Time-Frequency Analysis Reveals Pairwise Interactions in Insect Swarms

The macroscopic emergent behavior of social animal groups is a classic example of dynamical self-organization, and is thought to arise from the local interactions between individuals. Determining these interactions from empirical data sets of real animal groups, however, is challenging. Using multicamera imaging and tracking, we studied the motion of individual flying midges in laboratory mating swarms. By performing a time-frequency analysis of the midge trajectories, we show that the midge behavior can be segmented into two distinct modes: one that is independent and composed of low-frequency maneuvers, and one that consists of higher-frequency nearly harmonic oscillations conducted in synchrony with another midge. We characterize these pairwise interactions, and make a hypothesis as to their biological function.

Figure 1

Time-frequency analysis of the relative distance $r_{ij}(t)$ between midge pairs. (a) Time series of $r_{ij}$ for a randomly chosen insect pair as well as its continuous wavelet transform. Nearly all of the power in the signal for this noninteracting pair is at low frequencies. (b) Time series of $r_{ij}$ and CWT for an interacting pair. In the shaded region, $r_{ij}$ oscillates nearly harmonically with power at higher frequencies.

Figure 2

(a) Probability density functions (PDFs) of the separation between insects for all pairs, nearest neighbors, and interacting pairs. Interactions do not in general occur between nearest neighbors. (b) PDF of acceleration for all insects and those engaged in interactions. Interactions do not show distinct signatures in the acceleration statistics, and are thus not representable by a simple mean-field forcelike model. (c) PDF of speed (that is, the modulus of the velocity) for all insects and those engaged in interactions. The distribution is shifted to slightly faster speeds for interacting midges.

Figure 3

Fraction of flight time spent engaged in interactions as a function of the number of individuals in the swarm. Interactions are rare in small swarms, but occur about 15% of the time for larger swarms.

Figure 4

(a),(b) Velocity projected in the direction of the other individual for the two pairs shown in Fig. 1. Velocities are typically uncorrelated. But during an interaction, such as the shaded region in (b), the velocity signals for the two midges oscillate in phase. (c) Velocity cross-correlation functions for all midge pairs and for those engaged in interactions. During interactions, velocities are much more strongly correlated than they are for the population in general. The positive peak indicates antiparallel velocity vectors.

Figure 5

Time-frequency analysis of a single male midge and a virtual female. When the male detects the female wingbeat sound, as played back by a small speaker, it executes very high frequency motion (shaded region) before flying toward the speaker and landing on it.