The Brazilian forestry sector has a great potential for growth due to lower costs, production cycles, a higher productivity, and the variables that are less active to fluctuations in the finance market. Brazil has all competitive advantages of other countries in the forestry sector, due to its favorable natural conditions, scientific advances, and the entrepreneurial spirit, which results in a high growth potential (^{AMATA, 2009}; ^{ABRAF, 2013}). A species that has stood out in the forestry sector, and particularly in the foreign market, is the teak (Tectona grandis), originally from India, Myanmar, Thailand and Laos. It is species that flourishes in humid tropical climates with summer rains and dry winters. In Brazil, the teak grows best in areas with average annual rainfalls ranging between 1250 and 2500 mm and with an average temperature of 24 °C. A dry period of three to five months favors the quality of the wood ( ^{Cáceres Florestal, 1997}; ^{EMBRAPA, 2007}).

Various studies indicate that the teak has presented pathologies in Brazilian and international plantations. These diseases worry producers of this crop throughout the country, particularly, teak rust, given its aggressiveness (^{Pieri et al., 2011}). The disease presents yellow and powdery-looking pustules on the surface of the underside, and a premature defoliation takes place in all phenological phases of the culture, reducing the speed of growth of the plant, causing a reduction of the photosynthetic rate, and consequently impacting the rate of wood production (^{Arguedas-Gamboa, 2004}).

This disease was first reported in the American continent in Panama, in November 2003; later, in Costa Rica in January 2004 (^{Arguedas-Gamboa, 2004}); in Ecuador in September, and in Mexico in December 2005 (^{NAPPO, 2005}). In 2005, it was reported in Colombia (^{Céspedes and Yepes, 2007}), and in 2006, in Cuba (^{Pérez et al., 2008}). The first report of this disease in Brazil took place in 2009 and was later verified in several municipal areas of different Brazilian states (^{Pieri et al., 2011}).

The appropriate methods for the evaluation of the disease must allow a greater degree of accuracy, precision and repetitiveness, therefore such methods vary depending on the causal agents of the disease (^{Berger, 1980}). Severity is the variable used in the case of foliar diseases and the quantification of this variable is crucial for subsidizing different actions in agriculture, such as epidemiological studies, evaluations of control strategies, selecting resistant genotypes and carrying out tests with agrochemical products (^{Campbell and Madden, 1990}). The evaluation of severity is normally carried out in a subjective manner through visual analyses, and therefore the diagrammatic scales have become an important tool in these studies (^{Kranz, 1988}; ^{Nutter Jr. et al., 2006}). Scales are used in the normalization of the visual estimation; therefore, the evaluation is more precise and accurate between evaluators and it reduces errors in visual estimations (^{Campbell and Madden, 1990}).

Some of the most important characteristics in a diagrammatic scale are the ease of use, applicability in the face of a large variety of conditions with reproducible results, and the existence of intervals that represent all the stages of development of the disease (^{Berger, 1980}; ^{Bergamin Filho and Amorim, 1996}).

Proposing a standardized system to orient the evaluation of the severity of a particular disease is an important responsibility, since, if the system is deficient, the cost of its use may be higher than the benefits obtained with its use (^{Leite and Amorim, 2002}; ^{Nutter Jr. and Schultz, 1995}). However, a standardization of the disease evaluation methodology is highly desirable, since it helps compare results obtained in different institutions and locations (^{Bergamin Filho and Amorim, 1996}).

The aim of this study, therefore, was to develop and validate a diagrammatic scale to quantify teak rust in the field.

In order to do this, 200 adult teak leaves, aged 10 years, were gathered in an experimental field in the Hacienda Lageado - UNESP/FCA (Botucatu, São Paulo, Brasil) in the Tropical Flora company (Garça, São Paulo, Brasil), all of which presented different levels of damage due to rust; they were collected along with healthy leaves.

Each leaf was evaluated according to the proportion of the diseased area and the real severity of the disease, as a percentage. The healthy and affected areas were determined in RGB (red, green, blue) based on the methodology described by Masson et al. (2008). Later, the intermediate levels of the scale of severity were determined according to the Weber-Fechner law (^{Horsfall and Barratt, 1945}).

The scale was validated by 10 evaluators, who analyzed 50 digital images of adult teak leaves, both healthy and with symptoms of rust at different levels of severity. The evaluators had different levels of experience, some with previous knowledge of a scale, and others without experience or knowledge.

Each image of a leaf was projected for the evaluators using Power Point for 30 seconds in two stages: the first observation was performed without the use of a diagrammatic scale; the evaluators carried out the evaluation by placing a value, expressed as a percentage, in a previously established format. In the second stage, the evaluators received a new format along with the diagrammatic scale for reference. The images of the 50 teak leaves were projected for their evaluation against the scale.

Using the information obtained from the evaluations with and without scales, we determined the precision of the estimations obtained by calculating the coefficient of determination of the accuracy and the variance of absolute errors. A simple linear regression analysis was carried out, considering the real severity as the independent variable and the estimated severity, as the dependent variable. The precision of the estimations was evaluated using the precision or determination coefficient (r²) and the variance of the absolute errors (estimated severity minus real severity) (^{Kranz, 1988}; ^{Nutter Jr. et al., 1993}).

The diagrammatic scale of teak rust presented seven severity levels, base don the distribution of the sample: N0 = 0% (no symptoms or signs); N1 = 2.5%; N2 = 5%; N3 = 10%; N4 = 20%; N5 = 40%; N6 = 80%, exponentially, according to the Weber-Fechner law, as shown in Figure 1.

Figure 1 Diagrammatic scale for the evaluation of the severity of teak rust cause by the fungud Oliveae tectonae. Values in percentages of leaf area with symptoms.  

In the validation of the diagrammatic scale, the 10 evaluators presented differences in the perception of the severity levels of the disease. The evaluators presented a good accuracy, with and without scales, due to the estimated severity values being near the real values. Absolute errors decreased when the diagrammatic scale was used as an aid for evaluation (Figure 2).

Figure 2 Statistical validation of the diagrammatic scale to assess teak rust severity. Evaluators 5 and 7 where selected to represent the linear regression analysis between actual and estimated severity with and without using the diagrammatic scale. Those evaluators had the lowest and highest precision (r²), respectively.  

The evaluators displayed adequate estimations for repetitiveness, which can be viewed in the results of the regression between the first and second evaluation (with and without a scale). Due to the proximity of the estimated severity values and the real intensity values, the validation obtained very promising results (Figure 2).

The severity estimated using the scale and the regression lines obtained between the actual value and the estimation (continuous line) of rust in adult teak leaves are shown in Figure 2. The intercept (a) and slope coefficients (b) and determination r², obtained in the regressions between the real and the estimated, with and without the use of a diagram, are shown in Table 1.

There was a reduction in the absolute errors when the diagrammatic scale was used as an aid for evaluation (Figure 2).

With the adoption of the diagrammatic scale proposed, all evaluators improved the precision of the estimations (r²=0.93) in comparison with the result obtained without the use of the scale (r²=0.88).

Similar values between the estimated and real valued determine the accuracy of the evaluations. Precision is a factor to consider in the validation of a diagram scale, and it is defined as the precision o fan operation that supposed rigor and accuracy. Precision can be evaluated by determining the coefficient of regression analysis, which must be near to 1, and by the variation of absolute error (difference between estimated and real severity) (^{Bergamin Filho and Amorim, 1996}).

The difference between evaluators in the quantification of teak rust confirms observations by ^{Nutter Jr. and Schultz (1995)} regarding the variation in the ability between individuals to discriminate disease levels. The quality of the disease estimation is not only influenced by stimuli and psychological answers but can also be affected by factors such as the complexity of the sampling unit, size and shapes of the lesions, color and number of lesions in the sampling unit (^{Kranz, 1988}), fatigue and difficulty of concentration on the task (^{Shokes et al., 1987}).

The improvement in the accuracy of the estimations of the severity of rust in teak leaves with the use of the diagrammatic scale is similar to the results obtained in several studies carried out earlier, involving other pathosystems (^{Del Ponte et al., 2017}).

Even without the use of the diagrammatic scale, evaluators presented good levels of accuracy in the estimations, similar to the one confirmed in the validation of diagrammatic scales for rust in coffee (^{Capucho et al., 2011}), sugarcane (^{Klosowski et al., 2013}), bean (^{Godoy et al., 1997}) , soybean (^{Godoy et al., 2006}) and grapevine (^{Angelotti et al., 2008}), and may be a result of the ease of evaluation of the severity of the disease, due to the size of the rust pustules on leaves.

The evaluators presented certain levels of absolute errors in the estimations, even with the use of the diagrammatic scale. However, according to statements by ^{Stonehouse (1994)}, the presence of some level of error in the evaluations may be compensated by the speed and standardization that result from the use of diagrammatic scales. Likewise, as in most disease severity quantification methods, the use of diagrammatic scales is subjected to a certain degree of subjectivity, which can be minimized by training the evaluators (^{Nutter Jr. and Schultz, 1995}; ^{Nutter et al., 2006}).

The improvement in the repeatability of the disease severity estimations, as obtained in this study with the use of the diagrammatic scale, is important in developing standard disease evaluation methods, since it indicates that evaluations performed in different moments by a same evaluator presents a higher level of accuracy (^{Campbell and Madden, 1990}).

The diagrammatic scale proposed and validated in this study serves various items listed in a recent article (^{Del Ponte et al., 2017}) on the best practices for conducting and validating diagrammatic scales to quantify plant diseases.