Life history changes in Trogoderma variabile and T. inclusum due to mating delay with implications for mating disruption as a management tactic

Abstract Controlling postharvest pest species is a costly process with insecticide resistance and species‐specific control requiring multiple tactics. Mating disruption (MD) can be used to both decrease a female's access to males and delay timing of mating and decreases overall mating success in a population and population growth rate. Development of new commercially available MD products requires an understanding of life history parameters associated with mating delay. These can provide information for targeting proportions of reproducing individuals using MD. After delaying mating for females of two closely related beetle species, Trogoderma variabile and T. inclusum, we surveyed survivorship, number of eggs laid, and number of progeny emerged. With increases in mating age, total number of eggs laid and total number of progeny emerged significantly declined over time. T. inclusum typically had greater numbers of eggs laid and progeny emerged compared to T. variabile as female age at mating increased, suggesting that T. inclusum may be more resistant to long‐term delays in mating. Life span showed an increase as mating age increased but life span significantly decreased almost immediately following mating. Simulations depicting multiple distributions of mating within a population suggest that in a closed population, high levels of mating delay significantly reduced reproductive growth rates. Although reproductive growth rates were decreased with increased mating age, they are still large enough to maintain populations. This study highlights the differences in life history between two closely related species, suggesting that T. inclusum outperforms T. variabile over the course of a life span, but T. variabile has better reproductive capabilities early in life. MD may also be a viable component of a pest management system for these two species as it significantly decreased overall reproductive output and population growth.

Rather than think of efficacy of MD in terms of whether mating occurs or not, it is more accurate to think of how treatments impact the distribution of times that individuals mate. Complete disruption occurs if mating is delayed to where all individuals die or are no longer reproductively viable. However, under a MD treatment, some individuals may still be able to find each other and mate due to temporal or spatial gaps in treatment (e.g., pheromone concentration) or random encounters. These matings are likely to occur later than under optimal conditions, resulting in a shift in mating times and a corresponding reduction in fitness (Huang & Subramanyam, 2003). Delaying mating has been shown to decrease number of eggs laid, percent of eggs that are fertile, and increase time between mating and egg laying (Jones & Aihara-Sasaki, 2001;Mori & Evenden, 2013;Sgro & Partridge, 1999).
In Indianmeal moths, for example, number of spermatophores per female decreased as mating age increased and egg viability decreased by 22% per day according to female mating age (Huang & Subramanyam, 2003). The combination of effects due to not mating at all and increased age of mating can both contribute to decreasing populations (Cardé, 2007;Jones & Aihara-Sasaki, 2001;Sanders, 1997;Wyatt, 1997). Models of life history outcomes can include different ranges of effectiveness in MD as well as effectiveness of mating delay on multiple generations (Kiritani & Kanoh, 1984).
Populations contain a mixture of mated and unmated females, which can result from physiological receptivity, lack of opportunity, or infertility defects. For example, 26%-28% of Neodiprion setifer females were mated at any given time (Östrand et al., 1999), although specific mechanisms are not known. Flexibility in timing of mating is important for population survival, as availability of mates or competition may delay mating naturally (Carde, 1990;Jones & Aihara-Sasaki, 2001). Many insects have demonstrable optimal mating times (Ellis & Steele, 1982;Kawazu, Shintani, & Tatsuki, 2014;Proshold, Karpenko, & Graham, 1982;Spurgeon, Raulston, Lingren, & Shaver, 1997). For example, Cnaphalocrocis medinalis sex pheromone production increased from ages 2 to 4 days (Kawazu & Tatsuki, 2002) with delayed mating of 7 or 9 days significantly decreasing reproductive output (Kawazu et al., 2014). In comparison, Lymantria dispar mate immediately upon pupal emergence and by 3 days of age, the percent of successful mating significantly decreases (Proshold, 1996). Given that in a population, there is a distribution of mating times for females, understanding how fitness is impacted by time of mating and how a treatment such as synthetic pheromone associated with a MD program can shift this distribution of mating times can provide insight into how much of a shift is needed before population growth is negatively impacted.
Theoretically, effects of MD on a population can shift the distribution of mated females in different ways. Scenario 1 (Figure 2a) follows a distribution where the degree of mating is decreased over time, but there is no shift in timing of mating. This is a possible outcome of a noncompetitive model of MD (Miller et al., 2006b;Stelinski, Miller, & Rogers, 2008) where females are camouflaged by disruption sensory signals that are jamming males' attraction to females, temporarily "removing" males long enough that they die before they mate, decreasing overall numbers of females mated across time. In Scenario 2, optimal mating time is delayed, reducing the number of progeny, but F I G U R E 1 Photographs of Trogoderma variabile and T. inclusum females the number of individuals mating is not reduced. This could occur if it is more difficult for males to find females when a disrupting agent is present due to competitive mechanisms of MD such as false-trail following (Miller, Gut, De Lame, & Stelinski, 2006a;Miller et al., 2006b). In Scenario 3, some males are removed from the population via jammed signaling (noncompetitive), other males experience false-trail following (competitive), but there is still mating that occurs by chance or gaps in MD coverage (i.e., wind current changes). This may occur at large densities of insects where competitive and noncompetitive disruption are often indistinguishable from one another (Miller et al., 2006a(Miller et al., , 2006b and result in both a shift in optimal mating timing and a decrease in the number of mating males. In addition, efficiency of control (Figure 2b) can vary based on different factors that impact effectiveness of MD: for example, number of dispensers, gaps in coverage, nonchemical, or visual location of mates (Levinson & Hoppe, 1983). The inset graph ( Figure 2b) reflects a stable and consistent treatment, where MD provides a predictable and narrow level of control, which could effectively lead to enough control to negatively impact reproductive characteristics (e.g., net reproductive rate) and future persistence of populations.
However, and possibly more realistically, efficiency of control is not as narrow and stable ( Figure 2b) creating distributions where there are enough females still producing progeny that population persistence is not controlled by MD techniques (Jones & Aihara-Sasaki, 2001;Proshold et al., 1982;Spurgeon et al., 1997).
Many dermestid beetle species are important pests of stored food and other materials worldwide and includes the khapra beetle, Trogoderma granarium Everts, which is very destructive and is a quarantine pest in the US (Lindgren & Vincent, 1959;Lindgren, Vincent, & Krohne, 1955;Rees, Starick, & Wright, 2003). Trogoderma variabile Ballion ( Figure 1) is one of the most prevalent and damaging of dermestid species found in the United States (Campbell & Mullen, 2004;Campbell, Mullen, & Dowdy, 2002;Loschiavo, 1960) and is a potential target for the development of MD using sex pheromone as a control tactic. Trogoderma inclusum LeConte ( Figure 1) is a less damaging pest species that can co-occur with T. variabile. The two species have similar life history and demographic patterns, laying similar numbers of eggs with reported life expectancies that mirror one another (Partida & Strong, 1975;Strong, 1975) and are found across North America (Partida & Strong, 1975;Strong & Okumura, 1966), Australia, Europe, and temperate regions of Asia (Rees et al., 2003). A pheromone for T. inclusum is not currently commercially available, but the chemical compound used in T. variabile pheromone lures is also a pheromone component for T. inclusum and some response by T. inclusum to this pheromone component alone has been reported (Greenblatt et al., 1977). In addition, there is a lack of information on mating delay in dermestid beetles (Mori & Evenden, 2013), and this study will provide a foundational basis for application of mating disruption techniques on overall life history and reproductive capacity.
Here, we assessed overall life history characteristics of T. variabile and T. inclusum due to increased female mating age. We predicted that with an increased mating age, both species will have an increase in survivorship but will have decreases in numbers of eggs laid and progeny emerged and that these closely related species will have similar responses to mating age. If they are different, this would suggest that we need to consider specific life history characteristics when examining pest management goals. We also used Leslie Projection Matrices F I G U R E 2 Projected distributions as affected by mating disruption (MD). (a) Theoretical distributions of degree of mated females over time.
The natural distribution of mating over time is represented with a high peak in mating early after eclosion as adults with a tail over time. Scenario 1: MD leads to an overall decrease in number of individuals mating at any given time, that is, noncompetitive disruption. Scenario 2: MD causes a shift in optimal mating time, that is, competitive MD. Scenario 3: a combination of competitive and noncompetitive disruption. (b) Theoretical distribution of females within a population that are mated or unmated. There are three types of distributions of control in terms of mated to unmated individuals (Low, Medium, High control), which could be due to MD, at two different levels of skew (inset, gray; main, black). Inset: distributions are narrower and distinct from one another. As we move to the right along our x-axis, we exclude insects that experience no mating delay (mated). Main graph: broad distributions that include mated and unmated females at any given level of MD  (Leslie, 1945;Stark, Banks, & Acheampong, 2004) and survivorshipand progeny-based population simulations to make projections to future generations of insects. Finally, we used our laboratory data to model different proportions of mated and unmated females in a population to assess more realistic distributions created by MD within a population and the effects on life history characteristics. Pairs of males and aged females, and single female or male controls, were placed in 30-ml shell vials containing 1.75 g of presifted (70 mesh) flour and a 1 cm × 5 cm strip of filter paper and then sealed with a cotton stopper. Insects were transferred every 2 days to a new vial with fresh flour until the female died. Two days after adults were transferred out of the vial, the flour was sifted on a 60-mesh sieve, and eggs were collected and counted. Collected eggs were placed in a 236.6-ml (1/2 pint) mason jar with 20 g of flour and a filter paper lid.

Pupae of
Jars were incubated under the same conditions as stock populations, and adults were counted upon emergence.
For each female mating age group, we summarized data collected for: total number of eggs laid, number of days eggs were laid (oviposition period), and total adult progeny. We calculated life history statistics including survivorship (l x ) for each age class within each female age group, mortality (d x ), daily mortality rate (q

| RESULTS
Total number of eggs laid in a female's life span provides an estimate of their total fecundity potential. Trogoderma variabile and T. inclusum did not differ in total number of eggs laid when females' mating age was 1 or 3 days (p = .18 and p = .094), but T. inclusum laid significantly more eggs than T. variabile when mating age was 2, 4, 5, or 15 days (p ≤ .004; Table S2; Figure 3a-  Total progeny

Trogoderma inclusum Trogoderma variabile
(p = .025; Table 1). For T. inclusum (Table S4), decline in days laying eggs was gradual, with differences starting to occur at 5 days and only a mating age of 29 days being significantly fewer than all other mating ages ( Figure 3b). Trogoderma variabile females showed a similar gradual decline, with mating age of 5 days or more being significantly shorter in duration than a mating age of 1 day (Table S5; Figure 3c).
Total number of progeny provides a measure of whether the viability of eggs is also affected by mating age. The total number of progeny that emerged was significantly different between species and the interaction between mating age and species was significant (p = .0004; Table 1). T. inclusum and T. variabile females did not differ in total number of progeny after mating ages of 1, 3, and 4 days, but for mating ages of 2, 5, and 15 days T. inclusum had a greater number of total progeny (Table S2; Figure 3i-j), with total numbers of progeny being more similar between a mating age of 29 days for T. inclusum and 15 days for T. variabile (Figure 3i-j). Number of total progeny was also significantly different for mating age within each species (Table 1).
For T. inclusum, number of progeny did not change out to mating age of 5 days, but then decreased at 15 days and was lowest at mating age of 29 days (Table S4; Figure 3i). Similarly, females of T. variabile had significantly less total progeny after a mating age of 10 or 15 days compared to mating age of 1-5 days (Table S5; Figure 3j).
To predict the overall effect on population growth due differences in mating age, we calculated life history tables using collected progeny counts and life span data. Survivorship, mortality, daily mortality rate, and mean reproductive output were calculated for every age class for each mating age mating delay time of females (Table S1). Age class is defined as each day where females were placed in new vials and subsequently progeny was counted. Regardless of mating age, females had the highest mean reproductive output (m x ) on the first and second days that they mated. Females also tended to have higher daily mortality rates (q x ) between days 4 and 7 postmating.
Basic reproductive rate (R o ) with upper and lower 95% confidence intervals was also calculated (  Figure 4a-b).
Assessing survivorship of mated compared to virgin beetle estimates how costly reproduction is for these species. For both species, mated beetles had shorter life spans than control, unmated females (p < .0001; Figure 5). Unmated females lived significantly longer than those that were mated at any mating age for T. variabile (p < .0001 for mating ages 1 to 10; p = .0115 for mating age 15). For T. inclusum, unmated females lived longer than mated females (p < .0001), except after a mating age of 29 days when there was no difference in sur-  (Table   S7; Figure 6). This may suggest that T. inclusum has a more robust fecundity when faced with a longer-term mating delay as compared  Figure 4a).
With 80% of the population not mating, R o was 18.4 suggesting that a population with a distribution of mating and nonmating individuals will have a better overall persistence than a population that is all a mating age of 29 days, which is highly unrealistic. However, for T. variabile, a population with 80% of individuals not mating has a similar R o outcome to a population where all individuals are of mating age 15 days (R o = 9.5; Figure 4b). In addition, T. variabile sees a greater decrease in R o values between no mating delay and low mating delay than does T. inclusum, which actually sees a slight increase in R o (Figure 4c-d).

| DISCUSSION
The "Limited" is where most individuals mate without delay. "Low" is where most individuals are delayed 5 days, but there is still significant mating within the population. "Medium" occurs when most individuals are mating at levels of 10 days (T. variabile) or 15 days (T. inclusum) of mating age. "High" refers to a population where the majority individuals are mating at levels that correspond to mating ages of 15 days (T. variabile) or 29 days (T. inclusum). "80%" refers to a population where 80% of the population does not mate; there is some mating but with delays. All simulations are significantly different within and between species females and chance encounters between males and females (Carde, 1990). To achieve a more narrow distribution (Figure 2b, inset) through MD alone may be unrealistic given that the density of pheromone stations would also need to be at unrealistically high levels (Miller et al., 2006b).
In our models, we had a representative percentage of the population that mated at four different levels of mating ages. In pink bollworms, 75% of females were able to mate after less than 1 day delay, only 50% of females were mated at mating age of 5 days (Ellis & Steele, 1982;Lingren, Warner, & Henneberry, 1988;Proshold, 1996) with as few as 23% of females having a spermatophore in Indianmeal moths after a mating age of 5 days (Huang & Subramanyam, 2003).
However in other species such as the European grapevine moth, mating success was not affected at mating age of 12 days, with 96%-100% of females mated, but fertilization success significantly At longer-term delays in mating, T. inclusum is also more resistant to overall effects of delays in mating (Figure 4). Life span could be driving this difference, but T. inclusum also maintains the ability to lay a larger number of viable eggs than T. variabile at 15 days of delayed mating (Table S3; Figure 3). These two factors may go hand-in-hand; an extended life span may ultimately lead to the ability of a species to lay viable eggs for a longer period of time as well as adjust their timing of mating to defer negative impacts of a stressful environment which may lead to mating delays. Further physiological analysis is needed to tease apart the differences between these two species, but our data suggest that different mechanisms may be playing a role in combating exposure to mating delays in these two congeneric species.
Our species comparisons suggest that when applying MD as pest control we must consider individual life history characteristics of each species. Understanding when differences in mating age begin to affect reproductive output could help guide determining how amenable a species would be to MD as a pest management program and also to unmated females. Oviposition time, total progeny, and total eggs laid were significantly reduced as mating age increased, and optimal mating time was similar for both T. inclusum and T. variabile (Table   S1) (Ellis & Steele, 1982;Kawazu et al., 2014;Proshold et al., 1982;Spurgeon et al., 1997). In addition, predation and environmental fac-

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to reductions in egg production (Huang & Subramanyam, 2003) and overall hatchability rates (Kawazu et al., 2014), which could lead to increased variability and population control in populations under mating disruption.
The insects used in this study have been under laboratory culture which could influence the responses observed. Field collected insects often show a broader range of timing of mating than laboratory-reared insects (Huettel, 1976), and other factors occur under field conditions that were not considered in this study, such as previous mating experiences (Adeesan, Rahalkar, & Tamhankar, 1969). Different populations in the field may also have varying levels of heritability and plasticity which may also lead to variation in predicted life history characteristics and may shift our predicted simulation values (Romano et al., 2016). Laboratory-rearing conditions may also influence mating delay comparisons as laboratory conditions are often at the optimal temperature and humidity to promote best reproductive values with no field-induced mortality risks present. In this case, our estimates are most likely higher than what would be found in the field, which provides us with a margin of error for targeting mating delay in field populations, although in some cases, laboratory-reared and field insects have been shown to behave quite similarly (Schwalbe et al., 1974).
Our analyses demonstrate that net reproductive rates of both T. inclusum and T. variabile are significantly affected by increased mating ages but that decreases in R o may not be low enough to control the population through mating delay alone. Using several different methods, we can extend our laboratory data on eggs, progeny, and life span to include modeling population sizes several generations and populations with varying distributions of mated and unmated females. For both species of Trogoderma, populations will persist in high numbers even with mating delays implemented with T. inclusum showing a stronger resistance to longer mating delays that T. variabile. In addition, our models of population-wide mating delay suggest that we need greater than 80% of females do not mate to reach levels of R o that would reflect detrimental effects on future generations. By modeling these population distributions, we can begin to quantify realistic impacts of mating delay due to MD and understand necessary levels of mating delay to manage insect pest populations.

ACKNOWLEDGMENTS
We thank Rich Hammel and undergraduates for collecting data.

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