Empirical-deterministic prediction of disease and losses caused by Cercospora leaf spots in sugar beets

Empirisch-deterministische Prognose von Befall und Verlust verursacht durch die Cercospora-Blattfleckenkrankheit in Zuckerrüben

The IPM-(Integrated pest management) system presented here is aimed to get the most possible benefit of fungicide sprays in both, ecologically by reducing the chemical load on the environment and economically by saving costs and therefore optimizing the profit. Predictions of disease and losses are part of our IPM-system to control Cercospora leaf spots (Wolf et al., 2004; Wolf and Verreet, 2003; Wolf and Verreet, 2005b). This concept we called quaternary, because it consists of four elements, which complement themselves to one system. The need of IPM-tool combination resulted from the fact that single elements were not sufficient in view of keeping in the above mentioned principles of Integrated pest management.

The reasons were: (i) Prediction of disease onset is not accurate enough to decide on timings of fungicide sprays (Wolf and Verreet, 2005a). Only the risk of epidemic onset may be calculated by a so-called negative-prognosis where two periods are determined, one without risk and a following period with increasing risk. During the time of increasing risk the occurrence of first leaf spots has to be observed backed by a proper diagnosis. The latter is oriented to the typical asexual propagules, dark pigmented conidiophores and conidia appearing as black dots in the centre of the spots. (ii) Epidemic action thresholds may pinpoint fungicide sprays to optimize efficiency (Verreet et al., 1996; Wolf et al., 2001). But, on the other hand, epidemic action thresholds are defined as very early stages of the epidemic, and these stages are far away from direct yield loss. (iii) Therefore, in case of action threshold exceeding, an incidence resp. loss prediction is necessary to get insight, whether the economic damage threshold will be exceeded at harvest time (Wolf et al., 1998; Wolf et al., 2000). Only under this precondition fungicide sprays are justified, according to the principles of IPM.

This paper depicts the fourth element of the Quaternary IPM-concept by explaining the steps of developing an empirical-deterministic disease and loss prediction. The development is based on empirical field-data and is deterministic, because the actual disease situation determines the future disease development.

2 Materials and Methods

Fig. 1. Relational flow diagram of the disease and loss prediction model with calculated values in boxes and rate regulating influence parameters in the arrow boxes. Arrows with dotted lines indicate data input, used models or functions for parameter estimation.

Model development commenced with classification of field studies according to the criteria epidemic onset (CW_DIL5%) respectively the calendar week when ≥5% of beet leaves were showing symptoms and cultivar susceptibility which was either low or highly. In a next step, means were calculated for each class and curve fittings were performed using submodel (i) (Fig. 1). After receipt of all curve fitting data, equations (1a, 1b, 1c) for parameter estimation of the variables DS_max, a and b were derived from regressions in dependency of CW_DIL5%. The variable “a” is corresponding with the inflection point of the sigmoidal curve, respectively the calendar week where the increase of disease is the steepest. The variable “b” is controlling the conductance of the curve fit. Through the regressions, at CW_DIL5% all variables can be calculated and therefore, under use of submodel (i), the future disease course till end of the season. Moreover, this prediction reproduces weekly DS-values, which may be used for calculation of the AUDPC (area under disease progress curve)-value (Fig. 1). The AUDPC is calculated with equation (3) and expresses the entire disease curve comprising the beginning, progression and severity of incidence through one value (Kranz and Holz, 1993). Now, the AUDPC-value serves to indicate the significance of losses by comparing it with the economic damage threshold. Otherwise, disease loss relationships were created after regression of AUDPC-values and corresponding losses of beet yield (LBY, submodel (ii)) respectively recoverable sugar yield (LSY, submodel (iii)). Losses were calculated as the percentage of yield reduction in relation to the disease free “healthy control” as described above. For calculation of total loss amounts and economical loss assessments, indications of expected beet yield and sugar content on a regional basis is required (Fig. 1).

3 Results

The earlier the epidemic onset the more likely a severe disease progression is following. If CW_DIL5% <28, disease development may induce 65% loss of the leaf mass, but the disease curves slow down as later as the epidemic commences (Table 1-A). If the epidemic onset occurs after calendar week 32, the final DS remains below 5%. Generally, low susceptible cultivars reduce disease severity, but mostly the epidemic onset is delayed significantly, which is evident by a higher frequency of epidemic onset in late season (Table 1-B).

Now, the target of disease prediction is to reproduce the disease behaviour as empirical found.

Fig. 2. Two examples of field data assignment and calculation of DS-averages are shown; the criterion of DIL_5% was exceeded during the 27^th (Fig. 1-A, n=2 field studies, CW_DIL5%=27, highly susceptible cultivar) respectively the 30^th calendar week (Fig. 1-B, n=3 field studies, CW_DIL5%=30, low susceptible cultivar). Dots are means calculated from empirical field data (Tab. 1), the curves are fitted according to submodel (i) DS = DSmax/(1+exp(-(CW-a)/b)); error bars = standard deviation.

The procedure as shown by the above examples (Fig. 2) was applied to each class of cultivar susceptibility x CW_DIL5% (Table 1). Curve fit statistics of all assigned classes were listed in Table 2, in particular the values of the equation variables DS_max, a and b; in addition, the coefficients of determination, which are ≥0.99 in the period CW_DIL5% <32 respectively <30 in case of low susceptible cultivars. Hence, the aptitude of the selected submodel (i) concerning the reproduction of the disease course becomes evident. Moreover, it became apparent, that there were relationships between CW_DIL5% and the equation variables of submodel (i). DS_max is decreasing with delay of CW_DIL5%. The variable “a” is corresponding with the inflection point of the sigmoidal curve, respectively the calendar week where the increase of disease is the steepest. As logical, the value of variable “a” is increasing as later as the epidemic is initiated. The variable “b” is controlling the conductance of the curve fit. The b-values are also increasing along the epidemic onset is delayed. Thus, the curves are tending to get more flat (Table 2).

The overall conclusion is, in order to summarize Table 2 that the variables of submodel (i) depend on CW_DIL5% and cultivar susceptibility. This fact, therefore, offers the possibility to estimate the variables of submodel (i) through regressions. The relationship of CW_DIL5% and DS_max is negative sigmoidal (Fig. 3-A). Hence, the maximum DS is determined by 68%; the curves are slowing down along the epidemic onset is delayed and are tending asymptotic towards 0. Cultivar susceptibility is of substantial impact. Differences between highly and low susceptible cultivars account 10-15% DS, in particular during periods where the curves are the steepest. Estimation of parameters is quite accurate as coefficients of determination =0.99 (Table 3).

Fig. 3. Estimation of variables in dependency of CW_DIL5%^a and cultivar susceptibility for prediction of DS through submodel (i). A: DS_max, determining the maximum of the DS-curve; B: Variable “a”, corresponding with the inflection point of the curve; C: Variable “b”, controlling the conductance of the DS-curve. ^a CW_DIL5% = the calendar week when a leaf infection frequency of 5% is reached respectively a disease severity of 0.01% is exceeded.

If the “a”-values are regressed to CW_DIL5% the relationship is linear (Fig. 3-B, Table 3). Along the epidemic onset is delayed, the value of “a” is increasing. Differences between highly and low susceptible cultivars are slight in case of early epidemic onset and are increasing to 1 CW when CW_DIL5% is occurring in late season.

The relationship between CW_DIL5% and the variable “b” is the best to be reproduced through a polynomial function (Fig. 3-C, Table 3). The coefficient of determination is 0.96. There is a tendency of the values increasing slight over proportional when the epidemic onset is delayed. As a consequence, the calculated DS-curves are becoming more flat in case of late disease occurrence, according to the empirical records of disease development. Congruently to the behaviour of the “a”-variable, the differences between highly and low susceptible cultivars are increasing when the epidemic is delayed. This means that cultivar resistance is more effective under slight-moderate disease pressure.

Fig. 4. Disease loss relationship for prediction of beet yield loss^a (Fig. 4-A) and sugar yield loss^b (Fig. 4-B) depending on AUDPC^c. Dots represent the results of n=105 field studies. ^a Loss prediction according to submo­del (ii): LBY = 0.75*AUDPC, r² = 0.73. ^b Loss prediction according to submodel (iii): LSY = 40-40*exp (-AUDPC/19), r² = 0.83. ^c Calculation of AUDPC according to equation (3), see fig. 1.

The goodness of loss prediction, on one hand, may be assessed by the relationship of epidemic onset (CW_DIL5%) and AUDPC (Fig. 5). The crucial criterion here is the economic damage threshold of AUDPC 1 and, therefore, whether the time of threshold exceeding is predicted with high accuracy. The AUDPC-values marked as dots in Fig. 5 were calculated from DS-values recorded in the field till CW 40. Maximum AUDPC-values in the range of 20-30 result from early epidemic onset in CW 26-28 according to the first half of July; the values are declining rapidly along the epidemic onset is delayed. They tend asymptotic to 0 when CW_DIL5% ≥ 32. If the epidemic onset ≥CW 33 the AUDPC is <1 in all cases. This relationship is confirmed by the predicted values as indicated by the curves (Fig. 5), even though the regression is affected by a broad scattering of the single values, in particular at early epidemic onset. In general, low cultivar susceptibility is affecting a one week delay of disease development (Fig. 5, see dotted line).

Fig. 5. Relationship of epidemic onset=CW_DIL5%^a, and AUDPC^b at calendar week 40 (n=105 fieldstudies), Prediction of AUDPC is indicated through curves, full line representing highly susceptible respectively dotted line low susceptible cultivars. ^a CW_DIL5% = the calendar week when a leaf infection frequency of 5% is reached respectively a disease severity of 0.01% is exceeded. ^b Calculation of AUDPC according to equation (3), see fig 1.

On the other hand, in order to check the validity of loss prediction, the loss of recoverable sugar yield may be used as dependent variable (Fig. 6). The relationship is similar to Fig. 5 with high sugar losses of 25–35% occurring in case of early epidemic onset. Sugar losses are slowing down during the period of CW_DIL5% =31-34, congruently as the AUDPC-values have done, and approach to 0 beginning with CW_DIL5% 33 respectively 32 if cultivar susceptibility is low. Accordingly, losses are predicted to drop below 1% during this period. Also here we find a wide variation when considering single values. But crucial is here, in view of prediction, to distinguish periods of risk from such without any risk of losses.

Fig. 6. Relationship of epidemic onset (CW_DIL5%^a), and sugar yield loss^b, harvest time = CW 40-41. Prediction of sugar loss is indicated through curves, full line representing highly susceptible respectively dotted line low susceptible cultivars. ^a CW_DIL5% = the calendar week when a leaf infection frequency of 5% is reached respectively a disease severity of 0.01% is exceeded. ^b Sugar yield loss calculated by submodel (iii), see text.

The principles of our loss prediction model may be applied also for some other host parasite systems. Precondition is a data set spanning several years to record the disease variation depending on the climate and growing conditions. These empirical experiences can only be gained by field studies, which, in turn, can only reflect the situation of a specific environment. From this point of view, the results and therefore the specific definitions of prediction cannot be easily transferred to other growing regions, in particular, when the basic conditions of sugar beet cropping are different. And, moreover, there are an appropriate number of field studies necessary to reproduce the variation of disease. We gathered a dataset comprising more than 120 field studies – a big effort, but sometimes not enough to cover the range of disease variability sufficient. Thus, due to some lack of data, extrapolations had to be used, for instance concerning the effect of differing harvest times where only a few data were available. Some field studies were not appropriate due to high infection rates of other diseases, especially powdery mildew. That’s another impediment that diseases may interact what’s not wishful, and the losses must be able to relate them exceptionally to the main object. Therefore, suitable field studies must be selected following definite criteria, for example the epidemic of powdery mildew remaining under the DT of AUDPC=2 (Wolf, 2002).

In view of loss prediction, model development commenced with classification of field studies, depending on the time of epidemic onset respectively calendar week when the acting threshold of DIL 5% was exceeded and cultivar susceptibility. These factors substantially had impact on the severity of the epidemic (Wolf et al., 1998; Wolf et al., 2000; Wolf and Verreet, 1997) and are the only factors which determine the outcome of the disease course prediction. Thus, actual incidence situation is incorporated which, on the other hand, is the consequence of all past influences. Next to the actual incidence situation, future influences on disease progress consist preferably on cultivar susceptibility and weather. But weather forecasts are not reliable over long periods and, therefore, must be neglected. It can only be regressed to an annual average of disease progress which indirectly involves the typical climate of the growing region on an average base. Next step was the calculation of DS-means according to the classifications and curve fittings by application of a sigmoidal model. Determination coefficients mostly >0.95 confirmed the high aptitude of the chosen model. But more important was the finding of correlations between the model-variables and the classification criteria. So, besides prediction of disease severity curves through curve fittings, submodel (i) enabled to estimate the model variables through regressions. This could be seen as a big advantage because it makes the prediction much easier to handle.

Loss prediction based on the above mentioned principles has not been reported before. Our intention was directed to fill the gap in the development of the IPM sugar beet model, namely to get information about the likelihood whether the future disease course will exceed DT. A multivariate model for the estimation of yield losses in sugar beet was presented by Kelber (Kelber, 1977). Despite estimated losses did account the observed losses by 89%, the model cannot give indications about the yield risk during a current growing season. The estimation is retrospective because data of each quarter of the disease course are required. Therefore, important influence variables are only known at the end of the growing season. Rossi et al. (Rossi et al., 1994) presented the model CERCODEP. This model simulates the progress of disease severity over the course of a growing season with a time step of one day. By means of system analysis, the model considers the relationships between disease stages as infection, incubation and sporulation, etc., weather factors and host characteristics. Despite the model is reported to simulate the disease course with high accuracy, the authors concede that it’s rather scientific and less practical important (Racca and Jörg, 2003).

The vision of our model conception, on the contrary, was to meet the practical aspect of risk managing during a current growing season in order to back decisions on plant protection measures.