## 5 Plume Navigation Model
### The Interplay of Calling Time and Pheromone Amount on Male Fitness  
In this section, we consider the full mating problem with a stationary female generating the dynamically evolving plume \(c(\mathbf{x},t)\) presented in Equation (21). The \(N\) independent males seeking the female follow the plume according to Equation (20) and are characterized by a detection threshold \(C_{\text{tol}}\) and a speed \(v\); low \(C_{\text{tol}}\) and large \(v\) represent high-quality males. We study the mating process for a wide range of calling times and released pheromone amounts. In our simulations, the female is located at the origin and the \(N=10000\) non-interacting male moths are initialized \(500\) m downwind of her within a \(100\)-m line perpendicular to the direction of the wind flow as shown in Figure 11B. We assume mating occurs once the male is within \(r_{\text{cap}}=5\) m from the female. Once this distance is reached, the moth arrival time is recorded and the moth is removed from the simulation. Given the relatively large value of \(r_{\text{cap}}\), we do not adaptively change the time step \(\Delta t\) at the boundary of the female-generated plume (as in the simplified model) but keep it fixed. To represent male phenotypic variability, each male is assigned a \(C_{\text{tol}}\) value uniformly sampled in logarithmic space between \(10^{-10}\) and \(10^{-6}\) pg/m\({}^{2}\) and a flight speed \(v\) uniformly sampled between \(0.5\) and \(2\) m/s. Figure 11: (**A**) Schematic of the agent-based Plume Navigation Model as described in Section 5. A stationary female at the origin releases pheromone puffs while male moths fly upwind toward her. Note the capture radius \(r_{\text{cap}}\) and the presence of an advecting wind. (**B**) Representative female pheromone plume and male flight trajectories in our Plume Navigation Model simulations as described in Section 5. To simulate different female calling strategies, calling times \(t_{\text{call}}\) were varied from 1 to 8 h. Within each strategy, the emitted pheromone per puff was kept fixed at \(m_{i}=m_{\text{p}}\) and the puffs were emitted throughout the simulation at the rate of 1 puff per second. The \(m_{\text{p}}\) range we used across strategies was varied between 1 and 10 pg, corresponding to overall emitted pheromone of roughly 2 ng (1 pg emitted over a 30 min call) and 300 ng (10 pg emitted over an 8 h call), exceeding the range of typical values presented in Section 2.1. Each simulation represents one night of calling. Note that, since male moths are independent, concurrently simulating the arrival of \(N\) moths is equivalent to \(N\) simulations to study the arrival of a single moth. Finally, whereas moth quality in Section 3 was represented by \(\{R,D\}\), here, moth-quality indicators are \(\{C_{\text{tol}},v\}\). In Figure 12A, we show how the mating probability (the fraction of the \(N\) males that reach the female for all \(\{C_{\text{tol}},v\}\) values), depends on the calling time \(t_{\text{call}}\) and emitted pheromone \(m_{\text{p}}\). Simulations are run over the maximum calling time \(t_{\text{sim}}=8\) h when the female call ends. We then tally the total number of males that arrived from the onset of the simulation up to time \(t_{\text{call}}\) where \(t_{\text{call}}=1,\ldots,8\) h and compute all relevant statistics associated to \(t_{\text{call}}\), such as mating probability, mean speed, and mean chemosensitivity threshold. The results shown in Figure 12A thus represent cumulative subsamples of the maximum \(t_{\text{call}}=8\) h call. As can be seen, the mating likelihood is much more sensitive to \(t_{\text{call}}\) than to \(m_{\text{p}}\), as it increases only by approximately 10% over a tenfold increase in \(m_{\text{p}}\). This is in agreement with experimental observations where doubling the effective titer on a moth trap does not substantially affect the number of males that are captured ([PERSON] et al. [37]). Figure 12B shows the mean speed of successful males, regardless of \(C_{\text{tol}}\).