## 6 Discussion
Our models confirm that, if a female initially releases limited quantities of pheromone \(m_{\text{P}}\) per puff and the calling time \(t_{\text{call}}\) is brief, only the more motile and chemosensitive males may reach her. Mating likelihoods for moths of lesser quality improve once the amount of released pheromone or calling time increases. We found that the mean first capture and mating times and the mean arrival times can differ by several orders of magnitude, indicating that pheromone-based signaling may help balance the goal of selecting a high-quality male versus the need to mate within a finite time. We find that overall mating likelihood is more sensitive to \(t_{\text{call}}\) than to \(m_{\text{P}}\) but that modulating \(m_{\text{P}}\) allows the female to select for higher quality males with lower pheromone detection thresholds \(C_{\text{tol}}\). If we associate more chemosensitive males with lower \(C_{\text{tol}}\) levels to males with longer antennae, these findings are consistent with experimental observations where doubling the effective titer on a moth trap does not change the overall abundance of captured moths, but the antennae of males captured by single-female traps were observed to be longer than the antennae of males captured by double-female traps ([PERSON] et al. [37]). Simulations using MothPy performed over a 20-s timeframe when males are in close proximity to the female also confirm these findings, as shown in Appendix C.  
Antenna structure is an evolutionary aspect of moth anatomy. While some species display large, branching antennae to maximize surface area, sensilla count, and pheromone detection ([PERSON] et al. [64], [PERSON] et al. [16]), phylogeny shows that a majority of moths have simple non-branching antennae to minimize aerodynamic drag during flight ([PERSON] et al. [64]). In this case, sensilla and scales are carefully arranged so that chemical detection, pheromone retention, and flight capabilities are concurrently optimized ([PERSON] et al. [16]). Greater power and strength allow moths to sustain large antennae and elevated speeds, so that moth body and antenna sizes are often correlated ([PERSON] et al. [37]). Our results indicate that maintaining the same mating probability when pheromone detection thresholds decrease (so that the male is more chemosensitive) requires the male flight speed to decrease. Our models include several simplifying assumptions about moth behavior and interactions. For example, we consider the behavior of many independent males and a single calling female. These models could be expanded to study multiple females simultaneously emitting pheromones and their effects on male selection. Would female-female competition alter the optimal female strategies? There is also evidence that, in some species of moths, female calling attracts conspecific females as well as males ([PERSON] et al. [79]). This may lead to spatial clusters of females, which in turn produce larger aggregate plumes capable of attracting more males and males with higher \(C_{\text{tol}}\). This is another aspect of female-female behavioral interaction that may alter optimal female strategies. While our models assume that females mate only once and that the first male to reach the female mates with her, additional male-male competitive behaviors (e.g., multiple mating and spermatophore displacement) could be incorporated ([PERSON] and [PERSON] [34]). For species that engage in multiple mating, these behaviors may substantially change the selection pressures and female strategies as the last male to mate, rather than the first, would be considered the successful male. Additionally, while our models were built with a general moth in mind, species-specific parameter values could be used in cases where sufficient experimental data is available. When studying the Male Random Flight Model, we made the simplifying assumption for mathematical convenience that the plume is a static circle of radius \(r_{\text{mate}}\).