Disease progress curve. Plant disease epidemics are evaluated by measuring severity or incidence at several stages during the cropping season (see Estimation of Disease Severity). The graph of either severity or incidence (y axis) on a measure of time (x axis) is called ‘disease progress curve’ (DPC), which has being called the ‘signature’ of an epidemic, because it is critical for its analysis (3) . Obtaining DPCs is, therefore, the first step when analyzing an epidemic.

The representation of DPCs varies with the type of experiment. In un-replicated (usually exploratory) experiments, the DPC of a treatment (e.g., a cultivar, a fungicide, a combination of a cultivar and a fungicide, etc.) is a series of single points each of one representing the severity or incidence at a certain time. In contrast, in replicated experiments each of those points represents the average severity or incidence and has a plus-and-minus bar that represents a measure of variability (e.g., standard deviation of the mean). DPCs representing ‘observed’ epidemics (i.e., those from field, greenhouse, or laboratory) have their points usually not connected by lines. In contrast, DPCs representing ‘simulated’ epidemics (i.e., those obtained from a plant disease model) have usually their points connected by straight lines. Several DPCs can be plotted in the same figure to allow graphical comparisons among them. Figure 1 shows an example of observed and simulated DPCs from a replicated experiment.

Figure 1. Observed (circles) and simulated (continuous lines) disease progress curves (DPCs) of cultivars Tomasa and Amarilis infected with Phytophthora infestans in the location of Huancayo (Peru) in 2000. The simulated DPCs were obtained with a single simulation of the LATEBLIGHT model. Vertical lines represent the standard deviation of the observed mean blight severity (n = 4). Data from Andrade-Piedra et al. (1).

The DPC of a certain experimental treatment can be summarized with several descriptors (3):

Time of disease onset.

Initial amount of disease

Rate of disease increase.

Area under the disease progress curve (AUDPC).

Period until 50% severity or incidence.

Maximum amount of disease

Final amount of disease.

Epidemic duration.

Area under the disease progress curve. Epidemics of potato late blight (LB) are summarized usually with AUDPC. This descriptor has proved to be a reliable measure to estimate the effect of fungicide, host resistance (4) or pathogen fitness (8) on LB epidemics. It takes into account time of disease onset, rate of disease increase, and final severity (3). AUDPC is most frequently calculated with equation 1 (3):

where x_i = disease severity (percentage or proportion) at the i th evaluation, t_i = time (days, usually after planting or emergence, or Julian days) at the i th evaluation, and n = total number of evaluations. Figure 2 shows an example of the calculation of AUDPC on the following epidemic (n = 3):

t₁ = 10 days                 x₁ = 8%
t₂ = 20                         x₂ = 25
t₃ = 30                         x₃ = 65

Figure 2. Example of the calculation of the area under the disease progress curve (AUDPC) using equation 1 in an epidemic with 3 severity evaluations.

The units of AUDPC are percent-days (if severity was expressed as percentage, and time as days) or proportion-days (if severity was expressed as proportion) (3). The higher the AUDPC, the more severe the epidemic.

AUDPC values of epidemics with different durations can be compared using relative AUDPC, which is calculated by dividing the AUDPC by the total duration of the epidemic (4). Relative AUDPC has no units, their values vary from 0 to 100 (if severity was expressed as percentage) or from 0 to 1 (if expressed as proportion). It can be interpreted as the percentage (or proportion) of the maximum potential AUDPC (the AUDPC that a treatment would have if it had 100% severity at all evaluations).

Apparent infection rate. Epidemics of LB are also summarized with the rate of disease increase (r) (e.g. 2, 4References ). This is a parameter of several models which are used to study disease progress in a population of plants over time (3). Therefore, the first step is to choose the most appropriate model to describe the progress of LB in a certain treatment. The logistic model is usually used for polycyclic diseases (those with many cycles of infection during a single season) with sigmoid (s shape) DPCs, such as LB. In this model, the rate of disease increase is the slope of the logistic transformation of severity on time. The logistic transformation is called logit and is described in equation 2: 

logit = ln (x / [100 ─ x])                                      [2]

where ln = natural logarithm and x = disease severity (percentage) (if severity is expressed as proportion, substitute 100 by 1 in equation 2). The rate of disease increase of the logistic model is called apparent infection rate, because what is being evaluated is the apparently diseased tissue, since there is also infected tissue that is still asymptomatic.Continuing with the previous example, in order to calculate r, first transform severity into logits:

t₁ = 10 days                 x₁ = 8%             logit_x1 = -2.4

t₂ = 20 days                 x₂ = 25%           logit_x2 = -1.1

t₃ = 30 days                 x₃ = 65%           logit_x3 = 0.6

Then, estimate the slope of the linear regression of logits versus time using least square regression analysis (7) (Figure 3).

Figure 3. Example of the calculation of the apparent infection rate (r = 0.15) in an epidemic with 3 severity evaluations.

The units of r are logit^-1 day (if the unit of time was days). In the previous example, there is an increase of 0.15 logits for each day. This parameter represents a measure of the speed of disease increase over time (the higher the value, the faster the disease increase) and is determined by the pathogen aggressiveness, the plant susceptibility, and the environmental conditions (3).

 
The logistic transformation is undefined at values of x = 0% and x = 100% (or 1 if x is expressed as proportion) (3). Therefore, the x values included for the estimation of r must be higher than 0% and lower than 100%. The epidemics should be truncated at the first x value equal to 100%, and that value should be replaced by a value higher than the preceding, but lower than 100%. For example, to calculate r in the following epidemic:

 
t₁ = 10 days                 x₁ = 0%

t₂ = 20                         x₂ = 0.1

t₃ = 30                         x₃ = 10

t₄ = 40                         x₄ = 30

t₅ = 50                         x₅ = 70

t₆ = 60                         x₆ = 90

t₇ = 70                         x₇ = 99

t₈ = 80                         x₈ = 100

t₉ = 90                         x₉ = 100

t₁₀ = 100                     x₁₀ = 100

 
the evaluations at t₁, t₉ and t₁₀ should not be considered, and the x value at t₈ should be replaced by a value higher than x₇ (99%), but lower than 100% (e.g. 99.5%).

 
AUDPC has several advantages over r for summarizing epidemics. However, since r is a parameter of the logistic model, it is much better suited for analytical purposes than AUDPC. The advantages of AUDPC over r for summarizing epidemics are the following. First, the concept of AUDPC and the method to calculate it are simpler than those of r. Second, AUDPC does not require making any of the assumptions needed for growth curve models such as the logistic model. Among these assumptions, the most important are that environment, host resistance, and pathogen aggressiveness are uniform across the season (3). Finally, irregular DPCs (i.e, those that deviate from a sigmoid) are best summarized with AUDPC than with r. This type of curves may be obtained when an external factor (e.g., fungicide) has altered the disease progress.

 
AUDPC and r (and other descriptors, such as the period until 50% severity or incidence, the final amount of disease, etc.) are calculated for each repetition of a certain treatment. In that way, there will be a measure of variability that can be used for statistical comparison, e.g., analysis of variance. Finally, since AUDPC and r are calculated based on severity readings, several considerations for estimating severity in the field should be taken into account when calculating these epidemic descriptors. It is strongly suggested to study this section before continuing with Activities.