Overall efficacies of combined measures for controlling grape bunch rot can be estimated by multiplicative consideration of individual effects Research note

Methods and results: Field trials with the white Vitis vinifera cultivars Pinot gris and Riesling on the efficacy of three bunch rot control measures applied either alone or in combination were analyzed. Bunch rot disease severities prior to harvest were assessed and efficacies were calculated for each treatment. Observed efficacies of single measures were used to estimate the overall efficacies of all possible measure combinations. Calculated efficacies matched observed efficacies more accurately when assuming multiplicative interaction among the individual measures (R2 = 0.8574, p < 0.0001; average absolute deviation: 7.9%) than in case of assuming additive effects (R2 = 0.8280; average absolute deviation: 14.7%).


Introduction
Botrytis bunch rot caused by Botrytis cinerea Pers.:Fr.(teleomorph: Botryotinia fuckeliana (de Bary) Whetzel) is a major fungal disease of grapevine causing severe economic damage worldwide (Kassemeyer and Berkelmann-Löhnertz, 2009;Wilcox et al., 2015).Common bunch rot control strategies were traditionally based on the application of fungicides with known activity against B. cinerea (botryticides).Substantial evidence for a loss of fungicide efficacy due to resistance in B. cinerea was reported on several occasions [see for instance Leroch et al. (2011) or Walker et al. (2013)], illustrating the need for better fungicide resistance management and alternative control strategies beyond fungicides.In recent years, the high efficacy of non-chemical crop cultural measures such as preflowering or early post-flowering leaf removal in the cluster-zone (Molitor et al., 2011a;Poni et al., 2006;Poni et al., 2008;Sternad-Lemut et al., 2015), cluster division (Molitor et al., 2012), late first shoot topping (Molitor et al., 2015a), artificial shading (Basile et al., 2015), leaf anti-transpirants (Intrieri et al., 2013) and flower debris removal (Jaspers et al., 2016;Molitor et al., 2015b) has been demonstrated in different regions.The success of individual disease control measures is usually measured as first described by Abbott, 1925).
Being aware of the significant impact of annual meteorological conditions on bunch rot epidemics (González-Domínguez et al., 2015;Molitor et al., 2016), an estimation of the overall degree of control efficacy of complex strategies built on a set of modules is of interest for the annual bunch rot control strategy.Furthermore, it is crucial to avoid combining control methods that may act in an antagonistic manner with regard to the overall efficacy.
Ostensibly, a straightforward approach for estimating the cumulative efficacy (E ab…x ) of combined measures would be the accumulation (additive consideration) of the efficacies (E) of each single measure.This approach might deliver an acceptable estimation of the real efficacy at low efficacy levels and/or low numbers of measures combined.However, there is an obvious limitation to this approach at high efficacy levels and/or in case of high numbers of measures combined: the overall efficacy cannot, by definition, exceed 100%.However, theoretical efficacies above 100% might be reached when accumulating efficacies of several single measures.Furthermore, combining several control measures in other pathosystems indicated multiplicative rather than additive effects of combining control measures (Blandino et al., 2012;Edwards, 2004).
Consequently, we hypothesize that the efficacy of bunch rot control strategies combining two or more measures could be more correctly estimated based on the multiplicative consideration of the efficacies of single measures than based on additive consideration.
To test this hypothesis, three field examinations on the efficacy of three single non-chemical and/or chemical measures to control bunch rot as well as of all possible combinations of these measures were conducted and analyzed in the white Vitis vinifera L. cultivars Pinot gris and Riesling in the years 2009 and 2015 in Luxembourg.Fungicides with efficacy against Plasmopara viticola and Erysiphe necator were applied at 10-to 12-day intervals.No fungicides with known activity against B. cinerea were used.Each experiment was conducted as a randomized block design with four replicates of eight to twelve vines per plot.

Vineyard sites and experimental design
Treatments, precise dates of applications and the developmental stages of the grapevines recorded according to Lorenz et al. (1995) are summarized in Table 1.Treatments consisted of bioregulator application (Regalis ® ; active ingredient: prohexadione-Ca; application dose: 1500 mL ha -1 ), botryticide application (Teldor ® ; active ingredient: fenhexamid; application dose: 1600 g ha -1 ) or leaf removal in the cluster-zone on the north or east exposed sides of each row.For a precise description of the implementation of the treatments of trial A, see Molitor et al. (2011b).Assessment data of trial A have partly been published before (Molitor et al., 2011b).
Field trials B and C were performed specifically for the present analyses.Here, in treatments 3, 4, 7 and 8 two to four leaves were removed (depending on the number of clusters per shoot) in the cluster-zone.Vertical cluster division eliminating the lower part (approximately 50%) of each cluster took place in treatments 2, 4, 6 and 8 (for exact dates see Table 1).

Statistical analysis
Data sets consisting of average disease severities per plot were analyzed for the treatment effects by oneway ANOVAs using SPSS Statistics 19 (IBM, Chicago, IL, USA) after testing Gaussian distribution and homogeneity of variances.In case the nullhypothesis was rejected (p ≤ 0.05), multiple comparisons according to Tukey were performed.
Efficacies were calculated according to equation ( 1) as defined by Abbott (1925).(3) E= efficacy R= disease severity relative to control Estimated efficacies were compared with observed efficacies.Deviations (Δ) between the observed (E obs. ) and estimated efficacies (E est. ) were calculated for each combination of measures in all three trials and for both approaches.
Absolute deviations (Δ abs. ) (representing absolute values of deviations) were determined.Coefficients of determination (R 2 ) of linear regressions between estimated and observed efficacies were computed.Average values of deviations and absolute deviations were calculated for each trial.In addition, global averages of deviations and absolute deviations (representing averages of the data of all three trials) were computed.In case of multiplicative considerations, the ratio between observed (E obs. ) and estimated efficacies (E est. ) was calculated.

Results and discussion
As shown in  1).Generally, efficacies of the measures in 2015 tended to be higher in Pinot gris than in Riesling.This might be explained by the dense cluster structure of Pinot gris grapes in 2015.Here, control measures might have been more efficient than in Riesling, which showed less compact clusters in 2015.
Assuming additive effects, average deviations per trial between estimated and observed efficacies ranged from -1.0% to -21.3% with average absolute deviations between 6.7% and 21.3%.Here, the global average deviation was -10.6% and global average absolute deviation 14.7% (Table 1).The negative average deviations in all three trials suggest that additive considerations tend to overestimate the overall efficacies.This effect is, as expected, most pronounced in case of combining measures with high efficacies, as this was the case particularly in trial B. Here, assuming additive effects leads to estimated efficacies above 100%, confirming the limitations of this approach.
In case of the multiplicative consideration, the average deviations per trial between estimated and observed efficacies of combined measures ranged from 5.1% to 6.3% with average absolute deviations between 6.4% and 9.0%.Here, the global average   1).
Treatments in the same trial marked with the same letter did not differ significantly (p = 0.05).Observed (E obs. ) and estimated (E est. ) efficacies (i) according to equation (2) (additive consideration) or (ii) according to equation (3) (multiplicative consideration) as well as deviations (Δ) and absolute deviations (Δ abs. ) between observed and estimated efficacies are depicted.In case of multiplicative consideration, ratios between observed and predicted efficacies are shown.Generally, global averages represent averages calculated from the data of all three trials.
Estimated and observed efficacies were in both approaches significantly correlated.Coefficients of determination of linear regressions between estimated and observed efficacies were higher in case of the multiplicative consideration (R 2 = 0.8574; p < 0.0001) than in case of the additive consideration (R 2 = 0.8280; p < 0.0001) (Figure 1).The multiplicative approach assumes that each additional measure is affecting (in case of efficient measures: reducing) the disease severity level as the result of the previous/additional treatments rather than compared to the disease severity level in the untreated control.
Generally, the high goodness of fit as well as the observed low deviations between the estimated and the observed efficacies demonstrated the suitability of the approach assuming multiplicative effects to estimate the efficacy of combined viticultural measures.Ratios between observed and estimated efficacies (E obs./E est. ) > 1 mean that the overall efficacy of the combination of two or more measures is above the expected efficacy according to equation (3).Such ratios are indicating that besides multiplicative effects slight synergistic effects might exist, while, on the other hand, E obs./E est.ratios < 1 are indicating slight antagonistic effects.In the present investigations, both slightly synergistic as well as slightly antagonistic effects were observed in the different trials as well as in the different combinations.Generally, the fact that the global average ratio between observed and estimated efficacies of 1.10 was close to 1 demonstrates the usefulness of equation ( 3) with a slight tendency towards synergistic effects in some combinations: e.g., in treatments that combined leaf removal in the cluster-zone with other measures that lead to a reduction of the cluster compactness (such as cluster division or the application of a bioregulator), slightly synergistic effects were observed in all three trials, while in other combinations (e.g., cluster division + late first shoot topping), slight antagonistic effects Treatments in the same trial marked with the same letter did not differ significantly (p = 0.05).Observed (E obs .)and estimated (Eest.) efficacies (i) according to equation (2) (additive consideration) or (ii) according to equation (3) (multiplicative consideration) as well as deviations (Δ) and absolute deviations (Δ abs .) between observed and estimated efficacies are depicted.In case of multiplicative consideration, ratios between observed and predicted efficacies are shown.Generally, global averages represent averages calculated from the data of all three trials.
(E obs./E est.< 1) were recorded (Table 1).In the case of combining leaf removal with a late first shoot topping in 2015, synergistic efficacies were observed in Pinot gris (E obs./E est.= 1.09), while the efficacies in Riesling (0.98) were slightly antagonistic.The question of which combinations of measures under which conditions in which cultivar tend to show (besides generally multiplicative effects) synergistic or antagonistic effects and the underlying principles would merit further investigations based on a broader data set.Potentially, combining different measures affecting the complex pathosystem grapevine/bunch rot at distant loci, in different ways or at distant time points (e.g., bioregulator (effect on cluster compactness) + botryticide (direct effect on pathogen); Table 1) might tend to slightly synergistic effects while the combination of measures inhibiting the pathogen at similar positions (e.g., cluster division (effect on cluster structure) + late first shoot topping (effect on cluster structure); Table 1) might exhibit slight antagonistic effects (efficacy lower than expected based on the multiplicative consideration of single efficacies).
Under practical conditions, a broad spectrum of crop cultural measures is available to optimize the grape health status and hence to enable a prolongation of the maturation period (Molitor et al., 2012).Present (Table 1) as well as previous studies demonstrate that crop cultural measures (non-chemical control) are often of higher efficacy than the application of botryticides (chemical control) (Evers et al., 2010;Molitor et al., 2011b) and might save costs as well as energy (Sternad-Lemut et al., 2015).Consequently, such non-chemical crop cultural measures represent efficient tools for reducing or partially replacing the pesticide input in viticulture as intended in Integrated Pest Management.For instance, a chemical treatment (such as a botryticide application) can be replaced by an efficient crop cultural measure, without jeopardizing the efficacy of the bunch rot control regime.As an efficient risk management strategy, the combination of several measures is recommended in practical bunch rot control programs.According to the present results, the efficacy of the overall control strategy can be estimated based on multiplicative consideration of the expected effects of the single measures.Which and how many viticultural measures are integrated in the strategy is determined by the specific local conditions, the specific varietal degree of bunch rot susceptibility as well as the production target.

Field
investigations were carried out in the years 2009 and 2015 in the Luxembourgish Moselle Valley on the white Vitis vinifera L. cultivars Pinot gris and Riesling.Experimental vineyards were described in detail before [vineyard A (Pinot gris, Ahn): Molitor et al. (2011b); vineyards B (Pinot gris, Remich) and C (Riesling, Remich): Molitor et al. (2015a)].
R= disease severity relative to controlBased on the efficacies of single measures [calculated according to equation (1)], expected efficacies for combined measures were computed by: a. assuming additive effects according to equation (2) (2) E= efficacy R= disease severity relative to control b. assuming multiplicative effects according to equation (3):