^{ * }

^{ * }Luxembourg Institute of Science and Technology (LIST),

^{ * }Department “Environmental Research and Innovation (ERIN)”

^{ 4 }41, rue du Brill, L-4422 Belvaux, Luxembourg

^{ * }*Corresponding author: daniel.molitor@list.lu

^{ * }Abstract

^{ * }Aims: The present analyses aimed at evaluating the performance of two models for estimating the overall effect of combining two or more measures (leaf removal, cluster division, late shoot topping, botryticide application, bioregulator application) for controlling grape bunch rot based on the efficacy of the individual measures.

^{ * }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%).

^{ * }Conclusions: 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 additional treatments rather than compared to the disease severity level in the untreated control.

^{ * }Significance and impact of the study: The high goodness of fit as well as the observed low deviations between the estimated and the observed efficacies suggest that the multiplicative approach is appropriate for estimating the efficacy of combined viticultural measures in a complex practical bunch rot control strategy assembled of different modules.

^{ * }Key words: Botrytis cinerea, bunch rot, crop cultural measures, efficacy, Integrated Pest Management, multiplicative consideration, Vitis vinifera

Botrytis bunch rot caused by

Being aware of the significant impact of annual meteorological conditions on bunch rot epidemics (González-Domínguez

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

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

Field investigations were carried out in the years 2009 and 2015 in the Luxembourgish Moselle Valley on the white

Fungicides with efficacy against

Treatments, precise dates of applications and the developmental stages of the grapevines recorded according to Lorenz ^{®}; 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

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). In treatments 1 to 4, the first shoot topping was realized at BBCH 71-73 (P. gris) or 71 (Riesling) on 25/06, while in treatments 5 to 8 late first shoot topping took place 22 days later [17/07; BBCH 79 (P. gris) or 77-79 (Riesling)].

The final

Data sets consisting of average disease severities per plot were analyzed for the treatment effects by one-way ANOVAs using SPSS Statistics 19 (IBM, Chicago, IL, USA) after testing Gaussian distribution and homogeneity of variances. In case the null-hypothesis was rejected (p ≤ 0.05), multiple comparisons according to Tukey were performed.

Efficacies were calculated according to equation (1) as defined by Abbott (1925).

E= efficacy

DS= disease severity

R= disease severity relative to control

Based on the efficacies of single measures [calculated according to equation (1)], expected efficacies for combined measures were computed by:

assuming additive effects according to equation (2)

(2)

E= efficacy

R= disease severity relative to control

assuming multiplicative effects according to equation (3):

(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.

As shown in B.

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% (). 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 deviation was 5.5% and global average absolute deviation 7.9% ().

titre du tableau
_{obs.}
_{est.}
_{abs.}
_{est.}
_{abs.}
_{obs}
_{.}
_{est.}
A
2009
P. gris
1
untr. control
14.6±4
c
0.0
2
bioregulator
16/06
65
13.1±4
bc
9.9
3
leaf removal
18/06
71
4.6±1
ab
68.4
4
bioregulator+ leaf removal
16/06 18/06
65 71
2.4±0
a
83.7
78.4
5.4
5.4
71.6
12.2
12.2
1.17
5
botryticide
10/07
77
10.2±2
abc
29.9
6
bioregulator+ botryticide
16/06 10/07
65 77
7.6±2
abc
47.8
39.9
7.9
7.9
36.9
10.9
10.9
1.29
7
leaf removal+ botryticide
18/06 10/07
71 77
4.4±1
ab
70.1
98.3
-28.3
28.3
77.9
-7.8
7.8
0.90
8
bioregulator+ leaf removal+ botryticide
16/06 18/06 10/07
65 71 77
2.2±1
a
85.2
108.3
-23.1
23.1
80.1
5.2
5.2
1.06
average
-9.5
16.1
5.1
9.0
1.11
B
2015
P. gris
1
untr. control
40.3±3
d
0.0
2
cluster division
21/07
79
12.9±5
bc
68.0
3
leaf removal
18/06
68
18.5±2
c
54.2
4
cluster division+ leaf removal
21/07 18/06
79 68
2.6±0
ab
93.6
122.2
-28.6
28.6
85.3
8.2
8.2
1.10
5
late 1
^{st} sh. topp.17/07
79
34.1±2
d
15.4
6
cluster division+ late 1
^{st} sh. topp.21/07 17/07
79 79
11.9±2
abc
70.5
83.4
-13.0
13
72.9
-2.5
2.5
0.97
7
leaf removal+ late 1
^{st} sh. topp.18/06 17/07
68 79
13.4±2
c
66.7
69.6
-2.9
2.9
61.2
5.5
5.5
1.09
8
cluster division+ leaf removal+ late 1
^{st} sh. topp.21/07 18/06 17/07
79 68 79
1.3±0
a
96.9
137.6
-40.7
40.7
87.6
9.3
9.3
1.11
average
-21.3
21.3
5.1
6.4
1.06
C
2015
Riesling
1
untr. control
51.9±6
b
0.0
2
cluster division
21/07
79
33.8±3
ab
34.9
3
leaf removal
18/06
68
41.7±5
b
19.5
4
cluster division+ leaf removal
21/07 18/06
79 68
17.7±4
a
65.8
54.4
11.4
11.4
47.6
18.2
18.2
1.38
5
late 1
^{st} sh. topp.17/07
77-79
44.0±7
b
15.2
6
cluster division+ late 1
^{st} sh. topp.21/07 17/07
79 77-79
30.5±4
ab
41.2
50.0
-8.9
8.9
44.8
-3.6
3.6
0.92
7
leaf removal+ late 1
^{st} sh. topp.18/06 17/07
68 77-79
35.8±5
ab
31.0
34.7
-3.7
3.7
31.7
-0.8
0.8
0.98
8
cluster division+ leaf removal+ late 1
^{st} sh. topp.21/07 18/06 17/07
79 68 77-79
17.3±3
a
66.7
69.6
-2.9
2.9
55.5
11.1
11.1
1.20
average
-1.0
6.7
6.3
7.9
1.12
global average
-10.6
14.7
5.5
7.9
1.10

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) (). 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 (E_{obs.}/E_{est.} < 1) were recorded (). 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); ) 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); ) 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

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