## 2. **Moth Mating Mechanisms**
### Female Calling Strategies  
The release of pheromone by female moths is known as calling and is characterized by the female raising her abdomen to better disperse pheromone from the scent gland. The subsequent travel of pheromone molecules through the air forms odor plumes that are dispersed by the wind ([PERSON] et al. [38]). For nocturnal species, calling occurs during scotophase, the dark phase of the light-dark cycle, although the timing of calling onset, duration, and pheromone titer varies with species. Adult moths attempt to mate over several days before perishing, depending on their life span. In this section, we identify patterns of female calling and determine ranges of values for calling duration and pheromone titer. We assume a one-week mating period, as typical ([PERSON] [7], [PERSON] and [PERSON] [1]).  
The meta-analysis of [PERSON] et al. [17] reviewed 52 empirical studies of 44 _Lepidoptera_ species and categorized the reported female calling patterns of each. The calling effort was quantified as the time females spent calling males and/or as the amount of female pheromone titer. While most of the studies measured titer as the daily amount of chemicals present in female pheromone glands, a handful of others considered the amount of released pheromone per night. We do not distinguish between the two classifications and pool all reported values into one range. We thus implicitly assume that the amount of pheromone stored in the female body per day is the same as the cumulative amount of pheromone released during her nocturnal call. Note that it is experimentally difficult to measure pheromone ambient concentration and to infer its exact relationship to pheromone gland content ([PERSON] et al. [17]). Furthermore, there is great variability in the amount of pheromone stored and released by females both within a single species and across species and over the spatial extent of a pheromone plume ([PERSON] and [PERSON] [39]).  
Four possible categories of female calling patterns were considered in [PERSON] et al. [17]: _constant_ (the calling effort is the same every night), _increase_ (it is greater each night compared to the night before), _decrease_ (it is less each night compared to the night before), or _hat_ (it increases to a peak amount and then decreases). Among those studies that measured the time that females spent calling, approximately 70% reported that the effort followed the _increase_ pattern, 15% reported the _hat_ pattern, 9% reported the _decrease_ pattern, and 6% reported the _constant_ pattern. For studies that measured pheromone titer, approximately 40% reported that the effort followed the _hat_ pattern, 34% reported the _decrease_ pattern, 16% reported the _increase_ pattern, and 10% reported the _constant_ pattern. Due to variability, our models account for changes in both the time spent calling and the pheromone titer. A schematic is shown in Figure 1.  
Figure 1. Schematic of four female moth calling strategies, expressed as female calling effort over a typical seven night call. Calling effort is quantified as the time females spent calling males and/or the pheromone titer.  
Since our model aims to give a general picture of the dynamics of _Lepidoptera_ moth reproduction without focusing on a single species, we group all relevant estimates reviewed in [PERSON] et al. [17] for calling duration ([PERSON] and [PERSON] [40], [PERSON] and [PERSON] [41], [PERSON] et al. [42]) and pheromone titer ([PERSON] and [PERSON] [41], [PERSON] et al. [42], [PERSON] et al. [43], [PERSON] et al. [44], [PERSON] et al. [45]), to estimate the following:  
* _calling duration_: ranges from 0.5 to 8 h and
* _emitted pheromone_: ranges from 1 to 30 ng per night.  
[PERSON] et al. [46] estimated a pheromone release rate of 14 ng/h, corresponding to approximately 4 pg/s. As discussed above, we use these broad ranges as guiding estimates in our simulations but also consider larger values to capture the variation among species.