Table 1.
Summary of the entire experimental dataset.
Fig 1.
Sample spatio-temporal paired trajectory with the corresponding TDDC function, and observed delay values.
(A) Example of a paired flight trajectory subsampled for clarity with every other data point from the original 20 ms resolution. Non-grey symbols show interacting flight segments classified as either chase or coordinated flight extracted (see Methods) from the analysis of the TDDC plot, shown in panel (B), and the TDDS plot (not shown). For a given time and delay the TDDC plot shows the correlation between the headings of the two bats (1 is perfect alignment, 0 occurs when the relative headings is ±90°, -1 represents opposite alignments). Regions of the TTDC plot inside the area demarcated by the 0.95 correlation threshold correspond to relative heading values smaller than 18.2° in magnitude. The colour-coding of the movement paths is obtained from the coordinates (t, τ) of the disjoint black lines (time-ordered procedure) in panel (b), which assign delay response values between the bats at each instant in time. When no black line is present in the TDDC plot, the behaviour is deemed unclassified and the corresponding movement path in panel (a) is drawn grey. Panel (C) displays the observed delay values of coordinated and chase flights from all recorded trajectories through the analysis of the corresponding TDDS and TDDC plots.
Fig 2.
Bats’ relative locations with corresponding sound fields and summary statistics of all co-flying bats.
Panel (A): relative positions of co-flying bats with reactor’s sound fields. Symbols indicate locations of one individual relative to the position (centred) and heading (upwards) of the other: blue for chases, green for coordinated flights, and grey for unclassified behaviour. In the latter case, the individual at the centre is picked at random for each pair. Reactor is in the centre with upward heading with symbols showing actor’s positions and with red lines representing isocontours of the reactor’s calculated echolocation field. Parameters: cosine directionality with front-rear difference of 36 dB accounting for both emission and hearing directionality (see Equation (11) below). Source level is 110 dB [29] and absorption is 1.28 dB m−1[22]. Inset indicates separation distances dij, relative headings ϕij, i.e. the angular difference between the two velocity vectors, and exposure angles θij, i.e. the angular position of the actor with respect to the heading of the reactor. Panel (B), (C), and (D) display histograms of separation distances, absolute relative headings and exposure angles of co-flying bats obtained from panel (A).
Fig 3.
Model-generated spatio-temporal trajectories.
BSMI model output of the actor’s locations relative to the reactor, according to the TDDC and TDDS analysis, for different delayed response scenarios, each with echo amplitude reaction threshold at 10 dB. The blue and green points represent chase and coordinated flight respectively. The grey points represent non-interacting flights for which, having neither actor nor reactor, one of the pair was randomly placed at the center. (A) Spatial patterns when alignment response is immediate; when delay values are multiple of 100 ms and up to 500 ms; and (C) with reaction delay values multiple of 100 ms and between 600 ms and 2 s. For clarity only around three thousand randomly selected grey points have been plotted in each panel. Only short delay values, panel (B), reproduce the observed spatial relationship in Fig. 2 where actors are aligned within the sound field contour and chasees occupy the forward position directly in front of the chaser. Panels (A) and (C) corresponding to the model with instant and long delays respectively, fail to produce the same populating of the sound field and have chases absent or present at greater separations than recorded in the field, respectively.
Fig 4.
Fit of the model output to the observed interacting flights.
Contour level plot representing the fit of the coordinated flight movement patterns with those obtained from the model. The fitting procedure consists of comparing the relative position plot of coordinated flights from Fig. 2A and from the model with 1.5 × 1.5 m2 resolution. For each grid square (i, j) the normalised probability density, (i, j) is calculated and the lowest mean square error obtained via the expression
. The best fit is marked by the white point and corresponds to the model interaction field with parameters A = 16 and B = 10 dB.