2010}). Temperature (T), relative humidity (RH) and solar radiation (SR) were chosen to determine the expected scenarios, considering their greatest contribution to the development of the disease.

Observed scenario. Six tomato lines were evaluated, along with a control and two levels of susceptibility (S = susceptible, R = resistant, C= control); L-03 (S), L-51 (S), L-72 (S), L-92(S), L-43 (R), L-77(R), and Rio grande (C) (^{Leyva et al., 2013}). During the planting cycle, the plants were fertilized and the pest and weed controls were carried out. They were evaluated in the field with a complete random block experimental design with four repetitions (5 m in length, 0.80 m between furrows and 0.40 m between plants). The weekly readings of foliar infection were evaluated with the ^{Henfling scale (Henfling, 1987}) for a five-week period between August and September, 2017 and 2018, once the pathogen appeared naturally. Based on the initial symptoms after transplanting, the AUDPC was calculated progressively (^{Shaner and Finney, 1977}). The values derived from AUDPC were used to calculate the RAUDPC (^{Fry, 1978}; ^{Bonierbale et al., 2010}). Finally, the RAUDPC values were used to calculate the RaRAUDPC, using line 92 as the reference, which was possible during the experiment, following the procedure described by ^{Yuen and Forbes (2009}) and ^{Taipe et al. (2011}).

Simulated scenario. An algorithm named LATEBLIGH was produced using “SAS forWindows 9.0” (^{SAS, 2002}) considering the weather parameters and the level of the host resistant of the host within 2.4 m² of tomato plants, based on forms reported by ^{Díaz et al. (2014}).

Results And Discussion

Expected scenarios. When selecting the multiple regression model for the execution of the expected scenarios, temperature (T), relative humidity (RH) and solar radiation (SR) were found to be independent variables that presented the highest coefficient of determination (R² = 0.44). These variables are related to the presence, dissemination and effectiveness of P. infestans. Weather variables were recorded for a 10-year period (2007-2016) and averaged out in the tendency graph. Table 1 shows the minimum and maximum average records for weather variables derived from the application of two selection criterion for RH (80% ≤RH≤90% and RH> 90%). The upper limit of the average T, RH and SR records under the criterion of the 80% ≤RH≤90% was used to explain both the variability and the effect of these variables on the development of late blight. This comparison was made using the weather parameters for the expected scenarios with RH for 23.5 h and T 15.9 °C favoring the presence, dissemination and effectiveness of P. infestans, in comparison with the upper levels of the mean (^{Andrade-Piedra, et al., 2005c}; ^{Iglesias et al., 2010}). Based on the conditions obtained through T, RH and SR as the best multiple linear model, highest peak fluctuation and selection criterion 80% ≤RH≤90%, five expected scenarios were identified, with ranges of four to ten infection cycles of variable lengths ranging from 6 to 12 h by night, dawn and sunrise (19:00 to 08:00). Figure 1 shows the infection cycles of the expected scenarios (I to V). The tendency curves (high and low peaks) are joined for the three variables (T, RH and SR). Both the beginning and the end of each cycle are determined by the reduction of the RH and the increase in T, based on daily intervals of 60 min. A cold and humid weather is required for the development of a greater amount of inoculant in a short timeframe (^{Kamoun and Smart, 2005}). Darkness favors sporulation (^{Nowicki et al., 2012}) and the expression of the pathogens in Chapingo (^{Díaz et al., 2014}). The severity was favored with a T of 9.9 to 16.1 °C and an RH of 80.4 to 100% for 8 h in the tomato crop between June 18 and September 18 (Table 2). These conditions favor the beginning of an epidemic with temperatures at night below the condensation point for at least 4 h and a low temperature at night of 10 °C or below (Díaz et al., 2014; ^{Morales et al., 2011}; Nowicki et al., 2012). Significant differences (p <0.05) were observed between average registers for weather variables T and RH in the five expected scenarios analyzed.

Observed scenarios. In 2017 the genetic tolerance of Río grande and Line 77 was better than that of the tolerant Lines (Line 92 and Line 72), which were used as references in the initial progress of P. infestans, and in 2018, the expression of the tolerant line (Río grande) was greater to that of susceptible lines (Line 43, Line 51). In 2017, the infection observed in the field began on that same day, which led to the idea that both lines are susceptible to P. infestans under favorable conditions of RH and TR. Likewise, in 2018, the infection in lines 92 and Río grande began on the same day with a similar infection speed in comparison with 2017 according to the weather plan of conditions of that year (Figure 2). Weather conditions were favorable for the infection of leaves in susceptible lines. On days 90-91 after transplanting (ddt), plants of susceptible lines were infected by 73 % in 2017. A similar lag in the infection rates was also reported by ^{Cadena-Hinojosa et al. (2007}).

Figure 1 P. infestans infection cycles of five scenarios in tomato under the weather conditions in Chapingo, State of Mexico. (Temperature (°C), Relative humidity (%), Solar Radiation (Wm^-2).) 

Figure 2. Progress of the infection by P. infestans on a line of susceptible tomato during two seasons (2017, 2018) and one tolerant line (2017) under the weather conditions in Chapingo. (Temperatura (°C), Relative humidity (%), Solar radiation (Wm^-2), P. infestans). 

The progress of the infection of Line 92 (plants dead 100-104 ddt displayed the presence of favorable weather conditions for the dissemination of the pathogen, with a temperature of 10.6-15.4 °C, RH of 83-98% for 12 h during the night, dawn and part of the morning (20:00 to 08.00 h) coinciding with the expected VI-4 scenario. However, in 2018, the infection began and progressed later (in approximately 79-81 ddt) in comparison to 2017, with 12-16.2 °C, 90-99% RH, which coincides with scenarios 6, 7, 8 (Table 3).

In 2018, plants present no infection at 95-96 ddt, 10-14.6 °C, and 100 % RH for 12 h in the nighttime, dawn and sunrise (20:00-08:00 h), making it similar to expected scenario IV-4. In general, during both planting cycles (2017 and 2018), the progress of the infection by P. infestans was favored by scenarios with T of 10-16.7 °C and an RH 80-100% for 8-13 h at night, dawn and part of the morning (19:00-08:00 h) (^{Andrade-Piedra, et al., 2005c}; ^{Iglesias et al., 2010}). The average of 60-minute registers during the 102- to 104-day planting cycles in 2017 and 2018, displayed no significant differences between magnitudes of T (14.6 °C vs 15.4 °C) and RH (80% vs 83%). However, favorable conditions for the natural progression of the disease were observed and expected (based on the scenarios modelled). In 2017, the observed beginning of the infection coincided with scenarios I-2; in 2018, it coincided with scenarios II-3 and IV-5. In 2017, the point observed in which plants present no infection coincides with scenario IV-6, and in 2018, with scenario II-1 (Table 3).

The AUDPC, RAUDPC and RaRAUDPC were evaluated in a randomized experimental design with four blocks during 2017 and 2018. The results validated the proposed model, which was confirmed by the homogenous performance of the variance through an analysis of residues and the Shapiro-Wilk normality test, (^{SAS, 2002}) (Tables 4 and 5).

In 2017, the statistics of the tests produced the value of 0.45 for AUDPC, RAUDPC and RaRAUDPC with Pr <W 0.0001 and in 2018 the tree values were of 0.94. The Shapiro-Wilk normality validates the proposed model with a homogenous variance yield during both seasons. AUDPC, RAUDPC and RaRAUDPC were analyzed individually, although no differences were found between treatments with P <0.0001. During each planting cycle, the effect of the order of merit AUDPC, RAUDPC, and RaRAUDPC was greater in susceptible lines (line 92) in comparison with tolerant lines (Río grande). The t-test (LSD) and Tukey’s Honestly Significant Difference (HDS) Test for the variable AUDPC and its derivatives indicate that all possible comparisons between tolerant and susceptible lines were important in 2017.

RaRAUDPC was used to generate a susceptibility scale (1-8) for the degree of resistance or susceptibility of lines in two planting cycles (^{Yuen and Forbes, 2009}). This scale system is practical and easy to use, since it allows the minimum difference between observed averages of 7.6 vs 7.7 in the 2017 and 2018 cycles, respectively. This value becomes the maximum value (≤ 8) for susceptible and intermediate lines and the minimum value (<1) for the resistant cultivar (Tables 4 and 5). The minimum value was not observed in the two planting cycles, due to their being no statistical differences in the RaRAUDPC of the lines due to their high AUDPC value.

Simulated scenario. The model “LATEBLIGHT” involved the use of specific procedures, including magnitudes of parameters and epidemiological variables (Table 6), weather parameters from the specific surroundings, and the estimation of the initial inoculant of the pathogen (^{Andrade-Piedra et al., 2005c}). These procedures helped obtain observed and simulated AUDPC values, as well as to predict epidemics under natural infection conditions in Chapingo. In 2017, the model was used to obtain simulated and observed AUDPC values for each treatment(Figure 3). In addition, the model predicted the incidence of epidemics days before the natural infection in the field, which helps implement thorough control measures. Therefore, when predicting the outbreak, the model includes magnitudes of epidemiological variables and parameters (Table 6), as well as the weather parameters of T between 10.6 and 15.4 °C, RH between 80 and 100% for continuous periods of 9 to 13 h in the nighttime, dawn and morning.

Figure 3. Area under the disease progress curve (AUDPC) of the data observed (circles) and simulated (solid line) of seven late blight epidemics under field conditions in Chapingo, State of Mexico in 2017. The simulated progress curve was developed using the LB2004 version of “LATEBLIGHT”. Vertical lines represent the standard deviation of the mean for the observed severity of late blight. 

However, the magnitude of the relative humidity threshold did not remain fixed on 85 or 90% in this model, due to the variation caused by the weather conditions in Chapingo. The RH requires calibration, depending on the degree of susceptibility of the cultivars; specifically, at 80% for susceptible cultivars, and 88% for resistant cultivars. The top limit of 88% exists because humidity does not surpass 90% inside the canopy (^{Andrade-Piedra et al., 2005b}) (Table 7). The susceptible lines have values for AUDPC > 1956 in comparison to the tolerant line (AUDPC < 1753) (Table 7).

Figure 4. Area under the disease progress curve (AUDPC) of the data observed (circles) and simulated (solid line) of seven late blight epidemics under field conditions in Chapingo, State of Mexico in 2018. The simulated progress curve was developed using the LB2004 version of “LATEBLIGHT”. Vertical lines represent the standard deviation of the mean for the observed severity of late blight. 

During the 2018 cycle, the application of the model’s algorithm generated simulated AUDPC values near to those observed in the field, and in turn (Figure 4), the model predicted the incidence of epidemics two days before the natural infection observed in the field. The epidemic prediction was developed with the magnitudes of the epidemiological variables and parameters (Table 6), as well as the weather parameters of T between 10.6 and 15.4 °C, an RH of between 80 and 100% for a continuous period of 5 to 13.5 h in the nighttime and part of the dawn. However, the threshold magnitude of relative humidity did not remain fixed on 85 to 90% according to the model, due to the variation caused by weather conditions in Chapingo. As a result, RH was calibrated to 80-85% for susceptible lines and 86% for tolerant lines. This value was used because the maximum RH did not surpass 90% within the foliar canopy (^{Andrade-Piedra et al., 2005b}) (Table 8). The AUDPC distinguishes susceptible lines (AUDPC > 1426) from tolerant lines (AUDPC < 1333) (Table 8).

The expected scenarios were based on (1) a better multiple linear regression model; (2) a tendency graph, curves; and (3) selection criterion 80% ≤RH≤90% for T and RH. These criteria helped identify five favorable scenarios for P. infestans epidemics with four to ten P. infestans infection cycles with a duration of 5 to 12 h for the weather conditions in Chapingo. The infection rates observed during the 2017 and 2018 planting cycles confirmed that the real incidence of conditions favorable to P. infestans was influenced by (1) weather conditions (T and RH). The infection caused by P. infestans in the cycle observed in the field in 2017 was observed to coincide with expected scenarios IV-4 and III-1, and in 2018, it coincided with scenario V-2. The field experiment model is valid with a coefficient variation of <16%.

Conclusions

The number of infection cycles in the expected scenario was directly related with the severity presented by P. infestans in the scenarios observed. The higher the number of infection cycles related to favorable weather conditions, the higher the severity of late blight will be. The scenarios simulated with the LATEBLIGHT model predicted the severity of the scenarios observed two days in advance. This led to expected, observed and simulated scenarios having a broad relation for the prediction of P. infestans epidemics in tomato crops in Chapingo. In conclusion, the model proved to be able to predict infection epidemics in the field, facilitating the timely application of the thorough control methods, which would produce economic benefits and reduce the environmental impacts of agrochemicals.