Comparing the Life Table and Population Projection of Gaeolaelaps aculeifer and Stratiolaelaps scimitus (Acari: Laelapidae) Based on the Age-Stage, Two-Sex Life Table Theory

the Life Table and Population Projection of Gaeolaelaps aculeifer and Stratiolaelaps (Acari: Laelapidae) Based on the Age-Stage, Two-Sex Life Table Theory. Abstract: Predatory soil-dwelling mites, Gaeolaelaps aculeifer (Canestrini) and Stratiolaelaps scimitus (Womersley) (Mesostigmata: Laelapidae), are essential biocontrol agents of small soil arthropod pests. To understand the population characteristics of these two predatory mites, we investigated their development, survival, and fecundity under laboratory conditions. We used Tyrophagus putrescentiae (Schrank) as a food source and analyzed the data using the age-stage, two-sex life table. The duration from egg to adult for G. aculeifer was longer than that for S. scimitus, but larval duration was similar between the two species. Notably, G. aculeifer laid 74.88 eggs/female in 24.50 days, but S. scimitus laid 28.46 eggs/female in 19.1 days. Several population parameters, such as the intrinsic rate of increase, ﬁnite rate of increase, net reproductive rate, and gross reproductive rate of G. aculeifer , were signiﬁcantly higher than those of S. scimitus . Using the bootstrap technique with 100,000 samples, we demonstrated that the life tables constructed based on the 2.5th and 97.5th percentiles of ﬁnite rate of increase ( λ ) net reproductive rate ( R 0 ) may characterize the variability in the survival and fecundity curves, as well as predict population growth uncertainty. These data provide important information for the practical application of predatory soil mites to manage agricultural pests.

The best predators should survive prey scarcity [19], and their populations should be able to survive when the target pest population density is low due to their diverse host range [20]. Furthermore, this ability facilitates rearing on factitious preys, such as the mold mite Tyrophagus putrescentiae (Schrank) (Acari: Sarcoptiformes: Acaridae). T. putrescentiae is

Insect Rearing
The laboratory populations of G. aculeifer and S. scimitus were reared separately following a simple mass-rearing method [42,43]. The two predatory mite species were maintained in two closed plastic boxes (including an inner and outer box) at 25 ± 1 • C, 90% ± 5% relative humidity (RH), and a photoperiod of 16:8 (L:D) h.
The mold mite, T. putrescentiae, was used as prey for both predatory mites. The prey mites were also reared with rice bran as a food source following the same double box system [43].
The two predatory mites were collected from the stock population and reared in Petri dishes (50 mm D × 15 mm H). Cutting a 13.20-mm hole in each lid and covering the hole with a nylon mesh (0.053 mm) allowed ventilation in the Petri dishes. Rice husks (1 cc) were provided as a shelter for the mites in each Petri dish. To maintain constant humidity, water-saturated cotton was placed daily on the hole of each Petri dish ( Figure 1).

Life Table Study of G. aculeifer and S. scimitus
Life table studies were initiated using the egg stages of predatory mites. More than 100 pairs of G. aculeifer and S. scimitus adults were isolated from the mite culture and maintained in the Petri dishes to obtain the egg stages. After 24 h, each newly-laid egg was separated and collected into another Petri dish. Forty-eight G. aculeifer eggs and 41 S. scimitus eggs were used for the life table study. We supplied mixed life stages of T. putrescentiae daily to each Petri dish as prey. The predatory mites' developmental stage and survival rate were monitored every day. Emerged male and female adults of G. aculeifer and S. scimitus were paired, and each pair was transferred to a new Petri dish with new rice husks and prey. Males from the mass-rearing colony were used to mate with females from the life table cohort, since there were more females than males. The mass-rearing colony's males were omitted from the life table analysis, and daily oviposited eggs were recorded and discarded. The survival of each adult was recorded daily until the death

Life Table Study of G. aculeifer and S. scimitus
Life table studies were initiated using the egg stages of predatory mites. More than 100 pairs of G. aculeifer and S. scimitus adults were isolated from the mite culture and maintained in the Petri dishes to obtain the egg stages. After 24 h, each newly-laid egg was separated and collected into another Petri dish. Forty-eight G. aculeifer eggs and 41 S. scimitus eggs were used for the life table study. We supplied mixed life stages of T. putrescentiae daily to each Petri dish as prey. The predatory mites' developmental stage and survival rate were monitored every day. Emerged male and female adults of G. aculeifer and S. scimitus were paired, and each pair was transferred to a new Petri dish with new rice husks and prey. Males from the mass-rearing colony were used to mate with females from the life table cohort, since there were more females than males. The mass-rearing colony's males were omitted from the life table analysis, and daily oviposited eggs were recorded and discarded. The survival of each adult was recorded daily until the death of all individuals. These bioassays were conducted under laboratory conditions at the temperature and RH conditions described in Section 2.1.

Population Projection
The potential population growth of G. aculeifer and S. scimitus on T. putrescentiae was projected according to Chi [50] by incorporating the life table data into TIMING-MSChart [51]. The variability of population growth was projected as described by Huang et al. [49] using life tables representing the 2.5th and 97.5th percentiles, i.e., the 2500th and 97,500th sorted bootstrap results of the net reproductive rate (R0) and finite rate of increase (λ).

Life Table Data Analysis
The population parameters, including the intrinsic rate of increase (r), finite rate of increase (λ), net reproductive rate (R 0 ), mean generation time (T), age-stage-specific survival rate (s xj ), age-specific survival rate (l x ), age-specific fecundity (m x ), adult preoviposition period (APOP) and the total preoviposition period (TPOP), reproductive days (R d ), age-specific maternity (l x m x ), age-stage life expectancy (e xj ), and reproductive value (v xj ), were calculated, according to the age-stage, two-sex life table approach [35,[44][45][46] using TWOSEX-MSChart [47]. Population parameter variances and standard errors were calculated following the 100,000 random resampling bootstrap technique [48]. The differences in population parameters between G. aculeifer and S. scimitus were evaluated using a paired bootstrap test, based on the confidence intervals implemented in the TWOSEX-MSChart [46,47,49]. All graphs were generated using SigmaPlot v.12.5 (Systat Software Inc., San Jose, CA, USA, 2013).

Population Projection
The potential population growth of G. aculeifer and S. scimitus on T. putrescentiae was projected according to Chi [50] by incorporating the life table data into TIMING-MSChart [51]. The variability of population growth was projected as described by Huang et al. [49] using life tables representing the 2.5th and 97.5th percentiles, i.e., the 2500th and 97,500th sorted bootstrap results of the net reproductive rate (R 0 ) and finite rate of increase (λ).

Survival and Developmental Characteristics of G. aculeifer and S. scimitus
We observed that the two predatory mite species could complete development and produce offspring when fed on T. putrescentiae. Table 1 shows the developmental times of each stage, preadult duration, adult longevity, reproductive days, and fecundity of females for the two species. The mean developmental time of the egg stage for G. aculeifer and S. scimitus was 3.71 and 2.89 d, respectively (Table 1). The duration of the egg stage was significantly different between the two species (p < 0.0001). However, no significant differences were observed in the duration of larva (p = 0.2783), protonymph (p = 0.3577), and deutonymph (p = 0.6078) between G. aculeifer and S. scimitus. The preadult duration was significantly longer for G. aculeifer (11.51 d) than for S. scimitus (10.69 d). However, there were no significant differences in preadult survival rate (s a ) between the two species. Female longevity was significantly higher (p = 0.0165) for G. aculeifer (80.31 d) than S. scimitus (69.71 d). However, there were no significant differences in male longevity between the two species (p = 0.1242) ( Table 1). Significant differences were observed in APOP and TPOP between the two predatory mites. The maximum number of reproductive days was recorded for G. aculeifer (24.5 d), which was significantly higher than that for S. scimitus (19.12 d) (p = 0.0288). The fecundity of G. aculeifer (74.88 offspring/female) was also significantly higher than that of S. scimitus (28.46 offspring/female) (p = 0.0285). Standard errors (SEs) were estimated using 100,000 bootstraps. Mean values followed by the same letters in rows are not significantly different between the two species as assessed using the paired bootstrap test at the 5% significance level.

Life Table of G. aculeifer and S. scimitus fed on T. putrescentiae
The age-stage survival rate (s xj ) depicts the probability of whether a newly hatched individual would survive to age x and stage j ( Figure 2). Due to differences in developmental rate among individuals, there was an obvious stage overlap during the developmental period ( Figure 2). The female and male adults emerged at 8 and 10 d, respectively, for S. scimitus (Figure 2). In contrast, female and male adults appeared at 9 and 10 d, respectively, for G. aculeifer (Figure 2). The longer longevity of female adults compared to males could be observed in Figure 2. Figure 3 shows the age-specific survival rate (l x ), female age-specific fecundity (f x5 ) (the female adult being in the fifth life stage), age-specific fecundity (m x ), and age-specific maternity (l x m x ) for G. aculeifer and S. scimitus fed on T. putrescentiae. The l x curve of G. aculeifer was significantly decreased from age 50 d, whereas that of S. scimitus decreased from age 37 d (Figure 3). The parameter, f x5 , is the mean number of fertilized eggs produced by the female adult at age x. The highest peak of f x5 was observed for G. aculeifer fed on T. putrescentiae at age 18 d (f 18,5 = 4.8 eggs). Based on the curve, m x , the highest peaks occurred at age 18 d (with 3.04 offspring) for G. aculeifer, and at age 24 d (with 0.86 offspring) for S. scimitus (Figure 3). Based on both l x and m x , the maximum l x m x value of 3.04 offspring was recorded for G. aculeifer at age 18 d, whereas its value of 0.86 offspring was recorded for S. scimitus at age 24 d (Figure 3).
Life expectancy (e xj ) indicates the length of time an individual of age x and stage j is expected to survive. The curves of e xj of the egg, larva, protonymph, deutonymph, and adult of G. aculeifer fed on T. putrescentiae were higher than those of S. scimitus (Figure 4). respectively, for G. aculeifer (Figure 2). The longer longevity of female adults compared to males could be observed in Figure 2.  Figure 3 shows the age-specific survival rate (lx), female age-specific fecundity (fx5) (the female adult being in the fifth life stage), age-specific fecundity (mx), and age-specific maternity (lxmx) for G. aculeifer and S. scimitus fed on T. putrescentiae. The lx curve of G. aculeifer was significantly decreased from age 50 d, whereas that of S. scimitus decreased from age 37 d (Figure 3). The parameter, fx5, is the mean number of fertilized eggs produced by the female adult at age x. The highest peak of fx5 was observed for G. aculeifer fed on T. putrescentiae at age 18 d (f18,5 = 4.8 eggs). Based on the curve, mx, the highest peaks occurred at age 18 d (with 3.04 offspring) for G. aculeifer, and at age 24 d (with 0.86 offspring) for S. scimitus (Figure 3). Based on both lx and mx, the maximum lxmx value of 3.04 offspring was recorded for G. aculeifer at age 18 d, whereas its value of 0.86 offspring was recorded for S. scimitus at age 24 d (Figure 3). Life expectancy (exj) indicates the length of time an individual of age x and stage j is expected to survive. The curves of exj of the egg, larva, protonymph, deutonymph, and adult of G. aculeifer fed on T. putrescentiae were higher than those of S. scimitus (Figure 4). The life expectancy values of a newly-laid egg of G. aculeifer and S. scimitus were 67.33 and 60.34 d, respectively (Figure 4). Life expectancy (exj) indicates the length of time an individual of age x and stage j is expected to survive. The curves of exj of the egg, larva, protonymph, deutonymph, and adult of G. aculeifer fed on T. putrescentiae were higher than those of S. scimitus (Figure 4). The life expectancy values of a newly-laid egg of G. aculeifer and S. scimitus were 67.33 and 60.34 d, respectively (Figure 4).    Table 2 shows the population parameters of G. aculeifer and S. scimitus. The intrinsic  Table 2 shows the population parameters of G. aculeifer and S. scimitus. The intrinsic rate of increase (r), finite rate of increase (λ), net reproductive rate (R 0 ), and gross reproduction rate (GRR) of G. aculeifer fed on T. putrescentiae were 0.1733 d −1 , 1.1893 d −1 , 47.49 offspring, and 47.53 offspring, respectively. These parameters were significantly higher (p < 0.0001) than the values obtained for S. scimitus (0.1079 d −1 , 1.1139 d −1 , 18.97 offspring, and 22.03 offspring, respectively) ( Table 2). In contrast, the mean generation time (T) obtained for G. aculeifer (22.27 d) was significantly shorter (p < 0.0001) than that for S. scimitus (27.29 d) ( Table 2).

Population Projection
The growth capacities of G. aculeifer and S. scimitus were projected using life table data to demonstrate the increase in the pest population and stage structure during population growth on T. putrescentiae. The population growth and stage structure of G. aculeifer and S. scimitus fed on T. putrescentiae are depicted in Figure 6; the changes in the stage structure can be observed. The fastest population growth was observed for G. aculeifer fed on T. putrescentiae. Starting with 10 eggs, the population of G. aculeifer increased faster than that of S. scimitus fed on T. putrescentiae, which increased slowly ( Figure 6). According to the simulation, after 30 d, the total number of eggs, larvae, protonymphs, deutonymphs, female, and male adults of G. aculeifer was 112, 18, 55, 68, 46, and 29, respectively ( Figure 6). Figure 7 shows the total population sizes of the original cohort and those based on the 2.5th and 97.5th bootstrap percentiles of the finite rate and net reproductive rate, which helps understand the variability of population growth. The population growth rates of G. aculeifer and S. scimitus on T. putrescentiae were different. This could be attributed to differences in developmental time, viability, and fertility among individuals (Figure 7). The total population size of G. aculeifer and S. scimitus reached 76.76 and 27.93 individuals on day 30 when fed on T. putrescentiae, respectively (Figure 7). and S. scimitus fed on T. putrescentiae are depicted in Figure 6; the changes in the stage structure can be observed. The fastest population growth was observed for G. aculeifer fed on T. putrescentiae. Starting with 10 eggs, the population of G. aculeifer increased faster than that of S. scimitus fed on T. putrescentiae, which increased slowly ( Figure 6). According to the simulation, after 30 d, the total number of eggs, larvae, protonymphs, deutonymphs, female, and male adults of G. aculeifer was 112, 18, 55, 68, 46, and 29, respectively ( Figure 6).

Discussion
This study has shown that G. aculeifer had higher fecundity, intrinsic rate of increase, finite rate of increase, and shorter mean generation time than S. scimitus when fed on T. putrescentiae. Preadult survival and reproduction rates of insects on a prey that are higher indicate that the prey is more suitable [52]. Although this prey mite species has been used commercially for rearing G. aculeifer and S. scimitus [9,22], we used the age-stage, two-sex life table technique to compare the fitness traits of these two predatory mite species that feed on T. putrescentiae. The predator-prey interaction, population development, survival,

Discussion
This study has shown that G. aculeifer had higher fecundity, intrinsic rate of increase, finite rate of increase, and shorter mean generation time than S. scimitus when fed on T. putrescentiae. Preadult survival and reproduction rates of insects on a prey that are higher indicate that the prey is more suitable [52]. Although this prey mite species has been used commercially for rearing G. aculeifer and S. scimitus [9,22], we used the age-stage, two-sex life table technique to compare the fitness traits of these two predatory mite species that feed on T. putrescentiae. The predator-prey interaction, population development, survival, and reproduction can all be assessed using life table parameters [53,54].
In a predator-prey relationship, predator fitness is extremely important. It is affected by many factors, such as prey size and density [55,56], environmental factors, i.e., temperature, humidity [57,58], habitat complexity, and internal state of the predator [54,59]. Changes in the developmental rate, survival rate, fecundity, and reproductive age can all be attributed to these factors [60,61]. Our study showed that G. aculeifer and S. scimitus could complete their development and reproduction when fed on T. putrescentiae, but the fitness of these two species differed due to differences in survival, development, and fecundity. S. scimitus was found to be less suited to T. putrescentiae than G. aculeifer due to its prolonged TPOP and preadult length, as well as its lower fecundity and reproductive value. On the other hand, G. aculeifer is more suited and susceptible when fed on T. putrescentiae, because it has longer adult longevity, and life expectancy, higher fecundity, and population parameters (Tables 1 and 2).
Preys have been found to have an impact on the survival and development of numerous insects in previous studies [26,52,62]. Ajvad et al. [41] reported that female and male longevity of G. aculeifer fed on sciarid larvae was 67.7 and 60.3 d, respectively. Kakimoto et al. [63] revealed that the longevity of Orius similis Zheng females and males was 27.2 d and 13.2 d, respectively, compared with that of Orius sauteri (23.8 d and 14.5 d, respectively) when fed with Ephestia kuehniella Zeller. In another study, Asgari et al. [52] reported that male adult longevity (14.46 d) of Amblyseius swirskii Athias-Henriot was shorter than female adult longevity (16.61 d) when fed on T. putrescentiae. The same trend was observed in this study, where the total longevity of female and male adults (80.31 d and 73.33, respectively) of G. aculeifer was increased when fed on T. putrescentiae. Alternatively, the total longevity of females and males of S. scimitus was lower (69.71 d and 64.25 d, respectively) than G. aculeifer. This could be due to the nutritional content or quality of the specific diet/prey, decreased food pressure throughout development, physical defense or response of the prey, more feeding resources [62,64,65], predator preference behavior toward laying eggs [66,67], and complete physiological reactions in the insect body under selection pressure [68].
The life parameters, particularly r and λ, represent the various population features such as the developmental rate, fecundity, survival rate, and the population growth rate together to evaluate the population fitness. This theory supported the present study and showed that G. aculeifer showed higher R 0 , r, λ, and GRR values when fed on T. putrescentiae under our test conditions.
A population projection based on the age-stage, two-sex life table can reveal the change in stage structure during population growth. Understanding stage structure is vital to pest management, because predatory mites' dispersal and damage capability vary with stage. This study demonstrated that such a life table could provide a comprehensive description of predatory mite population's fitness on a given prey. The predicted population growth through time according to the age-stage, two-sex life table data can be described using the stages, as shown in Figure 6. Due to the incapability of traditional female age-specific life tables [31,32,34], to describe the stage differentiation, it would not be possible to show the stage structure, as shown in Figure 6.
We also demonstrated the variability of population growth using computer projections based on the bootstrap percentile confidence intervals. It is the first study to use the life tables of G. aculeifer and S. scimitus to depict the population growth range that is lower and upper 2.5th and 97.5th percentile to the most appropriate level of range for simulation ( Figure 7). The findings revealed that insect populations have a lot of fluctuation and that including the life table variability into population projections is critical.

Conclusions
In conclusion, our study's life table parameters and population prediction analysis demonstrated that G. aculeifer has greater efficiency as a natural enemy than S. scimitus. The obtained results support Hwang et al.'s study [43] indicating that the G. aculeifer population increased to a higher density than that of S. scimitus using a simple mass-rearing method. We strongly promote the use of age-stage, two-sex life table in pest management programs at the age stage to anticipate population growth, stage structure, and possible damage by including stage-specific consumption rates in their control strategies.

Data Availability Statement:
There is no supplementary information to reveal; all information is contained in this manuscript.