Field models for the prediction of leaf infection and latent period of Fusicladium oleagineum on olive based on rain, temperature and relative humidity

Authors


E-mail: philippe.nicot@avignon.inra.fr

Abstract

Although much is known about the effect of climatic conditions on the development of peacock leaf spot of olive, field-operational models predicting disease outbreaks are lacking. With the aim of developing such models, a 10-year survey was conducted to relate leaf infection to climate parameters that can be easily monitored in the field. As outbreaks of disease are known to be linked to rain, models were evaluated for their ability to predict whether infection would occur following a rain event, depending on air temperature and duration of relative humidity above 85%. A total of 134 rain events followed by confirmed leaf infection and 191 rain events not followed by detectable infection were examined. The field data were adequately fitted (both specificity and sensitivity >0·97) with either a multilayer neural network or with two of six tested regression models describing high boundary values of high humidity duration, above which no infection occurred over the temperature range, and low boundary values below which no infection occurred. The data also allowed the selection of a model successfully relating the duration of latent period (time between infection and the first detection of leaf spots) as a function of air temperature after the beginning of rain (R2 > 0·98). The predictive abilities of these models were confirmed during 2 years of testing in commercial olive orchards in southern France. They should thus provide useful forecasting tools for the rational application of treatments and foster a reduction in fungicide use against this major disease of olive.

Introduction

Peacock leaf spot, sometimes also referred to as olive scab, olive leaf spot or cycloconium leaf spot, is one of the most common diseases of olive (Olea europaea) trees worldwide (Obanor et al., 2008b). Its causal agent, formerly Spilocaea oleaginea, syn. Cycloconium oleagineum, was recently assigned to Fusicladium oleagineum on the basis of morphological and genotypic traits (Schubert et al., 2003; Crous et al., 2007; Sergeeva et al., 2009). Leaf symptoms consist of brown, circular and often zonate spots eventually surrounded by a yellow halo (Zarco et al., 2007). Over time, the leaves become chlorotic and defoliation may occur, which can significantly weaken the plant and reduce fruit yield on heavily infected trees (Graniti, 1993). It can also affect the quality of the fruits and reduce oil yield (Graniti, 1993). Most of the cultivars used for production are susceptible, even if a large range of disease prevalence can be observed among cultivars (MacDonald et al., 2000). On susceptible cultivars in conditions favourable for disease development, protection relies heavily on chemical control. In such situations in New Zealand, up to six sprays may be applied per year, corresponding to a total application of over 6 kg copper ha−1 (Obanor et al., 2008b). Such levels of copper use have also been observed in France in some orchards planted with the most susceptible cultivars in areas where climatic conditions are particularly favourable to disease development (S. Regis, unpublished data).

Infections result from the germination of conidia on the surface of leaves. The fungus rapidly penetrates the thick cuticle of the olive leaf and develops a colony, restricted to the subcuticular area of the epidermis, leading to the formation of a stroma (Graniti, 1993). The lesions remain undetectable to the naked eye until conidiophores are produced on the stroma, breaking the cuticular layer, and sporulation occurs (Graniti, 1993). The conidia are disseminated by wind (Lops et al., 1993) and rain (Tenerini, 1964) and can, in turn, produce new lesions. As olive is an evergreen tree, numerous cycles can take place year-round whenever conditions are favourable to disease development in the orchard. Contrary to the situation for apple scab, caused by a related species, Venturia inaequalis (Gadoury & MacHardy, 1982), no evidence has been reported for any epidemiological role of a hypothetical sexual stage in F. oleagineum. Furthermore, recent studies on the genotypic diversity of this fungus support the predominance of asexual reproduction (Obanor et al., 2010a).

Outbreaks of disease are strongly linked to rain events (Loussert & Brousse, 1978) and studies have been conducted on the effect of temperature and relative humidity (RH) on the infection process and on the latent period before symptom expression. Leaf infections were reported to occur at RH conditions as low as 80–85% (Chen & Zhang, 1983), but in most cases, wetness appeared to be necessary (Pappo & Pelec, 1958; Loussert & Brousse, 1978; Graniti, 1993). The minimum duration of leaf wetness was estimated to vary between 1 and 2 days depending on temperature, within a range of 5–25°C (Graniti, 1993). The widest reported range of temperature conducive to conidial germination was from 2 to 34°C (Graniti, 1993), with an estimated optimum between 12 and 15°C (Loussert & Brousse, 1978) or between 16 and 22°C (Chen & Zhang, 1983; Graniti, 1993). The time needed for symptom expression following leaf infection (referred to as ‘latent period’ in this work) was also reported to be highly dependent upon temperature, ranging from 12 days at 16–20°C to 16–19 days at 21–25°C (Chen & Zhang, 1983). In very hot or very cold conditions, the latent period was estimated to last for several weeks or even several months (Miller, 1949; Graniti, 1993) and this resulted in autumn infections which caused leaf spots that did not develop until the next spring or summer (Graniti, 1993).

Such knowledge of conditions favourable to disease development can be very useful to limit the application of fungicides according to the risk of infection. In the last 10 years, comprehensive multifactorial studies conducted in precisely controlled conditions have provided a useful basis for the construction of multiple regression models which characterize the relationships between disease severity or key steps of the disease cycle and environmental factors. A third-order polynomial equation was used to describe disease severity as a function of air temperature and the duration of leaf wetness (Viruega & Trapero, 2002), and second-order polynomial equations were used to describe spore germination or appressorium formation as affected by temperature and leaf wetness duration and for modelling the kinetics of germ tube growth for 180 h at each of five temperature levels (between 5 and 25°C) under continuous wetness (Obanor et al., 2008a). More recently, Obanor et al. (2010b) proposed a second-order polynomial model relating disease severity (estimated by the number of spots on batches of leaves examined on potted plants) to wetness duration, temperature and leaf age. They also showed that in conditions of continuously high RH (98% or higher) the quantitative relationship between disease severity and inoculum concentration was adequately represented by logistic equations for five different temperature levels between 5 and 25°C. The effect of wetness interruption and the effect of wetness duration prior to a 12-h dry period were also modelled with second-order polynomial equations for experiments conducted at either 10 or 20°C.

Such data constitute tremendous progress in the understanding of the epidemiology of the disease and provide key information for the development of risk prediction models in the field. In the present attempts to develop such a model, however, there were difficulties in measuring leaf wetness duration accurately and in a way that would be representative for most of the canopy in an orchard. To date, no wetness sensors have been endorsed by the World Meteorological Organization (Anonymous, 2008) and studies in orchards have shown that wetness assessment is highly influenced by the position of the sensors on the trees (Sentelhas et al., 2005). Furthermore, reported correlations between visual observations and information provided by wetness sensors can be low,with R2 coefficients below 0·6 (Magarey et al., 2006).

As a consequence, a different approach was initiated to develop predictive models for infection events and for the duration of the latent period, based on field-measured RH, rain duration and temperature. As infections are strongly related to rain in the field, the aim of this work was to identify the associated risk factors that could be easily integrated into an operational decision support system. The specific objectives of the present study were: (i) to identify climatic conditions that are needed, in addition to the presence of rain, to produce leaf infection in the field; and (ii) to estimate the duration of the latent period as a function of air temperature and RH.

Materials and methods

Experimental orchard

The study was conducted from 1999 to 2009 in the Baux-de-Provence production area in southern France in a 2-ha commercial olive orchard located at an altitude of 50 m a.s.l. The orchard was planted in 1960 with cv. Grossane, which is one of the most susceptible cultivars to F. oleagineum grown in France. The trees were pruned in a traditional vase shape. They were not irrigated and were cultivated according to local organic farming practices. Within this orchard, a 70-tree experimental plot which had received no pesticide treatment since 1990 was used. On 30 March 1999, at the beginning of the experiment, disease symptoms were present on 8% of the leaves in the experimental plot. In the surrounding orchard, disease was only detected in a few areas, where a maximum of 2% of the leaves were infected.

Monitoring of climatic data

Data were collected from a weather station (CIMEL 140, CIMEL Electronique) managed by a local administration (Comité Economique Agricole de l’Olivier at Aix en Provence). Located among olive trees 50 m south-east of the experimental plot, this weather station was equipped with sensors which allowed continuous recording of air temperature, RH and rain intensity (mm h−1 for rain events >0·2 mm).

Disease assessment

Ten trees were selected in the centre of the experimental plot and marked for future observations. They were examined one to three times a week between January 1999 and December 2009. From each tree, 10 fully expanded leaves (3–12 months old) were collected at random and examined for symptoms. As a result, 100 leaves were examined for every observation date. This sample size was chosen as an empirical compromise between the need for feasibility of frequent field surveys and the aim of minimizing the risk of missing small increases in disease incidence (the probability of observing no diseased leaves when sampling n leaves from a population with an actual 3% disease incidence is P ≈ 0·97n; accepting a 5% risk of missing a 3% disease incidence leads to a calculated sample size of 98·35). Each time, the number of leaves with visible spots was recorded and leaves without visible spots were processed to reveal latent infections. A method somewhat similar to that developed by Zarco et al. (2007) was used. The leaves were incubated for 30 min in 15% KOH at 18–22°C. Following this treatment, a leaf was considered as infected if at least one translucent spot was revealed (Fig. 1).

Figure 1.

 Latent infection of Fusicladium oleagineum (translucent spot) revealed by treatment of symptomless olive leaf with potassium hydroxide.

Linking rain events and leaf infection events

Rain is indispensible for leaf infection to occur, but certain rain events may not result in infection if available inoculum is insufficient or if microclimatic conditions are not favourable. The basis of this study was to examine 376 rain events (recorded between 1999 and 2009) and determine which of them resulted in subsequent infection. Two iterative steps were used to achieve this purpose. The first step used threshold values of temperature and wetness duration provided by previous studies to identify situations conducive to infection and situations for which infection was not possible. A rain event was considered to be ‘non-infectious’ in two situations: (i) if it occurred when air temperature was below 6°C (based on data of Chen & Zhang, 1983); or (ii) if it was followed by a high humidity period (RH > 85%) shorter than 6 h. A rain event was considered ‘infectious’ (presuming that inoculum was present) if it occurred when air temperature was between 10 and 20°C (based on data of Obanor et al., 2010b) and when it was followed by a high humidity period (RH > 85%) longer than 12 h. This first step resulted in the identification of unambiguous situations (either clearly infectious or clearly non-infectious rain events). For the remaining ambiguous rain events, a second iterative step was carried out to remove the ambiguity.

The second iterative step involved a detailed comparative examination of the weather data and the disease incidence data over the days following each of these ambiguous rain events. The dates of emergence of new leaf spots were compared with the estimated duration of the latent period following each of these rain events. The method used to estimate the duration of the latent period as a function of temperature and air humidity will be described below. When the estimated latent period elapsed without any emergence of leaf spots, the rain event was regarded as ‘non-infectious’. Conversely, a rain event was regarded as clearly ‘infectious’ if an outbreak of lesions occurred during the estimated latent period that followed and if no other rain events occurred during that period. It was thus possible to identify additional infectious or non-infectious events, leading to a substantially larger total data set. However, it was sometimes impossible to define whether a rain event was responsible for a subsequent outbreak of disease, for example when several rain events occurred within a short time span before the observation of new symptoms. Such unresolved ambiguous cases were excluded from the rest of the study.

Relating the duration of the latent period with air temperature after an infection event

An estimate for the duration of the latent period was a necessary tool to reduce the number of ambiguous cases described in the second iterative step above. The basis for establishing this estimate was the set of ‘infectious’ rain events clearly identified in the first iterative step above. For each of these rain events, the duration of the latent period was compared to the average air temperature during the time between the beginning of the rain and the field observation of the associated peacock spots. Regression analysis was used to fit second- to sixth-order polynomial models to the data. The goodness-of-fit of the models was compared on the basis of the correlation coefficients and the standard errors of the estimates computed as

image

where Yobs and Yest were the observed and model-estimated values respectively, n was the total number of data points and k the degrees of freedom of the model. The distributions of residuals were also examined as routinely carried out in regression analysis. The best model was then used in the second iterative step described above, leading to an enlarged set of infectious rain events. This final set of data was then used to conduct a second round of regression analysis, using the same types of models, in order to further refine the latent period model.

Relating the occurrence of infection with air temperature during rain and duration of high RH following rain events

Two methods were used for the analysis of data associated with the set of infectious and non-infectious rain events. One method consisted of regression analysis and the second method consisted of fitting neural network models.

Regression analysis

In a first step, an exploratory analysis of the data was realized by constructing a graph (Fig. 2) plotting rain events according to the average temperature recorded during the rain (TR, x-axis) and the duration of high RH after the rain (DHRH, y-axis), quantified as the number of hours with RH > 85%. Infectious rain events were distinguished from non-infectious ones, revealing conditions favourable to infection, conditions clearly not conducive to infection and ‘ambivalent conditions’ for which both infectious and non-infectious rains were present.

Figure 2.

 Characterization of rain events according to temperature and duration of high relative humidity after rain onset. Each rain event was assigned an ‘infectious’ status if it was followed by an increase in the incidence of olive peacock leaf spot (Fusicladium oleagineum) within the time frame and conditions described in the Materials and methods. Two sets of rain events were distinguished as boundary values. One set represented the rain events with the shortest durations of high humidity associated with infection and the second set represented the longest durations of high humidity associated with non-infectious rains.

In the second step, two sets of boundary values were determined across the range of recorded temperatures. One set of boundary values represented the shortest durations of high humidity associated with infectious rains and the second set represented the longest durations of high humidity associated with non-infectious rains (Fig. 2).

The third step consisted of fitting regression models to the boundary values identified in step two, in order to characterize the critical condition curve above which a rain was always infectious and the curve below which a rain was never infectious. Regression analysis was realized with the help of CurveExpert v. 1.3 software. Among the types of models available for evaluation with this software, six were selected for comparison (Table 1) because they provided curves with a high negative slope at low x values and a general L- or U-shape (Seber & Wild, 1989; Dourado et al., 2007) as shown by the data points (Fig. 2). The goodness-of-fit of the models was compared on the basis of the correlation coefficients, the standard errors of the estimates and the distribution of residuals, as indicated above. In addition, the Akaike Information Criterion (AIC; Akaike, 1969) was computed as

Table 1. Regression models fitted to the boundary values representing the shortest durations of high humidity associated with ‘infectious’ rains and the longest durations of high humidity associated with ‘non-infectious’ rains (Fig. 2) for olive peacock leaf spot caused by Fusicladium oleagineum
ModelEquationaHigh boundary for ‘non-infectious’ rainsbLow boundary for ‘infectious’ rainsb
ParametersStandard errorCorrelation coefficientAICcParametersStandard errorCorrelation coefficientAICc
  1. ay = duration of period with air relative humidity >85% from the start of a rain event (h) and = average air temperature during the rain (°C).

  2. bA rain event was considered as ‘infectious’ if it was followed by an increase in the incidence of peacock leaf spot within the time frame and conditions described in the Materials and methods.

  3. cAkaike Information Criterion.

  4. dND: not defined; the software was unable to fit this model to the data.

Logistic = a/(1 + exp (b−c*x))a = 4·8563, b = −18·5796, c = 42·06200·9380·9866·517a = 6·1582, b = −1069·8436, c = 0·93980·4180·9960·939
Vapour pressure = exp(a + b/+ c*ln(x))a = −16·4927, b = 72·8655, c = 4·83860·9600·9866·699a = −15·7267, b = 69·6551, c = 4·70980·5890·9893·322
Reciprocal quadratic = 1/(a + b*+ c*x^2)a = −0·4106, b = 0·0798, c = −0·00241·0140·9847·126a = −0·3951, b = 0·0767, c = −0·00241·2090·9668·319
Weibull = a−b*exp(−c*x^d)a = 40·4053, b = 35·6332, c = 1305233·5924, d = −7·31561·0260·9868·616a = 31·5441, b = 26·4244, c = 6106·7530, d = 0·55921·6450·93311·826
Hoerl = a*(b^x)*(x^c)a = 1994069·7871, b = 1·6352, c = −7·57381·1260·9817·945 NDdND 
Morgan–Mercer– Flodin (MMF) = (a*b + c*x^d)/(b + x^d)a = 2·1225, b = −84·0842, c = 4·5523, d = 2·25131·0520·9868·811 NDND 

AIC = n log(SSE/n) + 2(+ 1),

where SSE was the sum of squared errors:

SSE = Σ(Yobs− Yest)2

and p was the number of estimated parameters of a model.

Artificial neural network models

The data were also analysed using a multilayer feed-forward neural network (Peacock et al., 2007) to provide an appraisal of the occurrence of infection following a rain event. tanagra software (http://eric.univ-lyon2.fr/~ricco/tanagra/en/tanagra.html) was used with the same two variables as in the regression analysis above (TR and DHRH). The neural network was run with the standardized values of these variables ([raw value – average]/standard deviation), two neurons in the hidden layer and the learning parameters and stopping rules shown in Table 2. Its performance was evaluated by computing the overall prediction success, sensitivity and specificity as described by Peacock et al. (2007).

Table 2. Parameters and rules used for the construction of a multilayer neural network describing the advent of olive leaf infection by Fusicladium oleagineum following rain events
Learning parameters
 Validation set proportion0·20
 Learning rate0·15
Stopping rules
 Maximum number of iterations100
 Error rate threshold0·01
 Verify error stagnationNo

Results

Progress of infection over time

The observed incidence of leaves with typical peacock spots (visible infections) in the orchard varied widely over the 10-year study (from 0 to nearly 70%; Fig. 3). When taking into account the latent infections revealed by the laboratory test (referred to as total infections), the maximum incidence reached 90%. Reductions in the number of diseased leaves in the orchard were associated with defoliation, resulting from natural senescence of the leaves or disease-related abscission. This phenomenon was occasionally amplified by episodes of strong winds (wind speed >70 km h−1; Fig. 3).

Figure 3.

 Progression over time of Fusicladium oleagineum incidence (percentage of infected olive leaves). The lower curve (grey) represents leaves with typical peacock spots (visible infections). The upper curve (black) represents the total number of infected leaves, including those with latent infections revealed by laboratory tests. Individual dots in the upper part of the frame represent events of substantial leaf fall related to episodes of strong winds (>70 km h−1).

Linking rain events and leaf infection events

The first iterative step resulted in the unambiguous identification of 63 infectious and 165 non-infectious rain events among the 376 rain events examined.

The second iterative step allowed the identification of 71 additional infectious events and 26 non-infectious events, leading to a total data set of 134 infectious and 191 non-infectious rain events. The remaining unresolved ambiguous cases (excluded from the rest of the study) amounted to 51 out of a total of 376.

Relating the duration of the latent period to air temperature after an infection event

The final polynomial regression analysis was carried out on the total data set of 134 infectious rain events. Fitness improvement beyond the fourth-degree polynomial was marginal (Fig. 4). The equation for this model, represented in Figure 5, was:

Figure 4.

 Relationship between goodness-of-fit indicators and the order of polynomial models relating the duration of olive peacock leaf spot (Fusicladium oleagineum) latent period as a function of air temperature.

Figure 5.

 Relationship between the duration of the olive peacock leaf spot (Fusicladium oleagineum) latent period and air temperature. Each data point represents an infectious rain event. The curve shows a fourth-order polynomial model fitted to the data.

image

where Di and Ti represented the duration of the latent period and the average temperature during the period from leaf infection until symptom expression, respectively.

Relating the occurrence of infection to air temperature during rain and duration of high RH following rain events

Regression models

Among the six models tested, four adequately described both sets of boundary values defined in Figure 2 (critical conditions above which a rain event was always infectious and those below which a rain event was never infectious). The best fitness indicators were observed for the logistic model (Table 1) and for the vapour pressure model (Fig. 6).

Figure 6.

 Predictive models for the infection of olive leaves by Fusicladium oleagineum according to temperature and duration of high relative humidity after rain onset. In addition to a multilayer neural network model, regression models were fitted to the boundary values representing the lowest durations of high humidity associated with ‘infectious’ rains and the highest durations of high humidity associated with ‘non-infectious’ rains.

Neural network model

The feed-forward multilayer neural network was successfully used to define a model assigning a correct infection status to all but two of the 325 rain events examined in the study, resulting in a sensitivity value of 0·985. All rain events not followed by infection were correctly identified, resulting in a specificity value of 1. The parameters of this model are described in Table 3. Based on the model, a curve was constructed to delineate the critical high-humidity duration above which infection could occur over the temperature range (Fig. 6).

Table 3. Parameters of the fitted neural network model describing the advent of olive leaf infection by Fusicladium oleagineum following rain events
VariableAverageStandard deviation
  1. aAverage temperature recorded during the rain event.

  2. bDuration of high relative humidity (RH > 85%) after the rain event.

Parameters for input variable standardization
 TRa12·3566 4·4680
 DHRHb 9·6559 6·6573
Weights from input layer to hidden layer
 Neuron 1Neuron 2
 TR−5·0460 0·4371
 DHRH−1·1489−5·6071
 Bias−3·2367−3·8346
Weights from hidden layer to output layer
 No infectionInfection
 Neuron 1 4·87441612−4·87440901
 Neuron 2 5·30379161−5·30378556
 Bias−2·694614 2·69461031

Discussion

The analysis of the large data set collected in the 10-year study, using the results from previous work in controlled conditions (Viruega & Trapero, 2002; Obanor et al., 2008a, 2010b), allowed the successful fitting of models relating field-measured climate data to the occurrence of olive leaf infection by F. oleagineum and to the duration of the latent period following infection. This is apparently the first successful exploitation of field data on olive peacock spot to develop predictive models.

Two very different approaches were used for modelling leaf infection. The regression approach required the selection and separate analysis of two sets of boundary values (representing, respectively, the shortest durations of high humidity associated with infectious rains and the longest durations of high humidity associated with non-infectious rains). In contrast, the neural approach used the global data set, without any need for preliminary interpretation of the data, and provided a single boundary separating infectious and non-infectious rain events. Despite this advantage and its wide use for pattern or voice recognition, this type of model is still seldom used for plant protection studies (Peacock et al., 2007). Interestingly, the predictive curves provided by the two approaches were quite similar in shape (Fig. 6) and the sensitivity and specificity of the models were similarly high (Table 4). This supported a posteriori the choices made in the present study to distinguish the critical high and low boundary values (Fig. 2). For practical field application, however, the models provided by the regression approach were preferred for further work. The reason for this choice was that the difference in specificity and sensitivity of the two complementary curves (Table 4) allows the operator to select a model depending on an appreciation of the field situation and the level of acceptable risk. Using the curve showing low boundary values for infection (Fig. 6) as a decision threshold can lead to possible underestimation of the infection risk. In contrast, using the curve showing high boundary values for non-infection can lead to possible overestimation of the infection risk.

Table 4. Specificity and sensitivity of the models selected to describe the advent of olive leaf infection by Fusicladium oleagineum following rain events
ModelaSpecificitybSensitivityc
  1. aSee Figure 3 for a description of the models.

  2. bRate of correctly predicted absence of infection.

  3. cRate of correctly predicted infections.

Low threshold regression model (vapour pressure model)10·977
High threshold regression model (vapour pressure model)0·9741
Neural network model10·985

Among the six models used in the regression analysis of the high and low boundary values, two clearly provided the best fits: the logistic model and the vapour pressure model. Although the fitness indicators were slightly higher for the logistic model (Table 1), the vapour pressure model was selected for the development of a predictive tool. The reason which guided this choice was that the curves fitted to the data with the logistic model intersected at low temperatures (x-axis), casting doubt on their biological legitimacy because they delineated a zone where a rain event should be both infectious and non-infectious at the same time. The vapour pressure model did not present this drawback. Interestingly, the curves fitted with this model (Fig. 6), although they only pertain to infection versus non-infection, present a strong analogy in shape with those of the model recently used by Viruega et al. (2011) to describe disease severity according to wetness duration and temperature in a controlled-environment study.

Several future improvements in the predictive tool could be envisioned. Beyond knowing if weather conditions are conducive for infection to occur, the growers may wish to modulate the timing of their fungicide applications depending on the severity of the ensuing disease in the field. The recently established relationship between disease severity and climatic parameters (Viruega et al., 2011) constitutes a remarkable step toward such a goal. Several additional factors would need to be considered in the field, including the susceptibility of the olive cultivar (MacDonald et al., 2000) and inoculum pressure. The quantitative role of inoculum pressure has clearly been shown in controlled-environment studies, both in terms of disease incidence and disease severity (Obanor et al., 2010b; Viruega et al., 2011). For intensively studied diseases such as botrytis leaf blight of onion, direct field assessment of airborne inoculum has been used in conjunction with weather-based disease-prediction models (Van der Heyden et al., 2012). Alternatively, indirect estimates of inoculum pressure might also be simpler to implement in a field situation in the case of olive peacock disease. For example, quantifying the frequency of leaf infection on the trees might provide sufficient information for modelling purposes as fallen leaves in the orchard are not expected to liberate substantial amounts of inoculum (Prota, 1958; Laviola, 1966). However, implementing such improvements might not be sufficient as other complex factors may also be implicated in disease severity. For example, classes of leaf age would need to be distinguished, as most damaging infections were reported to occur in the spring (Shabi et al., 1994), possibly because the susceptibility of a leaf varies significantly with its age (Viruega et al., 2011). This in turn would also require the establishment of models to describe the production of new leaves by the trees, as well as their life span and the factors which influence their final abscission, providing an additional level of complexity. Although desirable, such improvements of the risk-prediction tools may be difficult to achieve soon in practice. Even for better-known diseases such as apple scab, to which much modelling effort has been devoted, quantification of risk has long been limited to predicting the release of primary inoculum according to climatic factors (Gadoury & MacHardy, 1982; Giosuèet al., 2000), suggesting that difficulties were encountered in the development of predictive tools taking disease severity into account. More recent advances include models attempting to predict scab severity based on host susceptibility and phenological stage as well as climatic factors (Rossi et al., 2007). However, modelling the severity of apple scab is complicated by at least two factors. One is the implication of both a sexual and an asexual form of inoculum. The second one is the difficulty in predicting the survival of pseudothecia and the amount of viable ascospores that they carry (Gadoury & MacHardy, 1986; Holb, 2006). This remains to be demonstrated, but faster progress could be anticipated for peacock leaf spot of olive as its epidemiology is somewhat simpler (because of the absence of sexual reproduction) and there is hope that the amount of conidial inoculum could be inferred from the number of diseased leaves present on the trees of an orchard.

In conclusion, despite (or possibly thanks to) their simplicity, the models obtained in the present study appear to constitute a promising tool for practical field application. During a 2-year period of field validation (2009–2011) by the French Phytosanitary Advisory Service over a sample of 40 sites in the French olive-growing region, each encompassing a 1-km radius around a weather station, only one infection failed to be predicted (S. Regis, unpublished data). That particular infection event could not be linked to any detected rain. It was thus probably the result of a very short rain event (< 0·5 mm) that failed to be detected by the sensor. With this single exception, the robustness of the predictive tool appears promising, although it cannot be excluded that growers may have failed to detect minor infection events, associated with very low increases in disease incidence. It is not possible to evaluate the frequency of falsely predicted infections, as growers sprayed in response to a predicted infection if they considered that current fungicide coverage was insufficient. The models are also currently used, together with archive meteorological data from 140 weather stations, to map the risk of olive peacock disease in southern France according to the average yearly number of infectious rains.

Acknowledgements

We thank the Centre d’Information Régional Agrométéorologique (CIRAME), the French Economic Committee of Olive (CEO), the French Interprofessional Olive Association (AFIDOL) and the Mas-de-la-Dame for facilitating data acquisition for the present study.

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