Predicting the impact of climate change on the potential distribution of the invasive tomato pinworm Phthorimaea absoluta (Meyrick) (Lepidoptera: Gelechiidae)

Phthorimaea absoluta (Meyrick) (= Tuta absoluta) (Lepidoptera: Gelechiidae), is the most damaging insect pest threatening the production of tomato and other solanaceous vegetables in many countries. In this study, we predicted the risk of establishment and number of generations for P. absoluta in the current and future climatic conditions under two Shared Socioeconomic Pathways (SSP2-4.5 and SSP5-8.5) of the years 2050 and 2070 using insect life cycle modelling (ILCYM) software. We used a temperature-dependent phenology model to project three risk indices viz., establishment risk index (ERI), generation index (GI), and activity index (AI) based on temperature data. The model projected large suitable areas for P. absoluta establishment in the Southern hemisphere under current and future climatic scenarios, compared to the Northern part. However, the risk of P. absoluta is expected to increase in Europe, USA, Southern Africa, and some parts of Asia in the future. Under current conditions, P. absoluta can complete between 6 and 16 generations per year in suitable areas. However, an increase in GI between 1 and 3 per year is projected for most parts of the world in the future, with an increase in AI between 1 and 4. Our results provide information on the risk of establishment of P. absoluta which could guide decision-makers to develop control strategies adapted for specific agro-ecological zones.


The establishment risk index (ERI) of Phthorimaea absoluta
We classified the establishment risk index (ERI) into five classes viz., unsuitable areas (ERI = 0.0-0.2),marginally suitable areas (ERI = 0.2-0.4),suitable areas (ERI = 0.4-0.6),highly suitable areas (ERI = 0.6-0.8)and optimal areas for survival (ERI ≤ 0.8).Overall, most parts of the Southern hemisphere of the world are projected to be highly suitable for P. absoluta establishment compared to Northern hemisphere under both current and future climatic scenarios (Fig. 1).Under the current climatic conditions, the pest could permanently establish (ERI ≤ 0.6) in most parts of sub-Saharan Africa except for the Sahara Desert which is projected to be unsuitable (Fig. 1A).Most countries in South America as well as some countries in Asia (i.e., Thailand, Myanmar, Bangladesh, Indonesia, and Malaysia), showed high or optimal suitability for P. absoluta establishment (Fig. 1A).Globally, under the SSP2-4.5 scenario of the year 2050, the suitable areas under current conditions will remain favorable for the pest's establishment but an increase in suitability is expected in some parts of Africa (e.g.South Africa, Botswana, and Namibia) and the Southern part of Australia (Fig. 1B).Although the optimal areas will dramatically decrease across the globe under the SSP2-4.5 scenario of the year 2050, they will remain highly suitable for P. absoluta to thrive (Fig. 1C).The same trend is projected for the year 2070 under both SSP2-4.5 (Fig. 1D) and SSP5-8.5 (Fig. 1E) scenarios, where ERI will be changing from optimal to suitable or highly suitable in most parts of Africa, South America, and Asia.
In the future, a major decrease in ERI is expected in South America, Central and West Africa, Australia, and Asia (India, Thailand, Myanmar, Cambodia, Philippines, Bangladesh, Indonesia, and Malaysia) under different SSPs for the years 2050 and 2070 (Fig. 2).The ERI is expected to increase by 0.05 under the SSP2-4.5 scenario for the year 2050 in most parts of Europe, the USA, the Middle East, some parts of Mexico and Asian countries (Fig. 2A).ERI might also increase by 0.1 in South America (Chile, Argentina, and Southern Brazil), and Africa (South Africa, Botswana, some parts of Madagascar, Kenya, Tanzania, and Ethiopia) (Fig. 2A) by 2050 under the same scenario.A similar increase is also expected under the SSP5-8.5 scenario for the year 2050 (Fig. 2B) and the SSP2-4.5 scenario for the year 2070 (Fig. 2C) for these countries.However, the highest increase in ERI is projected for the SSP5-8.5 scenario for the year 2070, where the establishment risk of the pest will increase by 0.1 in most parts of Europe, the USA as well as in some African countries (South Africa, Botswana, Namibia,  www.nature.com/scientificreports/Angola, Zambia, and Zimbabwe) (Fig. 2D).Also, an increase in ERI by 0.1 is projected for year 2070 in some parts of Mongolia and China and southern Australia under the SSP5-8.5 scenario (Fig. 2D).
From the total area of 30001150.78km 2 of the African continent, 41.5% (12461040 km 2 ), 25% (7500600 km 2 ), and 18.3% (5504112 km 2 ) are projected, respectively, to be suitable, highly suitable, and optimal for P. absoluta establishment under current climatic conditions (Table 1).Although the suitable areas are projected to decrease in 2050 by 4.7% (1412640 km 2 ) and 7.9% (2364228 km 2 ) under SSP2-4.5 and SSP5-8.5 scenarios, respectively, the highly suitable areas are projected to gain an additional 1121688 km 2 (3.7%) and 10249416 km 2 (9.2%) under the same scenarios, respectively (Table 1).A similar increase is also projected for the SSPs of the year 2070.In Asia, the marginally suitable areas (ERI = 0.2-0.4) will increase between 12.4 and 24%, while the suitable areas (ERI = 0.4-0.6)will increase by 0.2-1.3%depending on SSPs scenarios of the years 2050 and 2070 (Table 1).In Europe, unsuitable areas will be decreasing under all SSPs, and this will lead to an increase in the percentage of marginally suitable and suitable areas in the future.A similar trend is also expected in North America in the future, but the optimal areas are expected to decrease by 1.7% (404676 km 2 ) and 2% (480816 km 2 ) under SSP5-8.5 for the year 2050 and 2070, respectively, from the total area of the continent (24189364.53km 2 ) (Table 1).The optimal areas for P. absoluta establishment are expected to dramatically decrease in South America with a total area of 2108592 km 2 (11.9%) and 5813856 km 2 (32.7%) under SSP2-4.5 and SSP5-8.5 of the year 2050, respectively, and 6146928 km 2 (34.6) and 7327908 km 2 (41.3%) under SSP2-4.5 and SSP5-8.5 of the year 2070, respectively (Table 1).

Generation index of Phthorimaea absoluta
The generation index, which computes the mean number of generations that P. absoluta could complete per year under different climatic scenarios, is shown in Fig. 3.According to the model projection, in South America and sub-Saharan Africa, P. absoluta can complete between 6 and 16 generations per year under the current climatic scenario depending on the location.This situation is also expected in future SSPs but with an increased number of generations in some areas for the two regions (Figs. 3 and 4).However, in most European countries, P. absoluta Table 1.Projected area (km 2 ) for Phthorimaea absoluta establishment risk index (ERI) and the percent of area changes between current and future climatic scenarios for the years 2050 and 2070 under two Shared Socioeconomic Pathways (SSPs) (SSP2-4.5 and SSP5-8.5(SSPs).The asterisk represents the change in areas (gain or loss) between current and future climate scenarios.www.nature.com/scientificreports/can only complete between 3 and 6 generations per year except for Spain, Portugal, and Italy, where the pest can complete between 6 and 9 generations per year (Fig. 3A).Under SSPs of the year 2050, the number of generations per year is expected to increase across Europe, Asia, and the USA (Fig. 3A, B).A similar trend is projected under SSP2-4.5 (Fig. 3C) and SSP5-8.5 (Fig. 3D) scenarios for the year 2070.
The change in the number of generations for P. absoluta between the current and future climatic scenarios is shown in Fig. 4. Due to the expected increase in temperature, an additional one generation per year is predicted in most parts of the world especially Europe, Asia, and North America in the year 2050 under the SSP2-4.5 scenario (Fig. 4A).For the same year, under the SSP5-8.5 scenario, the number of generations of P. absoluta is expected to increase by two more generations per year across Europe, Brazil, and sub-Saharan Africa, especially the Democratic Republic of Congo, Tanzania, Congo, Gabon, Zambia, Malawi, Angola, Namibia, Botswana, South Africa and Cameroon (Fig. 4B).Globally, in the year 2070, the trend of the generation index under the SSP2-4.5 scenario is expected to be similar to that for SSP2-4.5 for the year 2050, except that the pest could produce an additional two generations across Brazil and the Democratic Republic of Congo (Fig. 4C).Similarly, under SSP5-8.5 for the year 2070, P. absoluta generation could increase by two to three generations per year, especially in Europe, sub-Saharan Africa, and some parts of the USA and China (Fig. 4D).

Activity index of Phthorimaea absoluta
The activity index (AI) which indicates the potential population growth rate of P. absoluta throughout the year under current and future climatic scenarios is shown in Fig. 5.Under the current climatic scenario, the potential activity index (AI) of P. absoluta is projected to be high in the tropical and subtropical regions, regardless of the climatic scenario, compared to the temperate regions, such as Europe, the USA, Mongolia, and China (Fig. 5A).
In the year 2050, the AI will remain high in Brazil, Mexico, Venezuela, Colombia, Ecuador, Peru, Bolivia, and Paraguay under both SSP2-4.5 (Fig. 5B) and SSP5-8.5 (Fig. 5C).The same is true for sub-Saharan African countries where AI will remain high under future climatic conditions (Fig. 5B, C).The potential AI of P. absoluta under SSP2-4.5 for the year 2070 is expected to be similar to that of the year 2050 with high AI projected in India, Thailand, Myanmar, Vietnam, Cambodia, Philippines, Bangladesh, Indonesia, and Malaysia (Fig. 5D).However, under SSP5-8.5 for the year 2070, the AI might decrease in Brazil and some parts of Bolivia, Paraguay, and Argentina (Fig. 5E).
The change in AI between current and future climatic scenarios is shown in Fig. 6.An increase in AI by 1 indicates that the population will increase by ten-fold over the current scenario.Overall, the AI is expected to increase between 1 and 4, indicating an increase in P. absoluta population by 10-40-fold per year (Fig. 6).An increase in AI by 1 to 3 is expected in 2050 under both SSP2-4.5 (Fig. 6A) and SSP5-8.5 (Fig. 6B) in most www.nature.com/scientificreports/sub-Saharan African countries, except Somalia, Nigeria, Benin, Ghana, and Ivory Coast, where AI is expected to decrease by 1.In South America, a decrease in AI between 2 and 4 is projected for Brazil, Venezuela, Colombia, Ecuador, Peru, and Bolivia under both SSPs of 2050 (Fig. 6A, B) and SSP2-4.5 for the year 2070 (Fig. 6C).
Most parts of Asia also showed an increase in AI by 2 under the same scenarios with the exception of Thailand, Myanmar, Vietnam, Cambodia, Philippines, Bangladesh, Indonesia, and Malaysia where AI might decrease by 2 (Fig. 6A, B).The highest increase in AI is projected under SSP5-8.5 for the year 2070 in most parts of Europe, Asia, and East and South Africa (Fig. 6D).

Discussion
In this study, we used a complete life cycle of P. absoluta (phenology model) described by Mohamed et al. 31 to predict its establishment and number of generations under current and future climatic scenarios using insect life cycle modelling software.The phenology model calculated the thermal requirement for each developmental parameter including the development time, development rate, mortality rate, fecundity, adult senescence, and the life table parameters that determine the population growth rate.The advantage of this method is that it provides comprehensive information on the effect of temperature on the overall insect growth, and therefore a more accurate prediction of its potential geographical distribution under different climate change scenarios.
Our predictions indicate worsening scenarios of the impact of P. absoluta in Europe, Asia, and South and East Africa under future climatic conditions in terms of establishment, increased number of generations and activity indices, which might lead to more potential damage to tomato and other host crops.Under current climate conditions, our results showed that P. absoluta could permanently establish itself in tropical and sub-tropical regions (ERI ≥ 0.6).Our model prediction closely matches the current distribution of this pest worldwide.For example, P. absoluta has invaded most parts of sub-Saharan Africa, where our model showed ERI between 0.4 and 1.Similarly, some parts of Spain, the country where P. absoluta was first detected following its transatlantic invasion 4,5 , showed high suitability for its establishment (ERI = 0.4-0.6).Also, the outcome of our model prediction for the current scenario was similar to that of Santana et al. 29 .Using a CLIMEX model, the authors projected large suitable areas for P. absoluta establishment in Central and South Americas, Africa, Asia and Australia under the current climatic scenario, where our model also showed high climate suitability for this pest to thrive.Likewise, Desneux et al. 4 projected some parts of Tunisia, Algeria and Morocco in North Africa to be suitable for T. absoluta, which agrees with our findings that showed suitable climate conditions for this pest to establish in these areas under the current climate scenario.
Although our model showed high climate suitability for P. absoluta, in the Central African Republic, Congo, Gabon, Ivory Coast, Liberia, and Sierra Leone, as well as some Asian countries, the pest is yet to be officially reported in these countries 32 .Nonetheless, P. absoluta could spread into suitable uninvaded areas as it was recently reported in Togo 6 , where the model predicted high climate suitability.Contrary to the finding by Tonnang et al. 27 who predicted a high risk of the establishment of the pest across the USA and some parts of Canada under the current situation, our model projected marginal suitability for P. absoluta establishment in these countries except of some parts in Southern USA.The discrepancy between the outcome of the two studies could be explained by the different datasets that were used for prediction.Tonnang et al. 27 used records for P. absoluta occurrence in South America to predict the potential distribution of the pest worldwide.In addition, the authors used thermal requirements for P. absoluta obtained from a degree day model, unlike our study which used a complete phenology model that described the thermal requirements of the complete life cycle of the pest.In fact, the degree day model predicts only the development rate of insect pest, and the use of such model has some limitations.For example, the development rate of insect increases linearly with an increase in temperature until the optimum point, and then, it decreases until reaching the highest thermal threshold for development.However, such an increase in the development rate does not always translate to an improvement in the overall performance for the insect.The optimal temperature for development rate usually leads to high mortality of immature stages, and subsequently lower population growth rate 33 .Unlike the degree day model, the phenology model provides the thermal requirements for a complete life cycle of the pest including development time, development rate, mortality rate, fecundity, adult senescence, and the life table parameters that determine the population growth rate.We considered all these parameters in our study to predict the suitable areas for P. absoluta establishment.Based on our model prediction, under future climatic scenarios (the years 2050 and 2070), the ERI will increase across Europe, North America, Northern Asia, South Australia, and South and East Africa.However, the establishment risk for P. absoluta is expected to be higher under SSP5-8.5 scenario compared to SSP2-4.5.Although our results under current conditions were in line with those reported by Santana et al. 29 , the projected future scenarios were slightly different.For example, Santana et al. 29 , projected West and Central Africa to be unsuitable for P. absoluta under SRES A2 scenario for the year 2050 (= SSP5-8.5),while our results showed a high risk of establishment in these areas.Indeed, P. absoluta has already invaded many countries in West and Central Africa where the pest is currently causing huge damage to small-scale farmers 32 .Similarly, our future projection for India also differed from that of Fand et al. 30 who projected marginal habitat suitability for P. absoluta occurrence using the Maxent model, compared to our model that showed moderate to high suitability for P. absoluta establishment.These discrepancies may be explained by the different climatic datasets used for modelling as Santana et al. 29 used SRES A2 scenario and Fand et al. 30 used A1B emission scenario, compared to SSPs scenarios that we used.In fact, the reliability of future climate projections has some level of uncertainty 34 , thus different climate models may produce different results when used in species distribution modelling.The second explanation for these differences could be attributed to different modelling tools that were used by these studies which have different levels of complexity in their fitting.
Compared to the tropical regions, the projected ERI for P. absoluta in the temperate region is relatively low (ERI = 0.2-0.4),although the pest is present in part of this region causing severe damage to tomato crops 27,35 .This is mainly attributed to the extreme temperature variation within the year in temperate regions which limits the survival of immature stages for a few months.Our prediction indicates that all life stages of P. absoluta could survive between 3 and 5 months per year in Europe and other temperate regions.In this region, the lower temperature reaches below zero degree Celsius in winter, which is not conducive for the survival of P. absoluta.However, some studies revealed that the pest goes into diapause during winter and successfully passes the harsh environmental conditions [8][9][10]36 , and this explains the occurrence of the pest in temperate regions.
The present study showed that P. absoluta could complete 3-16 generations per year, depending on the environmental conditions.A study by Abolmaaty et al. 37 predicted 11-13 generations per year under open field conditions in Egypt using a degree-day accumulation model.This agreed with our results that showed P. absoluta can produce between 9 and 13 generations per year in Egypt under current conditions.Martins et al. 38 reported 17 generations per year at a constant temperature of 33 °C, while de Campos et al. 9 argued that the pest could complete between 6 and 9 generations per year in Mediterranean Basin under a warmer temperate climate, which also is in line with our findings.Our model also predicted an increase in the number of generations per year in many locations under future climatic conditions.For example, an additional 2-3 generations per year are expected by the years 2050 and 2070 in most parts of Europe, Africa, Asia, and South America.This is mainly due to the expected temperature rise, as a result of global warming, which will lead to a shorter developmental time of P. absoluta, hence more generations per year.
The AI, which is computed based on the finite rate of population increase (λ), served as a good indicator of the potential population growth rate and it signifies the spread risk and severity of the insect pest.Under current conditions, AI ranged between 2 and 20 in areas where P. absoluta could well establish and cause damage.This was similar to AI of closely related species Phthorimaea operculella in potato production areas worldwide which ranged between 1 and 24 17 .However, under future scenarios, this index will increase by 2-4 in most parts of sub-Saharan Africa, Asia, and Europe.This implies that the populations of P. absoluta will increase by 20-40-fold per year in these areas under future conditions if the temperature is considered to be the only factor that affects the pest population.As the number of generations for P. absoluta increases, the population abundance and damage (AI) for the pest is also increasing.Thus, the increase in the number of generations within the cropping season or year as a result of climate change may aggravate the risk of P. absoluta under future climatic conditions, thus causing more damage to the crops.
The change in temperature significantly affects the distribution, abundance, reproductive success and establishment of the insect pest 18,20 .Therefore, the increase in temperature as a result of global warming may have a serious effect on the potential distribution and spread of P. absoluta toward new areas and this might lead to huge crop losses.In this regard, our study could serve as an early warning tool that could guide policy makers to prevent the future spread of P. absoluta into new areas and curb the current invasion through the development of effective phytosanitary measures and efficient control strategies.Identification of suitable regions that are at high risk of invasion by P. absoluta is very important for pest surveillance and monitoring.Therefore, our results will be useful for regulatory bodies such as national plant protection, particularly in uninvaded countries to determine pest risk analysis areas to prevent the invasion of P. absoluta and safeguard future spread.

Model limitations
In this study, we provided predictions that used a combination of temperature data and P. absoluta physiological parameters.Our model accurately predicted the current distribution of the pest as the real-world records of P. absoluta distribution closely aligned with our findings.However, one of the limitations of the current study is that the results obtained are based only on temperature as a factor influencing the distribution of P. absoluta and it does not consider other factors such as host plant, natural enemies, rainfall, and relative humidity.Also, the model does not consider the areas in which the climatic conditions could be artificially changed such as the use of greenhouses.This is very important for countries such as North America, where about 20% of the crop is produced in greenhouses 39 .An important observation is a discrepancy between models' outputs.In this regard, we propose an ensemble approach that combines features and skills obtained from the individual modeling methods.Therefore, a "generalizer" meta-mapping that learns from a weighted combination of the key intrinsic features embedded in each suitability map could be applied to improve accuracy relative to any individual map obtained from a single model.

Modelling tool
In this study, we used insect life cycle modelling (ILCYM version 3.0) tool 17,20 to predict the future distribution and number of generations of P. absoluta under different climatic scenarios.ILCYM consists of three modules, namely the model builder module, the validation and simulations module, and the population analysis and mapping module that is used to study the population ecology of insect pests 20 .The model builder contains several empirical linear and nonlinear functions that are used to predict the effect of temperature on insect developmental time, developmental rate, mortality rate, oviposition and adult longevity based on life table data collected at different constant temperatures.These functions are known as phenology models or process-based models, and they are used to determine the relationship between temperature and insect development.The validation and simulations module in ILCYM compiles the all the function in one phenology model that is used to estimate the life table parameters that determine the population growth rate of insect pests under both constant and fluctuating temperatures.This module also validates the phenology model using life table data of the insect pests collected under fluctuating temperatures.Finally, the population analysis and mapping module links the phenology model with geographical information system (GIS) platforms that allow spatial simulations and estimation of the pest risk indices based on insect life cycle and temperature data 17,20 .In our previous study by Mohamed et al. 31 , we used model builder and validation and simulations modules to construct, simulate and validate the temperature-dependent phenology models of P. absoluta.In the current study, we complied these models and used them in the population analysis and mapping module in ILCYM to spatially predict three risk indices of P. absoluta including establishment risk index (ERI), generation index (GI), and activity index (AI) of P. absoluta.

Temperature-dependent phenology model for Phthorimaea absoluta
A temperature-dependent phenology model for P. absoluta developed by Mohamed et al. 31 was used to predict three risk indices of the pest viz., ERIGI, and AI, under current and future climatic conditions.The phenology model was developed in ILCYM (version 3) 20 using life table data of P. absoluta collected in the laboratory at five constants temperatures of 15, 20, 25, 30, and 35 °C (Fig. 7).The developed model consists of a set of mathematical functions that were used to describe temperature dependency of development time, development rate, and mortality rate of P. absoluta immature stages as well as female fecundity and adult senescence (see Mohamed et al. 31 for more details about the functions).These functions include the complementary log-log (CLL) fitted to the normalized development time of egg and pupal stages as well as female and male longevity; logit function fitted to the normalized development time of larval stage; Sharpe and DeMichele function 1 40 fitted to the development rate of egg and larva; Briere function 1 41 fitted to the development rate of pupa, Wang function 1 42 fitted to the mortality rate of all immature stages; Exponential modified function 3 fitted to cumulative fecundity; Taylor function 1 fitted to mean fecundity of the female, and Exponential simple function fitted the male and female senescence.These functions were compiled (phenology model) and validated with life table data collected from a study conducted under fluctuating temperatures (Fig. 7) (see Mohamed et al. 31 for more details).The model predicted that a temperature range between 20 and 25 °C is optimal for P. absoluta immature stages development in which high population growth is occurring with an intrinsic rate of increase ranging between 0.09 and 0.13 31 .

Temperature data
Monthly minimum and maximum temperature data (2.5 arcmin) were obtained from WorldClim database (http:// www.world clim.org/) and used to estimate the risk indices of P. absoluta under current and future climatic scenarios.To simulate the risk under the current scenario, we used interpolated historical temperature data of the years 2015.For future climatic scenarios, data of the Beijing Climate Center Climate System Model (BCC-CSM) 43 for the years 2050 and 2070 under two Shared Socio-economic Pathways (SSPs) SSP2-4.5, and SSP5-8.5 were used to simulate the impact of temperature increase on the invasion risk of P. absoluta.Data were downloaded in "TIF" format and then were converted to "ASCII" format before they were used for the spatial analysis.

Spatial analysis and mapping of the risk indices
The scheme implemented to simulate P. absoluta risk indices is shown in Fig. 7.The developed temperaturedependent phenology model was used to simulate the life table parameters of P. absoluta.These parameters include the gross and net reproductive rates, mean generation time, intrinsic rate of population increase, doubling time, and the finite rate of population increase as reported in Mohamed et al. 31 .The simulations considered the daily minimum and maximum temperatures as a cosine function to calculate temperature-dependent population parameters at each 15 min time step while accounting for daily temperature variability as described by Kroschel et al. 17 .The mathematical equation developed by these authors was used to estimate the temperature of the first half-day where T i is the temperature (°C) at time step i ( i = 1, 2, 3, …, 48), and Min and Max are the daily minimum and maximum temperatures, respectively.The same equation was applied to calculate T i for the second half- day using the minimum temperature of the next day.We used average monthly temperature data obtained from WorldClim database.Hence the daily temperatures were replaced with monthly averages for the half-day  temperature to predict each 15 min time step in the above function.Using the simulated population growth parameters of P. absoluta based on the phenology model and temperature data, the following risk indices were estimated under SSP2-4.5 and SSP5-8 5 of the years 2050 and 2070 and visualized using QGIS: (1) Establishment risk index (ERI).
The ERI identifies the suitable areas for pest establishment under a specific thermal condition and it is calculated based on the daily survival of the immature stage 17 and the species reproduction ability 44 .ERI has probability values between 0 and 1, with 1 indicating a possibility for individuals in each immature life stage (egg, larva, pupa) to survive, reaching the adult stage (throughout the year; 365 days), and the adult laying eggs for the species life cycle to continue.The function used by Ngowi et al. 44 was employed to compute ERI as follows: where ERI is the establishment risk index, I i is the number of days i within the year ( i = 1, 2, 3, …, 365) and I I is the total number of days within the year (365 days).
Generation index herein refers to the number of generations that P. absoluta may produce in a specific location in one year.GI was calculated based on the mean generation time (in days) using the equation described by Kroschel et al. 17  where GI is the generation index (number of generations per year), 365 is the number of days in the year and Tc is generation time (in days) calculated for each day i ( i =1, 2, 3, …, 365).
The IA is strongly associated with the finite rate of population increase, and it takes into consideration the whole life history traits of the pest.AI was calculated by taking the log of the products of estimated finite rates of population increase calculated for each day of the year using function described by Kroschel et al. 17  where AI is the activity index, i is the finite rate of the population increase within the year at each day i ( i =1,2,3, …, 365).For instance, a value of 4 for this index indicates a potential population increase by a factor of 10,000 within a year.

Figure 2 .
Figure 2. The change in establishment risk index (ERI) of Phthorimaea absoluta between current and future climatic scenarios for the years 2050 and 2070: (A) difference between current and future scenarios for 2050 (SSP2-4.5),(B) difference between current and future scenarios for 2050 (SSP5-8.5),(C) difference between current and future scenarios for 2070 (SSP2-4.5)and (D) difference between current and future scenarios for 2070 (SSP5-8.5).

Figure 4 .
Figure 4.The change in generation index (GI) of Phthorimaea absoluta between current and future climatic scenarios for the years 2050 and 2070: (A) difference between current and future scenarios for 2050 (SSP2-4.5),(B) difference between current and future scenarios of 2050 (SSP5-8.5),(C) difference between current and future scenarios for 2070 (SSP2-4.5)and (D) difference between current and future scenarios for 2070 (SSP5-8.5).

Figure 7 .
Figure 7.The scheme implemented in Insect Life Cycle Modelling (ILCYM) and QGIS software to simulate and map the risk indices of Phthorimaea absoluta.
as follows: as follows: