Image composites of fixations (pauses – typically 50-150ms) during three different examples of scanning behaviours in Melophorus bagoti, all taken within 1m of the nest entrance, in inexperienced ants forming their route to a feeder.

Images were extracted and compiled from highspeed video taken at 600fps at 1080p using a Chronos 2.1HD camera (field of view, 30 cm × 17 cm). For each image, fixations are indicated by consecutively numbered black arrows denoting the ant’s orientation (except reversal). Rotational movement between fixations, saccades, are classified as either away (pink) or towards (green) the goal direction (∼90°). When a fixation precedes a change in turning (from left to right in these examples), this fixation is classified as a reversal (orange). (A) Denotes a scanning example where it reverses direction once but then turns in a complete loop with no reversal (fixations 6-16). (B) Shows a scan which contains multiple reversals (two). (C) Illustrates a scan with one reversal, ∼180° from the goal direction. Black dotted arrows denote pre/post scan forward movement.

Schematic of neural circuit model and its outputs across navigation relevant brain regions.

(A) The central complex (CX), a mid-brain region whose subregions compare representations of the goal heading with a representation of the agent’s compass-based current heading. The CX outputs bilateral signals to turn the left (red line) and right (blue line) to the Lateral Accessory Lobes (LAL). (B) Within the LAL oscillator, left (L) and right (R) neurons reciprocally inhibit one another (red and blue connections), while attempting to maintain a basal firing rate via internal feedback (circular black arrows), forming an oscillator which outputs a stable anti-phasic oscillatory activity between the L and R neurons across time (red and blue lines). (C) A steering signal is outputted from the LAL and results in the agent’s forward and angular movement. This steering signal stopped via an external inhibitory ‘freeze signal’, that breaks the angular and forward speed central pattern generators (CPG), initiating the scan. A threshold was implemented for the underlying angular drive to restart the CPG after each fixation period, resulting in a saccade whose magnitude was determined by this accumulated angular drive. The agent’s angular speed was normalised by the forward speed (linear normalisation - angular speed = angular drive/(forward speed + 0.1)) so the agent produces larger saccades magnitudes during scans. Threshold was determined to roughly mirror saccade magnitudes in real-world ants. Scan duration was implemented as an exponential duration distribution through a dice-roll at each simulation step. (D) Characteristics of an example path, with a single scanning bout, generated by the model. Black dots represent the agent’s head position at each simulated step coupled with coloured bars which indicate both the forward speed (arbitrary scale) and heading direction of each step. During the scanning bout, the agent’s forward speed is zero and the model produces several fixations in separate directions. The fixations of this scanning bout are zoomed and separated into a sequence of fixations. Coloured arrows indicate saccades, rotational movements between fixations which were defined as either away (pink) or towards (green) the goal direction. (E) The modelled CX’s turning signal output towards the goal direction, based on if the agent’s heading direction is to the left or right of the goal. (F) The oscillatory activity between the R and L neurons in the LAL during the example path. The agent’s (G) heading direction, (H) angular speed, and (I) forward at each step during the path.

Saccade angle distribution and the effect of CX steering guidance on saccade angle magnitude.

Saccade angle distributions in (A) the modelled agent and (B) real ants with all scan conditions combined. After each fixation, the subsequent saccade angle is plotted against the fixation’s angular divergence from the goal direction in both (C) the model agent and (D) real ants with all conditions combined. The general trends of the model are classified through coloured arrows (away-green, towards-pink) representing the increasing next saccade angle towards the goal direction and the decreasing next saccade angle away from the goal direction of the modelled agent when fixation orientation from the goal direction was large. This pattern is consistent with the model assumption that CX steering strength varies with angular divergence from the goal; easier to turn towards goal and thus large saccades, while harder to turn further away and small saccades. A similar pattern is observed in the ant data. For the box and whisker plots in panels C and D, the box spans the interquartile range while the horizontal line indicates the mean. Whiskers extend to the IQR X 1.5 while outliers beyond this range are shown as ‘+’ symbols. The indentation of the bar around the mean indicates the 95% confidence interval.

Relationship between fixation duration and reversal.

(A) Sequence of fixation directions and their duration for an example scan containing multiple reversals (orange), showcasing that the longest fixations tend to occur when the ant reverses directions on the next saccade (fixation duration continuum, blue-min; yellow-max). (B) shows changes in the cumulative turning drive over the course of the example scan. To initiate a saccade, the drive must surpass a threshold (line). This threshold possesses a level of noise which leads to variance in when a saccade appears as well as to the variance in saccade magnitude. Reversals occur when the oscillatory cycle changes phase (±), which are associated with longer times for turning drive to accumulate beyond threshold (orange). (C) Angular speed through the simulation, spikes represent saccades to the left and right and the change from positive to negative illustrates reversal periods (orange). Relationship between fixation duration and oscillatory cycle changes (orange) and subsequently reversals, occur in (D) modelled and (E) real ants. In both, the longest fixation duration typically occurs at the reversal (0), increasing as the reversal approaches (-), while decreasing post reversal (+). For these box and whisker plots, the box spans the inter quartile range while the horizontal line indicates the mean. Whiskers extend to the IQR X 1.5 while outliers beyond this range are shown as ‘+’ symbols. The indentation of the bar around the mean indicates the 95% confidence interval. Correlation between fixation duration and the next saccade angle in (F) modelled and (G) real ants. Data are split into the lower 25% (Q1, Blue) and upper 75% (Q2-Q4, Pink) of the distribution. In both, the general tendency in Q1 is significantly positive (real ant; Linear regression model; F(1, 281) = 11.00, p = 0.001), while beyond this (Q2-Q4) the tendency is significantly negative (F(1, 795) = 5.97, p = 0.015). The ‘unlikely’ zone in grey depicts the area of high saccade magnitudes following very short fixations, which should be highly unlikely given the low threshold drive must accumulate needed to break fixation in these instances.

Scans start and end irrespective of oscillator state and saccade number distributions.

In the modelled agent, (A) the number of saccades within a scanning sweep (before first reversal) was compared with the post-reversal sweep number showing a general upward trend. (B) the number of saccades within the penultimate sweep compared to the final sweep of the scanning bout, showing a downward trend. In real ants, (C) comparison of the number of saccades in the first and second sweep and (D) the penultimate and final scanning sweeps. Both model and real ant sweep comparisons only contain scans which contained two or more reversals, in order to compare the starting/stopping sweeps with a full, within reversals sweep (second/penultimate). Statistical comparisons were made using Wilcoxon tests. The distribution of saccade counts in each scanning bout within (E) the model, showing a Poisson distribution and in (F) real ants, showing a ‘Poisson-like’ distribution.

The strength of the CX’s corrective turn signal, and its inverse relationship with navigational uncertainty.

The model predicts an inverse relationship between CX signal strength and navigational uncertainty. Signal strength is predicted to be high when navigational uncertainty is low, such as in experienced foragers, and low when uncertainty is high, such as during route formation. (A) Model-predicted first reversal direction (relative to goal direction) as a function of CX signal strength. (B) First reversal direction in real ant data, comparing experienced and inexperienced foragers. (C) Model-predicted saccade angle as a function of CX signal strength. (D) Saccade angle amplitude in real ant data, comparing experienced and inexperienced foragers. For all box and whisker plots, the box spans the inter quartile range while the horizontal line indicates the mean. Whiskers extend to the IQR X 1.5 while outliers beyond this range are shown as ‘+’ symbols. The indentation of the bar around the mean indicates the 95% confidence interval.

Diverse behaviours emerge from interactions between the central complex’s (CX) steering signal and the modulation of the agent’s forward speed.

(A) A single ‘Full Loop’ scan (Video 5), the agent terminates forward speed and exhibits a scanning bout with both fixations and saccades. Here, the CX’s corrective steering excites the oscillator and reverses its phase (black arrow), resulting in the agent continuing the loop rotation rather than reversing. These full loop behaviours are rare within scanning (most scans reverse) but are observed in ants (Video 1-3). (B) Shows a double ‘Full Loop’ scan example where the agent performs two full loop rotations in a scan. As in panel A, (Simulations - Video 6). Here, the oscillator’s phase is reversed by the CX twice (black arrows). (C) A ‘volte’ is a full rotation performed without stopping forward movement, unlike the full loop in A and B.” (Simulation - Video 7). A common behaviour in Cataglyphis desert ants (Fleischmann et al., 2017). This behaviour arises in the agent when forward speed is low but not stopped, boosting angular speed and allowing the CX steering output to reverse oscillator phase without fixations. (D) An example of a ‘Myrmecia-like’ path in the agent, characterized by moderate forward speed and larger lateral oscillations, reminiscent of real world Myrmecia ants (Clément, Schwarz and Wystrach, 2023; e.g. Video - 4). Here, moderate forward speed allows for larger alternating turns and lateral displacement.

Summary of the behavioural spectrum produced by the modelled agent as a function of forward speed inhibition facilitating angular speed.

High forward speed results in an agent that ‘sprints’, with its straight paths resembling desert ants (Melophorus bagoti and Cataglyphis). Decreasing forward speed progressively increases angular speed facilitation, leading to the large oscillations of Myrmecia under moderate forward speed (Clément, Schwarz and Wystrach, 2023; Video 4), ‘voltes’ under low forward speed, and ultimately scanning behaviours when forward speed reaches zero. Here, angular facilitation plateaus, the central pattern generator (CPG) is disrupted and the agent scans, with the choreography of scanning being dictated by interactions between CX signal strength and the oscillator, as observed in ants (Real Ants - Video 1-3; Simulations - Video 5,6)