The Tar Spot Complex (TSC), associated with the Phyllachora maydis Maubl and Monographella maydis Müller & Samuels fungi, is a disease that has turned into the main limiting factor for maize production (Zea mays L.) in a number of humid/sub-humid, tropical regions and transitional zones (^{Hock et al., 1989}) in several regions of Mexico and Central America. The incidence of TSC causes severe yield losses and deteriorates the quality of the fodder; furthermore, it has the potential to entirely destroy parcels of land (^{Pereyda et al., 2009}). In Mexico, the disease is considered potentially significant in around 800 thousand hectares distributed among the states of Michoacán, Puebla, Veracruz, Guerrero, Oaxaca and Chiapas (^{Gómez et al., 2013}).

In the field, it has been observed that the maize is first infected by P. maydis, causing small black stains in the form of exalted carbonaceous scabs, that due to their appearance are denominated asphalt stains (^{Hock et al., 1989}). Subsequently, a necrotic diameter is formed around each one of the lesions of P. maydis due to the secondary infection of M. maydis, originating the so called fish-eye symptom (^{Hock et al., 1992}). From all the organisms associated with M. maydis, the one that causes foliar necrosis has the most devastating effect. Under favorable conditions, the foliage of the plant may completely dry out in less than eight days due to the fusion of the lesions of the two pathogenic organisms and due to the possible production of a toxin (Hock et al. 1995).

Given the increasing importance of the Tar Spot Complex, standardized methods for the quantification of the disease are required, methods that allow the conduction of accurate, precise, and reproducible epidemiological studies; understanding 'accuracy' as the proximity that an estimated value has to the real value, 'precision' as the variation or repeatability associated with an estimation, and 'reproducibility' as the absence of change in the estimations when several evaluators quantify the same characteristics (^{Nascimiento et al., 2005}).

Among the methods of measurement for the intensity of a disease, the use of diagrammatic logarithmic scales is the most widely used. These scales consist in the representation of a series of plants or parts of plants that show the symptoms of a disease in varying degrees of severity (^{Nascimiento et al., 2005}) and are based on the Weber-Fechner law which states that the visual acuity of the damage is proportional to the stimulus logarithm up until a 50% severity, and from this value on, the relation is inversely proportional to the stimulus logarithm caused by the quantity of remaining healthy tissue (^{Mora et al., 2000}).

Despite the increasing importance of TSC in maize and the resulting need to carry out epidemiological or control studies, there is no standardized quantification method of the disease that provides easily reproducible results among investigators or institutions; therefore, the objective of this investigation was to design and validate a diagrammatic logarithmic severity scale for the maize - Phyllachora maydis and Monographella maydis - pathosystem that allows the evaluation of the damage caused by the disease in fields, analyzing the accuracy, precision and reproducible values generated with its use.

Design of the diagrammatic logarithmic scale. The methodology proposed by ^{Mora et al. (2000)} was employed, utilizing 50 leaves with a wide range of severity levels, originating from different hybrids with different genetic basis, which allowed the representation of different severity levels.

The photographic documentation was obtained from the parcels in the experimental station Agua Fría CIMMYT, Puebla and from communities in Chilpancingo, Guerrero in 2013. The total foliar area and the total diseased area of each digitalized image was determined through the Image Tool 3.0 software; the ratio of the healthy and diseased tissue allowed the calculation of the severity of the disease. The logarithmic scale was generated through the 2-Log V1.0 program, proposed by ^{Mora et al. (2000)}.

Validation of the diagrammatic scale. A sequence of 50 photographs of leaves and maize plants with different TSC severity levels was used, previously determining the affected area of each one of them. The severity of each image was evaluated by ten evaluators with the help of the scale, five of them with experience in the quantification of disease severity and five without direct experience in the phytopathological area. The accuracy and precision of each evaluator was determined through a simple analysis of linear regression as described by ^{Nutter et al. (1991)}.

The accuracy of each evaluator was determined through the T test applied to the intercept of the linear regression (b₀), to verify the H₀: b₀=0 hypothesis; and with the coefficient of the slope of the line (b₁) to estimate if it was different from 1 (H₀: b₁=1), with P ≤ 0.01. The accuracy of the tests was estimated with the coefficient of determination (r²⁾ of the same linear regression and with the absolute deviation of the error. The simple linear regression analysis was done through the GLM procedure of the SAS 9.0 statistical package.

In the field, the maximum severity value of TSC observed was 100 %, causing the premature senescence and death of the entire plant; conversely, the inferior limit had 0% severity. Considering both limits, the diagrammatic logarithmic scale was constituted by seven classes, represented by the intervals 0(0-0), 3(1-6), 12(7-22), 38(23-55), 72(56-84), 91(85-95) and 98(96-100)% of the necrotic foliar area (Figure 1).

Figure 1 Diagrammatic severity scale for the Tar Stain Complex in Maize. 

The accuracy, represented by the degree of proximity of the estimated values to the real values (^{Nutter et al. 1991}), measured by the b₀ intercept and by the b₁ coefficient of the linear model, was greater for the evaluators with experience in the quantification of diseases (Table 1). The values of the b₀ intercept were closer to zero for the first group. The value of the b₀ intercept was positive in almost all cases, which indicates that there is a tendency to overestimate the severity of the disease; this tendency was greater for the evaluators without experience. Based on the null hypothesis (a=0 o b=1), the coefficient b₁ was statistically equal to 1 (P<0.01) for most of the evaluators, indicating that the assessment of TSC generates results that are close to the real values, even when there is a tendency to overestimate them. ^{Nascimiento et al. (2005)} point out that an overestimation of the majority of evaluators indicates the presence of positive constant deviations for all levels of severity of the disease.

Table 1 Estimate of the interception parameters (b0), slope (b1), and coefficient of determination (r2) of the simple linear regression analysis calculated between the real and estimated severity of TSC, carried out by 10 evaluators with and without experience in the quantification of diseases. 

*, **Situation where the intercept value of the line (b₀) or the coefficient of the slope (b₁) were statistically different from 0 and 1 respectively; based on the T test with α=0.05 and 0.01, respectively.

According to ^{Sherwood et al., (1983)} the leaves with similar severities but with a different number of lesions generate a tendency to overestimate the disease, mainly when the number of lesions is high and their size is small, such is the case of TSC, where the usual symptom denominated "fish-eye" is presented in a high number of lesions. The overestimation of the severity levels using logarithmic scales has been common in several pathosystem. This has been reported, among others, by ^{Barbosa et al., (2006)} for Puccinia horiana; and ^{Aquino et al., (2008)} for Ramularia gossypii.

The precision (reproducibility or variation associated with an estimation), estimated by the coefficient of determination (r²⁾ and by the variability of the absolute errors (^{Nutter et al., 1991}), was greater for those evaluators with experience, fluctuating in the range of 0.81 to 0.92 (Table 1; Figure 2). The precision levels observed indicate that the first contact with the scale is appropriate for successful implementation in the evaluation of TSC. In regards to this, ^{Michereff et al., (2006)} determined precision values appropriate for a first evaluation with the use of scales; conversely, ^{Tovar et al., (2002)} had to familiarize the evaluators in order to increase precision and accuracy.

Figure 2 Errores absolutos (severidad real - severidad estimada) de las evaluaciones del CMA con el uso de la escala logarítmica; en la parte superior los evaluadores con experiencia en la cuantificación de enfermedades, en la parte inferior los evaluadores sin experiencia. 

The precision values observed in the evaluators without experience are acceptable; prior training could have a positive influence on the quality of the evaluations. This has been demonstrated for other pathosystems: ^{Barbosa et al.,(2006)} and ^{Aquino et al., (2008)} considerably elevated the accuracy and precision of the estimations of the evaluators without experience after prior training. The same author indicates that there was no significant improvement for the experienced evaluators.

The reproducibility of the scale was high using the same scale for the assessment of the material, given different evaluators estimated similar severity percentages. The linear regression of the severities estimated by the evaluators produced coefficients of determination that varied within the range of 65 to 91 (Table 1). Therefore, the use of the diagrammatic scale for the evaluation of TSC generates a high concurrence with the real severity values, reflected in a high precision among the evaluators.

^{Hock et al., (1992)} developed a scale that was also based on the logarithmic law for the in-field evaluation of the severity of TSC; however, the obtained precision values were not adequate. This was due to the complicated quantification system and to the elevated number of classes with which it was developed; furthermore, it considered the symptoms caused by both infectious agents separately. In this study, the symptoms of P. maydis and M. maydis were considered together, resulting in the observance of the combined symptoms of the disease by the evaluator.

Finally, the use of standardized systems for the quantification of maize diseases, and those of any other crop, proves to be a powerful tool as it allows the perfect comparison of experiments carried out by different institutions and investigators. The diagrammatic logarithmic scale for the TSC proposed in this study represents a standardized quantification method for the disease that will help obtain easily reproducible results, due to its high levels of accuracy and precision among several evaluators, therefore, it can be used as supporting material for different kinds of studies related to the quantification of the severity of TSC.