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Keywords:

  • agricultural economics;
  • disease forecasting;
  • fungicides;
  • septoria leaf blotch;
  • Septoria tritici

Abstract

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Appendix

A method was developed to evaluate crop disease predictive models for their economic and environmental benefits. Benefits were quantified as the value of a prediction measured by costs saved and fungicide dose saved. The value of prediction was defined as the net gain made by using predictions, measured as the difference between a scenario where predictions are available and used and a scenario without prediction. Comparable ‘with’ and ‘without’ scenarios were created with the use of risk levels. These risk levels were derived from a probability distribution fitted to observed disease severities. These distributions were used to calculate the probability that a certain disease induced economic loss was incurred. The method was exemplified by using it to evaluate a model developed for Mycosphaerella graminicola risk prediction. Based on the value of prediction, the tested model may have economic and environmental benefits to growers if used to guide treatment decisions on resistant cultivars. It is shown that the value of prediction measured by fungicide dose saved and costs saved is constant with the risk level. The model could also be used to evaluate similar crop disease predictive models.


Introduction

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Appendix

Testing of empirically derived disease risk prediction models on independent data usually only relates to model accuracy, e.g. the percentage of correct predictions. Although important, accuracy alone does not adequately describe the potential benefits of model predictions. Disease risk prediction models that aim to adjust crop management for improved profitability and reduced environmental impact should be tested against those criteria (Royle & Shaw, 1988). One rare example of such an approach in crop science is the work of Fabre et al. (2007), which addressed the financial advantage of using binary decision rules. Other examples of evaluating predictive models directly on benefits resulting from predictions can be found in other disciplines. In meteorology, the economic value of the weather forecast is used to select models (Murphy, 1977; Thornes & Stephenson, 2001; Wilks, 2001; Mylne, 2002). In medical science the ‘clinical usefulness’– the extent to which a model improves medical decision making, sometimes combined with a cost-benefit analysis – is used instead of model accuracy (Metz, 1978; Zweig & Campbell, 1993). The method introduced in this paper uses the same ‘value of prediction’-driven methodology.

A common way to define the value of a prediction in other disciplines is as the difference between a scenario where model predictions are used and a scenario where model predictions are not used (Thornes & Stephenson, 2001). The difficulty is to specify these scenarios. If decisions are binary, scenarios can be formulated around the decision on whether to act (e.g. apply fungicide) or not to act (e.g. not apply fungicide) (Fabre et al., 2007). If the decision is not binary, but instead concerns a quantitative level of fungicide dose, then these scenarios are more complex to define. Also, analysis of benefits should account for what growers are trying to achieve. This is not necessarily to treat at the average economic optimal dose. They may also want to reduce the risk of a severe economic loss and may be willing to pay small additional costs in the majority of years to reduce such a risk resulting from infrequent exceptionally high disease seasons.

In this paper we introduce risk levels to define such scenarios. Risk levels are derived from an exponential probability distribution fitted to disease severities observed for a wide range of sites, seasons and cultivars, and represent the probability of a certain economic loss. By calculating both ‘with’ and ‘without’ prediction scenarios at the same risk level, comparable scenarios are created from which the value of prediction can be calculated. The procedure is exemplified using a disease risk prediction model for Mycosphaerella graminicola (anamorph Septoria tritici) described in te Beest et al. (2009). Mycosphaerella graminicola is the most damaging foliar disease of winter wheat in the UK and one of the main drivers of fungicide use (Hardwick et al., 2001). The model predicts the occurrence of an economically damaging disease infection and is designed to give a prediction sufficiently early in the season to influence decision making about fungicide sprays. Benefits result from a lower fungicide input and can be quantified as economic benefits of lower costs of fungicide and potential environmental benefits of a smaller quantity of fungicides released into the environment.

Materials and methods

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Appendix

The predictive model

The predictive model for M. graminicola evaluated in this paper is described in detail by te Beest et al. (2009). The model gives an indication of disease risk just before the first fungicide spray is applied. In the UK it is common practice to apply three fungicide sprays, predominantly to control M. graminicola, in correspondence with wheat leaf emergence (Paveley et al., 2009). The first spray is timed when the third leaf (counting down from the top of the plant) is fully emerged, typically at growth stage 31/32 (first/second node detectable, typically mid-April); a second spray at growth stage 39 (flag leaf fully emerged, typically end of May); and a third spray at growth stage 59 (emergence of head complete, typically mid-June). The prediction is timed at growth stage 31 (1st node detectable).

The model predicts the presence or absence of a ‘damaging epidemic’, defined as 5% or more disease severity at growth stage 75 (medium milk). This 5% threshold has been used before as the economic injury level for M. graminicola on winter wheat in the UK (Gladders et al., 2001, Pietravalle et al., 2003). The model is the result of ‘window pane’ statistical analysis (Coakley & Line, 1982; Pietravalle et al., 2003), with which key weather variables suitable for prediction were identified, resulting in the following discriminant model:

  • image(1)

A damaging epidemic is predicted if the outcome of Eqn 1, F(Rain,MinT), is larger than 0. The first variable used in the M. graminicola predictive model is daily rain above 3 mm accumulated in the 80-day period preceding growth stage 31 (Rain, Eqn 1). This variable works as follows: if, for example, the daily rainfalls over a 4-day period were 5 mm, 2 mm, 5 mm and 10 mm, this would contribute 2 mm, 0 mm, 2 mm and 7 mm to the accumulation, which would be 11 mm in total. The second variable is the daily minimum temperature above 0°C accumulated in a window that starts 120 days before growth stage 31 and ends 70 days before growth stage 31 (MinT, Eqn 1).

Data

The disease data used for the evaluation originate from the Cropmonitor project (http://www.cropmonitor.co.uk), which assesses and reports disease severity from experimental sites across the UK (Table 1). The Cropmonitor data are independent of the data used to build the predictive model, and are described in te Beest et al. (2009). These data were measured in 2003–05, while the model was constructed on data from the period 1994 to 2002. At each year–site combination observations of disease severity were made on cultivars differing in their disease resistance. All observations were from plots untreated with fungicides. Averaged over 2003–05, the predictive model predicted a damaging epidemic in 61% of the experiments in these data. Disease severity on leaf 2 at growth stage 75, commonly used as a benchmark (Thomas et al., 1989), was used to summarize the observations and to relate disease severity to yield loss (Table 2). The disease-severity observations were divided into two groups according to HGCA Recommended List resistance rating (Anonymous, 2003–05). This rating system ranges from 1 to 9, with 1 being very susceptible and 9 very resistant. The highest resistance rating in the dataset was 7 and the lowest was 3. The resistant group contained cultivars with resistance ratings of 6 and 7 and the susceptible group contained cultivars with ratings of 3, 4 and 5. This split was chosen so that both groups (and subgroups) were large enough for fitting a severity probability distribution. The collection of observations in a group represented the situation without prediction. Two subgroups were constructed in each group, one consisting of the observations for which a damaging epidemic was predicted and one where no damaging epidemic was predicted. To calculate the model predictions, weather data (minimum temperature and rain) were retrieved from meteorological stations near the experimental site (Table 1) from the BBSRC meteorological website (http://www.bits.bbsrc.ac.uk/metweb).

Table 1.   Overview of years and sites used with model predictions and realized outcomes for Mycosphaerella graminicola on winter wheat
SiteYearPredictionaResistantbSusceptiblec
  1. aDamaging epidemic predicted (E); no damaging epidemic predicted (N).

  2. bFirst figure is the number of observations (site-year-cultivar combinations) for resistant, second is the number of observations with a damaging epidemic.

  3. cAs b,but for susceptible cultivars.

Askham Bryan (Yorkshire)2004E3/02/2
Boxworth (Cambridgeshire)2003N 1/0
2004E3/21/1
Drayton (Warkwickshire)2003N 1/1
2004E3/12/2
2005N2/02/0
Exeter (Devon)2003E 1/1
2004E3/12/2
Gleadthorpe (Nottinghamshire)2003N 1/1
2004E3/32/2
High Mowthorpe (Yorkshire)2003N 0/0
2004E3/32/2
2005E2/02/2
Lavenham (Suffolk)2003E 1/0
2004N3/12/2
2005N2/02/0
Newcastle (Tyne & Wear)2004E3/02/2
2005E2/02/1
Rosemaund (Herefordshire)2003N 1/1
2004E3/32/2
2005E2/22/2
Terrington (Norfolk)2003N 1/1
2005E2/02/2
Wye (Kent)2003N 1/1
York (Yorkshire)2005E2/22/2
Table 2.   Summary of the data by subgroup for Mycosphaerella graminicola on winter wheat
 Severity (mean %)ObservationsYear-site combinationsαa Fitb
  1. aParameter of the exponential probability distribution fitted to the disease data.

  2. bP-value of a Kolmogorov-Smirnov goodness-of-fit test for the exponential probability distribution fitted to the disease data.

All cultivars9·5812510·60·45
No epidemic predicted5·0201020·20·17
Epidemic predicted10·961159·20·66
Resistant cultivars5·9411616·90·21
No epidemic predicted1·37374·60·10
Epidemic predicted6·8341314·70·35
Susceptible cultivars13·140257·60·41
No epidemic predicted6·9131014·50·74
Epidemic predicted16·127156·20·26

Disease risk

To quantify the economic benefit of using the model predictions we first derived the risk levels needed to define the scenarios. An exponential probability density distribution, α·e-αS, in which S is the disease severity and α is the exponential probability distribution parameter, was fitted to each subgroup (Fig. 1). The exponential distribution quantified the probability that, for a given year–site combination, disease severity S develops. A Kolmogorov-Smirnov goodness-of-fit test was performed with genstat (Payne et al., 2004) to test whether the fitted data were significantly different from an exponential distribution. Based on the P-values (Table 2) all fits were acceptable and not significantly different from an exponential distribution.

image

Figure 1.  Histograms of disease severities for Mycosphaerella graminicola on winter wheat with the exponential probability distribution fitted (Eqn 2). Values of α and goodness-of-fit are specified in Table 2.

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Yield loss increases with disease severity, and the disease severity which causes a certain economic loss (specified later) is termed the ‘critical disease severity’. The probability of a disease severity (S) equal to or greater than this critical disease severity (Sc) is equal to the area under the upper tail of the exponential distribution. By integrating over the domain [Sc,∞] the probability of a disease severity greater than Sc can be derived according to:

  • image(2)

where α is a parameter of the exponential distribution and K is the probability of disease with a severity equal to or greater than the critical disease severity (Sc).

Gross margin, M. graminicola-related costs, and economic optimal dose

To quantify the economic benefit of using the model predictions, we quantified the expected costs related to M. graminicola. The gross margin (Nix, 2005) is defined as the economic output per hectare minus the variable costs per hectare. The economic output per hectare is calculated as the production (P) in tonnes per hectare multiplied by the grain price (PW) per tonne. The variable costs are all costs that vary with crop area, such as purchase of seeds, chemicals and fertilizer. This excludes fixed costs such as building and machinery maintenance or mortgage payments, which are all not directly dependent on crop area and can differ considerably between farms. The variable costs were subdivided into costs that were, and costs that were not, related to M. graminicola. The gross margin was then calculated according to:

  • image(3)

where VC were the variable costs unrelated to M. graminicola, and MC were the variable costs related to M. graminicola, defined as:

  • image(4)

The costs related to M. graminicola (MC) were the sum of the costs of fungicides and the costs resulting from M. graminicola-related yield loss. Costs of fungicides were calculated by multiplying the fungicide price (PD), in £ per dose, by the fungicide dose (D), in dose per hectare. The yield loss was calculated from the expected disease severity without treatment [E(S)], the percentage yield loss for each percent disease severity (L), and the percentage of disease remaining after fungicide dose D was applied (DR). Disease severity remaining (DR) was defined as the percentage of disease severity that occurred at growth stage 75 after using fungicide dose D compared to the disease severity that would have occurred without using fungicides. By multiplying the percentage yield loss with the production of wheat in tonnes per hectare (P) and the price of wheat in £ per tonne (PW) yield loss was quantified into costs in £ per hectare.

The relationship between disease severity and yield loss is typically described with a simple empirically derived equation with a yield-loss ratio describing the percentage yield loss per percent disease (Gaunt, 1995). For M. graminicola such relationships have been previously derived by King et al. (1983), Thomas et al. (1989) and Paveley et al. (1997). There is also evidence for a disease density dependent relationship (Shaw & Royle, 1989), but because of the variability in yield loss, such relationships seldom provide a better estimation. Based on yield-loss data over the years 2003–05 from the UK HGCA Recommend List trials (http://www.hgca.com) a yield-loss ratio (L) was calculated (Table 3).

Table 3.   Overview of the parameters used and their dimensions and values
Variable nameSymbolValueDimension
  1. aShould be taken as fraction in equations.

Wheat yieldP  9·15t ha
Wheat pricePW100£ t−1
Fungicide price per dosePD25£ per dose
Yield-loss ratioL  0·81-
Dose-response factork  2·8ha per dose
Maximum reduction 3 spraysRD 99·6a%
Variable costs excluding fungicidesVC230£ ha−1
Seed cost 40£ ha−1
Fertilizer cost 100£ ha−1
Chemical cost excl. M. gram. fungicides 90£ ha−1

Yield loss is typically described by the maximum attainable yield minus the actual yield (Nutter et al., 1993). An indication of both over the years 2003–05 was obtained from the UK HGCA Recommended list trials (http://www.hgca.com), where the mean yield in fungicide-treated plots was 10 t ha−1 (at 85% dry matter) and the mean yield in plots untreated with fungicides was 8·3 t ha−1. Assuming half the damage was caused by M. graminicola gave a yield loss caused by M. graminicola of 0·85 t ha−1. The attainable wheat yield (P) while only considering M. graminicola then became 9·15 t ha−1. The yield-loss ratio was calculated by relating the disease severity over 2003–05 to the yield loss in 2003 to 2005. Data from Tables 1 and 2 were used to quantify M. graminicola disease severities on leaf 2 and the HGCA data were used as an indication of yield loss (disease severity data from leaf 2 are not available from the HGCA trials, and yield loss data were not available for the data from Tables 1 and 2). As both the HGCA data and the data in Tables 1 and 2 were from a wide range of sites and cultivars, they were assumed to represent countrywide averages over the years 2003–05. With an attainable wheat yield (P) of 9·15 tonnes, a yield loss of 0·85 tonne, and a M. graminicola percentage of 11·4%, the yield-loss ratio became 0·81% yield loss per percentage M. graminicola on leaf 2. In Thomas et al. (1989) a yield-loss ratio of 0·42 was calculated and in King et al. (1983) a yield-loss ratio of 0·55 was estimated. The ratio calculated here is higher than both these ratios, but recent work suggests there has been a decrease in tolerance to M. graminicola in wheat (Parker et al., 2004; Foulkes et al., 2006), which suggests that a higher yield-loss ratio may be appropriate.

The grain price (PW) in £ per tonne is market-dependent and variable and was fixed at a value which was representative of a typical value during recent decades based on data from the HGCA (http://www.hgca.com).

The percentage disease severity remaining at growth stage 75 after applying fungicide dose D (DR) depends on the maximum amount of reduction obtainable with fungicides (RD) and the fungicide response factor (k) and was modelled with an exponential dose-response curve (Paveley et al., 2000, 2001):

  • image(5)

where S is the disease severity without fungicide treatment, RD is the maximum percentage of reduction in disease severity possible with an infinite fungicide dose, and k describes the curvature of the response curve.

Epoxiconazole was used as an example fungicide, because it is one of most effective and widely used fungicides against M. graminicola. One litre of the commercial product Opus (BASF plc) per hectare is one recommended dose and contains 125 g of the active substance epoxiconazole. It was assumed that all epoxiconazole used without mixture on commercial crops (Garthwaite et al., 2004) was used predominantly against M. graminicola and that other fungicides were used simultaneously to control other diseases. The product label limits the total dose applied in any one season to a maximum of 2 L commercial product ha−1. Values for RD and k were calculated for the period 2003–05. A single dose of Opus had an average k value of 3·55 (ks) over the years 2001–03 and a disease-reduction percentage (RDs) of 84% (Lockley & Clark, 2005). There are typically three fungicide sprays applied per season to wheat in the UK, each at approximately half the recommended dose (as specified on the product label; Finney, 1993). The disease reduction percentage (RD) for triple sprays was calculated as (1−RDS)3 (Paveley et al., 2003), in which RDs is the disease-reduction percentage of a single spray. The k value was calculated by fitting a single dose response curve, (1−RD + RD·e−k·Dose), over a triple dose response curve, inline image, assuming all three sprays are of equal dose in which ks stands for the k value for a single fungicide spray. Variable costs were based on data from Nix (2005).

The yield loss [YL(D)] caused by M. graminicola as a function of fungicide dose D can be calculated from Eqns 4 and 5 as:

  • image(6)

To calculate the expected yield loss caused by M. graminicola,Eqn 6 is multiplied by the probability density function of disease severities (Eqn 2) and integrated over the possible range of disease severities from 0 to infinity:

  • image(7)

This can also be written as:

  • image(8)

In this calculation, the integral is the equivalent of the mean expected severity [E(S)]. By combining Eqns 4–8 the expected costs at a dose D can be calculated as:

  • image(9)

If the fungicide dose is increased, the costs of fungicide will increase and the costs of M. graminicola yield loss will decrease. For any given disease severity which would have occurred without treatment, there is a dose where the combination of these two costs is minimal. This dose will be called the economic optimal dose as defined by Paveley et al. (2001). To calculate this economic optimal dose, Eqn 9 is differentiated with respect to dose D, the derivative set to 0, and the derivative is rewritten as a function of the economic optimal dose (DE), resulting:

  • image(10)

Costs with risk

Although Eqn 10 defines the economic optimal dose that minimizes the costs and maximizes the gross margin, as argued in the introduction, the actual aim of growers in a spray decision may not necessarily be to find the average economic optimal dose, but to reduce the risk of a severe economic loss.

The risk of a certain economic loss, measured with the costs or the (reduction in) gross margin, was earlier defined as being equal to the risk of a ‘critical disease severity’ as risk level K (Eqn 2). What level of disease severity is critical depends on what costs are acceptable. To calculate the critical disease severity, Sc, Eqn 9 can be rewritten as:

  • image(11)

The probability of certain costs (MC) can then be calculated by substituting Eqn 11 (Sc) into Eqn 2, resulting in:

  • image(12)

From equation 12 the costs with risk (MCK) can be calculated according to Eqn 13, where MCk are those costs where the actual costs in a certain year can be expected to be higher with probability of K (risk), and lower with probability 1−K:

  • image(13)

The dose at which the costs at risk level K are minimal (DK) can then be calculated by differentiating Eqn 13 with respect to fungicide dose D and equating the derivative to zero:

  • image(14)

Equation 13 is similar to the equation for expected costs (Eqn 9) with the expected severity E(S) replaced by -ln(K)/α. Since for the exponential distribution E(S) = 1/α both equations have the same outcome for =  e−1 = 0·37.

All parameter values used in the calculations were derived from literature (Table 3). In correspondence with the disease data, all parameters were, where possible, estimated for the period 2003–05 for the UK.

Value of prediction

The value of prediction can be quantified in fungicide dose or costs. The value of prediction measured by fungicide dose is the dose that would be saved if predictions were followed. The value of prediction measured by costs can be calculated in expected costs, which quantifies the gain in income that can be expected if predictions are followed. The value of prediction is calculated as the difference between scenarios with and without model predictions. Both are calculated with the same risk level to allow comparison. In general, the value of prediction (VP) is calculated as:

  • image(15)

where Sce(WP) is the measure (fungicide dose or costs) resulting from the scenario without predictions, Sce(E) is the measure if a damaging epidemic is predicted, and Sce(A) is the measure if no epidemic is predicted. The scenario with model predictions is calculated by combining Sce(A) and Sce(E) according to a weighted average based on the proportion of cases in which a damaging epidemic is predicted (θ). On average the risk prediction model predicts a damaging epidemic in 61% (Table 1) of the cases on the dataset (θ is 0·61). This means that in this paper the result of predicting a damaging epidemic has greater weight in calculating the value of prediction.

In the scenario without model predictions, the optimum fungicide dose is calculated using all data in a particular resistance rating group (Fig. 1a, d, g) and the appropriate α value (Table 2). In the scenario with model predictions, the optimum fungicide dose is calculated separately for the subgroups of data where a damaging epidemic is predicted (Fig. 1c, e, i) and where no damaging epidemic is predicted (Fig. 1b, e, h), also with the appropriate α value (Table 2). To calculate the value of prediction measured by fungicide dose, Eqn 14 is substituted for Sce() in Eqn 15 according to Eqn 16 (see appendix). For the value of prediction measured by expected costs the optimum dose at a certain risk level, Eqn 14 is substituted into Eqn 9, which is then substituted for Sce() in Eqn 15 according to Eqn 18 (see appendix).

Results

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Appendix

First we describe the general associations between risk, expected severity, fungicide dose and costs. From these general associations we describe how they relate to the value of prediction.

The risk level is reduced if a higher fungicide spray is used (Table 4). This is because a higher fungicide dose offers more protection against disease and decreases the probability that a disease-induced economic loss occurs. Furthermore, cultivar resistance reduces the optimum fungicide dose because a higher cultivar resistance results in lower expected disease severity. How large the increase or decrease in optimum dose is depends on the level of cultivar resistance (Table 4). The optimum fungicide dose can also change as a result of prediction. The increase or decrease in optimum dose then depends on how much the expected severity changes with prediction (Table 4; Fig. 2). The value of prediction is a result of the shift in dose that results from prediction.

Table 4.   Fungicide dose (where one dose unit = one recommended dose of 1 L ha−1 of the commercial product Opus) and value of prediction in fungicide dose for all cultivars, resistant cultivars and susceptible cultivars at two risk levels (= 0·37 and = 0·01) for Mycosphaerella graminicola on winter wheat
 KaPredictionAll cultivarsResistantSusceptible
  1. aRisk level K used in the calculation.

  2. bCalculated with Eqn 14.

  3. cCalculated with Eqns 16/17.

  4. dValue of prediction expressed as percentage of the fungicide dose without prediction, e.g. (0·06/0·7)*100.

0·37Withoutb0·70·60·9
 Absenceb0·50·040·6
 Epidemicb0·80·60·9
 Value of predictionc0·060·170·04
 Percentaged8%31%5%
0·01Withoutb1·31·11·4
 Absenceb1·00·61·2
 Epidemicb1·31·21·5
 Value of predictionc0·060·170·04
 Percentaged5%16%3%
image

Figure 2.  Cost curves with and without prediction, calculated according to Eqn 9 for Mycosphaerella graminicola on winter wheat. Graph illustrates costs (at risk level = 0·37) for all cultivars. A similar shift occurs with susceptible and resistant cultivars and with different risk levels.

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The decrease in optimum dose if no damaging epidemic is predicted is larger than the increase in dose if a damaging epidemic is predicted (Table 4). These shifts in optimum dose are largest for resistant cultivars and considerably smaller for susceptible cultivars. This difference between cultivar groups is largely the result of the high accuracy in predicting the absence of a damaging epidemic for resistant cultivars. The value of prediction measured by fungicide dose saved is largest for resistant cultivars and substantially smaller for susceptible cultivars and for all cultivars considered together. In percentage fungicide use reduction, the gain from prediction is also largest for resistant cultivars.

As with fungicide dose, shifts in expected costs are also larger for resistant than for susceptible cultivars (Fig. 2; Table 5). The value of prediction measured by costs saved is also largest for resistant cultivars and substantially smaller for susceptible cultivars and for all cultivars considered together (Tables 5 and 6). Surprisingly, the value of prediction (in absolute but not percentage units) is independent of the risk level K (appendixEqns 17 and 19). From Eqn 17, it can also be concluded that the value of prediction measured by fungicide dose is only influenced by the difference between the α values of the two prediction subgroups, how they are weighted (θ), and the dose response factor (k). Notably, it is not dependent on the maximum disease reduction percentage (RD) or the fungicide dose price (PD). The value of prediction measured by costs depends on all parameters apart from the risk level K.

Table 5.   Costs and value of prediction in costs (£ ha−1) for all cultivars, resistant cultivars and susceptible cultivars at two risk levels (= 0·37 and = 0·01) for Mycosphaerella graminicola on winter wheat
Ka PredictionAll cultivarsResistantSusceptible
  1. aRisk level K used in the calculation.

  2. bCalculated with Eqn 9 with D calculated according to Eqn 14.

  3. cCalculated with Eqns 18/19.

  4. dValue of prediction expressed as percentage of the costs without prediction, e.g. (1·5/27·6)*100.

0·37Withoutb27·623·230·6
 Absenceb21·79·924·7
 Epidemicb28·924·632·5
 Value of predictionc1·54·41·1
 Percentaged5%19%4%
0·01Withoutb34·229·937·2
 Absenceb28·316·531·3
 Epidemicb35·631·239·2
 Value of predictionc1·54·41·1
 Percentaged 4%15%3%

Discussion

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Appendix

In this paper we developed an evaluation procedure with which predictive models can be evaluated for their economic and potential environmental benefits. As part of this evaluation procedure we introduced risk levels based on disease severity and a method to calculate the optimum fungicide dose at a given risk level.

If any predictive model is to be adopted by growers it must provide clear economic benefits for them. The evaluation procedure developed in this paper identifies situations where making use of predictions may lead to benefits and situations where it may not. The value of prediction calculated in the evaluation procedure can be used to indicate whether a predictive model is likely or not to be adopted. Based on the value of prediction, the M. graminicola early warning model tested in this paper may have economic and environmental benefits to growers if used to guide treatment decisions on resistant cultivars. This was the result of the low number of damaging epidemics (false negatives) that occurred if no damaging epidemic was predicted. The value of prediction on susceptible cultivars was substantially smaller and adjusting fungicide dose according to predictions may not lead to benefits in this case. The evaluated predictive model is thus less suitable for use with susceptible cultivars.

The value of prediction is calculated from two comparable scenarios defined with risk levels. To calculate the value of prediction in practical situations it might be expected that it would be important to know what risk levels (and thus fungicide doses) are appropriate to model those practical situations. However, with disease distributed exponentially and a linear disease–yield-loss relation, the value of prediction in fungicide dose and costs are independent of risk level. The value of prediction can therefore be calculated without knowing the actual risk level and is independent of the initial fungicide dose used. This means that the initial fungicide dose used by a grower does not influence the benefits from the predictive model, greatly improving the usefulness of the method described. It is, however, important to know how the expected disease severity changes with prediction.

Fabre et al. (2007) introduced methodology to evaluate binary decisions, i.e. to spray or not. In this analysis, the costs reduction obtained by following predictions was quantified. Decisions on applying control measures are often more complex and concern the level of control. The method introduced in this paper looks at quantitative decisions, i.e. how much to spray. This method of evaluating predictive models is particularly of interest for diseases where the economic injury level is exceeded in most crops in most years and where applying control measures is standard practice. This method can be parameterized for different diseases and crops, and could be expanded to multiple diseases or different fungicide-spraying regimes.

Acknowledgements

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Appendix

This project has been funded by the Department for Environment, Food and Rural Affairs (DEFRA), United Kingdom. Rothamsted Research receives support from the Biotechnology and Biological Sciences Research Council (BBSRC) of the United Kingdom. Weather data used is Crown copyright data supplied by the UK Met Office.

References

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Appendix

Appendix

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Appendix

The value of prediction (VP) measured by fungicide dose is obtained by substituting Eqn 14 into Eqn 15 to give:

  • image(16)

where α1 is the exponential distribution parameter resulting from the distributions without prediction (Fig. 1a, d, g), α2 is the exponential distribution parameter resulting from the subsets where no damaging epidemic is predicted (Fig. 1b, e, h) and α3 is the distribution parameter resulting from the subsets where a damaging epidemic is predicted (Fig. 1c, f, i). Equation 16 can be simplified to:

  • image(17)

Value of prediction measured by expected costs is obtained by substituting the dose (DK) calculated in Eqn 14, into Eqn 9 and then into Eqn 15 to give:

  • image(18)

which, with E(S) = 1/α, can be simplified to:

  • image(19)