## 2. **Moth Mating Mechanisms**
### Male Navigational Strategies  
Male moths from diverse species exhibit a set of well-known navigational behaviors in the presence of female pheromone plumes ([PERSON] [30], [PERSON] and [PERSON] [31], [PERSON] and [PERSON] [32], [PERSON] and [PERSON] [21], [PERSON] et al. [28], [PERSON] et al. [33]). While vertical motion is observed in the presence of trees and thick canopies and under conditions of high moth density ([PERSON] et al. [47]), in most unobstructed cases, males stabilize their flight at a fixed altitude and motion along the vertical axis is limited ([PERSON] et al. [48], [PERSON] et al. [49]). Male moths typically execute planar random walk flights during which their sensilla gather environmental information. Upon detection of a species-specific plume by antennal chemoreceptors, male moths orient upwind using antennal mechanoreceptors, and subsequently cease random flight and surge, flying directly upwind, towards the source.  
Since turbulence of the ambient air makes pheromone plumes intermittent and filamentous, a male moth may lose contact with the plume as it surges toward the female ([PERSON] et al. [20]). Upon loss of pheromone signal, the moth adopts a zigzag trajectory perpendicular to the direction of wind flow at a fixed altitude. This behavior is called casting and is thought to increase the probability that the male moth would recapture the pheromone plume ([PERSON] et al. [50]). If casting is unsuccessful for a given period of time, the male moth resumes random flight.  
Estimates reported in the literature ([PERSON] and [PERSON] [21], [PERSON] and [PERSON] [51], [PERSON] and [PERSON] [52], [PERSON] et al. [48], [PERSON] [53]) lead us to the following male flight speed range and turning rate:  
* _male flight speed_: ranges from 0.5 to 5 m/s
* _male turning rate_: ranges from 3 to 4 turns/s  
Although flight speed and turning rates depend on whether male moths are engaged in a random flight, surging, or casting behavior, we assume that males broadly move and turn within the above ranges at all times. These values lead us to estimate typical random walk diffusivities \(D\sim 1\) to \(10^{-2}\) m\({}^{2}\)/s, as also confirmed by other studies on _Lepidoptera_ diffusivity estimated at \(D\sim 1\) to \(10^{-1}\) m\({}^{2}\)/s ([PERSON] [54], [PERSON] [55]). For transitions between flight modes, the time necessary for males to measure pheromone concentrations is less than 100 ms, while the time to realize that the pheromone plume is lost is estimated as 300-500 ms ([PERSON] [5], [PERSON] and [PERSON] [56], [PERSON] and [PERSON] [57]). Since the typical time spent in any flight mode varies between seconds and hours, several orders of magnitude larger than the above awareness/decision times, we neglect the time lag between transitions. Finally, studies on pheromone-specific receptor neurons reveal that male moth sensilla are able to detect pheromones at very low concentrations, allowing for males to detect the plume at large distances ([PERSON] et al. [58], [PERSON] et al. [59]). If we assume a typical plume length of 2 km and estimate male flight speed at 1 m/s, we can also give the rough estimate of 30 min as the time a male moth spends in the female-generated plume. Most nocturnal male moths begin flying in the evening and until the predawn hours, indicating that male activity normally occurs away from the plume or when searching for it ([PERSON] et al. [60]).