Ants determine their next move at rest: motor planning and causality in complex systems

Abstract

To find useful work to do for their colony, individual eusocial animals have to move, somehow staying attentive to relevant social information. Recent research on individual Temnothorax albipennis ants moving inside their colony's nest found a power-law relationship between a movement's duration and its average speed; and a universal speed profile for movements showing that they mostly fluctuate around a constant average speed. From this predictability it was inferred that movement durations are somehow determined before the movement itself. Here, we find similar results in lone T. albipennis ants exploring a large arena outside the nest, both when the arena is clean and when it contains chemical information left by previous nest-mates. This implies that these movement characteristics originate from the same individual neural and/or physiological mechanism(s), operating without immediate regard to social influences. However, the presence of pheromones and/or other cues was found to affect the inter-event speed correlations. Hence we suggest that ants' motor planning results in intermittent response to the social environment: movement duration is adjusted in response to social information only between movements, not during them. This environmentally flexible, intermittently responsive movement behaviour points towards a spatially allocated division of labour in this species. It also prompts more general questions on collective animal movement and the role of intermittent causation from higher to lower organizational levels in the stability of complex systems.

Keywords: complex social systems; division of labour; intermittent top-down causality; motor planning; movement; self-similarity.

Figure 1.

(a) The experimental arena. (b) Side view. The paper mask covers the 7.5×5 cm ant nest, and a removable 1.5 cm cover over the nest entrance allows ants to be released into the arena one by one.

Figure 2.

(a) The speed distribution of all ants at λ=8. The empirically determined activity event speed threshold v_e is shown as the vertical magenta line, at 0.9 mm s⁻¹. (b) Illustration of the event definition process. A 60 s period of exploration is shown for λ=8. Estimated error bars in speed are shown as a blue band around the mean. To define the end of a period of activity, the speed must be less than or equal to a threshold of 0.9 mm s⁻¹ for a single time step or longer. The speed threshold is shown as the horizontal magenta line, while bands of red on the y-axis indicate a stopping period according to this criterion. Higher λ leads to tighter error bars and hence a lower speed threshold because one-step displacements are larger, leading to reduced fractional error in the speed with a fixed tracking error.

Figure 3.

(a) Examples of average event speed profiles 〈v(t;T)〉: speed versus time t averaged over all events with duration T for the six ants in ${\mathrm{C}}_{\mathrm{C}}^2$. The event speed profiles have durations T=4.8 s (orange), 9.6 s (green), 19.2 s (blue), 38.4 s (magenta) and 59.2 s (cyan), and the number of events N_T is 41, 22, 8, 6 and 1, respectively. In general, the longer the event T, the higher the average event speed for the particular profile 〈v(T)〉_t. (b) The number of events N_T versus event duration T for ${\mathrm{C}}_{\mathrm{C}}^2$. The trend is for the number of events to decrease with event duration, which is binned into units of 0.8 s. The highlighted events are those displayed in (a). The total number of events shown $\sum _T{N}_T=1024$.

Figure 4.

The distribution of stopping durations for the (a) no cleaning and (b) cleaning treatments (all colonies). The arithmetic mean stopping duration is indicated by a magenta line; the geometric mean is not significantly different between treatments (figure 5b; electronic supplementary material, table S3). Note that there are 15 ants in the no cleaning treatment and 18 in the cleaning treatment.

Figure 5.

95% confidence intervals (CIs) of the mean shown, two vertical axes are employed. (a) Outside the nest, the geometric mean event duration is significantly longer in the no cleaning treatment. Inside the nest, it is not significantly different between nest sizes. (b) Outside the nest, the geometric mean stopping duration is not significantly different between cleaning and no cleaning treatments. Inside the nest, ants stop moving for longer in the larger nest. (c) Outside the nest, the average event speed is significantly higher in the no cleaning treatment. Inside the nest, the average event speed is significantly higher in the larger nest.

Figure 6.

Average event speed 〈v(T)〉_t versus event duration T for (a) no cleaning treatment and (b) cleaning treatment. Data for C¹. Error bars indicate 95% CI around the mean. Data points without an error bar originate from one event only. The red line on the log–log plot indicates a power-law relationship 〈v(T)_t〉=aT^β. Across all colonies, β_NC=0.22±0.02,β_C=0.24±0.03,a_NC=2.82± 0.27 and a_C=2.45±0.27, indicating a sub-linear increase in average speed with the duration of an event. There is a departure from trend for very short and very long events, which we suggest is attributable to insufficient acceleration time and a plateauing effect at an individual ant’s maximum speed.

Figure 7.

(a) The power-law relation 〈v(T)_t〉=aT^β shown for the average exponents across the four treatments studied with a representative range of durations. Log scale shown on axes in (b). (1) Inside the nest, nest dimensions enlarged—β changes (increases), a constant. (2) Shift from inside the nest to outside the nest—β changes (decreases), a changes (increases). (3) Remaining outside the nest, social information introduced—β unchanged, a changes (increases).

Figure 8.

(a) Rescaled event speed 〈v(t;T)〉/〈v(T)〉_t versus rescaled time t/T. Data for colony ${\mathrm{C}}_{\mathrm{C}}^2$. Rescaling the speeds in an event of duration T with its average speed aligns the event speed profiles. Grey lines represent the rescaled event speed profiles for all the $\sum _T{N}_T=1024$ events. The highlighted events indicated with orange, green, blue, magenta and cyan are the same as in figure 3. The average rescaled event speed profile (black curve) indicates the scaling function $\mathcal{G}$. Error bars show 1 s.e.m. (b) Scaling function $\mathcal{G}$ for the three colonies in both no cleaning (red) and cleaning (blue) treatments. After a period of acceleration the average speed is reached for most of the event, followed by a shorter period of deceleration at the end. This patterns holds in both treatments.

Figure 9.

Weighted correlation r_w between successive average event speeds, inside and outside the nest, for different treatments. The outside, cleaning treatment correlation is the highest, when individual ants encounter no social information (physical or chemical) from other ants. 95% CIs shown. See also the electronic supplementary material, table S6.