The spatial frequency tuning of optic-flow-dependent behaviors in the bumblebee Bombus impatiens

Abstract

Insects use visual estimates of flight speed for a variety of behaviors, including visual navigation, odometry, grazing landings and flight speed control, but the neuronal mechanisms underlying speed detection remain unknown. Although many models and theories have been proposed for how the brain extracts the angular speed of the retinal image, termed optic flow, we lack the detailed electrophysiological and behavioral data necessary to conclusively support any one model. One key property by which different models of motion detection can be differentiated is their spatiotemporal frequency tuning. Numerous studies have suggested that optic-flow-dependent behaviors are largely insensitive to the spatial frequency of a visual stimulus, but they have sampled only a narrow range of spatial frequencies, have not always used narrowband stimuli, and have yielded slightly different results between studies based on the behaviors being investigated. In this study, we present a detailed analysis of the spatial frequency dependence of the centering response in the bumblebee Bombus impatiens using sinusoidal and square wave patterns.

Fig. 1.

Experimental setup. A box containing a bumblebee colony was connected directly to a clear acrylic tunnel through which the bees navigated to reach the sugar solution housed inside of the feeder box. Bees traveling through the shaded region of the tunnel were recorded using a tripod-mounted video camera situated above the tunnel. The inside walls of the tunnel were lined with different patterns; in the case illustrated, two sinusoidal gratings of different spatial frequencies.

Fig. 2.

Representative flight paths. All the recorded flight paths are shown for experimental trials comparing (A) two gray walls (zero spatial frequency), (B) a 0.05 cycles cm⁻¹ sinusoidal grating and a gray wall, and (C) 0.6 and 0.15 cycles cm⁻¹ sinusoidal gratings. The dashed line denotes the center of the tunnel.

Fig. 3.

Gray wall experiments. (A) The mean lateral distance from the center of the tunnel (black circles) is plotted for bees flying through a tunnel lined with a uniform gray pattern on one wall (constant wall) and a sinusoidal pattern of varying spatial frequency on the opposite wall (variable wall). For comparison, two control trials in which both walls carried the same sinusoidal grating (dark gray squares) are also plotted. (B) The average flight speed is plotted against spatial frequency (black circles) and compared with control trials (dark gray squares). Error bars denote the 95% confidence intervals between groups derived from a Tukey–Kramer multiple comparison test on the one-way ANOVA results. The number of paths analyzed was N=1139, with a minimum of 34 and maximum of 144 paths per trial. Zero spatial frequency represents a uniform gray pattern.

Fig. 4.

Spatial frequency tuning curves of the centering response. (A) The dependence of the mean lateral flight position on spatial frequency is compared for experiments in which one pattern was held constant (constant wall) at either 0.15 cycles cm⁻¹ (black triangles) or 0.6 cycles cm⁻¹ (gray circles) while the spatial frequency of the opposite wall was varied. The dashed lines indicate the predicted zero crossings when both walls hold the same pattern of either 0.15 cycles cm⁻¹ (black) or 0.6 cycles cm⁻¹ (gray). (B) The average speed of the bees versus the spatial frequency of the variable wall. Error bars represent the 95% confidence intervals for N=1961 unique paths (minimum of 35 and maximum of 188 paths per trial).

Fig. 5.

Contrast sensitivity of the centering response. The mean distance from the center of the tunnel when one wall was lined with a 0.6 cycles cm⁻¹ sinusoidal, 0.06 contrast pattern (constant wall) and the other wall was lined with a 0.15 cycles cm⁻¹ gratings with varying contrast. Data from the first and second colonies are shown in black and gray, respectively. The single black square denotes the combined mean lateral positions for controls in which both walls had either 0.6 cycles cm⁻¹ or 0.15 cycles cm⁻¹ patterns. The lines denote two exponential functions fitted to the data of either the first (black solid line) or the second (dashed gray line) colony. The error bars indicate the 95% confidence intervals for N=942 paths (minimum of 38 and maximum of 201 paths per trial).

Fig. 6.

Response differences between square wave and sinusoidal stimuli. The mean distance from the center of the tunnel is plotted when the constant wall holds a sinusoidal pattern with a spatial frequency of 0.15 cycles cm⁻¹ (black triangles, solid line) or 0.6 cycles deg.⁻¹ (dark gray circles, solid line) while the variable wall is lined with square wave and sine wave gratings of different spatial frequencies. The squares represent the mean distance from the center when the constant wall has either a 0.15 cycles cm⁻¹ (black) or a 0.6 cycles cm⁻¹ (gray) square grating. Vertical dashed lines indicate the predicted zero crossing when the constant wall has a 0.15 cycles cm⁻¹ (black) or 0.6 cycles cm⁻¹ (gray) sinusoidal pattern. Error bars indicate the 95% confidence intervals for N=1091 paths (minimum of 41 and maximum of 188 paths per trial).