Modeling Thermal Developmental Trajectories and Thermal Requirements of the Ladybird Stethorus gilvifrons

Simple Summary The ladybird Stethorus gilvifrons is an important natural enemy of herbivorous two-spotted spider mites, Tetranychus urticae. Here, we modeled the effect of temperature, which is the most significant abiotic environmental factor, on the development and thermal thresholds of S. gilvifrons. Thermal parameters and developmental trajectories were estimated by fitting two linear and 20 non-linear models to experimental data measured at seven temperature regimes ranging from 15 to 38 °C. Our findings demonstrate that S. gilvifrons is able to complete development at a broad range of temperatures and is well-adapted to temperatures occurring in temperate, Mediterranean, and subtropical climates. The thermal development models presented here represent a significant step towards an in-depth evaluation of S. gilvifrons as a biological control agent of T. urticae under different temperature regimes. The models can be used to predict the phenology of this predator, to forecast its population dynamics in the field, and to optimize mass-rearing efforts. Abstract The development rate of the predatory ladybird, Stethorus gilvifrons (Mulsant), fed on Tetranychus urticae Koch, was determined at 15, 20, 25, 27, 30, 34, and 38 °C. The total development time from egg to adult emergence for females was estimated to be 61.4, 31.6, 14.4, 13.3, 12.5, and 11.7 days, respectively. The development time decreased with increasing temperature from 15 to 34 °C, but all eggs failed to hatch at 38 °C. The lower temperature threshold (T0) for the entire development period and the thermal constant (K) for female S. gilvifrons were estimated to be 11.64 °C and 194.50 degree-days (DD) using the common linear model, and 11.96 °C and 187.87 DD using the Ikemoto and Takai model, respectively. Data were fitted to 20 non-linear development rate models and the thermal thresholds (Tmin and Tmax) and optimal temperature (Topt) were estimated. Among non-linear models, the Briere-2 and Ikemoto and Takai linear model provided adequate descriptions of the temperature-dependent development of S. gilvifrons. The upper-temperature threshold was estimated to be about 44 °C using the Logan-10 non-linear model. The estimated thermal development characteristics can be used to predict the occurrence and the population dynamics, as well as to improve the mass rearing and release, of S. gilvifrons for the biological control of T. urticae.


Introduction
In recent decades, herbivorous spider mites (Acari: Tetranychidae), such as the twospotted spider mite Tetranychus urticae Koch, which can attack a wide range of crops, have become some of the most important agricultural and horticultural pests worldwide [1,2]. In Table 1. Linear and non-linear models used to simulate the developmental rates of S. gilvifrons at various constant temperatures.

Equation Model
References Ordinary linear regression [35] DT = K + t min D Ikemoto & Takai

Equation Model
Reference Lactin-1 [42] R(T) = e ρ×T − e (ρ×T max −( Tmax −T ∆T ))+λ m Analytis [44,45] R(T) = ax 3 + bx 2 + cx + d Polynomial 3rd order [46] Kontodimas-16 [ Lamb [52] 1 D = a(T − t min ) 2 (t max − T) Equation-16 [37] 1 [55] Using an existing dataset of temperature-dependent development of S. gilvifrons [23], here, our aim was to determine the thermal developmental trajectories and thermal thresholds of all immature stages of S. gilvifrons under semi-natural conditions by using linear and non-linear models. Such models are important by allowing the development of sampling and monitoring methods with simple rules for the timely detection and prediction of the presence and activity of the predators. Moreover, such models can be useful for developing mass-rearing techniques and estimating and comparing the dynamics and population growth of pests and their natural enemies.

Mite and Coccinellid Stock Colonies
The laboratory stock colonies of T. urticae and S. gilvifrons were established two months before starting the experiments with~200 adult individuals of each species collected from two sugarcane fields ( [23]. Tetranychus urticae was reared on young maize plants (Zea mays var. KSC 704), which were grown from seeds in plastic pots (24 cm diameter and 26 cm depth) filled with a mixture of sandy loam, loam, and compost in equal proportions. No pesticides were used during plant growing. All plants were grown in a greenhouse at 27 ± 2 • C, 50 ± 10% RH, and natural photoperiod (~13-15:11-9 h L:D). The predatory beetles were reared in mesh covered aluminum cages (70 × 70 × 120 cm) on maize seedlings infested with spider mites. The cages were kept in the laboratory at 27 ± 1 • C and 50 ± 5% RH and natural photoperiod (~13-15:11-9 h L:D). The colony was maintained by the addition of spider mite-infested maize seedlings at weekly intervals. Additional maize plants were grown to produce leaves used in the life history experiments [23].

Experimental Design
To establish a cohort, twenty pairs of coccinellid females and males were incubated at 27 • C on maize leaf discs (8 cm diameter), with moist cotton pads provided as free water source, which were placed in a transparent plastic container (19 × 14 × 4 cm). Newly laid eggs of S. gilvifrons were individually transferred onto maize leaf squares (4 × 4 cm) resting on slightly moistened cotton pads in plastic dishes (6 cm diameter), which were stored in growth chambers set at 15,20,25,27,30,34, and 38 • C, 50 ± 5% RH and a photoperiod of 16:8 h (L:D). The numbers of individuals (age < 24 h) at the beginning of the experiment were 200, 140, 120, 120, 120, 120, and 120 eggs at the above temperatures. Survivorship and the life stage of each individual at each temperature were checked and recorded daily. The different larval instars of S. gilvifrons were fed daily with T. urticae (about 100 mixed stages) and their life stages were determined based on their body size and the presence of the exuvium, which was used as the criterion of successful molting. Based on the recorded data, the incubation period, and the larval and pupal periods were determined for each individual. In addition, the total developmental time from the date of oviposition to adult emergence was calculated.

The Relationship between Temperature and Developmental Rate
Two linear and 20 non-linear models were examined to find the best-fitting model to describe the relationship between temperature and developmental rate of S. gilvifrons ( Table 1). The common linear model or degree-day (DD) model, which is frequently used to determine the thermal constant (K) and lower temperature threshold, is as follows: where T is the temperature ( • C), D r is the development rate (days −1 ), a is the intercept, and b is the slope. The lower temperature threshold (T 0 ) and the thermal constant (K, degree-days) were estimated using the parameters: T 0 = −a/b and K = 1/b [35]. Ikemoto and Takai [39] proposed another linear model based on the development time formula as follows: (DT) = K + tD where D is developmental time (days), T is the temperature ( • C), t is the lower temperature threshold, and K is the thermal constant. This equation is derived from the common linear model (1). The Ikemoto and Takai linear model represents a straight line with X = T and Y = DT [39]. The twenty nonlinear models (Table 1) were applied to estimate the lower and uppertemperature threshold and optimal temperature for development, each model was evaluated based on the following criteria: 1.
The coefficient of determination (R 2 ). A higher value R 2 indicates better fit.

2.
The residual sum of squares (RSS). A smaller value of RSS indicated better fit. The coefficient of determination and residual sum of the square is commonly used for model evaluation. However, the R 2 value is not appropriate for discrimination between models with a different number of parameters because models with more parameters will provide a better fit. Therefore, we used the Akaike information criterion (AIC) and the adjusted coefficient of determination R 2 adj , which are independent of the number of parameters.

1.
The Akaike information criterion. A good model must explicitly include smaller values of AIC [56,57], where AIC is where n is the number of observations, p is the number of model parameters, including the intercept, and SSE is the sum of squared error.

2.
The adjusted coefficient of determination (R 2 adj ). A higher value of R 2 adj indicates better fit [38]. R 2 adj was calculated from the following equation: where n is the number of observations, p is the number of model parameters, and R 2 is the coefficient of determination or coefficient of nonlinear regression.

Linear Modeling
The raw life history data for the development of S. gilvifrons [23] were analyzed with the age-stage, two-sex life table [58,59] using the computer program TWO SEX-MSChart [60]. The variances and standard errors of the population parameters were estimated by the bootstrap technique [61], with 100.000 re-samplings to obtain stable estimates [62]. Then, paired bootstrap tests were used to examine the differences between the temperature treatments [23].
The relationship between temperature (T) and developmental rate (r = 1/d) for the immature stages was modeled using linear regression, where r(T) = a + bT, within the temperature range in which the relationship is linear (15 to 34 • C). The model was fitted using Microsoft Office Excel 2007. The lower developmental threshold temperature was estimated by extrapolating the regression line to the temperature axis, t b = −a/b. In addition, degree-day estimations for development were calculated using the formula K = (T − t b ) Dev, where K is degree-days, Dev is the mean number of days to complete development at a constant temperature (T), and t b is the lower threshold temperature [63].

Non-Linear Modeling
Temperature-dependent mean rates of development, r(T), were modeled using twenty descriptive nonlinear models ( Table 1). The parameters of the non-linear models were estimated with the non-linear regression model of Marquardt [64] using the JMP (IN 4.lnk) and Excel (version 2007) programs. Lower and upper developmental thresholds were estimated from the equations.

Developmental Time (Data from [23])
The predators completed development from egg to adult at all temperatures examined, except at 38 • C ( Table 2). At 38 • C, all eggs failed to hatch. The duration of the immature stages decreased sharply with increasing temperature. The mean incubation period decreased with increasing temperature up to 34 • C. The developmental period of eggs ranged from 15.7 and 15.7 d at 15 • C to 3.7 and 3.5 d at 34 • C for females and males, respectively. Similarly, the larval period was affected significantly by temperature and the shortest larval period was observed at 34 • C. There were no statistically significant differences between the larval periods at 25 and 27 • C for females and at 25, 27, and 30 • C for males. Pupal development ranged from a mean of 11.8 and 12.1 days at 15 • C to 2.6 and 2.9 days at 34 • C for females and males, respectively.

Linear Models
The common linear model and the Ikemoto and Takai model were applied only to data within the temperature range of 15 to 27 • C since the data at 30 and 34 • C deviated from linearity. Both linear models fitted the stage-specific developmental rate well ( Figure 1) and showed an acceptable fit to data for all immature stages combined. The linear regression equation, the lower-temperature threshold (T min ), and the thermal constant (K) of S. gilvifrons were calculated for each immature stage ( Table 3). Neither of the two linear models provides an optimal temperature or an upper-temperature threshold. The Ikemoto and Takai linear model had higher R 2 and R 2 adj values than the common linear model (Table 3), indicating a slightly higher degree of confidence in parameter estimates provided by the Ikemoto and Takai model. The Ikemoto and Takai model tended to give higher estimates of T min and lower estimates of the thermal constant than the common linear model for egg to pupa development (Table 3). Table 3. Linear regression equations, lower temperature threshold (T min ), and thermal constant (degree-days) of S. gilvifrons immature stages using two linear models.

Linear Model
Stage Thermal Range Linear Equation  Figure 1).
The values of R 2 , RSS, AIC, and R 2 adj used to evaluate the goodness-of-fit for each model showed that Briere-2, with the highest values for R 2 and R 2 adj and the lowest values for RSS and AIC, had the best fit to the development of each immature stage and total immature development, and was thus used to estimate the lower-temperature threshold and the optimal temperature. Logan-10 was used to estimate the upper-temperature threshold. The Briere-1 model had the poorest fit to data among all twenty non-linear models (Table 5).       The values of R 2 , RSS, AIC, and R 2 adj used to evaluate the goodness-of-fit for each model showed that Briere-2, with the highest values for R 2 and R 2 adj and the lowest values for RSS and AIC, had the best fit to the development of each immature stage and total immature development, and was thus used to estimate the lower-temperature threshold and the optimal temperature. Logan-10 was used to estimate the upper-temperature  Table 6. Estimated optimal temperature, temperature thresholds, and models applied to estimate these parameters for different immature stages and total development of S. gilvifrons.

Discussion
This study is the first to model temperature-dependent development and the thermal requirements of the ladybird S. gilvifrons. By providing fundamental information on the thermal biology of this predator, this study may benefit implementation of the use of this predator as biological control agent of spider mites.
The study underlying the modeling presented here [23] demonstrated that the temperaturespecific developmental times of S. gilvifrons are sex-specific. There were small but significant differences between the development times from egg to adult measured for females (61.4, 31.6, 14.8, 13.3, 12.5, and 11.7 days) and those for males (63.2, 28.5, 13.2, 13.4, 12.2, and 12.3 days) at 15,20,25,27,30, and 34 • C [23]. Interestingly, males developed more slowly than females at the extremes, at 15 and 34 • C, but somewhat faster at moderate temperatures 20, 25, and 30 • C. These results slightly differ from the total developmental time estimated by Taghizadeh [20] for S. gilvifrons (56.4, 31.1, 18.5, 17.5, 12.4, and 9.2 days at 15, 20, 2, 2, 3, and 35 • C). Roy [29] reported that S. punctillum successfully developed between 14 and 34 • C, with 68.5 and 12.1 days, respectively, but egg hatching failed at 12 and 36 • C. Jafari [23] showed that the total developmental time of S. gilvifrons on T. urticae at 25 • C was 14.4 for females and 13.2 days for males, whereas Taghizadeh [20] and Aksit [65] observed 18.5 days and 14.6 days at the same temperature. Roy [29] determined this parameter for S. punctillum on T. mcdanieli at 24 • C to be 17.1 days, Shih [66]) for S. loi on T. kanzawai at 23.8 • C to be 15.2 days, Fiaboe [67] for S. tridense on T. evansi at 24 • C to be 17.4 days, Khan and Spooner-Hart [68] for S. vagans on T. urticae at 25 • C to be 13.1 days, and Mori [69] for S. japonicus on T. urticae at 25 • C to be 17.1 days. Apart from species-specific characteristics, differences among these studies might also be due to different rearing techniques and experimental conditions, host plants used in the experiments, prey mite species, photoperiod, along with differences in data analysis. Taken together, the total developmental duration in the range of 25 to 27 • C was 19 to 13 days for both females and males in all the different Stethorus spp. tested [70][71][72][73].
The common linear model [35] has been widely used for its simplicity and suitability to calculate the thermal constant (K) [37,74]. When comparing the two linear models using the R 2 and R 2 adj coefficients, the Ikemoto and Takai model indicated a better fit for the development of all immature stages of S. gilvifrons than the common linear model and was thus used to estimate T 0 and the thermal constant. In line with previous studies, demonstrating a similar lower-temperature threshold in Stethorus spp., no development was observed at 10-12 • C [21,29,67,69], with development starting at around 15 • C among the temperatures tested. Estimation of the lower-temperature thresholds in our study revealed around 12 • C T 0, using the common linear and Ikemoto and Takai models (Table 3). It remains to be shown whether fluctuating temperatures exert different effects to constant temperatures [75] on the development and lower thermal threshold of S. gilvifrons. Pertinent studies on encyrtid and eulophid parasitoids found indeed differences in developmental times and lower thresholds between fluctuating and constant temperature regimes [76,77]. Moreover, the vapor pressure deficit, which changes with temperature at the same ambient relative humidity, might be a factor in temperature-specific developmental rates (e.g., [78]).
The estimated T 0 and thermal constant (11.96 • C and 187.87 DD, respectively) estimated by the Ikemoto linear model for total development (Table 3) were lower than the corresponding values reported for S. gilvifrons (12.47 • C and 222.72 DD) estimated by the common linear model [21].
Most non-linear models used in our study showed a statistically highly significant goodness of fit according to R 2 , R 2 adj, RSS, and AIC values. Therefore, in addition to the above, the temperature-related biological parameters T 0 , T opt and T max were used to select the best model for describing the relationship between the developmental rates of S. gilvifrons and temperature. The Sigmoid, Logan-6, Logan-10, Lactin-1, Janisch, Stinner, Lamb, Polynomial 3rd-order, Sharpe and DeMichele, Taylor, and Bieri-2 models could not be used to estimate T 0 because there was no intersection with the temperature axis ( Table 4; Figure 1).
The Polynomial 3rd-order, Equation-16, Kontodimas-16, and Analytis models overestimated T max for S. gilvifrons in all immature stages and some provided an inaccurate estimation of the lower-temperature threshold. In contrast, the Sigmoid, Lamb, Janisch, Stinner, Sharpe and DeMichele, and Taylor models underestimated T max . The estimated T opt by the Janisch model was lower than the experimental values for all immature stages. Among all non-linear models, the Briere-2 model was the most efficient for the description of temperature-dependent development of the predators regarding T 0 and T opt . The Logan-10 model provided the best estimate of T max (Table 6). Roy [29] determined an optimum temperature of about 30 to 32 • C using the Briere-1 model for S. punctillum. In our study, the optimal temperature for the development of S. gilvifrons was about 33 • C for total development and the upper-thermal threshold varied between 38 and 44 • C depending on the model, which indicates that these predators can thrive under the same broad range of temperatures (15-37 • C) as their prey T. urticae. Several studies have shown that the optimal temperature for T. urticae is around 35 • C and that the lower-and uppertemperature thresholds are about 10 and 38 • C, respectively [79][80][81][82][83]. Afshari [84] reported that S. gilvifrons successfully developed between 35.25 to 37.80 • C during the warm growing season (May-September), in the sugarcane fields of Ahvaz, Southwestern Iran. While these field observations suggested that S. gilvifrons well tolerates higher temperatures (up to 37 • C), our study shows that the upper-temperature threshold estimated by the Logan-10 model lies between 36.97 and 44.03 • C (Table 6), or at about 40 • C, calculated by other non-linear models [21]. In biological control, the estimation of the temperature thresholds, thermal constants, and optimal temperature for the development of natural enemies can substantially contribute to the selection of the most suitable natural enemy to be used under different environmental conditions [6,29,85].
The results of our study indicate that S. gilvifrons can be a promising biological control agent for spider mites over a broad range of temperatures that are common in subtropical and tropical climates. Stethorus spp. are distributed in many different climates, ranging from tropical (S. gilvifrons, S. tridens and S. loi) [20,21,23,65,66] to temperate (S. punctillum, S. japonicus, S. vagans and S. pauperculus) [29,[68][69][70]. All Stethorus spp. occurring in temperate and subtropical climates overwinter in the adult stage, whereas tropical species seldomly enter diapause [15]. Degree-day models developed from constant temperature experiments can be used to predict the emergence of S. gilvifrons in the field. Combining estimates from linear and non-linear models provides for a useful prediction of the first emergence of adult S. gilvifrons during the vegetative season. Undoubtedly, the development rate of S. gilvifrons is also influenced by factors other than temperature, such as nutrition, humidity, and photoperiod, which were not included in the models presented here. The parameter estimates obtained by our models were derived from laboratory studies conducted at strictly defined climatic conditions [23], while in natural and agricultural environments the predators are subjected to more complex and fluctuating conditions. Nevertheless, the models presented here indicate that S. gilvifrons is also a promising candidate for utilization as a biological control agent at more extreme low and high temperatures, as compared to other predators of T. urticae, in terms of temperature tolerance [19,23,[86][87][88][89]. Estimating temperature-dependent development and modeling the thermal requirements of S. gilvifrons is important for creating forecasting models. Understanding its thermal adaptations allows to predict the temporal synchrony with its prey and to choose the best time for releasing the predators under both field and greenhouse conditions.

Data Availability Statement:
The data presented in this study are available on request from the first author (M.J.).

Conflicts of Interest:
The authors declare no conflict of interest.