The dance of male Anopheles gambiae in wild mating swarms

Abstract

An important element of mating in the malaria vector Anopheles gambiae Giles in nature is the crepuscular mating aggregation (swarm) composed almost entirely of males, where most coupling and insemination is generally believed to occur. In this study, we mathematically characterize the oscillatory movement of male An. gambiae in terms of an established individual-based mechanistic model that parameterizes the attraction of a mosquito toward the center of the swarm using the natural frequency of oscillation and the resistance to its motion, characterized by the damping ratio. Using three-dimensional trajectory data of ten wild mosquito swarms filmed in Mali, Africa, we show two new results for low and moderate wind conditions, and indicate how these results may vary in high wind. First, we show that in low and moderate wind the vertical component of the mosquito motion has a lower frequency of oscillation and higher damping ratio than horizontal motion. In high wind, the vertical and horizontal motions are similar to one another and the natural frequencies are higher than in low and moderate wind. Second, we show that the predicted average disagreement in the direction of motion of swarming mosquitoes moving randomly is greater than the average disagreement we observed between each mosquito and its three closest neighbors, with the smallest level of disagreement occurring for the nearest neighbor in seven out of 10 swarms. The alignment of the direction of motion between nearest neighbors is the highest in high wind. This result provides evidence for flight-path coordination between swarming male mosquitoes.

Figure 1

Three-dimensional position (a) and velocity (b) of a single mosquito (solid line) from Sep. 1, 2010 sequence that had a wind speed of 0.67 m/s in the compass direction 252°. The shaded region corresponds to $3\sigma$ bounds for position and velocity of all mosquitoes in the swarm, and the broken line is the mean. The origin of the inertial frame is located at the ground level under the camera rig.

Figure 2

Velocity autocorrelation along downwind, crosswind, and vertical dimensions (solid black) and the respective function fits (dashed) for sequences from (a) Aug. 21 and (b) Aug. 28. The residual measure is the sum of the square error in the function fit. (c) Natural frequency ( ${\omega }_0$), damping ratio (ξ), overall level of motion (A) and residual fitting error for ten mosquito swarms sorted left to right in the order of wind speed. The inertial frame is oriented along downwind (black), crosswind (grey), and vertical (white), except for Aug. 21 for which the inertial frame is oriented north-south and east-west, wind speed was not available.

Figure 3

The plot of natural frequency ( ${\omega }_0$) versus damping ratio (ξ) for all swarms shows that the motion of the swarm is underdamped in the horizontal plane (square=downwind, triangle=crosswind) and overdamped in the vertical (circle). PCR results wherever available show the swarm molecular form. Solid markers are for Aug. 28, 2010 sequence with high wind.

Figure 4

Mean first (circle), second (triangle), and third (square) nearest-neighbor distance versus average velocity disagreement for all swarms. Solid markers are for Aug. 28, 2010 sequence with high wind.