## 2 Materials and Methods
For the summer/autumn protocol, boards were checked until 17 days after the beginning of the last VarroMed(r) treatment, considering the number of days of efficacy on dispersal mites (6 days as described in the leaflet) and for more than 11 days to evaluate the eventual efficacy of the treatment on mites inside the capped brood cells susceptible to Varroa (Figures 1-3). \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Location**} & \multirow{2}{*}{**Protocol**} & \multirow{2}{*}{**Apiary Code**} & \multicolumn{2}{c}{**Number of**} & \multirow{2}{*}{**Treatment**} \\  & & & **Treated** & & **Period** \\  & & & **Colonies/Control** & & \\  & & & **Colonies** & & \\ \hline Zutendaal, & Summer/autumn & & & & \\ Belgium & (\(\times\)5) 1  & BELGIUM & 10/10 & 23.9–3.11.2018 \\ Rome, Italy & & Summer/autumn & & \\  & (\(\times\)5) & ITALY\_IZSLT & 10/10 & 6.8–20.9.2018 \\ Brdo pri Kranju, & Summer/autumn & & & \\ Slovenia & (\(\times\)5) & SLOVENIA & 8/7 3  & 13.9–15.10.2018 \\ Karlovac, & Summer/autumn & & & \\ Croatia & (\(\times\)3) 2  & CROATIA & 10/10 & 20.7–2.8.2018 \\ Levico Terme, & Winter & ITALY\_FEM & 10/10 & 22.11–6.12.2018 \\ Italy & Winter & ITALY\_IZSLT & 10/10 & \\ Bassano del & Winter & ITALY\_IZSVE & 10/10 & 17.11–1.12.2018 \\ Grappa, Italy & Karlovac, & Winter & CROATIA & 10/10 & 29.1–20.2.2018 \\ Croatia & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Number of hives used in each trial and location. For the winter protocol, boards were checked until 14 days after the VarroMed(r) treatment. A follow-up treatment consisting of the application of synthetic micitcides with different mechanism of action based on amitraz and tau-fluxalinate (in combination or in double dose), in order to avoid low efficacy due to possible mite resistance to one of the active substances, was applied to verify the residual number of mites. We used VPMs registered for honey bees with active substances not present in VarroMed(r). In the summer/autumn protocol, all queens were caged in VAR-CONTROL cages (Api-Mo.Bru, Campodoro, Padova, Italy--[[http://www.apimobru.com](http://www.apimobru.com)]([http://www.apimobru.com](http://www.apimobru.com)) (accessed on 13 September 2021) for 24 days. The follow-up treatment was applied during the caging period and for more 18 days. The residual number of mites was counted on sticky boards during the whole timeframe [25,30]. In brood absence (winter treatment), residual mites were counted on the sticky boards for 14 days after the follow-up treatment [25,30]. The untreated colonies of all control groups were checked for the natural mite fall and received the same follow-up treatment. The percentage of acaricidal efficacy (AE) in each hive was evaluated using the formula: \(\text{AE}=(\text{V}_{\text{T}}/\text{V}_{\text{T+follow-up}})\times 100\), where \(\text{V}_{\text{T}}\) is the total number of mites killed by the VarroMed(r) treatment, not considering the mites fallen during the queen caging period, and \(\text{V}_{\text{T+follow-up}}\) represents the total number of mites killed by the tested treatment and the follow-up treatments [31]. During the experiments, mean environmental temperatures were recorded by weather stations near the apiaries. Statistical analysis was performed using XLSTAT(tm) software [32]. It was verified if differences in acaricide efficacy were statistically significant using a Mann-Whitney Test [33]. The amount of adult honey bees and brood coverage between groups (treated and control) was evaluated using Kruskal-Wallis Test [34]. For the latter, multiple pairwise comparison with Dunn's Test [35] was applied with Bonferroni correction.