A temperature- dependent phenology model for Apanteles subandinus Blanchard, parasitoid of Phthorimaea operculella Zeller and Symmetrischema tangolias (Gyen)

The potato tuber moth ( Phthorimaea operculella Zeller) is a major invasive pest of po tato ( Solanum tuberosum L.) worldwide. Classical biological control using parasitoids had been of primary interest during the last decades to control this pest. More than twenty parasitoid species have been reported parasitizing P. operculella . Apanteles subandinus Blanchard had been successfully used in different countries. Determination of the para -sitoid's temperature- dependent development is crucial for better predicting the poten tial of the parasitoid to establish in a new region and to control the target pest. Therefore, the effect of temperature on the development and reproduction of A. subandinus was studied at five constant temperatures ranging from 11– 30°C in its main host P. operculella . The Insect Life Cycle Modeling (ILCYM) software was used to fit nonlinear equations to collected life table data and to establish an overall phenology model to simulate life table parameters based on temperature. The parasitoid completed its life cycle at con stant temperatures from 15 to 30°C. Temperature of 11°C was lethal to pupae, and at 35°C no larvae development was possible. The theoretical lower threshold temperatures for the development of egg- larvae and pupae were 10.3°C and 11.8°C respectively. The model predicted limits for survival at around 12°C and 33°C. The lowest senescence rate was observed within the temperature range of 15– 25°C. Oviposition time decreased significantly with increasing temperature from 12.2 days (15°C) to 1.8 days (30°C). The highest fertility was predicted at 27°C. Maximum population growth is expected around 26.78°C with a finite rate of increase, λ of 1.0445, which corresponds to a population doubling time of 15.9 days. The highest values for gross reproduction rate (GRR) and net reproduction rate (R0) were found between 24 and 25°C, and the shortest mean gen eration time (T) was observed at 30°C (23.48 d). The use of the phenology model in the context of classical biological control of P. operculella is discussed.


| INTRODUC TI ON
The potato tuber moth (Phthorimaea operculella Zeller) (Lepidoptera, Gelechiidae) probably originated from tropical mountainous regions of South America. It has become a cosmopolitan invasive potato pest in more than 90 countries worldwide and is reported the most damaging insect pest of potato (Solanum tuberosum L.) in almost all tropical and subtropical regions of the world. The Andean potato tuber moth, Symmetrischema tangolias (Gyen), originated in the mountainous regions of Peru and Bolivia. It is widely distributed at midelevation in the Andes in Colombia, Ecuador, Peru and Bolivia, but its presence has been also reported in Australia, Tasmania, New Zealand and Indonesia (Kroschel & Schaub, 2013). S. tangolias has been shown to be much less invasive than P. operculella, which is adapted to a wider range of agroecological zones and higher temperatures (Sporleder, Schaub, et al., 2016). Chemical control has been the most frequent control method used by farmers worldwide compromising farmer's health (Orozco et al., 2009) and the environment (Devine et al., 2008), although good examples of integrated pest management for potato tuber moths had been developed  and implemented in different countries (e.g. Australia: Peru: Keller, 2003; Republic of Yemen: Kroschel, 1995).
Temperature is one of the most important factors affecting the development, survival and reproduction rates of insect pests and hence strongly determines demographic parameters, which are required for understanding population growth and dynamics, development rates and seasonal occurrence (Bale et al., 2002;Logan et al., 1976;Uvarov, 1931). Detailed temperature effects on the population growth potentials of P. operculella and S. tangolias are wellknown through extensive field and laboratory studies (Keller, 2003;Kroschel & Koch, 1994;Roux & Baumgärtner, 1995). Moreover, temperature-based phenology models have been developed and validated for both pests (Sporleder et al., 2004, Sporleder, Schaub et al., 2016 and used to map the pest's establishment risk and growth potentials in potato regions worldwide under current and future climates influenced by climate change (P. operculella: S. tangolias . For properly planning classical biocontrol programmes based on the use of parasitoids and understanding their potential to establish in new environments as well as to successfully control the target pests, it is important to understand the temperature-dependent development of both the host (pest) and the parasitoid and their possible synchrony of development under different climatic (temperature) conditions. Cardona and Oatman (1975)

| Origin and rearing of A. subandinus
The specimens used in this study were derived from the laboratory colony maintained at the International Potato Center (CIP), Lima, Peru. Although the parasitoid had been originally reported to occur in Peru (Tenorio, 1996;Vera, 1999), it could not be iden- A rearing method for larval parasitoids of P. operculella was established. Reared adults were maintained at 25 ± 1°C, >70% relative humidity and natural photoperiod. Thirty pairs of A. subandinus were placed in a parasitizing chamber (transparent ethylene boxes of a size of 40 × 20 × 20 cm) and fed with a solution of honey and water (in a ratio of 1:2). After 2 days of mating, three slices of potato (variety Yungay) infested with >30 neonate larvae of P. operculella were placed inside the chamber. After 2 days of parasitism, the potato slices were removed and transferred to 0.5-litre plastic containers (between two or three slices per container) and incubated at room temperature until the emergence of A. subandinus adults. After approximately 20 days, developed adults were recuperated by sucking the individuals with an aspirator.

| Origin and rearing of P. operculella
Eggs of P. operculella were obtained from a colony maintained at the International Potato Center (CIP) on potato tubers (variety Peruanita) at room temperature (23-26°C), 60%-70% relative humidity and natural photoperiod. After hatching, neonate larvae were placed in plastic containers (30 × 20 × 7.5 cm) containing potato tuber as food and sand as a pupation medium. Pupae were recovered approximately after 20 days, disinfected in 0.3% sodium hypochlorite solution and placed in oviposition cups (½ litre) covered with cheesecloth. A filter paper on the cheesecloth provided an oviposition site for new adults. Adults were fed with 5% sugar solution dropped on top of the cheesecloth. The filter paper was changed daily, and eggs employed for further rearing or bioassays.

| Experimental procedure and data collection
The effect of temperature on the development and reproduction of A. subandinus was studied in controlled incubation chambers (Thermo Fisher Scientific Inc., MA) at five constant temperatures of 11, 15, 20, 25 and 30°C. Data loggers (Hobo H8, Onset, MA) were used to monitor the temperature conditions. Relative humidity in the chambers was maintained at about 60% by placing containers with water; the photoperiod was kept at 12:12 (L:D) h.

| Development of immature stages and survival
For A. subandinus, observations on successful parasitism and egg development are not possible without the dissection of P. operculella larvae. Therefore, depending on the temperature under study, every 12 hr at 30°C, because development from egg to larva was realized in <12 hr, and every 24 hr at all lower temperatures, 30 larvae were dissected to evaluate and determine parasitism rate and the development of eggs to larvae until all eggs had hatched.
Development of parasitoid larvae could be observed within host larvae by using the stereo microscope. The study was carried out as follows. Two hundred 3-day-old larvae of P. operculella, individually put on small potato squares (1.0 × 1.0 × 0.4 cm), were placed in 8 L containers with 40 pairs of A. subandinus after a period of 1 day of mating. After 12 hr of parasitism at the temperature used for general rearing (25°C), the potato squares were placed in small plastic containers with a volume of 2 cm 3 and stored in incubators at the five constant temperatures. For each temperature, not less than one hundred P. operculella larvae were inspected using the stereo microscope. Larvae were observed until pupation to determine the larval development time as well as to record survival.
When larvae of A. subandinus entered the pupae stage, remaining parts of the potato square were removed, and pupae maintained at the same constant temperature conditions until the emergence of adults. Adult emergence was recorded twice daily to determine development time of pupae and sex. This made it possible to evaluate total immature development time for both males and females of A. subandinus. When the A. subandinus larva was not visible under the stereo microscope, the moth larva was dissected to verify whether it was parasitized. In the life table, egg development time was included in the larva development time (egg-larva).
The experiment was repeated three times.

| Adult longevity
At the day of emergence, adults were sexed, isolated and placed in small glass tubes (10 × 50 mm), with a mesh on top and fastened with a rubber band. Adults were fed with a solution of honey and water in a ratio of 1:2. The glass tubes containing the adults were placed in incubators at the five constant temperatures, and observations on survival time were made daily until all insects had died. The mean survival time was recorded for both sexes, and the inverse of it was plotted against the respective constant temperature.

| Reproduction capacity
At the day of emergence, one female and two males were jointly released in a plastic container of 0.5 L and incubated at the five constant temperatures. Adults were fed with a solution of honey and water in a ratio of 1:2. The provided copulation time depended on the temperature (Table 1). After this period, three potato slices infested with 50 larvae were put in the container and replaced in different time intervals depending on the temperature until the female had died (Table 1). To record the parasitism rate, the larvae were reared under the same temperature conditions up to the emergence of adults of P. opercullela and A. subandinus; the number of female and male parasitoids was recorded. The experiment was also used to record the longevity of mated adults. The experiment had 10 repetitions and was at least three times replicated at the different constant temperatures in time. However, at 11°C, no experiments were carried out due to the mortality of pupae of 100% (

| Model parameterization and analysis
The development of the A. subandinus phenology model and its life  perature and observed development rates (Campbell et al., 1974) using only data points within the linear range (data points at high temperature outside the linear range were deleted

| Mapping suitable release regions
For mapping suitable release regions, we implemented the presented A. subandinus phenology model in ILCYM's potential population distribution and risk mapping module following the methodology described by Sporleder et al. (2017Sporleder et al. ( , 2020 and . For analyzing the potential establishment and efficacy of A. subandinus to control P. operculella in potato regions globally, we used the Establishment Index (EI) and Generation Index (GI), and generated a new index based on the differences in generations (ΔGI = GI parasitoid −GI host ) developed annually by the parasitoid and its host P. operculella in the different potato growing regions.
The three indices are simulated and displayed for potato production regions for which the potential establishment and distribution of P. operculella has been confirmed (i.e. with an Establishment Risk Index [ERI] of >0.7, according to   Figure 1).

| Development rate
Temperature-dependent median developmental rates were well described by the Taylor model (Taylor, 1981) for the egg-larvae stage and the modified Janisch-1 model (Janisch, 1932) for the pupae stage (

| Immature mortality
Mortality showed significant differences among treatments for stages of egg-larvae (F = 1669.1, df = 4, 479, p < .0001) and pupae (F = 2375.3, df = 3, 335, p < .0001). Pupae were the most susceptible immature stages to temperature variation. Egg-larvae mortality was high at extreme temperatures (94% and 100% at 11 and 35°C, respectively), with lowest mortality at 25°C. For pupae, mortality rate was highest at 11°C (100%), and lowest at 25°C (16%) and 20°C (21%) respectively. The total immature mortality had the lowest value at 25°C (44%) and the highest at 30°C (81%). The effects of temperature on the mortality of A. subandinus immature stages egglarvae and pupae were best described by the Wang 1 model (Wang et al., 1982) (Table 4, Figure 3). The model predicted increasing mortality as temperature deviates from the optimum temperature, indicating limits for survival at around 12 and 33°C (Figure 3). where r(T) is the development rate at temperature T; r m (intrinsic rate of increase) is a measure of the rate of growth of a population. This is the instantaneous rate of change (per individual per time interval), assuming the population is in stable age distribution. It is equal to the natural log (In) of the finite rate of increase. T opt is the temperature at which the development rate is at maximum, B and H are the fitted parameters. T roh is a shape parameter giving the spread of the curve. Janish-1: where r(T) is the development rate at temperature T, T opt is the temperature at which the development rate is at maximum, and D min and K are fitted constants. b Numbers in parenthesis are standard errors.

| Adult longevity and fecundity
The sex ratio was highly affected by temperature, with a predominance of males at lower temperature of 15°C (1:6.6 for female:male), and a sex ratio of almost 1:1 at a temperature range of 20°-30°C.
The longevity of adult female and male A. subandinus decreased with increasing temperature (Table 5), with significant differences be-  Hilber and Logan 3 model was fitted to determine the relationship between senescence rates of female adults and temperature, and for male adults, an exponential model was selected (Table 6, Figure 4).
The lowest senescence rates were observed within the temperature range of 15-25°C.
The AFT model revealed a significant effect of temperature on the oviposition time. Median oviposition time decreased significantly with increasing temperature from 12.2 days at 15°C to 1.8 days at 30°C (Table 5). The effects of temperature on fecundity were described by the Wang 10 model with predicted highest fecundity at 27°C (Table 6, Figure 5a). The relationship between temperature and survival time of adult A. subandinus females and males and oviposition rate were best described by an exponential model (

| Life table parameters
Simulations

| Validation of the model
Phenology model validation of A. subandinus was carried out using fluctuating temperature data at a range from 18-33°C, with an average mean temperature of 24.8°C. Simulated population parameters were mostly well predicted when compared with observed data collected under fluctuating temperature. The most significant discrepancy was with the mean generation time (Table 7).

| Suitable release regions
An respectively, indicating an overall good biocontrol potential and capacity of A. subandinus in these regions (Figure 9).
Preliminary studies to understand the effects of temperature on the development of A. subandinus were conducted by Cardona and Oatman (1975 than reported by Cardona and Oatman (1975) and Kfir (1981)

for
A. subandinus. This could be due to the high humidity (>60%) in our study, which negatively affects insect longevity (Emana, 2007;Evans, 1983). According to Roux and Baumgartner (1995) and Lightle et al. (2010) also nutrition can be a possible cause for the reduction of adult longevity and the production of progenies. Sporleder et al. (2004) emphasized that larvae nutrition and light intensity may affect oviposition and adult senescence and may mask the effect of temperature.
In classical biological control programmes for P. operculella, A. subandinus was released as an exotic parasitoid mostly in combination with the encyrtid Copidosoma koehleri and the braconid Orgilus lepidus. The parasitoids established in several countries, but the control efficacy was not consistent among the regions (Cañedo et al., 2016). Understanding the parasitoids likelihood for establishment in new target environments as well as their population growth potential is crucial for effectively planning and implementing classical biocontrol programmes. Failure of biological control programmes has been deeply influenced by climatic factors (Messenger and van den Bosch, 1971). It has been therefore proposed that biological control agents are best obtained from areas where climatic conditions match the areas in which they are to be released (Hoelmer & Kirk, 2005). As a result, climate-matching techniques have been used in biological control to identify climatically suitable regions for biological control agents to be released on invasive alien plants (Byrne et al., 2002;Sutherst et al., 2007). Another approach is the use of complex phenological models, which form a thorough basis for developing deductive species distribution models (Orlandini et al., 2019). This approach is applied in the model builder of the Insect Life Cycle Modeling (ILCYM) software (www.cipot ato.org/ilcym; Sporleder et al., 2013Sporleder et al., , 2020 by the parasitoid and its host]) applied in this study to identify suitable release areas for the parasitoid A. subandinus were only displayed in potato production regions globally for which the potential establishment and distribution of its primary host P. operculella has been confirmed . Good biocontrol agents produce large numbers of offspring, and ideally, parasites complete more than one generation during each generation of the pest (Meyer, 2003  F I G U R E 9 Potential efficacy of A. subandinus to control P. operculella according to model predictions using the differences in the annual number of generations developed by the parasitoid and its primary host (ΔGI = GI parasitoid −GI host ) for the year 2018 and displayed in potato production regions globally for which the potential establishment and distribution of P. operculella is confirmed.

CO N FLI C T O F I NTE R E S T
There is no conflict of interest.

DATA AVA I L A B I L I T Y S TAT E M E N T
Data are openly available in a public repository that issues data-