###### Abstract  
Male and female moths communicate in complex ways to search for and to select a mate. In a process termed calling, females emit small quantities of pheromones, generating plumes that spread in the environment. Males detect the plume through their antennae and navigate toward the female. The reproductive process is marked by female choice and male-male competition, since multiple males aim to reach the female but only the first can mate with her. This provides an opportunity for female selection on male traits such as chemosensitivity to pheromone molecules and mobility. We develop a mathematical framework to investigate the overall mating likelihood, the mean first arrival time, and the quality of the first male to reach the female for four experimentally observed female calling strategies unfolding over a typical one-week mating period. We present both analytical solutions of a simplified model as well as results from agent-based numerical simulations. Our findings suggest that, by adjusting call times and the amount of released pheromone, females can optimize the mating process. In particular, shorter calling times and lower pheromone titers at onset of the mating period that gradually increase over time allow females to aim for higher-quality males while still ensuring that mating occurs by the end of the mating period. m 2020 10 6  
the egg, larva, pupa, and adult stages. The length of these periods depends on the specific species, habitat, climate, and available food sources, but in most cases, the adult stage varies between a few days (the yucca and silkworm moths) to a few months (the common brown house moth). A moth's mating period mostly coincides with the adult stage ([PERSON] and [PERSON] [1]). The complex process of searching for a mate for copulation involves male and female moths communicating in complementary ways. Although some repuscular and diurnal species have been identified, most moths are nocturnal. The predominant communication mechanism of nocturnal species is via the release of pheromones by females, termed calling, and the subsequent sensing of these chemical cues by males ([PERSON] [2], [PERSON] et al. [3]). A continuous period of calling is known as a call. During a call, female moths emit pheromone molecules from dedicated glands at the end of their abdomens via short, discrete pulses called puffs that are dispersed in the atmosphere through convective and diffusive motion. Collectively, these puffs define a plume. Typical emission rates are on the order of a few puffs per second ([PERSON] et al. [4]). Male moths detect the female-generated pheromone plumes through sensilla, sensory receptors located on their antennae and follow the scent toward the source ([PERSON] [5], [PERSON] [6], [PERSON] [7]). Due to the great olfactory sensitivity of male antennae, adaptive species-specific pheromone blends can be distinguished from other background, food, or plant odors even at low concentrations, and males are able to follow trails over long distances, up to several kilometers ([PERSON] et al. [8], [PERSON] et al. [9]). The reproductive process is marked by female choice and male-male competition, since typically multiple males aim to reach the female but only the first can mate with her ([PERSON] [10]). This translates into a high opportunity for sexual selection on desirable male traits, such as those regarding body weight, antenna structure, wing length, genital clasper length, and symmetry ([PERSON] et al. [11]). However, maximizing these traits can come at a cost. For example, while larger antennae may be able to detect pheromone more efficiently, there will be more aerodynamic drag during flight and energy limitations due to more neural tissue ([PERSON] et al. [12], [PERSON] [13], [PERSON] et al. [14], [PERSON] et al. [15], [PERSON] et al. [16]). Females utilize several pheromone-producing strategies to maximize benefits and to minimize costs. If too little pheromone is released, the likelihood of being reached by a male is low and the call may result in no mating.