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Honey bee colony loss and parasites across space and timeHoney bee colony loss strongly depends on spatio-temporal factors33,42, which in turn have to be jointly modeled with other stressors. Focusing on CONUS climatic regions, defined by the National Centers for Environmental Information40 (see Fig. 1), this is supported by the box plots in Fig. 2 which depict appropriately normalized honey bee colony loss (upper panel) and presence of V. destructor (lower panel) quarterly between 2015 and 2021. Specifically, Fig. 2a highlights that the first quarter generally accounts for a higher and more variable proportion of losses. Average losses are typically lower and less dispersed during the second quarter, and then tend to increase again during the third and fourth quarters. The Central region, which reports the highest median losses during the first quarter (larger than 20%) exemplifies this pattern, which is in line with existing studies that link overwintering with honey bee colony loss6,29,30,31,32,33,43. On the other hand, the West North Central region follows a different pattern, where losses are typically lower during the first quarter and peak during the third. This holds, albeit less markedly, also for Northwest and Southwest regions. These differing patterns are also depicted in Fig. 3, which shows the time series of normalized colony loss for each state belonging to Central and West North Central regions – with the smoothed conditional means highlighted in black and red, respectively. Figure 2b shows that also the presence of V. destructor tends to follow a specific pattern; in most regions it increases from the first to the third quarter, and then it decreases in the fourth – with the exception of the Southwest region, where it keeps increasing. This is most likely because most beekeepers try to get V. destructor levels low by fall, so that colonies are as healthy as possible going into winter, and also because of the population dynamics of V. destructor alongside honey bee colonies – i.e., their presence typically increases as the colony grows and has more brood cycles, since this parasite develops inside honey bee brood cells44,45. The West region (which encompasses only California since Nevada was missing in the honey bee dataset; see Data) reports high levels of V. destructor throughout the year, with very small variability. A comparison of Fig. 2a and b shows that honey bee colony loss and the presence of V. destructor tend to be higher than the corresponding medians during the third quarter, suggesting a positive association. This is further confirmed in Fig. 4, which shows a scatter plot of normalized colony loss against V. destructor presence, documenting a positive association in all quarters. Although with the data at hand we are not able to capture honey bee movement across states, as well as intra-quarter losses and honey production, these preliminary findings can be useful to support commercial beekeeper strategies and require further investigation.Figure 2Empirical distribution of honey bee (Apis mellifera) colony loss (a) and Varroa destructor presence (b) across quarters (the first one being January-March) and climatic regions; red dashed lines indicate the overall medians. (a) Box plots of normalized colony loss (number of lost colonies over the maximum number of colonies) for each quarter of 2015–2021 and each climatic region. At the contiguous United States level, this follows a stable pattern across the years, with higher and more variable losses during the first quarter (see Supplementary Figs. S2-S6), but some regions do depart from this pattern (e.g., West North Central). (b) Box plots of normalized V. destructor presence (number of colonies affected by V. destructor over the maximum number of colonies) for each quarter of 2015–2021 and each climatic region. The maximum number of colonies is defined as the number of colonies at the beginning of a quarter, plus all colonies moved into that region during the same quarter.Full size imageFigure 3Comparison of normalized honey bee (Apis mellifera) colony loss (number of lost colonies over the maximum number of colonies) between Central and West North Central climatic regions for each quarter of 2015–2021 (the first quarter being January-March). (a) Trajectory of each state belonging to Central (yellow) and West North Central (blue) climatic regions. (b) Smoothed conditional means for each of the two sets of curves based on a locally weighted running line smoother where the width of the sliding window is equal to 0.2 and corresponding standard error bands are based on a 0.95 confidence level46.Full size imageFigure 4Scatter plot of normalized honey bee (Apis mellifera) colony loss (number of lost colonies over the maximum number of colonies) against normalized Varroa destructor presence (number of colonies affected by V. destructor over the maximum number of colonies) for each state and each quarter of 2015–2021 (the first quarter being January-March). Points are color-coded by quarter, and ordinary least squares fits (with corresponding standard error bands based on a 0.95 confidence level) computed by quarter are superimposed to visualize the positive association.Full size imageUp-scaling weather dataThe data sets available to us for weather related variables had a much finer spatio-temporal resolution (daily and on a (4 times 4) kilometer grid) than the colony loss data (quarterly and at the state level). Therefore, we aggregated the former to match the latter. For similar data up-scaling tasks, sums or means are commonly employed to summarize the variables available at finer resolution47. The problem with aggregating data in such a manner is that one only preserves information on the “center” of the distributions – thus losing a potentially considerable amount of information. To retain richer weather related information in our study, we considered additional summaries capturing more complex characteristics, e.g., the tails of the distributions or their entropy, to ascertain whether they may help in predicting honey bee colony loss. Within each state and quarter we therefore computed, in addition to means, indexes such as standard deviation, skewness, kurtosis, (L_2)-norm (or energy), entropy and tail indexes48. This was done for minimum and maximum temperatures, as well as precipitation data (see Data processing for details).Next, as a first way to validate the proposed weather data up-scaling approach, we performed a likelihood ratio test between nested models. Specifically, we considered a linear regression for colony loss (see Statistical model) and compared an ordinary least squares fit comprising all the computed indexes as predictors (the full model) against one comprising only means and standard deviations (the reduced model). The test showed that the use of additional indexes provides a statistically significant improvement in the fit (p-(text {value}=0.03)). This test, which can be replicated for other choices of models and estimation methods (see Supplementary Table S5), supports the use of our up-scaling approach.Figure 5 provides a spatial representation of (normalized) honey bee colony losses and of three indexes relative to the minimum temperature distribution; namely, mean, kurtosis and skewness (these all turn out to be relevant predictors based on subsequent analyses; see Table 1). For each of the four quantities, the maps are color-coded by state based on the median of first quarter values over the period 2015-2021 (first quarters typically have the highest losses, but similar patterns can be observed for other quarters; see Supplementary Figs. S12-S14). Notably, the indexes capture characteristics of the within-state distributions of minimum temperatures that do vary geographically. For example, considering minimum temperature, skewness is an index that (broadly speaking) provides information on whether the data tends to accumulate at one end or the other of the observed range of minimum temperatures (i.e., a positive/negative skewness indicates that the data accumulates towards the lower/upper range, respectively). On the other hand, kurtosis is an index that captures the presence of “extreme” values in the tails of the data (i.e., a low/high value of kurtosis indicates that the tail minimum temperatures are relatively close/very far from the typical minimum temperatures). With this in mind, going back to Fig. 5, we can see that minimum temperatures in states in the north-west present large kurtosis (a prevalence of extreme values in the tails) and negative skewness (a tendency to accumulate towards the upper values of the minimum temperature range), while the opposite is true for states in the south-east. More generally, the mean minimum temperature separates northern vs southern states, kurtosis is higher for states located in the central band of the CONUS, and skewness separates western vs eastern states.We further note that the states with lower losses during the first quarter (e.g., Montana and Wyoming) do not report extreme values in any of the considered indexes. Although these states are generally characterized by low minimum temperatures, these are somewhat “stable” (they do not show marked kurtosis or skewness in their distributions) – perhaps allowing honey bees and beekeepers to adapt to more predictable conditions. On the other hand, states with higher losses during the first quarter such as New Mexico have higher minimum temperatures as well as marked kurtosis, and thus higher chances of extreme minimum temperatures – which may indeed affect honey bee behavior and colony loss. Overall, across all quarters of the years 2015-2021, we found that normalized colony losses and mean minimum temperatures are negatively associated (the Pearson correlation is -0.17 with a p-(text {value} More

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