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Keywords:

  • dose–response curves;
  • effective dose;
  • fungicide programmes;
  • multiplicative survival model;
  • Septoria tritici;
  • tebuconazole

Abstract

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

A function was derived to predict fungicide efficacy when more than one application of a single active ingredient is made to a crop, given parameters describing the dose–response curves of the component single-spray applications. In the function, a second application is considered to act on that proportion of the total pathogen population which was uncontrollable at the time of the first application (represented by the lower asymptote of the dose–response curve for the first treatment), plus any additional part of the population which survived the first application as a result of a finite dose being applied. Data to estimate the single-spray dose–response curve parameters and validate predictions of two-spray programme efficacy were obtained from separate subsets of treatments in four field experiments. A systemic fungicide spray was applied to wheat at a range of doses, at one or both of two times (t1 and t2), in all dose combinations. Observed values of the area under the disease progress curve (AUDPC) for septoria leaf blotch (Mycosphaerella graminicola) were used to construct response surfaces of dose at t1 by dose at t2 for each culm leaf layer. Parameters were estimated from single-spray and zero-dose treatment data only. The model predicted a high proportion (R2 = 71–95%) of the variation in efficacy of the two-spray programmes. AUDPC isobols showed that the dose required at t2 was inversely related to the dose at t1, but the slope of the relationship varied with the relative timings of t1 and t2 in relation to culm leaf emergence. Isobols were curved, so the effective dose – the total dose required to achieve a given level of disease suppression – was lower when administered as two applications.


Introduction

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

A single fungicide application to wheat provides efficient control of foliar disease on the culm leaf layer which emerges (and is therefore exposed to infection) shortly before application (Paveley et al., 2000). Less effective control is obtained on preceding and succeeding layers. Consequently, when the weather is particularly conducive to disease or host resistance is inadequate, a single fungicide application may not provide sufficient control to prevent premature green-area loss from all the upper leaf layers that are important to yield formation. There is little theory to describe or predict the joint effect of two or more fungicide applications within a spray programme. Such theory should support decisions on the appropriate dose (Paveley et al., 2001) for the current application, for any given dose applied previously. It might also help to discriminate between circumstances under which the total dose required to achieve a given level of disease control (the effective dose, ED) would be minimized by applying a lower dose more often, or a higher dose less often.

Simple models to describe the joint effect of active ingredients applied simultaneously in a spray mixture are long established (Bliss, 1939; Wadley, 1945; Scardavi, 1966; Colby, 1967; Rummens, 1975), and have been tested against experimental data for control of weeds, invertebrate pests and fungal diseases (Morse, 1978; Kozial & Witkowski, 1982; Gisi et al., 1985; Grabski & Gisi, 1987; Streibig & Kudsk, 1993). Kosman & Cohen (1996) extended mixture theory to account for nonsimultaneous action of mixtures in which, for example, one fungicide affects spore germination, and another affects mycelial growth but not spore germination. Hence the components could be considered as acting at different times. This paper explores whether such models might be adapted to predict the efficacy of fungicide spray programmes from the performance of their component applications, where those applications are of the same active ingredient but applied at different times. Two mixture models have been widely reported: the multiplicative survival model (MSM) and the additive dose model (ADM). Each has proponents and critics, but consensus suggests that the ADM and MSM are most appropriate when the components of the mixture have the same or different modes of action, respectively (Morse, 1978).

The ADM assumes a constant ratio between equipotential doses, which implies parallelism of the dose–response curves of the components, after log dose transformation (Kosman & Cohen, 1996). Paveley et al. (2000) described fungicide dose–response curves by a parsimonious function which can be expressed as:

  • Dd = D0[1 − b(1 − ekdose)](1)

where Dd and D0 are disease severity at dose d and dose = 0, respectively, b the amount of disease that might potentially be controlled with an infinite dose (expressed as a proportion of D0), and k defines the rate of change of disease severity with dose.

The k parameter was shown to be constant across spray timings, whereas b varies substantially and predictably according to the timing of application in relation to culm leaf emergence. Hence, if two sprays were applied some days apart, the lower asymptote (D0 − b) would differ between the two applications. Thus the curves for the two component applications cannot be parallel, making use of the ADM inappropriate.

The MSM does not require parallelism, but assumes that the mixture components can be thought of as acting independently and sequentially. Hence active substance B acts with the same efficacy as if it were applied alone, but only on that part of the pathogen population which ‘survives’ the effect of active substance A. This notion fits well with the sequential spray case. The approximation to independence of action of the two components arises in the mixture case by the two modes of action working on different target sites within the pathogen. Where sequential sprays are of the same mode of action, independence of action might still occur, as different subsets of individuals in the pathogen population are likely to be in a susceptible phase of their life cycle at different times. In effect, the second application might be considered as acting on that part of the total pathogen population which was uncontrollable at the time of the first application (represented by the lower asymptote of the dose–response curve from the first application), plus any additional part of the population that survived the first application as a result of a finite dose being applied.

These principles were used to derive a function to predict fungicide efficacy when more than one fungicide application of a single active ingredient is made in a crop, given parameters describing the dose–response curves of the component single-spray applications. Predictive value was tested against experimental data, using septoria leaf blotch (causal organism Septoria tritici, anamorph of Mycosphaerella graminicola) and winter wheat (Triticum aestivum) as the test pathosystem.

Materials and methods

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

Theory: extension to a two-spray programme

To extend Eqn 1 to describe a two-spray programme, using MSM principles, let spray 1 have parameters k and b1 and be applied at dose d1, and let spray 2 have parameters k and b2 and be applied at dose d2. The amount of disease, D, remaining after both applications is given by:

  • image(2)

The first and second terms (in square parentheses) represent the proportions of disease remaining after the effects of d1 and d2, respectively. Dose can be measured either in absolute units or as proportions of the recommended dose (the dose recommended for use on a particular crop by the fungicide manufacturer and approved by the pesticide regulatory authority), with estimates for k varying accordingly. Proportions of the recommended dose are used here.

Because control might be pest density-dependent, Kosman & Cohen (1996) suggested that where action was nonsimultaneous, the efficacy of the second mixture component should be determined against a pest population of the same density minus the efficacy of the first component. This is impractical in field conditions. Thus it was assumed that the proportional efficacy of the second application was unaffected by the amount of disease remaining after the first treatment.

Experimental design and treatments

Four field experiments were conducted during the 1996/97 and 1997/98 seasons on winter wheat cv. Riband, which is susceptible to septoria leaf blotch, at ADAS Rosemaund, Hereford, England. Experiments were established using a plot drill on 10 October 1996 and 4 October 1997 (experiments 1 and 2, respectively) in a three-replicate randomized block design. Plot sizes were 18 × 2 m in 1996 and 24 × 2 m in 1997. At Markle Mains, East Lothian, Scotland, experiments were marked out in existing crops drilled on 8 October 1996 and 27 September 1997 (experiments 3 and 4, respectively) and were arranged in fully randomized and randomized block designs, respectively, with four replicates of each treatment. Plot sizes were 20 × 2 m.

With the exception of fungicide applications, the experimental areas were treated according to local commercial practice. Fungicide treatments of tebuconazole (as the commercial product Folicur, 250 g active ingredient L−1, Bayer plc, Bury St Edmunds, UK) were applied using a hand-held sprayer in 225–250 L water ha−1 at 250 kPa through Lurmark F110-04 nozzles (Lurmark Ltd, Longstanton, Cambridge, UK) at the doses and timings given in Table 1. Doses above the recommended rate were used for experimental purposes, to better estimate dose–response curve lower asymptotes. There was no evidence of phytotoxicity resulting from these high-dose treatments. Tebuconazole was selected as a representative of the widely used ergosterol biosynthesis-inhibiting group, with eradicant and protective activity against S. tritici. This group of active ingredients plays a key role in wheat disease control, used in combination with fungicides of other modes of action (Paveley & Clark, 2000). All growth stages (GS) quoted are from the decimal code (Tottman, 1987).

Table 1.  Spray timings and doses of treatments applied to randomized and replicated field plots of winter wheat cv. Riband in each of experiments 1–4
Treatment numberFungicide dosea applied at
Timing 1 (GS 32)bTiming 2 (GS 33)b
  • a

    Tebuconazole as commercial product Folicur (L ha−1 at 250 g ai L−1).

  • b

    Treatments at timings 1 and 2 were applied when leaf III or II, respectively, was the youngest emerged leaf with ligule visible on more than 50% of shoots. Timing 1 dates were 1 May, 29 April, 6 May and 5 May in experiments 1–4, respectively; timing 2 dates were 15, 13, 20 and 19 May, respectively.

10·0 (untreated)0·0 (untreated)
20·00·25
30·00·50
40·01·00
50·02·00
60·250·0
70·250·25
80·250·50
90·251·00
100·252·00
110·500·0
120·500·25
130·500·50
140·501·00
150·502·00
161·000·0
171·000·25
181·000·50
191·001·00
201·002·00
212·000·0
222·000·25
232·000·50
242·001·00
252·002·00

First treatments (at GS 32) were applied 1–3 days before full emergence of leaf III (where leaf layers are counted downwards from the flag leaf, leaf I). The date of full emergence was defined as the first assessment on which the leaf ligule was visible on at least 50% of shoots. Second treatments were applied when leaf II was fully emerged (at GS 33). The precise timing of fungicide sprays to target particular leaf layers was determined by dissecting five randomly selected shoots from across the experiment every 3 or 4 days from GS31. Leaves II and III were targeted as there was a greater likelihood of obtaining high disease severities to discriminate treatment effects, than on leaf I.

Disease assessments

Disease severity was measured as the percentage of leaf area affected by septoria leaf blotch in all plots at weekly intervals from the time of the first fungicide treatment until crop senescence. On each occasion, 10 randomly selected shoots per plot were assessed using disease assessment keys (Anonymous, 1972). At each assessment date prior to GS 39, shoots were dissected to allow disease scores to be recorded under the positions that they would eventually occupy on the mature plant. In experiments 1 and 2 at ADAS Rosemaund, every leaf layer with green leaf area remaining was assessed, and data for leaves I–III are presented. In experiments 3 and 4 at Markle Mains, only leaf II was assessed.

Analysis

The severity of the leaf blotch epidemic was expressed as the area under the disease progress curve (AUDPC) from sequential assessments, to avoid confounding the effects of treatment and assessment timing. AUDPC values (% days) were calculated from the severity data by numerical integration using the trapezoidal rule, and provided a measure of the damage caused by the disease, integrated over the life of the leaf.

AUDPC dose–response surfaces

The analysis proceeded in two distinct steps: parameter estimation for Eqn 2, then the test of the equation with independent data. To test the extent to which Eqn 2 predicted the efficacy of two-spray treatments (closed triangles in Figs 1–2), response surfaces were derived, using parameters describing the component single-spray dose–response curves (estimated from observations of zero-dose and single-spray treatments; closed circles in Figs 1–2). For each leaf layer in each experiment, the parameters of Eqn 2, namely D0 (AUDPC at dose = zero), b1 and b2 (proportions of disease that might potentially be controlled with an infinite dose of fungicide applied at t1 or t2, respectively), and k (rate of change of AUDPC with dose) were estimated using FITNONLINEAR in genstat (Payne et al., 1993) using only the AUDPC values from plots making up the dose–response curves for single sprays (those that were untreated or received only a single spray treatment at either t1 or t2). Fitted dose–response surfaces were plotted with dose applied at t1 (d1), dose applied at t2 (d2), and AUDPC in the x, y and z dimensions, respectively. Two sets of percentage fit (R2) values were calculated. The first (inline image) described the variance in the single-spray dose–response curves accounted for by the fitted function. The second (inline image) quantified the proportion of the variation in the efficacy of two-spray treatments predicted by Eqn 2, using parameters from the fitted single-spray dose–response curves.

image

Figure 1. Response surfaces of AUDPC (% days) on fungicide dose (proportion of recommended dose) applied at time 1 (emergence of leaf III) and time 2 (emergence of leaf II), for the upper three culm leaves. Surfaces (a) (c) (e) and (b) (d) (f) are for leaves I, II and III in experiments 1 and 2, respectively. Observed data from zero-dose (untreated) and single-spray treatments (•) were used to estimate parameters for Eqn 2 (see text) to derive the response surface. Observed data from two-spray treatments (▴) were used to test the predicted joint efficacy represented by the response surface.

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image

Figure 2. Response surfaces of AUDPC on fungicide dose applied at time 1 and time 2 for leaf II in experiments 3 (a) and 4 (b). Observed data from zero-dose and single-spray treatments (•) were used to estimate parameters for Eqn 2 (see text) to derive the response surface. Observed data from two-spray treatments (▴) were used to test the predicted joint efficacy represented by the response surface.

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Results

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

Septoria leaf blotch was severe on leaves I, II and III in all experiments, except for moderate severity on leaf I in experiments 1 and 2. Other foliar diseases remained at zero or low levels, and would not have interfered with leaf blotch epidemic development.

AUDPC dose–response surfaces

The 3D response surfaces fitted to the single-spray and untreated points are shown in Figs 1 and 2 for experiments 1–4, with first dose, second dose and AUDPC on the x, y and z axes, respectively, and parameter estimates (with their units and standard errors) in Table 2. Data points are shown attached to their t1 and t2 dose points on the 3D surface by vertical lines.

Table 2.  Parameter estimates with units, standard errors (in brackets) and percentage fit values for AUDPC dose–response surfaces fitted to data from plots receiving zero-dose (untreated) and single-spray treatments, plus percentage fit values for predictive precision of two-spray programme efficacy
 D0 (% days)b1b2k (dose−1)aib (dose)aR2test (%)cR2test (%)d
(dimensionless)
  • a

    Expressed as proportions of the recommended dose.

  • b

    Amount by which the dose at one time should exceed the dose at the other time in order to minimize the total dose applied. Derived from fitted parameters via Eqn 6; see text.

  • cR2 for percentage fit of AUDPC values observed from the zero-dose (untreated) and single-spray treatments to values calculated by Eqn 2 (see text) after parameter estimation (calibration) using those values.

  • dR2 for percentage fit of AUDPC values observed from two-spray treatments to values predicted by Eqn 2, given parameters estimated using independent observed AUDPC data from zero-dose (untreated) and single-spray treatments only.

  • nd, not determined; na, not applicable.

Experiment 1
 Leaf I 3570·210·843·550·893·288·8
  (29)(0·09)(0·07)(1·07)(nd)(na)(na)
 Leaf II 9650·380·973·901·080·994·9
(147)(0·14)(0·12)(1·83)(nd)(na)(na)
 Leaf III14940·850·821·71−0·182·992·5
(162)(0·12)(0·12)(0·68)(nd)(na)(na)
Experiment 2
 Leaf I 4900·670·743·150·181·271·3
  (51)(0·08)(0·08)(1·07)(nd)(na)(na)
 Leaf II 9170·710·743·410·092·692·0
  (59)(0·05)(0·05)(0·69)(nd)(na)(na)
 Leaf III10820·810·712·82−0·290·193·0
  (87)(0·06)(0·06)(0·70)(nd)(na)(na)
Experiment 3
 Leaf II10230·320·812·610·981·686·0
(119)(0·12)(0·11)(1·19)(nd)(na)(na)
Experiment 4
 Leaf II13690·150·781·322·398·892·6
  (31)(0·03)(0·05)(0·20)(nd)(na)(na)
Parameter estimation

Equation 2 provided a good description of the variation in AUDPC with single fungicide sprays of varying dose (including zero) and timing. Percentage variance accounted for (inline image) by the fits to the untreated and single-spray AUDPC values ranged from 80·9 to 98·8% between sites and leaf layers (Table 2). Tests for correlations between parameters suggested a negative association between D0 and k (correlation coefficient = −0·75) and a weak negative association (−0·46) between b1 and b2.

Test of predictive precision

Prediction of the variation in AUDPC with two-spray treatments of varying dose and timing, using dose–response curve parameters estimated from the single-spray treatments, was good. Fits of the predicted values to observed data from the two-spray treatments gave values for percentage variance accounted for (inline image) ranging from 71·3 to 94·9% (Table 2), and F probability values were always P < 0·001. Plots of residuals provided no consistent evidence of bias, so unexplained variation represented random error in the data.

Interpretation of response surfaces

The response surfaces (Figs 1 and 2) show AUDPC decreasing with increasing dose in both x and y dimensions, with each additional increment of dose having a decreasing effect. However, the extent to which a unit dose decreased disease severity was determined by the b parameter. On leaf II in all experiments b2 was greater than b1 (albeit not always significantly so, according to the standard errors), indicating the greater efficacy of the t2 applications, which were administered closer to the time when the leaf was fully emerged. The t1 dose was less influential in reducing disease severity. In experiments 1 and 2, where leaves I and III were also assessed, the pattern of effects seen on leaf I was similar to that observed on leaf II, with greater efficacy per unit dose from the t2 timing. Values for b1 and b2 were not significantly different on leaf III, but in both experiments the estimate for the former exceeded the latter. Differences between b1 and b2, and changes in their relative values between leaf layers, were less marked in experiment 2 than in experiment 1. Nevertheless, on all leaf layers in all experiments, good efficacy (indicated by large b values) was obtained from the treatment timing nearest to full leaf emergence.

The k parameter was positively related to the degree of curvature of the dose–response. Standard errors indicated that estimated values for k varied little, with few significant differences within experiments and no consistent trends across leaf layers (Table 2). Minimum and maximum values across the experiments were, respectively, 1·32 on leaf II in experiment 4, and 3·9 on leaf II in experiment 1. In the latter case the dose–response curvature was such that AUDPC values were close to their asymptote values at dose = 1, whereas in the former case AUDPC values were still decreasing beyond dose = 1.

Effective dose isobols

Contour diagrams corresponding with Figs 1 and 2 are shown in Figs 3 and 4, respectively (axes are arranged to allow direct comparison between the two sets of figures). The lines of equal effect or isobols (Loewe & Muischnek, 1926; Tammes, 1964) represent the effective total dose (EDtot) at each timing required to achieve a given percentage control from 10% (EDtot10) to 90% (EDtot90), i.e. for an EDtot of x%, AUDPC = D0(1 − x/100). Hence the isobols quantify how the dose at t2 required to achieve a given efficacy relates to the dose at t1. In the UK, the recommended dose is the maximum that can be applied. Thus where an isobol crosses an axis at a value below or equal to unity, that level of disease control is achievable with a single application of a legal dose at the time represented by that axis. However, that level of control may be obtainable with a lower total dose, or higher levels of control may be attainable by applying two sprays. To test this, a set of parallel lines were considered, each running diagonally across the isobol diagram and joining points of equal total dose (for example, the line AB for leaf III in Fig. 3e). Point C, at which a line of equal total dose meets an isobol, defines the point at which the total dose required to achieve a given level of control is minimized.

image

Figure 3. Isobol diagrams (contours of equal efficacy) for fungicide dose (proportion of recommended dose) applied at time 1 (emergence of leaf III) and time 2 (emergence of leaf II), for the upper three culm leaves. Surfaces (a) (c) (e) and (b) (d) (f) are for leaves I, II and III in experiments 1 and 2, respectively. Contours are shown at AUDPC values corresponding to effective doses (ED) at 10% intervals from ED10 to ED90 (doses required to achieve 10 and 90% control, respectively). Dotted lines join points at which the total dose to achieve a given level of efficacy is minimized. In (e) line AB is a line of equal total dose; C, at which a line of equal total dose meets an isobol, defines the point at which the total dose required to achieve the level of efficacy represented by that isobol is minimized; the square (F) encloses dose combinations that do not exceed the statutory maximum dose and can therefore be used in farm practice.

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image

Figure 4. Isobol diagrams for fungicide dose applied at time 1 and time 2, for leaf II in experiments 3 (a) and 4 (b). Contours are shown at AUDPC values corresponding to effective doses (ED) at 10% intervals from ED10 to ED90. The dotted line joins points at which the total dose to achieve a given level of efficacy is minimized. The equivalent line in (b) is off the scale.

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The minimum total dose points were calculated for each isobol by calculating the point at which the tangent of the isobol was −1. Equation 2 was rearranged to give the contour curve for dose d2 as a function of dose d1, at a given disease level Da, by making d2 the subject:

  • image(3)

To obtain the values of d2 and d1 for a given tangent, Eqn 3 was differentiated with respect to d1 and the resulting expression made equal to the required tangent value – in this case, to unity. The differential of Eqn 3 with respect to d1 is:

  • image(4)

The expression has a negative sign as the tangents of the isobols represented by Eqn 3 are negative, because d2 decreases as d1 increases. By setting Eqn 4 equal to −1 so that, in effect, the numerator is equal to the denominator, the resulting expression can be solved for the specific dose (inline image) on the isobol which fulfils the condition, giving the quadratic:

  • image(5)

The positive sign before the square root was found to give the correct value of inline image for further analysis. This value of inline image, when put into Eqn 3, gave the corresponding value, inline image, for the minimum total dose point on the isobol.

Line of minimum total dose

The form of Eqn 2 dictates that, for all experiments and leaf layers, the minimum total dose points must lie in a straight line (for example, DE for leaf III in Fig. 3e) where inline image, about which the isobols, and hence the surfaces that they represent, are symmetrical. The constant represents the intercept (i) on the y axis: the amount by which the dose at one time should exceed the dose at the other in order to minimize the total dose (dtot) applied.

Simplifying the expression for d2 (Eqn 3) minus the expression for d1 (Eqn 5) provided the intercept (i) (Table 2) as a function of b1, b2 and k, so:

  • image(6)

The size of the constant i, that defines the position of the line of minimum total dose, depends on the relationship between amounts of controllable disease b1 and b2. When two spray timings are of approximately equal efficacy, so b1 ≈ b2, the response surface is symmetrical about a line close to d2 = d1 (Fig. 3e, leaf III; Fig. 3b, leaf I and II), so i ≈ 0. In contrast, where d1 and d2 differ in efficacy, so b1 is < or > b2, respectively (Fig. 3a,c and Fig. 4a,b), then i has a substantial positive or negative value. The form of Eqn 6 dictates that for any given difference between b1 and b2, i will increase as k tends towards zero.

Minimum total dose–response curve

A vertical section through the response surface along the line of minimum total dose (line DE in Fig. 3e) would show the relationship between dtot and Da when the amount of dtot applied at t1 and t2 was optimized. The function for this minimum total dose–response curve can be derived because, along the line of minimum total dose, inline image.

Substituting these functions for d1 and d2 in Eqn 2 gives:

  • image(7)

By defining each of the component doses as a function of dtot and the intercept, in effect Eqn 2 for the response surface is constrained only to calculate Da along the line of minimum total dose.

Similarly, along the line of minimum total dose inline image, hence combining Eqn 5 for inline image with Eqn 6 for i provides the function for the minimum total dose (inline image) required to achieve any given disease level, Da:

  • image(8)

In countries where a maximum legal dose per application is defined by regulatory authorities (one dose unit), only those parts of the isobol diagram (and hence those parts of the line of minimum total dose) that are enclosed by the square labelled F in Fig. 3a are of practical interest. Higher doses are of experimental value to estimate the shape of the response surface more precisely.

Relative efficacy of single- and two-spray programmes

Equation 8 allows comparisons between the dose required to achieve a given level of efficacy from single- or two-spray programmes. Maximum efficacy obtainable with legal doses can also be quantified by comparing the points at which isobols intercept the axes within the range 0–1 dose units, against the point at which the line of minimum total dose crosses the highest ED isobol before exceeding dose = 1 at either spray timing. Three contrasting examples illustrate the pattern of effects.

In the first example (leaf II in experiment 1), t2 was close to the optimum spray timing, with high efficacy denoted by b2 approximating to 1 and an ED90 of 0·68. In contrast, t1 was too early, with low efficacy denoted by a low b1 value and effective doses above ED30 exceeding 1. As a result, the line of minimum total dose was substantially displaced from the origin (large positive intercept, i) so that two-spray programmes were always less efficient than a single spray at t2. In the second case (leaf III in experiment 1), t1 and t2 were equally displaced either side of the optimum timing, resulting in equivalent efficacy, so b1 ≈ b2 and i ≈ 0. ED60 was the highest legal effective dose at both timings, with d1 = 0·72 and d2 = 0·78. The EDtot60 for a two-spray programme along the line of minimum total dose was 0·68. Eighty per cent efficacy could be obtained with a total dose below the maximum permitted, as EDtot80 = 1·27. In the third example (leaf III in experiment 2), t1 was closer to the optimum timing than t2. ED70 and ED60 were the highest permitted effective doses for t1 and t2, respectively, at 0·70 and 0·65. The EDtot70 for a two-spray programme was 0·63 and EDtot90 = 1·58.

When compared across experiments and leaf layers, isobol curvature was dependent on k and expressed most at high ED levels – see, for example, the isobol diagrams for leaf III in experiments 1 and 2 shown in Fig. 3a,b and their k values given in Table 2.

Theory: extension to a multiple spray programme

Equation 2 and its derivatives could be expanded to predict the combined efficacy of multiple sprays of doses d1, d2 dn at times t1, t1 tn, by adding additional terms. Each application would be considered to act on that proportion of the population which survived the combined effect of all previous applications. Similarly, the theory could be expanded to allow the effects of changing the timing of the component sprays to be investigated, because variation in b with spray time was found to be described well by the normal function (Paveley et al., 2000), which could therefore be substituted for b in Eqn 2, thus:

  • image(9)

AUDPC is minimized when t = µ (mean of normal distribution) and increases at a rate dependent on σ (standard deviation of normal function) as t increases or decreases from µ. θ is the maximum of the normal term (expressed here as a proportion of D0) when t = µ, hence θ is inversely proportional to the minimum value of AUDPC. Validation of Eqn 9 requires experimental data from a wider range of spray timings than those tested here, in order to obtain reliable estimates of σ, µ and θ.

Discussion

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

This paper demonstrates theoretically and experimentally that it is possible to predict the efficacy of two-spray programmes from the performance of their component single sprays. The assumption underlying use of the MSM model – that the subsets of the population on which the two sprays were acting should be substantially distinct – was acceptable for the pathosystem and fungicide treatments tested. If the theory is extended to other systems, limitations on the proximity of adjacent applications in the programme will need to be respected. Provided the treatment interval is greater than, or a substantial proportion of, one latent period (as in the data presented here), then adjacent applications act on largely distinct generations, and the model should provide reliable predictions of programme efficacy.

There now follows an assessment of the objectives described in the introduction: (i) to support decisions on the appropriate dose for the current application for any given dose applied previously; and (ii) to identify circumstances under which the total effective dose would be minimized by applying a lower dose more often, or a higher dose less often.

Effective doses at different application timings

Effective doses at the second application were inversely related to the dose at the first application, but the slope of the relationship (represented by the isobols) varied according to the relative efficacy of the two applications. Hence (i) where two timings are equally effective, equal doses should be applied at each time; (ii) if one time is more effective, more of the total dose should be applied at that timing; and (iii) in extreme cases, where i is large, all of the dose should be applied at the more effective timing, as the limited isobol curvature within the range of legal doses does not compensate for the poor efficacy of the less effective timing. The decision on the amount of total dose that should be applied at each timing is simplified because i is constant, regardless of the appropriate total dose. In practice, fungicide dose decisions are subject to considerable uncertainty. If, in retrospect, the dose applied at the first timing is considered to be excessive or insufficient, the isobol diagrams show that there is scope to compensate by adjusting the dose of the second application in the opposite direction. However, the total effective dose will be higher than if optimal doses are applied at each timing. Spray timing may be less critical when conditions are not conducive to spore transfer and infection. In experiment 1, full emergence of each of leaves III, II and I was followed by substantial rainfall events, whereas emergence of the upper leaves in experiment 2 coincided with a predominantly dry period. Differences in efficacy of the two spray timings were less marked in experiment 2 than in experiment 1.

Minimizing total effective dose

In the pathosystem tested, the total effective dose required was reduced when administered as two applications. For a single spray, the optimum application timing is a compromise between decreasing effects on epidemic onset and increasing effects on the relative epidemic growth rate, as the spray is delayed beyond full leaf emergence (Paveley et al., 2000). The isobol curvature reported here may arise because two well timed spray applications allow delayed epidemic onset from the first application to be combined with reduced growth rate from the second. At any point in time, there is a proportion of the pathogen population that is not in a fungicide-susceptible phase of its life cycle, as those individuals have yet to arrive on the target leaf or have already expressed symptoms. That proportion of the population is represented by the lower asymptote of the dose–response curve for a fungicide application at that time. Increasing the dose of a single application has only a diminishing effect on the susceptible part of the population, whereas two applications reduce the lower asymptote by catching a higher proportion of the pathogen population in a susceptible state. The beneficial effect of two spray applications on the total effective dose was greatest when there was high isobol curvature within the legal range of doses. This occurred when efficacy at the two timings was similar (small i values), and at high ED and k values. Hence spray programmes of fungicides with high dose–response curvature can achieve high efficacy at low total dose. However, this beneficial effect does not comply with the strict definition of ‘synergy’ between the two applications, as the observed efficacy for two-spray treatments agreed with the calculated expected efficacy, according to the specified theory of nonsynergistic action (Morse, 1978; Kosman & Cohen, 1996).

Although a lower total dose was usually required to achieve a given level of control when split between two applications, the isobols were seldom sufficiently curved for the financial saving from the lower dose to compensate for the labour and machinery costs of the additional spray (Nix, 2001). Also, repeated applications may increase the risk of fungicide resistance (Metcalfe et al., 2000). However, with a susceptible cultivar, favourable weather and high pathogen inoculum concentrations, two sprays were required to achieve acceptable disease control across the upper three leaves, important to resource capture. Where two or more applications are justified on these grounds, isobol curvature should be accounted for when determining the appropriate dose, otherwise an excessive amount may be applied. Equation 9 allows theoretical exploration of the optimum separation of the component sprays in a fungicide programme and the number of applications needed. These should be determined jointly by the period over which a single spray can achieve effective control (quantified by σ), and the difference between optimum application timings (µ) for different parts of the crop canopy. In wheat, the upper culm leaf layers intercept most of the incident photosynthetically active radiation during the yield-forming period. These leaves emerge and expand within a short period (Sylvester-Bradley et al., 1997). The long latent period of Mycosphaerella graminicola contributes to σ values that are sufficiently large in relation to the differences in µ between upper leaf layers, that two well timed sprays (Hardwick et al., 2001) can provide close to optimal control of leaf blotch on those leaf layers critical to resource capture. However, in contrasting pathosystems where canopy expansion is prolonged and the latent period short, closely spaced multiple treatments may be required to obtain effective control.

Acknowledgements

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

Funding of this work by the Home-Grown Cereals Authority is gratefully acknowledged. Thanks are due to host farmers for provision of experimental sites, many colleagues for conducting the experiments and statistical advice, and anonymous referees for constructive criticism of the manuscript. The contributions of Simon Oxley of SAC, and Alice Milne and Eric Audsley of Silsoe Research Institute are acknowledged.

References

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  • Anonymous, 1972. Guide for Assessment of Cereal Diseases. Harpenden, UK: Ministry of Agriculture, Fisheries and Food, Plant Pathology Laboratory.
  • Bliss CI, 1939. The toxicity of poisons applied jointly. Annals of Applied Biology 26, 585615.
  • Colby SR, 1967. Calculating synergistic and antagonistic responses of herbicide combinations. Weeds 15, 202.
  • Gisi U, Binder H, Rimbach E, 1985. Synergistic interactions of fungicides with different modes of action. Transactions of the British Mycological Society 85, 299306.
  • Grabski C, Gisi U, 1987. Quantification of synergistic interactions of fungicides against Plasmopara and Phytophthora. Crop Protection 6, 6471.
  • Hardwick NV, Jones DR, Slough JE, 2001. Factors affecting diseases of winter wheat in England and Wales, 1989–98. Plant Pathology 50, 45362.
  • Kosman E, Cohen Y, 1996. Procedures for calculating and differentiating synergism and antagonism in action of fungicide mixtures. Phytopathology 86, 126372.
  • Kozial FS, Witkowski JF, 1982. Synergism studies with binary mixtures of permethrin plus methyl parathion, chlorpyrifos and malathion on European corn borer. Journal of Economic Entomology 75, 2830.
  • Loewe S, Muischnek H, 1926. Ueber kombinationswirkungen. Archiv fur Experimentelle Pathologie und Pharmakologie 114, 31326.
  • Metcalfe RJ, Shaw MW, Russell PE, 2000. The effect of dose and mobility on the strength of selection for DMI fungicide resistance in inoculated field experiments. Plant Pathology 49, 54657.
  • Morse PM, 1978. Some comments on the assessment of joint action in herbicide mixtures. Weed Science 26, 5871.
  • Nix J, 2001. Farm Management Pocketbook. Wye, UK: Imperial College.
  • Paveley ND, Clark WS, 2000. The Wheat Disease Management Guide. London, UK: Home-Grown Cereals Authority.
  • Paveley ND, Lockley D, Vaughan TB, Thomas J, Schmidt K, 2000. Predicting effective fungicide doses through observation of leaf emergence. Plant Pathology 49, 74866.
  • Paveley ND, Sylvester-Bradley R, Scott RK, Craigon J, Day W, 2001. Steps in predicting the relationship of yield on fungicide dose. Phytopathology 91, 70816.
  • Payne RW, Lane PW, Digby PGN, Harding SA, Leech PK, Morgan GW, Todd AD, Thompson R, Tunnicliffe Wilson G, Whelam SJ, White RP, 1993. GENSTAT Reference Manual, Release 3. Oxford, UK: Clarendon Press.
  • Rummens FHA, 1975. An improved definition of synergistic and antagonistic effects. Weed Science 23, 46.
  • Scardavi A, 1966. Synergism among fungicides. Annual Review of Phytopathology 4, 33548.
  • Streibig JC, Kudsk P, 1993. Herbicide Bioassays. Boca Raton, FL, USA: CRC Press.
  • Sylvester-Bradley R, Scott RK, Clare RW, Kettlewell PS, Kirby EJM, Stokes DT, Weightman RM, Gillett AG, Macbeth JE, Gay A, Foulkes MJ, Spink JH, Hoad SH, Russell G, Mills A, Duffield SJ, Crout NMJ, 1997. The Wheat Growth Guide. London, UK: Home-Grown Cereals Authority.
  • Tammes PML, 1964. Isoboles, a graphic representation of synergism in pesticides. Netherlands Journal of Plant Pathology 70, 7380.
  • Tottman DR, 1987. The decimal code for the growth stages of cereals with illustrations. Annals of Applied Biology 110, 44154.
  • Wadley FM, 1945. The Evidence Required to Show Synergistic Action of Insecticides and a Short Cut in Analysis. US Department of Agriculture publication ET-223. Washington, DC, USA: US Department of Agriculture.