In Mexico, 67% of the total production of barley is for rainfed crops (spring-summer) and remaining 33% is irrigated (autumn- winter). The region where it is grown under irrigation is El Bajio, corresponding to the States of Querétaro, Guanajuato, Michoacan and Jalisco (^{Islas, 2008}); in the period of 2003-2009, the average yield in El Bajío was 4.7 t ha^-1 (^{SIAP-SAGARPA, 2009}). The barley stripe rust, caused by Puccinia striiformis f. sp. hordei, is a serious disease in the shoal, as the crop is set in the watering cycle autumn-winter, and the fungus is favoured during this period because it is a pathogen of low temperature and is a major problem in places where the cold, moist climate prevail (^{Stubbs, 1988}).

The optimum temperature range for germination of spores is 9-13 °C and 12-15 °C for development and sporulation (^{Roelfs et al., 1992}). The rusts can be controlled by spraying fungicides; however, growing costs and damage to the environment are increased (^{Sandoval et al., 1999}). The intensity of the disease changes from cycle to cycle in response to weather conditions. Today, integrated management schemes use information from the host, the pathogen and weather conditions as well, but none can alert or predict the onset of infection or pathogen development.

Dynamic models enable integration of the variables associated with pathosystem, besides calculating changes attributable to weather conditions to obtain sufficient information to support the application of products to control the disease. For this, we made a model that estimates the onset of infection and development of stripe rust of barley (P. striiformis f. sp. hordei) in the State of Guanajuato, in order to use it as a tool for decision in the prevention and management of this disease.

The work was done in the INIFAP (Campo Experimental Bajío) in Celaya, Guanajuato. The agroclimatic monitoring was conducted through the network of meteorological stations of Guanajuato Produce Foundation and portable stations Mark Davis. For developing the model a computer with OS (Windows 7) was used; software (Vensim^® 5.6d), (SIMPEC and ESRI^® ArcMap^™ 10.0).

The model was constructed based on systems theory, using the methodology of system dynamics given by ^{Rabbinge et al. (1989}) . The model calculates the deposition based on the initial spore inoculum secondary inoculum and then spore germination calculated according to the temperature conditions (<= 11 °C) and relative humidity (> 80%) and the frequency of infection, the germinated spores give rise to lesions (pustules) that produce new spores (secondary inoculum) finally severity is calculated by dividing the infected between the available leaf area and multiplied by 100 to express it as a percentage area. The diagram shown in Figure 1. For model calibration monitoring data stripe rust severity of barley were used in the Bajío Experimental INIFAP.

Figure 1 Diagram model of infection and development of P. striiformis f. sp. hordei, showing the interactions and types of variables. 

Data correspond to cycles autumn-winter 2009-2010, 2010-2011, 2011-2012 and 2012-2013 in materials susceptible (Apizaco) and moderately susceptible (Alina, Armida and Esperanza) to stripe rust. Simulations for five sowing dates (November 1, 15 November 1 December 15 December and 1 January) were performed, and the corresponding comparisons for each date and each cycle is made. A map of risk of disease for the Sate was developed by the interpolation method IDW (inverse distance weighted) using the database of the National Weather Service (NWS-CNA), depending on the days with favourable conditions on February, highlighting the main municipalities in terms of production of barley. For the analysis of climate the SIMPEC software was used.

The total of the simulations are shown in Table 1, using the maximum value recorded by the model. The 2009- 2010 cycle was an exceptional case because heavy rains in early February were recorded and this was reflected in severity; in 2010-2011 no extraordinary conditions were presented; in 2011-2012 light rains were recorded the first days of January, but this was enough to promote optimal conditions for the pathogen; finally the 2012-2013 cycle recorded three days of very late frost in March and this resulted in an increase in severity for late planting dates.

Table 1 Severity data of P. striiformis f. sp. hordei real and simulated of different barley varieties registered in five sowing dates for four crop cycles. 

The parameters described in the literature indicated that, the optimum temperature for stripe rust infection is 11 °C; however, these data obtained indicated that infection cycles increased when the temperature dropped, therefore, the model is adjusted according to these observations. Simulations with the model for the 2009-2010 cycle, showed a strong association with the data observed in the field (Figures 2 and 3), showing an R 2 of 0.96, for this the highest severity data recorded by the model was used. Which indicates the model fit resulted in a high accuracy.

Figure 2 Percentage graph of simulated severity in five planting dates for 2009-2010 in the city of Celaya, Guanajuato. 

Figure 3 Linear regression graph between the simulated and observed severity of stripe rust in five sowing dates in 2009-2010 in the city of Celaya, Guanajuato severity. 

In Figure 4, the risk map to stripe rust shows during the month of February, the analysis was conducted in the municipalities of the production area of Guanajuato, which covers the municipalities of Valle de Santiago, Salamanca, Cortazar, Irapuato, Jaral del Progreso and Abasolo. As shown, all the area has at least 10 days with favourable conditions for the pathogen, which is a high probability that the disease is present.

Figure 4 Definition of risk areas to stripe rust in Guanajuato, depending on weather conditions favourable for infection in February. 

In particular, the town of Valle de Santiago, as well as some areas of the municipalities of Jaral del Progreso, Salamanca and Abasolo area represent the highest risk for this condition, logging more than 20 days with favourable conditions for infection in the month of February.