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First published online May 2, 2008
Journal of Experimental Biology 211, 1635-1644 (2008)
Published by The Company of Biologists 2008
doi: 10.1242/jeb.013425
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Variability in the encoding of spatial information by dancing bees

Rodrigo J. De Marco*, Juan M. Gurevitz{dagger} and Randolf Menzel

Freie Universität Berlin, Fachbereich Biologie/Chemie/Pharmazie, Institut für Biologie–Neurobiologie, Königin-Luise-Strasse 28-30, D-14195 Berlin, Germany


Figure 1
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  		Fig. 1. An analysis of within-individual variations in the encoding of distance information in the dance. To compare information from different bees and distances, the data from each waggle phase was incorporated into a frequency distribution using the difference between the duration of that waggle phase and the mean duration from all the waggle phases of the dancer, and dividing this difference by the mean. Each of these values is referred to as the `divergence' between the distance information encoded in a single waggle phase and that from all of a dancer's waggle phases. The relationship between the flown distance and the frequency distribution of such divergences, in percentages, is shown in (A–C); the variance of the distributions decreases as the flown distance increases. (D–F) To answer how the precision of the distance indication changes with increasing waggle-phase duration, we used the number and duration of the dancers' wagging movements (WMs) to re-calculate the distributions of the divergences according to the number of WMs of the single waggle phases. Within-individual variations in the encoding of distance thus appeared to be invariant to the actual flown distance. (G,H) To confirm this, we analyzed the relationship between the flown distance and the frequency distribution of `actual' divergences, i.e. those involving at least one WM of a dancer's body, either below (G) or above (H) the mean. The values obtained for each category were divided by the total number of individual measurements. Data from different bees were then averaged, and the resulting frequency distributions were separately analyzed according to the flown distance. N1, number of dancers; N2, number of waggle phases. The asterisk in G denotes statistical differences between the corresponding bars (see Results for statistics and details.)

 

Figure 2
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  		Fig. 2. (A) An analysis of the scatter of a dancer's number of wagging movements (WMs) around the mean. Data from waggle phases following either left (light grey) or right (dark grey) turns are shown separately. (B) The number of WMs occurring during the waggle phase as a function of the dancer's mean orientation with respect to vertical; left and right waggle phases (see Materials and methods) are shown separately. (C) Mean number of WMs as a function of to the dancer's mean orientation with respect to vertical. Data from left and right waggle phases were pooled separately; vertical lines indicate 95% C.I.; different letters denote significant differences between groups (P<0.05).

 

Figure 3
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  		Fig. 3. (A) An analysis of the scatter of directions of single waggle phases around the mean. Data from waggle phases following either left (light grey) or right (dark grey) turns are shown separately. (B) Average standard error (s.e.), in degrees, of the mean direction of a dancer's waggle phases as a function of the average dance orientation; for each orientation, we averaged standard errors from 10 different random resamplings in order to balance the sample size across categories. (C) The `residual misdirection' of the dance as a function of the time of day. (D) The angular divergence of the dance as a function of the average dance orientation; white circles denote the mean angular divergence (± s.e.m.), whereas colours depict the frequency distribution of the divergences as a function of the average dance orientation. Different letters denote significant differences (P<0.05) across groups. (E,F) Frequency distribution of the scatter of directions of left (E) and right (F) waggle phases around the mean as a function of the average dance orientation.

 

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  		Fig. 4. The accuracy and precision of the encoding of spatial information in the dance, as related to the field locations indicated by the endpoints of the vectors encoded in 1414 waggle phases (N3) from 145 dances (N2) by 29 dancers (N1). Data are from to the second experimental series. The colour scale refers to the absolute number of observations within categories (bin size=10) in a two-dimension system of coordinates. The square denotes the position of the hive (H), and the circle that of the feeder (F).

 

Figure 5
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  		Fig. 5. An analysis of the level of uncertainty associated with the encoding of both direction (A,C) and distance (B,D) information as a function of the number of observed waggle phases. For each given number of waggle phases, we used 50 000 random resamples and computed the proportion of those resamples yielding a certain level of precision, defined on the basis of their respective deviations from the mean. Cumulative frequencies thus denote the probability of achieving a certain level of precision based on an increasing number of waggle phases. In A and B, each line corresponds to a different number (sample size) of observed waggle phases. For the sake of comparison, the same results are shown in C and D, where the precision in the encoding of distance is shown in meters; `W-Phs' is the number of waggle phases; the average precision for direction and distance information is shown in degrees (C) and meters (D), respectively.

 

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© The Company of Biologists Ltd 2008