Fig 1.
A sketch of a series of discrete puffs, released at a constant pulsing rate, and the trajectories of a male moth (view from above).
A female moth is denoted as a small circle in the origin. The lowest detectable concentration of each puff is marked by a dashed contour line. A dash-dotted envelope denotes the limits of an average long term concentration distribution of a virtual plume. This figure manifests the major feature of the patchy plume—the size of patches of pheromone, the distance between them and the width of an isoline of the long time averaged concentration (i.e. “virtual plume”) grow proportionally in any given turbulent flow. The cross symbol × denotes schematically the turning point where the new casting search starts. The lateral spread of the search is equivalent to the size of the last patch, marked by two small circles on the moth path line.
Fig 2.
Typical velocity field and puff locations.
Arrows—instantaneous two dimensional velocity field U(x, y); circles—puff locations (symbols size is arbitrary and not related to the puff size). Velocity field is a sum of the wind velocity and random, turbulent fluctuations, defined by turbulent intensity.
Fig 3.
Flow chart of the search navigation algorithm.
Fig 4.
Typical paths of a navigator for different turbulent intensities and representative sets of flier coordinates (xm, ym), αs ∈ (30° − 120°).
(a) low 5% turbulence intensity; (b) 15% intermediate turbulence intensity; (c) 30% high turbulence intensity. (d) A typical flight path with symbols showing the detection points of puffs and their identification number.
Fig 5.
Probability of success as a function of increasing turbulent intensity for three different radii around the pheromone source.
Error bars demonstrate the standard deviation of 1000 simulation runs for random initial positions and simulated turbulent flow fields.
Fig 6.
Probability density function of lateral deviation (defined as a sum of all lateral deviations from a straight line between the first and last trajectory points, normalized by the length of the straight line) for different values of turbulent intensity shown in the legend.
Insets shown the average values and the standard deviations of the distributions as a function of turbulent intensity.
Table 1.
Summary of simulation results (average 〈x〉 and standard deviation Sx) for the three levels of turbulent intensity: trajectory length, time of flight, lateral deviations, number of search cycles and number of counter-turns.
The 0.05 (low) turbulence intensity pertains to field or wind tunnel conditions, 0.15 to a typical value in open field atmospheric boundary layer, and the 0.3 (high) turbulent intensity pertains to the air conditions in dense canopy layers, for example, in forests.
Fig 7.
Effect of meandering and gusts on search success for different values of meandering or gusts shown in the legend.
Graphs shown the average values.
Fig 8.
Success rate for a navigation strategy with an internal counter for different values of the counter.
The point at zero is the success rate of a proposed navigation strategy with dynamically counter equal to tc.