Fig 1.
Data processing to obtain the most frequent amplitude in overnight recordings.
(A) A typical vibrational spectrum averaged over 3 minutes from an accelerometer in the hive. Note the pronounced peaks at 125 Hz and 250 Hz, a feature common to all honeybee vibrational spectra collected from the comb. (B) A histogram of amplitude values from the same data shown in panel A. The majority of amplitudes are found between 1x10-6 m/s-2 and 5x10-6 m/s-2, as clearly seen in (A). Note that the information regarding frequency is lost. (C) Vibrational spectra (averaged over 3 minutes) collected from midnight to 7 a.m shown as a spectrogram. Each vertical line is the equivalent of the spectrum in (A) but with the amplitude now colour coded (blue = 0 ms-2, red = 3x10-5 ms-2). The large number of spectra available each night results in the histogram shown in (D) which is much smoother. In subsequent figures all histograms shown have been further normalised to their maximum value, this would be approximately 340 in the case of panel D.
Fig 2.
Overnight vibrational amplitude distributions for three colonies.
In colony No. 5, the most common vibrational amplitude oscillates regularly over the entire summer, whilst in colony No. 6, a period without a peak in May takes place three weeks after the primary swarm (the date of which is indicated with the yellow tick in early April). Visual inspection revealed that colony No. 2 was temporarily 'drone laying' in July, and this is also reflected as a clear perturbation of the cycle. Histograms are all normalised to their maximum (red pixel). The data for all colonies is available in S1 Fig.
Fig 3.
Overnight vibrational amplitude distributions in four contiguous frames within one colony.
Note the absence of oscillation in the winter time, the variations in the phase of the oscillation in differing frames, and the lack of oscillation three weeks after the primary swarm in the middle of April (shown by the yellow tick). The data shown here come from the UK apiary.
Fig 4.
Spectral analysis of the distributions oscillations for 20 colonies of one apiary.
All 20 colonies from one apiary are shown, including those used in Fig 2. The spectra have been normalised to their maximum and subsequently sorted to show the colonies with the shortest period (top) to the longest (bottom). Note many spectral maxima in remarkable agreement, between 21 and 26 days. Colony 2, which was found 'drone laying' for a month or so, exhibits small peaks that are additional to the single one seen for Colony 5 and 6. Only one colony (No. 4) out of 20 does not exhibit a clear peak in the range 21 to 26 days. Only four colonies out of 20 do not have their maximum in that same range. Two of these (No. 12, and No. 14) are colonies that failed a month after their primary swarm took place.
Fig 5.
Whole frame condition against vibrational amplitude.
Only the three colonies from Fig 2 are considered here (Colony No. 2 is represented by red squares, No. 5 by black circles, and No. 6 by blue triangles), at seven points in time when the frames condition were assessed visually. When colonies are considered individually, the linear combination of frame condition can be correlated to the extracted vibrational signal but the multiplying factors (α, β and δ) are not the same for each frame (red (α, β, δ) = (0.414,0.147,-0.668)x10-7, black (α, β, δ) = (0.402,-0.109,0.441)x10-7, blue (α, β, δ) = (-0.439,0.0006,0.68)x10-7).
Fig 6.
Outcome of numerical discrimination for raw vibrational amplitude spectra.
One averaged spectral measurement is collapsed onto a 3D point with coordinates named DF score 1, 2, and 3. Black dots: low amplitude state measurements (any colony 2, 5, 6, 7 or 15). Other dots: high amplitude state measurements for Colony 5 (red), 2 (blue), 6 (green), 7 (cyan) and 15 (magenta). Good discrimination is achieved for 30 minute long measurements except for Colony 6. The last figure gives the discriminant functions, which must be cross-correlated with the mean spectrum to give DF score 1, 2 and 3.
Fig 7.
Outcome of numerical discrimination for spectra normalised to their maximum.
The colour coding is the same as in Fig 6. Here 60 minute long averaging is required, and Colony 6 still exhibits overlap between the two states being discriminated. The fourth figure gives the relevant discriminant functions.
Fig 8.
Vibrational amplitude oscillation tracked by spectral shape analysis.
One hour long averaged spectra are normalised prior to being cross correlated with the three discriminant functions shown in Fig 7. The outcome is used to compute an indicator of the vibrational amplitude oscillation, which is shown from midnight to 6 am as a colour coded image. The indicator is not only good at tracking the amplitude oscillations (except for Colony No. 6) which is shown with the white curve, it also suffers less drift, as clearly demonstrated on Colony No. 5, 7, and 15. The white curve's quantitative axis is displayed on the right hand side of the individual plots. The indicator is obtained by first collapsing a one hour long averaged spectrum onto a 3D point, by computing three separate cross correlations with the curves shown in Fig 7D. The distance, D1, between the 3D point and the centroid of the black cloud in Fig 7 is further calculated, as well as the distance, D2, between the 3D point and the centroid of the other clouds. The colour-coded indicator is the ratio D2/D1.
Fig 9.
Vibrational amplitude oscillation tracked by spectral shape analysis for colonies that did not contribute to the DFA numerical search.
The three discriminant functions shown in Fig 7 are used on the colonies that have not contributed to the DFA numerical search. The resulting predictive indicator is shown again from midnight to 6 am as a colour coded image. The indicator is good at tracking the amplitude oscillations (shown with the white curve) on Colonies 1, 3, 8, 10, 11, 19 and 20, but exhibits poor performance on other colonies, in particular those with very high amplitudes (Colonies 4 and 13) or those where the depth of the oscillation of interest is much less pronounced. The white curve's quantitative axis is displayed on the right hand side of the individual plots. The data for the remaining colonies is shown in S3 Fig.