The results describe the importance of a particular predictor for predicting a response variable, the direction of the predicted effect on the response variable, and the extent to which the primary relationship is modulated by secondary and tertiary predictors. Within each figure, the central subfigure shows the relationship between the primary predictor and the response variable if the influence of the other two secondary predictors (top and right) is neutral. Because these secondary predictors mostly co-vary (i.e. Fig. 1: Brood 80 at Time 20 is more likely than Brood 200 at Time 20) the three subfigures on the leading diagonal are the most likely outcomes, while the remaining six subfigures are primarily for explaining and understanding the interactions. A summary of the original data can be found in Fig. S1 and Table S1. Throughout the results variables have capital letters.
Predicting clinical symptoms from spore counts
All response variables were relevant for predicting Symptoms (Table 2: P[effect>0] = 100% for all predictors). Spores were a strong predictor of the Symptoms in all four models, both directly and through its interaction with the other variables (Table 1: M1-M4), and because subtracting the effect of secondary predictors from the Spores predictor left a high probability of an effect size larger than zero (Table 2: Spores-Brood P[effect>0] = 91.3%; Spores-Time P[effect>0] = 94.3%). Brood and Time were equally predictive for Symptoms (Table 2: Brood-Time P[effect>0] = 55.6%), though much less so than Spores. The Symptoms increased first slightly and then strongly with increasing Spores, regardless of the Time and Brood (Fig.1: Time 50/Brood 130). Symptoms increased over Time, both in absolute terms and in relation to a given spore count level (see also Fig. S2), and Symptoms also increased with increasing Brood (see also Fig. S3).
Brood was a stronger modulator of the Spores-Symptoms relationship than Time since the Spores×Brood interaction received more weight than the Spores×Time interaction (Table 1: M2 includes Spores×Brood and not Spores×Time). This is also illustrated by a stronger change of the Spores-Symptoms relationship along Brood than along Time (Fig. 1).
Lastly we calculated the probability of encountering Symptoms if no Spores are detected in an adult bee sample (Spores = 0), which resulted in a probability around 0.22.
Predicting spore counts from clinical Symptoms
All response variables were relevant for predicting Spores (Table 2). Symptoms were the strongest predictors of Spores, both directly and through its many significant interactions with other predictors; three out of the four selected models (Table 1), and since subtracting the effects of secondary predictors from Symptoms left a high probability of an effect size larger than zero (Table 2). Bees seemed more important than Time for predicting Spores (Table 2).
Regardless of Time and Bees, Spores increased with increasing clinical Symptoms (Fig.2: Time 50/FOB 9; see also Fig. S4 for the full range of spore counts). In general though, Spores decreased over Time, as is illustrated by the decrease over Time for any given level of Symptoms (see also Fig. S5). Spores also decreased with increasing Bees irrespective of Time or Symptoms (Fig. S6). However, early in the season Spores increased with increasing number of Bees.
Time was a stronger modulator of the Symptoms-Spores relationship than number of Bees, since the model including only the Symptoms×Time interaction received 50% of the Akaike weight (Table 1). This is illustrated by a greater change in the slope of the Symptoms-Spores relationship in relation to Time than in relation to Bees (Fig. 2, Fig. S4).
We furthermore estimated the number of expected Spores in an adult bee sample if Symptoms are at level zero or level one, which resulted in around 158 and 228 Spores, respectively. Lastly, we calculated the posterior of the difference for extreme and likely values of Spores in order to investigate a dilution effect of sampling 100 bees while colony size differed (see ESM 3).
Predicting the effect of AFB disease on colony strength
All response variables were relevant for predicting the first variable of colony size, the number of adult bees (Table 2). Brood was the strongest predictor of Bees, as revealed by the importance of its interactions with the other variables in all four selected models (Table 1). This importance is further illustrated by the high probability of an effect larger than zero after subtracting the effect of Spores or Time as a co-predictor. The time post-infection seemed to be a much more important co-predictor of the number of bees than the number of spores (Table 2).
Regardless of Time or Brood the number of bees increased with increasing spore numbers (Fig.3: Time 50/Brood 130). Similarly, regardless of Spores and Brood, Bees increased with Time (Fig. 3: see at zero spore count and in Fig. S7 at Spores 850) and Bees increase with increasing Brood if the other predictors are held at their mean/median values (Fig. 3: zero Time point; Fig. S8: Spores 850).
Time was a stronger modulator of the Bees-Spores relationship in the colonies than Brood as the model with the Spores×Time interaction was ranked higher than the model including the Spores×Brood interaction (Table 1). This is illustrated by the strong change over Time in the slope, from a positive to a negative relationship, while the changes with respect to Brood are less prominent (Fig. 3).
Regarding the second measure of colony strength, i.e. the amount of Brood, we saw that all response variables were relevant for predicting Brood amount (Table 2). The number of Bees was by far the strongest predictor of Brood amount in the first model, which included only the Symptoms×Bees interaction, and received 99 % of all the predictors’ weight (Table 1). Therefore, here we only used M13 for the predictions instead of a weighted combination of all 4 models.
The importance of Bees for predicting the amount of Brood is further illustrated by the high portability of an effect larger than zero after subtracting the co-predictor Symptoms or Time. Symptoms seemed more important than the Time for predicting Brood (Table 2).
Regardless of Time and Bees, the Brood increased with increasing Symptoms (Fig.3: Time 50/Bees 9). Similarly, Brood decreased with Time irrespective of the Symptoms and Bees (Fig. 4 and Fig. S9, any symptom score). Brood also increases with Bees (Fig. 4), although at very high Symptoms, more Bees did not lead to more Brood anymore.
Bees was an overwhelmingly stronger modulator of the Brood-Symptoms relationship relative to Time since Symptoms×Bees was the only relevant interaction (Table 1). This is illustrated by the strong change in the slope of the Brood-Symptoms relationship in relation to the number of Bees, relative to the slope in relation to Time (Fig. 4).