Bioclimatic Thresholds, Thermal Constants and Survival of Mealybug, Phenacoccus solenopsis (Hemiptera: Pseudococcidae) in Response to Constant Temperatures on Hibiscus

Temperature-driven development and survival rates of the mealybug, Phenacoccussolenopsis Tinsley (Hemiptera: Pseudococcidae) were examined at nine constant temperatures (15, 20, 25, 27, 30, 32, 35 and 40°C) on hibiscus ( Hibiscus rosa -sinensis L.). Crawlers successfully completed development to adult stage between 15 and 35°C, although their survival was affected at low temperatures. Two linear and four nonlinear models were fitted to describe developmental rates of P . solenopsis as a function of temperature, and for estimating thermal constants and bioclimatic thresholds (lower, optimum and upper temperature thresholds for development: Tmin, Topt and Tmax, respectively). Estimated thresholds between the two linear models were statistically similar. Ikemoto and Takai’s linear model permitted testing the equivalence of lower developmental thresholds for life stages of P . solenopsis reared on two hosts, hibiscus and cotton. Thermal constants required for completion of cumulative development of female and male nymphs and for the whole generation were significantly lower on hibiscus (222.2, 237.0, 308.6 degree-days, respectively) compared to cotton. Three nonlinear models performed better in describing the developmental rate for immature instars and cumulative life stages of female and male and for generation based on goodness-of-fit criteria. The simplified β type distribution function estimated Topt values closer to the observed maximum rates. Thermodynamic SSI model indicated no significant differences in the intrinsic optimum temperature estimates for different geographical populations of P . solenopsis . The estimated bioclimatic thresholds and the observed survival rates of P . solenopsis indicate the species to be high-temperature adaptive, and explained the field abundance of P . solenopsis on its host plants.


Introduction
Mealybugs (Hemiptera: Pseudococcidae) are important pests worldwide causing economic damage to several crops. The Solenopsis mealybug, Phenacoccus solenopsis Tinsley, first described from New Mexico, USA [1] was reported to infest cotton (Gossypium hirsutum L.) and 29 other hosts in Texas, USA [2]. This invasive species currently has a worldwide distribution spanning Central America, the Caribbean and Ecuador [3], Brazil [4], Pakistan and India [5], China [6], Nigeria [7] and Australia [8]. P. solenopsis is highly polyphagous with a record of 194 host plants [9]. Hibiscus rosa-sinensis L. is an evergreen herbaceous ornamental and landscape shrub, native to China and widely distributed in the tropics and sub-tropics. In the US, hibiscus is a popular flowering plant maintained in greenhouses all over the country [10]. In India, it is a common ornamental plant in the backyards and gardens nurtured for its bright and large flowers as religious offering. Hibiscus is a recorded host for P. solenopsis in Nigeria [7], China [6,11] and the Indian subcontinent [9,12]. As a perennial host, hibiscus appears to play an important role in the population dynamics of P. solenopsis on cotton during the crop season. After harvest of rainy season cotton by December, P. solenopsis survives mostly on alternate hosts such as Abutilon indicum (L.) and Parthenium hysterophorus L. [9]. As these weeds dry up in the hot summer during April-May in the rainfed tracts, P. solenopsis is mostly found surviving on H. rosa-sinensis. With the onset of monsoon rains in June, P. solenopsis population spreads to adjacent weeds that spring up early, and subsequently appears in adjoining fields planted to cotton [13]. Since H. rosa-sinensis is a popular and economically important ornamental species worldwide, and it serves as a host for P. solenopsis during summer time in the Indian subcontinent, the present study on development and survival on hibiscus gains significance.
Temperature is one of the major environmental factors influencing insects. Development, survival, adult longevity and fecundity data are vital for understanding the population dynamics of any insect species on a particular host [14]. Development of the polyphagous mealybug species, Maconellicoccus hirsutus (Green) at the same temperature was different when reared on five different hosts [15]. Understanding phenology of an insect species at different temperatures is crucial for predicting its seasonal occurrence and planning for integrated management. Many mathematical models describe insect developmental rate as a function of temperature [16][17][18][19]. Linear model [20] is widely used to explain the straight line relationship between the developmental rate and temperature in the limited range (15-30°C) and calculate lower developmental thresholds and thermal constants required to complete development of life stages. To describe the developmental rate more realistically and over a wider temperature range, several nonlinear models have been applied [21,22] to provide estimated values for optimum and maximum temperatures for development. However, estimation of thermal constant cannot be achieved by nonlinear models. They usually give a good fit to most experimental data, and many of them incorporate physiological and biochemical constants [16,17,21]. The biophysical explanation for the temperature-development relationship is that enzymes catalyze reactions such as those responsible for development within organisms. Exposure to extreme temperatures affects rates of enzyme activity by changing their conformation, and in some cases denaturing the proteins that regulate the biophysical processes of development, thereby stunting developmental rates [23][24][25].
In this paper, we applied several mathematical functions to describe the developmental rate of P. solenopsis on H. rosasinensis at nine constant temperatures (15 to 40°C). Development of P. solenopsis on cotton was proportional to temperature in the linear portion of the developmental rate curve [26]. We hypothesized a similar relationship on hibiscus and fitted linear models to the developmental rate data in the temperature range of 15-32°C to calculate the lower thresholds and thermal summation values useful to predict timing and phenology of life cycle events of P. solenopsis. As developmental times were longer at the upper temperature (35°C), we applied nonlinear models to describe this relationship and estimate the optimum and upper threshold temperatures for development. Prolific development of P. solenopsis field populations on hibiscus in the hot summer indicated a higher survival at warmer temperatures. We compared our results on the developmental thresholds, thermal constants and survival of P. solenopsis on hibiscus with that on cotton in India [26], on pumpkin and hibiscus in China [11,27]. Better understanding of the life history parameters of P. solenopsis on its key off-season host, hibiscus could provide leads to improve its prediction on cotton during the cropping season.

Mealybug colony establishment
Initial cultures of P. solenopsis collected on cotton (RRS No. 777-792/11, Insect Identification Service, IARI, New Delhi) were maintained for three generations on twigs of H. rosasinensis (bloom -pinkish red, no spots or splashes with eye zone small and red; leaves -semi-glossy, ovate with serrated margins). Different stages of P. solenopsis required for various experiments were drawn from this culture maintained at 27 ± 1°C, 65±5% relative humidity (RH) and 12: 12 h (L:D) photoperiod. In all the experiments, leaves of H. rosa-sinensis were used as host tissue. Fully expanded healthy leaves were excised, wiped with wet tissue and petioles were individually wrapped around with wet adsorbent cotton and placed in petri dishes (9 cm diameter) prior to release of insects. Leaves were changed every 3 to 4 days at 15-30°C and daily at 32-40°C.

Development and survival
Development and survival of P. solenopsis was assessed at 9 constant temperatures: 15, 18, 20, 25, 27, 30, 32, 35 and 40°C (±1°C). For each temperature experiment, 20 mated females (30-35 d old) were transferred individually onto hibiscus leaves in petri dishes, and placed in an environmental growth chamber (MLR 350H, Sanyo, Japan) set at the test temperatures, 65 ± 5% RH, and a photoperiod of 12: 12 h (L:D). Neonate crawlers emerging from an ovisac of a mated female were transferred to a freshly prepared hibiscus leaf in a separate petri dish (10 crawlers/dish) and returned to the set temperature in the growth chamber. Twenty such replicates were maintained for each temperature. Petri dishes were examined daily using a stereomicroscope for shed exuviae which marked the successful completion of the current instar duration. Sex of each nymph was determined at the time of the second molt. From this point onwards, developmental times of males and females were recorded separately in segregated petri dishes. Daily mortality was recorded and instar survival in each replicate was determined as the percentage of surviving individuals at the start of each instar for female nymphs. For males, survival was assessed as the percentage of winged males that emerged from puparia formed at the end of the second molt. Survival from crawler to adult emergence was calculated as the percentage of crawlers that survived to adult stage. The percentage of female adults was calculated as a secondary sex ratio estimate. Preoviposition period was assessed by individually pairing each newly emerged female (<2 d) with 1-2 adult males developed at the same temperature.

Linear models
Two models were evaluated to estimate the linear relationship between ecologically relevant temperatures and the rate of development of P. solenopsis. The first was the thermal summation model [20] which is given by the expression: where, r is the rate of development (=1/ Development time (D) in days), T is ambient temperature ( o C); intercept (a) and slope (b) are the model parameters. Thermal constant, k (= 1/b), is the number of degree-days (DDs) or heat units above the threshold needed for completion of an instar (Table S1). Lower temperature threshold (T min ) was determined as the xintercept (= -a/b) which is the estimated lower temperature at which the rate of development is either zero or no measurable development occurs. Standard error (SE) values of T min and k were calculated as described by Campbell [20]. The second linear model by Ikemoto and Takai [28] is given as: where, DT is the product of the duration of development, D (days), and temperature, T ( o C), k is thermal constant and T min is the lower developmental threshold.

Nonlinear models
Three empirical nonlinear models were fitted to the instar specific developmental rate data to estimate the optimum temperature threshold (T opt ) and upper temperature threshold (T max ). T opt is the threshold temperature at which developmental rate is maximal, while T max is the lethal threshold at which development ceases. Lactin-2 model [21], Briere-1 model [22] and simplified β type distribution function [29] were applied to assess the nonlinear relationship. In addition, a thermodynamic model referred to as the Sharpe-Schoolfield-Ikemoto model (SSI model) was used to estimate intrinsic optimum temperature for P. solenopsis [30]. All the nonlinear models described the relationship between developmental rate (1/D) and temperature (T).
The Lactin-2 model [21] is given by the expression: where, D is the mean development duration in days, ρ is the composite value for critical enzyme-catalyzed biochemical reactions as T increases to T opt , Δ is the difference between T opt and T max when thermal breakdown becomes the overriding influence and λ is a fitted coefficient that forces the nonlinear curve to intersect the x-axis and allows the estimation of lower developmental threshold. Although T max is a parameter in the Lactin-2 model, it does not actually represent the upper temperature at which growth rate equals to zero (the upper developmental threshold). The true developmental threshold predicted by the model can be obtained only by simulation [31]. Thus both T min and T max were numerical approximations obtained as the roots of the fitted model by running the Newton-Raphson algorithm (SAS 9.2). Similarly, T opt was obtained from the Lactin-2 equation by iterating the temperature parameter until the developmental rate was maximized [31].
The Briere-1 model [22] is given by the expression: where, r is the developmental rate as a function of temperature (T), and 'a' is an empirical constant.
The simplified β type distribution function [29] fitted to the data is given by the expression: where k, α and β are model parameters estimated by Marquardt's nonlinear method. In this model, T max and T opt could not be derived directly from the equation as parameters. T max was estimated graphically from the rapid decline of the right descending branch [29] and T opt was derived using optimization [26].
The nonlinear thermodynamic SSI model [23][24][25] is given by the expression: where, developmental rate (r) is a function of temperature, T (in absolute temperature, K) (273.15K = 0°C), R is the gas constant (1.987 cal/deg/mol), ΔH A is the enthalpy of activation of the reaction that is catalyzed by the enzyme (cal/mol), ΔH L is the change in enthalpy associated with low-temperature inactivation of the enzyme (cal/mol), ΔH H is the change in enthalpy associated with high-temperature inactivation of the enzyme (cal/mol), T L is the temperature at which the enzyme is half active and half low-temperature inactive (K), T H is the temperature at which the enzyme is half active and half hightemperature inactive (K), T ϕ is the intrinsic optimum temperature at which the probability of enzyme being in the active state is maximal (K), and ρ ϕ is the mean development rate at the intrinsic optimum temperature (T ϕ ) assuming no enzyme inactivation (day -1 ).

Statistical analysis
Generalized linear model with logit link function was used to model survival data with temperature as a fixed factor. The developmental duration data was checked for normality and found to be positively skewed. Cramer-von Mises and Anderson-Darling goodness-of-fit tests confirmed that the developmental duration data followed the gamma distribution. PROC GLIMMIX was applied to the nested design by assuming temperature as a fixed effect, and female-Id and crawlers nested within female-Id as random effects. Further, mean survival and development durations were separated using the Tukey-Kramer HSD (honestly significant difference) test at 5% level of significance.
Regression (Equation 1) was performed with replicate data using PROC REG to determine linear relationship between developmental rate (1/D) and temperature (T) to obtain a and b as regression parameters. Also the product of duration (D) and temperature (T) was regressed (Equation 2) on duration (D) to obtain T min and k as the regression parameters. The two linear models were tested for significant differences in the estimates of T min and thermal constants for different life stages by nonparametric Wilcoxon Signed Rank test.
PROC NLIN was performed to estimate parameters of nonlinear equation 3 (λ, ρ, T max and Δ) and equation 4 (a, T min and T max ). PROC OPTMODEL was used to estimate the T opt of the fitted models. Similarly, parameters of equation 5 (k, α and β) were estimated using PROC NLIN [32] and were used to derive T opt . The SSI model parameters in equation 6 were estimated by using the OptimSSI function in SSI package version 2.7 in R software using the default option of setting lower developmental threshold as the initial value of T L (optT L = 1). Confidence intervals (95%) for T ϕ were estimated by the modified accelerated and bias corrected bootstrap method [30]. Model performance evaluation of the four nonlinear models was made based on goodness-of-fit statistics: Akaike information criterion (AIC), adjusted R 2 and root mean square error (RMSE). To compare developmental thresholds, thermal constants and survival among geographical populations of P. solenopsis, we extracted mean developmental data from published data sets [11,27]. Each author applied a different model to development duration data making it difficult to compare parameter estimates of different populations. Therefore, we adopted equation 6 to recalculate the lower developmental threshold (LDT, same as T min ) and sum of effective temperature (SET, same as k) for different populations for a meaningful comparison. In one case, we could obtain replicate data sets of development duration at different temperatures from our previous study on cotton from the same laboratory [26] and hence it was possible to test the equality of LDTs and SETs for the local Warangal population on the two hosts: hibiscus in this study with those on cotton using equation 2 through analysis of covariance (ANCOVA) [33][34][35].
Pair-wise comparison of intrinsic optimum temperatures estimated from equation 6 for the same life stage between two geographical populations (data sets from [11,27]) or the local Warangal population on two hosts (this study and data set from [26]) was tested by calculating the 95% confidence interval (CI) of the difference between two groups of bootstrap replications of T ϕ [30]. If the interval of difference contained 0, intrinsic optimum temperatures (T ϕ ) of the first and second population were not statistically different [25].
To know how well the estimated bioclimatic thresholds explained the field abundance of P. solenopsis, we monitored the field incidence of the mealybug regularly on cotton during the crop season and on other hosts during off-season at identified locations in the south-central (18-22° N) and in the northern belt (28-32° N). Daily air temperatures were collected from the nearest meteorological observatory.

Survival
Phenacoccus solenopsis successfully completed its development from crawler to adult emergence at all the temperatures between 15-35°C (Table 1). At 40°C, only eggs were produced which did not hatch. Crawlers were the most susceptible to temperature extremes while second and third instar females exhibited a high degree of survival. In case of male nymphs, no mortality was observed and adult males emerged from puparia at all temperatures (15-35°C). Overall, survival of crawlers to adult emergence was at its lowest (10.2%) at 15°C and at its highest (72.6%) at 32°C. Further, sex ratio in terms of proportion of females was >70% with higher female bias in the lower temperature range.

Development
Temperature significantly influenced the development of P. solenopsis nymphal instars and their cumulative development to adulthood (Table 2). However, maternal influence was not significant when included as a random effect in the analysis. In the temperature range of 15-32°C, developmental duration decreased with increase in temperature for both female and male nymphs. Time spent in each instar was the longest at 15°C and shortest at 32°C. Fastest developmental times were recorded for the second instar in females and pupal instar in

Developmental thresholds and thermal constants
The linear relationship between developmental rate and temperatures in the range of 15 to 32°C for female and male instars and their cumulative development was explained well by both the linear models (R 2 > 0.91, P < 0.0001) except for male pupa (Table 3). However, the linear relationship was much stronger for the combined instars of male prepupa and pupa (data not shown, R 2 = 0.94, P < 0.0001). Equation 2 gave consistently narrower estimates of standard errors of T min for all the instars. Thermal constants (k) estimated from equation 1 were 222.2 and 237.0 DDs compared to 230.4 and 246.7 DDs from equation 2 for cumulative female and cumulative male, respectively. Thermal constants for generation estimated by the two linear models were close (308.6 and 306.3 DDs). Wilcoxon signed rank test revealed that T min (S = 14.5, P = 0.1602) and SET (S=16.5, P = 0.1055) for all individual nymphal instars and their cumulative life stages obtained from linear equation 1 were not significantly different from those obtained from linear equation 2. ANCOVA test confirmed rate isomorphy as the interaction term (development duration × host) was not significant (P > 0.05) for cumulative female (F = 3.51, P = 0.06), cumulative male (F = 0.17, P = 0.68) and for generation (F = 0.02, P = 0.89) ( Table 4). Thus, there was no significant difference in the slopes of equation 2 corresponding to the two hosts, hibiscus and cotton. However, ANCOVA without the interaction term, gave p-values of slopes <0.05. Hence, the thermal constants for these stages of the local population were significantly lower on hibiscus compared to cotton.
The nonlinear relationship between developmental rate and temperature for different life stages of P. solenopsis on hibiscus was fitted well by all the four nonlinear models viz., Lactin-2, Briere-1 and β type distribution function and SSI model by additionally including rates at 35 and 40°C (Figures 1  and 2, Table 5). T min estimated using nonlinear Briere-1 and Lactin-2 models for cumulative female were close to the linear model estimates, but the standard error values of T min provided by Briere-1 model were higher. Optimum temperature (T opt ) thresholds obtained were in the range of 33.9 to 34.6°C from Lactin-2 model, while they were 32.9 to 33.9°C with Briere-1 and 31.  (Table 5) indicating a better fit compared to the other nonlinear models. Lactin-2 and β type distribution function performed better in case of cumulative female (adjusted R 2 = 0.96, RMSE = 0.007 and AIC range = -86.7 to -87.0). In case of the cumulative male, both SSI and Lactin-2 models performed better while for generation, beta type distribution function performed better based on the goodness-of-fit criteria.
Metaanalysis of mean development data by applying SSI model to the published data sets yielded estimates of intrinsic optimum temperature for different geographical populations of P. solenopsis. T ϕ estimates for cumulative development of the female nymphs for the local population was 22.9°C on hibiscus, 22.8°C on cotton; 23.0°C for the Guangzhou population on hibiscus, and 18.7°C for the Zhejiang population reared on pumpkin (Table 6). T ϕ estimates were comparatively higher for cumulative development of male on all the hosts.

Discussion Survival and development
Temperature is the most important environmental factor that influences insect development and survival. Due to its invasive spread to distant places from its origin in USA and ability to survive on different host plants, many recent studies focused on the temperature dependent biology of P. solenopsis populations from different geographical areas. Constant temperature response experiments were used to estimate parameters of phenology models to bring out the thermal differences in development times or their inverse, development rates. However, these studies differed in host plants, constant temperature range and models used. Two studies adopted the widely used equation 1 [11,26], while another study [27] used the logistic model. Few other studies confined their results to application of ANOVA to the developmental duration data of life stages [36,37]. The geographical populations of P. solenopsis showed variation in development time, lower threshold and thermal constant. These differences can be attributed to multiple factors such as experimental conditions, host-plant quality and thermal adaptation to the geographical area [38]. Survival during the life stage is another factor measured in experiments designed to estimate development time using constant temperatures. The resultant observations of survival are typically modal with poorest survival at low and high temperatures [39]. The causes of reduced survival near threshold temperatures can include heat or cold injury as well as bottlenecks when discrete developmental events such as egg hatch or nymphal moult cannot occur. Among mealybug species, P. solenopsis could successfully complete its  Table 4. Results of ANCOVA for testing equivalence of lower developmental threshold (T min ) estimates for the local population of P. solenopsis reared on hibiscus (this study) and cotton [26].  [10] or eggs of M. hirsutus which failed to eclose [41]. However, the survival of P. solenopsis was greatly reduced at this lower temperature.
Males could successfully emerge out of puparia at all the temperatures tested, as observed in another Phenacoccus species, P. madeirensis [40]. Overall survival of crawlers to adult stage was higher on hibiscus at 35°C (Table 1) compared to cotton [26].
Temperature had a pronounced effect on P. solenopsis reared on hibiscus with accelerated development to a maximum rate at 32°C, beyond which it decelerated and ceased at 40°C (Figures 1 and 2). In this study, the average cumulative developmental times for P. solenopsis female nymphs at 20 and 30°C on hibiscus were markedly faster compared to the development on cotton [26] and pumpkin [27] but were closer to those reported on the same host, hibiscus (this study and [11]). Preoviposition period of mated females in this study was 2-3 days shorter on hibiscus compared to     cotton. Observed differences related to the geographical populations and hosts are discussed later on the basis of parameter estimates of linear and nonlinear models.

Evaluation of models
A linear approximation of relationship between developmental rate and temperature gives the most appropriate fit within the quasi-linear range of temperatures [16]. Outside this range, developmental rate deviates from the straight line and hence some data points are to be excluded in the linear fit [17,28,35]. We selected the linear range of 18-30°C (Table 3) after taking into account higher R 2 values, lower survival of crawlers to adulthood at 15°C, and rapid development of instars at 32°C. The data points at 15 and 32°C were excluded while fitting the longest developmental times of P. solenopsis i.e. cumulative female, cumulative male and generation due to low sample numbers at the lower temperature and use of daily observation data in this study even at the higher temperature [42]. Equation 1 is widely used for calculating the lower temperature thresholds [17][18][19] and it is the simplest method for estimation of thermal constant [43]. We employed equation 2 to increase precision of parameter estimates as demonstrated by Iketmoto and Takai [28]. Although, higher R 2 were obtained with equation 2, parameter estimates were statistically similar. Even though there was no apparent advantage with equation 2 over equation 1, the former allowed testing of developmental rate isomorphy for the local population of P. solenopsis on two hosts ( Table 4).
All the nonlinear models described well the developmental rate curve for all the instars and their cumulative development (Figures 1 and 2, Table 5). The fact that the nonlinear models include developmental data from higher temperatures where the relationship is no longer linear is considered an advantage in estimating the theoretical T opt and T max [29]. The advantage of Lactin-2 over the simplified β type distribution function and Briere-1 model was the incorporation of parameters which have a biological interpretation. However, T opt values from Lactin-2 model were slightly overestimated compared to the temperature at which the maximum developmental rate was observed. Simplified β type distribution function gave a more biological reason to prefer it to other models as T opt values were in accordance with the fastest development rates observed at 32°C on hibiscus (Tables 2 and 5) and on cotton [26]. The estimates of T H values from SSI model (Table S2) were lower than the upper lethal temperatures (T max ). This was reflected in the higher survival of nymphal instars and the overall survival of crawlers to adulthood observed at 35°C (Table 1). T H estimates indicated that the enzymes were half active and half inactive between 35.1 and 38.6°C and provided a physiological basis for the nonlinear development observed in different instars at the higher temperatures.
Mated females of P. solenopsis exhibit ovoviviparous reproduction as the crawlers are observed on the same day of egg deposition [26]. As a result, preimaginal development is synonymous with nymphal stage without a distinct egg stage unlike in P. madeirensis [40]. Therefore, we could not apply the rate isomorphy principle where the proportion of time spent in preimaginal developmental stages of a population does not change with temperature [44]. However, if rate isomorphy is common, there should be little variation in the lower developmental threshold between stages within species and populations [25,42] which was found true for the local population of P. solenopsis on two hosts, hibiscus and cotton. However, the local population required significantly lower thermal constants on hibiscus than on cotton. Shorter development times are indicative of better host suitability [15].
Variation in LDTs of the same developmental stage among different geographical populations suggest genetic capacity of a species to shift its thermal sensitivity for adapting to different climatic conditions. LDT tends to vary with the temperature of the niche to which the organism is adapted and there is a trade-off between LDT and SET among conspecifics [42,45]. In this study, we applied the SSI model to recalculate LDT and SET values, and estimated intrinsic optimum temperatures (T ϕ ) from the mean developmental data of geographical populations which permitted statistical comparison of bioclimatic thresholds on different hosts. There were no significant differences in LDT and SET estimates between the Warangal population (this study) and the Guangzhou population [11], both reared on hibiscus (Table S3). However, these values differed significantly with that of Zhejiang population reared on pumpkin [27]. Undue prolongation of developmental times reflected in larger thermal constants for completing life stages suggested that pumpkin is not a suitable host for P. solenopsis. Thermal characteristics among different populations of species may vary with the food source [46]. Further studies may be required to test whether the significantly different LDT estimate of Zhejiang population of P. solenopsis on pumpkin is host induced or reflects a shift in thermal sensitivity to its niche field environment in the higher latitudes (30° N).
The most important parameter estimated by the nonlinear thermodynamic SSI model is the intrinsic optimum temperature (T ϕ ) which is the temperature at which the probability of enzymes being in the active state is maximal [23]. It is considered as the most suitable temperature for an insect to exist and reflects its adaptation to the thermal environment. T ϕ estimated from mean values of developmental rates at different temperatures means that the probability of the enzymes being active for the population is maximal and hence applies to the whole population. Also, T ϕ might be constant for an insect species. This means that among different geographical populations there is presumably no significant difference in this parameter [25]. The pair-wise comparison of the intrinsic optimum temperatures of geographical populations revealed no differences for T ϕ (Table S4), thus, substantiating constancy in T ϕ among geographical populations of P. solenopsis. Intrinsic optimum temperatures of geographical populations of diamond back moth reared on different hosts did not differ and the peak crop damage coincided when the daily average air temperatures equalled or approximated T ϕ [25].
Further, we applied the bioclimatic thresholds to explain the field abundance of P. solenopsis in the south-central cotton growing belt of India. In this tract, cotton is sown during June-July and harvested by December-January. Mean daily air temperatures in the optimum range for maximum development rate (T opt , 32-33°C) estimated from β type distribution function (Table 5) prevailed during summer (April-May). During this period, P. solenopsis was mostly recorded on its alternate host, H. rosa-sinensis. Mean daily air temperatures in the range of 95% CIs of intrinsic optimum temperature (T ϕ, 18.7 to 26.5°C) estimated for cumulative female on hibiscus (this study) from the thermodynamic SSI model (Table 5) prevailed between October and February. Peak abundance of P. solenopsis was recorded on cotton in this window period (October to November). It is inferred that the average air temperatures closer to T opt coincided with the abundance of the mealybug during the off-season on its alternate host, H. rosa-sinensis, while the average air temperatures within the 95% CI of intrinsic optimum temperature coincided with its abundance on its main host, cotton. Abundance of P. solenopsis on cotton is perhaps also aided by the withdrawal of pesticide sprays by farmers towards the crop maturity. The population subsequently shifted to the available alternate hosts after the termination of the cotton crop during December-January. Further, in this south-central cotton belt of India (18-22° N), daily minimum temperatures are >LDT (12.5°C for cumulative female, Table 3) in the coldest month of January and T max (40°C) during the hottest month of May. Similarly, in the northern latitudes (Haryana and Punjab, 28-32° N), minimum temperatures fall below 5°C and daily mean air temperatures are closer to LDT during January, while daily maximum temperatures reach above 40°C during June. Therefore, estimated LDT and >T max thresholds for P. solenopsis could possibly explain the wider annual population fluctuations in the northern belt [47]. However, there are factors other than temperature, such as nutrition, humidity, photoperiod and natural enemies that regulate population dynamics of a species.
Use of ecologically relevant constant temperatures and use of appropriate models in this study on hibiscus made it possible to compare the developmental thresholds of P. solenopsis with those estimated on cotton, its seasonal host [26]. For the local population, we found no significant difference in LDTs between the life stages reared on hibiscus and cotton. The estimates of T opt and T max from the empirical nonlinear models were similar on both the hosts and were closer to the observed rates of development and survival. However, cumulative preimaginal development of female and male nymphs, and generation were much faster on hibiscus and required lower thermal constants (DDs) for completion. Overall, higher values of bioclimatic thresholds (T min , T opt and T max ), lower thermal constants, higher survival rates and shorter preoviposition period at higher temperatures suggest that P. solenopsis exhibits the traits of a high-temperature adapted tropical species [45].
In this paper, we applied the thermodynamic SSI model to the published mean developmental duration data and found no significant differences in LDT and T ϕ estimates for the geographical populations of P. solenopsis on different hosts with the exception of P. solenopsis population on pumpkin. T ϕ estimates for P. solenopsis are within the usual range of predicted intrinsic optimum temperatures (18-23°C) based on development rate for some insects [23][24][25]. We made an attempt to make use of the estimated model parameters (T opt and T ϕ ) to understand the annual cycle of P. solenopsis and its seasonal phenology in the cotton agro-ecosystems of the south-central India. Bioclimatic parameter estimates from this study could be used to map the potential geographical distribution of P. solenopsis. These estimates along with other eco-climatic indices can be used as inputs for simulation modeling [47,48] or as empirical evidence for model validation. Such a method was applied for forecasting of Helicoverpa populations in Australia [49]. Our results suggest that H. rosasinensis is among the preferred off-season hosts for P. solenopsis and supports its development and survival at higher temperatures during summer. This implies that the population regulation of Solenopsis mealybug during summer by periodical monitoring, pruning and destroying of mealybug infested shoot apices on hibiscus is very crucial for its effective management to reduce infestation on cotton in the ensuing season. The world over, hibiscus is an important ornamental plant. Hence, the developmental data of P. solenopsis on hibiscus provided in this study would be useful for monitoring and planning control strategies on this plant and several other crops as well.