## 6 Discussion  
In this work, we studied different sexual selection methods used by female moths to attract males with high-quality traits: faster flight speed/diffusivity and better ability to sense small concentrations of pheromone, i.e., chemosensitivity. Specifically, we considered four experimentally observed calling strategies where the female varies calling times and amounts of emitted pheromone over a one-week period in an attempt to optimize both mating success and quality of the first male to mate. Since male moth navigation and pheromone dynamics typically occur at fixed altitude, we only considered two-dimensional representations. We developed an initial simplified agent-based model (the Male Random Flight Model) where the female-generated pheromone plume is assumed to be static and circular and male moths are assumed to be random walkers before reaching the plume, which allowed us to find analytical estimates for the mean first arrival time. We considered a cohort of \(N\) independent males, with diffusion constant \(D\), who can sense the female-generated plume at a distance \(r_{\text{mate}}\) that started at a distance \(r_{0}>r_{\text{mate}}\) from the female. For a single calling period of fixed duration, the mean first arrival is found to scale as \(\mathbb{E}[t_{\text{a}}]\simeq(r_{0}-r_{\text{mate}})^{2}/(D\ln N)\). We identified \(r_{\text{mate}}\) and \(D\) with male quality: large values of \(r_{\text{mate}}\)  
Figure 13: Simulation results from the agent-based Plume Navigation Model described in Section 5 for \(N=10,\!000\) moths attempting to reach a female calling for \(t_{\text{call}}=8\) h via the continued release of \(m_{\text{p}}=1\) pg per second. (**A**) Contour plot of mean first arrival time \(\mathbb{E}[t_{\text{a}}]\) of males in \(\{C_{\text{tol}},v\}\) phase space. (**B**) Contour plot of the mean arrival time of males in \(\{C_{\text{tol}},v\}\) phase space. Both mean first arrival times and mean arrival times are measured in hours. indicate moths that sense the female at larger distances, and large values of \(D\) indicate moths that can more readily explore the environment. An interesting avenue for future research would be to extend these results to a variety of random walk models such as those analyzed in [PERSON] et al. [77] and in [PERSON] and [PERSON] [78]. We also considered multiple calling periods distributed over seven nights according to an _increase_, _decrease_, _hat_, or _constant_ pattern such that the total possible calling time, which is a measure of effort on the female's part, remains constant across strategies. We find that the optimal calling strategy that minimizes expenditure while maximizing male quality and overall mating likelihood is the _increase_ strategy, as has also been shown by experimental studies. Our more complex agent-based model (the Plume Navigation Model) allowed us to include realistic female-generated plumes that evolve dynamically due to advection by wind and atmospheric dispersion over timescales of several hours. Male navigation is modeled in a more detailed manner: prior to sensing the plume, males are assumed to perform Brownian motion; once the pheromone is detected, they surge upwind toward the female. If the plume is lost, the moth will engage in casting behavior to relocate the plume. At the end of the casting phase, if the pheromone remains undetected, the moth will return to performing Brownian motion, else it will surge toward the female. We used the pheromone detection threshold of male moths, \(C_{\text{tol}}\), and their diffusive velocity \(v\) as proxies for male quality. Finally, we allowed male moths to search for the female plume over realistic periods of up to eight hours per night. Where possible, we used experimental studies to inform parameter values. Ideally, a female reproduces at the beginning of adulthood with a high-quality male; however this may not always be possible and the female may need to adjust her calling strategy to attract males of lesser quality before the mating period ends.