Aim, design and setting of the study
To assess how sexual selection dynamics change over the course of a lifetime in a polygamous moth species, we investigated the direct reproductive costs and benefits of multiple matings, as well as the role of sperm competition in reproductive success. To identify the factors that may affect reproductive success, we used two different setups: repeated matings and polygamous matings, following [following 54] and described in detail below (experimental design). Using computer simulations, we also explored differences in absolute reproductive success between males and females. All experiments were conducted between November 2014 and February 2016 in the laboratory at the Institute for Biodiversity and Ecosystem Dynamics, University of Amsterdam.
Description of materials
Populations of H. virescens moths have been laboratory reared at the Institute for Biodiversity and Ecosystem Dynamics, University of Amsterdam, since 2011. The rearings originate from North Carolina, where eggs were first collected from the field in 1988 , supplemented with new field collections over the years, and reared at the Max Planck Institute for Chemical Ecology from 2003 until 2011 (see also [66, 67]).
Larvae were reared individually on artificial pinto bean diet under controlled conditions in a climate chamber (60% relative humidity (RH); 25 degrees C; 14 h light: 10 h dark with lights off at 11.00 am). Pupae were checked daily for eclosion. Newly emerged adults were sexed and placed individually into a plastic cup (37 ml; Solo, Lake Forest, Illinois) with sugar water (cotton soaked with 10% sucrose). In all mating experiments, we used two- to three-day old virgin moths, and pairs were always from different families to avoid inbreeding effects. All experiments were conducted in clear plastic beakers (473 ml; Solo, Lake Forest, Illinois) covered with gauze, so that the moths could be observed but could not escape.
We determined the longevity and lifetime fecundity and fertility of individual moths, making use of the experimental design that compares repeated matings with polygamous matings  to control for the factors partners and matings separately. Bateman gradient is defined as the slope of regression of the number of offspring on the number of mates . To measure Bateman gradients, the data were combined from four treatments in our study. Specifically, four treatments were set up (see Table 1): a) one virgin male or female was placed per beaker and observed for five consecutive nights (treatment 1: no matings, females n = 30; males n = 30), b) virgin individuals were paired with a virgin mate on the first night, after which the sexes were separated into different beakers (treatment 2: mated once, females n = 29; males n = 31), c) individual moths were paired with a new, virgin mate every night for five consecutive nights (treatment 3: polygamous matings, females n= 59; males n = 63), d) individual moths were paired with the same mate every night (treatment 4: repeated matings, females n = 52; males n = 52) for five consecutive nights. To pair the individuals with a virgin mate every night, after each night the couples were separated into different beakers and given a new virgin mate. Individuals paired with different and same mates that died prior to the fifth night were excluded from the analyses (5 females and 2 males in treatment 3, four couples in treatment 4). Female fecundity was defined as the lifetime egg production of a female and female fertility was defined as the total percentage of eggs that hatched. Male fecundity and fertility was measured indirectly by counting the total number of eggs laid and the total percentage of eggs that hatched from his female partners.
Successful copulations were determined as follows. Moths are completely inactive during the daytime and become sexually active at specific hours at night . Heliothis virescens is sexually active between three and 6-7 hours after sunset [44, 45] and matings last on average 3 h . Therefore, for five consecutive nights individual moths of all four treatments were observed every half hour with a red light to note copulating pairs, starting at the onset of the dark period (scotophase), in a climate chamber with the same conditions as described above. As spermatophores are formed during mating and remain in the bursa of the female, the number of successful matings can be determined by dissecting the female at the end of her life [37, 42]. To measure their longevity, all moths from the experiments were kept separately and fed with sugar water (cotton soaked with 10% sucrose) every two days until death. Therefore, after death adult females were dissected under a microscope to count the number of spermatophores inside each female, which was taken as the number of successful copulations.
Effects of mating history
To assess the effects of successful matings with virgin partners or partners with different mating histories, we first determined the number of successful copulations, as described above, after which we assessed the successful mating incidences of males and females in treatments 3 and 4. To evaluate the effect of previous successful male mating history on the reproduction of singly mated females, only the males from the “polygamous matings” (treatment 3) were used, because in the “repeated matings” treatment we could not be sure in which night(s) a male had mated successfully with the paired female (i.e., when a mating resulted in a spermatophore) – we could only ascertain her cumulative mating status afterwards by dissection (see above).
To determine the fecundity of each moth, during the 5 days of the mating experiments, the eggs laid were collected and the moths were transferred into new beakers every day. After the experiments, all eggs from each cup were collected every second day and the number of eggs was counted using a grid under the microscope. Fecundity was calculated as the total number of eggs laid by each female during her life span. Fecundity of males could also be determined in this way, at least in treatment 3, by keeping track of each female that one male had mated with. In this way, we analyzed the fertility and fecundity of females and males that had mated with 0, 1, 2, 3 or 4 previously mated partners.
To determine the number of fertile eggs, the collected eggs were kept in separate cups (250 ml) until the eggs hatched. The number of hatched eggs (i.e., black eggs, which indicate developing larvae, and larvae) were counted 3 days after egg hatch started. Fertility was calculated as the percentage of eggs hatching.
Reproductive success with sperm precedence
Using data from the mating experiments described above and available in the literature, we theoretically investigated various sperm precedence scenarios by modeling the mating dynamics in a population of moths through deterministic calculations. Specifically, we assumed that mating probabilities were proportional to the available males and females in each night, that mating probability deterministically determines mating rate, and that 60 % of the females that mated in one night were available for mating the next night, as was found to be the case in the “polygamous matings” treatment (see Fig. 3b). We assumed relative cumulative reproductive output as a function of the number of matings as fitted for our data (Fig. 3a), and division of reproductive output over days since first mating as measured for singly mated females by Proshold et al. . To determine the effect of remating on reproductive success for males, we used four paternity scenarios: a) 100 % first-male sperm precedence: all offspring is sired by the first male a female mated with, and thus 0 % is sired by any subsequent male, b) 0.33 last-male paternity: fertilization probability of sperm from earlier matings decreases by 33 % each time a female mates with a new male, c) 0.66 last-male paternity, and d) 100% last-male sperm precedence: 100 % of offspring is sired by the last male a female mated with. For females, we assumed that additional matings would result in more offspring as measured in the mating experiment, using the fitted relation between relative offspring production and relative mating success (see Fig. 3a and explanation below).
All statistical analyses were performed in R software version 3.4.1 . Survival analysis was conducted on the longevity data using Cox proportional hazards model (package: survival in R, ). The following covariates and their interactions were considered to be incorporated in these models: treatment, sex, number of matings. These models were simplified using analysis of deviance and AICc criteria. The model that was used to compare the longevity between males and females contained treatment, number of matings and sex without interactions as covariates. A separate Cox regression model was fitted for males and females to investigate the effect of multiple matings and treatment. These models contained treatment and the number of matings without interactions as covariates. To compare the effect of treatment on longevity, we used a Tukey post-hoc test at the 5 % probability level for multiple comparisons (package: multcomp in R, ).
Separate Bateman curves were fitted for males and females. We regressed the number of live offspring on the number of matings (mating success) using linear models. To generate conventional Bateman curves that are comparable to results reported for other species, we only used the data obtained from treatment 3, i.e., individuals receiving a different virgin partner every night for five consecutive nights.
The effects of mating history on fecundity and fertility of singly mated females were analyzed using a generalized linear model (GLM) with a quasi-Poisson distribution (due to overdispersion), where either fecundity or fertility were the dependent variables and the number of previous matings as the independent variable. Tukey post-hoc tests at the 5 % probability level for multiple comparisons were conducted to assess differences between previous male mating histories. To calculate the Coefficient of Variation (CV) in reproductive success, only the data of treatment 3 were used, where individuals received 5 virgin partners on five consecutive nights. The CV in reproductive success was calculated as the ratio of the standard deviation of the number of offspring and the mean number of offspring.