Temperature-dependent modelling and spatial prediction reveal suitable geographical areas for deployment of two Metarhizium anisopliae isolates for Tuta absoluta management

Tuta absoluta is one of the most devastating pests of Solanaceae crops in Africa. We previously demonstrated the efficacy of Metarhizium anisopliae isolates ICIPE 18, ICIPE 20 and ICIPE 665 against adult T. absoluta. However, adequate strain selection and accurate spatial prediction are fundamental to optimize their efficacy and formulations before field deployment. This study therefore assessed the thermotolerance, conidial yield and virulence (between 15 and 35 °C) of these potent isolates. Over 90% of conidia germinated at 20, 25 and 30 °C while no germination occurred at 15 °C. Growth of the three isolates occurred at all temperatures, but was slower at 15, 33 and 35 °C as compared to 20, 25 and 30 °C. Optimum temperatures for mycelial growth and spore production were 30 and 25 °C, respectively. Furthermore, ICIPE 18 produced higher amount of spores than ICIPE 20 and ICIPE 665. The highest mortality occurred at 30 °C for all the three isolates, while the LT50 values of ICIPE 18 and ICIPE 20 were significantly lower at 25 and 30 °C compared to those of ICIPE 665. Subsequently, several nonlinear equations were fitted to the mortality data to model the virulence of ICIPE 18 and ICIPE 20 against adult T. absoluta using the Entomopathogenic Fungi Application (EPFA) software. Spatial prediction revealed suitable locations for ICIPE 18 and ICIPE 20 deployment against T. absoluta in Kenya, Tanzania and Uganda. Our findings suggest that ICIPE 18 and ICIPE 20 could be considered as effective candidate biopesticides for an improved T. absoluta management based on temperature and location-specific approach.

Tomato, Solanum lycopersicum L. is one of the most valuable cultivated vegetable crops in sub-Saharan Africa providing a source of direct and indirect employment for many people 1 . In Kenya, tomato is a food and nutrition security vegetable crop mostly cultivated by smallholder farmers for both domestic and export markets 2 . The rapid growth of the tomato industry has been coupled with the emergence of devastating indigenous and invasive insect pests and diseases 3 . As a result of these pests infestation, significant annual losses of up to 70% of tomato production have been estimated in Africa 3 , providing a clear constraint on current and future yields. Among these biotic constraints, the tomato leafminer, Tuta absoluta (Meyrick) (Lepidoptera: Gelechiidae) is ranked as the most current devastating pest of the crop 4,5 . Tuta absoluta is an invasive species native to South America 6 , which was first detected in 2008 on the African continent following a transatlantic invasion of tomato fields in 2006 in Spain 7,8 . More than a decade after its first detection in Africa, the pest has since spread to nearly every country on the continent destroying thousands of hectares of tomato fields and other solanaceous crops (e.g. potato, Solanum tuberosum L. and black nightshade, Solanum nigrum L.), frequently causing total crop losses 9 .
The management of invasive pests on the African continent, especially for the tomato leafminer has taken a scary and reactive approach leading to sporadic and uncoordinated actions to control the pest which has over the years established a foothold in the continent 10 . The extent of damage and the associated alarming level of economic losses (estimated at US$ 1.1 billion) being reported annually due to T. absoluta are enormous and are likely to increase significantly if left uncontrolled, leading to additional production costs to manage the pest 3 .
In response to this challenging situation, smallholder vegetable farmers have been desperately applying cocktails of synthetic pesticides 11 , largely driven by government-subsidized agrochemical input schemes, aggressive marketing by pesticide company representatives and out of desperation to reduce the pest infestation. Yet, the widespread use of synthetic insecticides has rarely delivered a satisfactory level of control due to the cryptic feeding behavior of the pest immature stages and the rapid development of resistance to many classes of insecticides known for T. absoluta population in other parts of the world 6,[12][13][14] , and consequently jeopardizing the pest control efforts. Additionally, pesticides resistance resulting from indiscriminate applications has caused unprecedented disruption of the resilience of natural ecosystems and has attracted growing public concerns over effects on non-target organisms, environmental and human health 15 . These resulted in the search for alternatives to pesticides to manage T. absoluta infestations with a great interest in developing biological control approaches using natural enemies (predators, parasitoids or microbials) to reduce pesticides use and limit insecticidal resistance development in both the adult and immature stages of T. absoluta [16][17][18][19] . Among the microbials being explored, entomopathogenic fungi (EPF) offer effective and viable alternative to control insect pests of economic importance, as they cause epizootics in the target host population while minimizing impacts on beneficial and other non-target organisms as well as increasing the quality of agricultural products 20,21 . These make them also potential option as biopesticides for controlling the tomato leafminer, T. absoluta 18 .
The mode of action of EPF against insects starts with spore adhesion to the host, followed by formation of appressoria that penetrate the cuticle, which later reach and invade the hemocoel and finally interferes with the host immune system 22 . However, the level of infection depends on the physiological properties (virulence, sporulation and persistence) of fungal strains which are regarded as a major obstacle to the success of their development as biocontrol agents 23,24 . Also under natural conditions, fungal infection is increasingly associated with stressful abiotic factors such as UV, humidity and temperature which modulate the virulence of the pathogen 25 . Indeed, there is increasing evidence that temperature is the dominant abiotic factor that has a significant influence on the infectivity profiles of fungal strains [26][27][28][29] whose application in the field as biopesticide products result sometimes in inconsistent performance/efficacy, limiting their use 30 . It is therefore important to explore the effect of this key abiotic stress, temperature on the efficacy of the identified potent EPF isolates 18 to sustainably manage T. absoluta in different agroecological systems, especially under the continuous climate change scenario. Furthermore, different nonlinear and linear models are used to estimate fungal growth over a wide range of temperature regimes and to predict the effect of EPF virulence in epizootic development among target insect pest populations 31,32 . Consequently, accurate prediction of the potential ecological fitness of these virulent fungal isolates is fundamental to optimize their efficacy in field application against the tomato leafminer.
Akutse et al. 18 recently reported the efficacy of three Metarhizium anisopliae (Metchnikoff) Sorokin fungal strains (ICIPE 18, ICIPE 20 and ICIPE 665) as the most potent isolates which hold promise as biocontrol agents for managing adults T. absoluta. However, the interactions between their performance and abiotic factors that could affect their field efficacy are paramount to be established for an effective selection of the most virulent fungal isolate(s) best suited for mass-production prior to its/their formulations and field deployment. To achieve this, it is important to simulate the effects of different temperature regimes on M. anisopliae ICIPE 18, 20 and 665 mass-production and their efficacy/virulent against T. asboluta, and subsequently predict potential suitable areas of application of these biopesticides or strengthen their efficacy through appropriate new formulations. Therefore, this study aimed to (i) assess the germination, growth and conidial production of the three candidate isolates, (ii) evaluate their virulence against adult T. absoluta under different temperature regimes, (iii) determine mass-production indices for the three fungal isolates and (iv) develop spatial predictions on potential areas where the candidate fungal isolates could cause significant epizootics in T. absoluta populations.

Spatial prediction of the virulence of Metarhizium anisopliae isolates ICIPE 18 and ICIPE 20
against adult Tuta absoluta in East Africa. Spatial predictions using EPFA for the performance or   (Fig. 7A,B); unlike in some parts of Nakuru and Nyandarua where the model predicted very low performance of the fungal pathogen ranging from 16 to 34% mortality (Fig. 7A,B). Moreover, the model predicted a very high probability of mortality of adult T. absoluta in several regions in Tanzania (Lindi, Morogoro, Tabora, Tanga) for ICIPE 18 and a moderate mortality in Iringa and Njombe (Fig. 8A). Similarly, for ICIPE 20, the model predicted a high mortality pattern in regions of Singida, Dodoma, Mbeya, Manyara; but predicted moderate virulence pattern of ICIPE 20 in Iringa and Njombe (Fig. 8B). In Uganda, the virulence pattern was almost similar for the two isolates with high probability of mortality predicted in Lango, West Nile, Teso and Acholi; and very low to moderate mortality predicted in Elgon (Fig. 9A,B). In general, environmental conditions appeared to be conducive to the pathogens' virulence across the three countries (Kenya, Tanzania and Uganda).

Discussion
All the three M. anisopliae isolates (ICIPE 18, ICIPE 20 and ICIPE 665) tested in this study showed significant variation in germination, radial growth, conidial production and virulence against adult T. absoluta across the various temperature regimes with ICIPE 18 and ICIPE 20 showing their superiority as the best candidate biopesticides for sustainable management of the pest. Our results also showed that Kenya, Tanzania and Uganda where these potent isolates are expected to be registered, commercialized and upscaled for T. absoluta control exhibit different patterns in spatial virulence of the two candidate isolates (ICIPE 18 and ICIPE 20); which clearly demonstrates the importance of using spatial modelling as a decision-support tool for the optimization of  www.nature.com/scientificreports/ biopesticides deployment in different agroecological zones. Furthermore, our study indicated that M. anisolpiae ICIPE 18 yielded the highest weight of conidia powder followed by ICIPE 20 and ICIPE 665 when using rice as growth substrate for mass-production of the candidate isolates. The ability of an EPF isolate to germinate under given environmental temperature regimes is a critical determinant of its efficacy 34 . Here, our findings revealed that over 90% of conidia germinated at 20, 25 and 30 °C, while only between 35 and 50% germinated at 35 °C. At 15 °C, no spore germination was recorded after 18 h incubation, but low germination was observed after longer time (delayed germination) which consequently translates into low hyphal growth and low sporulation. This is in agreement with previous studies that revealed that no germination occurred at low temperatures (< 15 °C) for M. anisopliae fungal isolates 23,26 . Ekesi et al. 35 also observed an absence or delayed conidial germination at low temperatures indicating that conditions were not favourable for spores to initiate germination within 18 h post-incubation. In contrast, Dimbi et al. 28 recorded spores germination at 15 °C after 24 h inoculation for several M. anisopliae isolates including ICIPE 18 and ICIPE 20. Similarly, De Croos and Bidochka 36 found that some M. anisopliae isolates were cold-active due to their ability to germinate and grow at temperatures as low as 8 °C. This suggests that spore germination may be related to the geographical origin of the strains or influenced by the conditions under which the spores are formed, highlighting the significant intra-specific variation in the germination among M. anisolpliae strains [36][37][38][39] . Importantly, germination occurred at 20 °C for all the three isolates; which marks the transition from a resting state to active development mostly driven by metabolic changes 40 . Our findings also showed that M. anisopliae isolates ICIPE 18 and ICIPE 20 had the highest germination rate at all temperature regimes compared to ICIPE 665 with an optimum at 25-30 °C. Hywel-Jones and Gillespie 38 also reported an intra-specific variation in the germination among M. anisopliae strains with the highest germination rate achieved at 25 and 30 °C.
Growth of the three fungal isolates was adversely affected at 15, 33 and 35 °C. This finding concurs with previous studies that reported growth inhibition of fungal pathogens exposed to extreme temperatures 27,28 . The extremely low growth rate of the isolates observed at 15, 33 and 35 °C indicates that these temperatures were unsuitable for spores' development and were close to the insect survival lower and upper thermal limits. Indeed, T. absoluta has a lower thermal threshold ranging from 5.37 to 7.38 °C while its upper thermal threshold varies between 33.82 to 35.69°C 41 . However, fungal growth for the three isolates became evident at 20 °C reaching an optimum at 30 °C predicted by the linear and Brière-1 models, even though ICIPE 665 grew more slowly than the other two isolates. This is in an agreement with Bayissa et al. 22 and Ekesi et al. 34 who reported that M. ansiopliae species are mesophilic fungi that grow well between 15 and 30 °C with an optimal temperature range of 20-30 °C. Vidal et al. 42 reported similar growth pattern for Paecilomyces fumosoroseus fungal species exhibiting high growth rate between 8 and 30 °C with thermal optima ranging from 20 to 30 °C. It is important to note that www.nature.com/scientificreports/ for fungal isolates of tropical origin, growth does not occur below a lower thermal threshold (10 °C) and gradually the growth increases with increase in temperature to a maximum at optimal temperature (25-28 °C), and finally decreases rapidly to zero at an upper threshold (32-35 °C) which is considered as the lethal temperature 42,43 .
Although the germination and fungal growth rate reached their optimum at 30 °C for isolates ICIPE 18 and ICIPE 20, we observed a significant decrease in spore production at the same temperature. Nevertheless, isolates ICIPE 18 and ICIPE 20 yielded the highest conidia production at all the temperature regimes compared to ICIPE 665 with an optimum at 25 °C. The poor yield of conidia observed at 33 and 35 °C illustrates the requirement/importance of optimum temperature to sustain conidia production and consequently boost fungal mass-production. This finding is consistent with the observation that optimum temperature for spore production is at 25°C 44 . Adults T. absoluta exposed to dry conidia showed a sharp increase in mortality at temperatures between 10 and 30 °C. The highest level of infection was observed at 25 and 30 °C for all the three fungal isolates, presumably representing the optimum temperatures at which fungal infection is most affecting the insect. This virulence pattern observed is therefore important in the selection of key application zones of these fungal candidates since their virulence is showed to be temperature-dependent. The effect of temperature on virulence of M. anisopliae dry conidia against adult stages of insect pests has previously been reported by Onsongo et al. 27 in adult Tephritid fruit flies Zeugodacus cucurbitae (Coquillet) (Diptera: Tephritidae) which succumbed to fungal infection over a wide temperature range (15-30 °C), with an optimum of 25 °C. A similar mortality pattern was observed with M. anisopliae isolate ICIPE 69 which was found effective against adult legume pod borer Maruca vitrata Fabricius (Lepidoptera: Crambidae) at temperature ranging from 15 to 33 °C, with an optimal temperature infection ranging between 25-30°C 26 . The lowest LT 50 values were recorded at 25 and 30 °C for the most two virulent isolates, ICIPE 18 and ICIPE 20. The rapid germination and growth of these two fungal isolates at almost all the temperature range could probably explain the fastest death they induced to the insects observed in this study. This confirms the observation that fungal isolates tend to kill most rapidly at the optimum temperature of their vegetative growth 26 . These two candidate isolates could therefore be deployed in the field with different temperature variation (20-30 °C) using an autodissemination device against adult T. absoluta through an "attract-and-infect" strategy, as they were found to be compatible with the commercial Tuta pheromone lure (TUA-Optima®) 18 .
Mathematical models have become an important tool for understanding and predicting the virulence and suitable application areas of entomopathogenic fungi against insect pests of economic importance often occurring in unpredictable environmental conditions 31,45 . Here, we used T. absoluta occurrence in East Africa 4 to model the virulence of the candidate isolates (ICIPE 18 and ICIPE 20) against the pest. The decision-support tool revealed that in some areas across Kenya, Tanzania and Uganda (where the potent fungal-based biopesticides are planned www.nature.com/scientificreports/ to be registered, commercialized and upscaled), the candidate fungal isolates might be effective as an excellent control and management tool for T. absoluta while in other areas the predicted level of virulence tend to be very low. For example, in the southern and northern part of Kenya, the models predicted higher virulence of both isolates while very low to moderate virulence has been predicted in the Central part of the country. Interestingly, tomato production is highly concentrated in Kirinyaga, Kajiado, Bungoma, Kwale and Taita Taveta counties 4 where ICIPE 18 and ICIPE 20 are expected to perform by inducing high infection to the pest. In Tanzania, tomato is mainly cultivated in Iringa, Morogoro and Tanga regions 46 while in Uganda, the main tomato production areas are Central, Eastern and Western regions 47 where the model predicted high mortality pattern of the pest for the two candidate isolates. As such, deploying fungal-based biopesticides in these locations will have a high probability of managing T. absoluta. However the microclimate conditions in some counties of Kenya (e.g. Naivasha in Nakuru county) where tomato is produced in greenhouses could be suitable for the infection of the pest by the fungal isolates and this requires investigating further. Klass et al. 32 predicted the effects of temperature on performance of a fungus-based biopesticide for controlling locusts and grasshoppers. The authors also predicted considerable spatial variation in M. anisopliae var. acridum and its virulence across different regions where the two voracious pests (locusts and grasshoppers) occur. These three countries (Kenya, Tanzania and Uganda) are among the countries where most biopesticides developed by icipe are also registered and commercialized. With a pest like T. absoluta, which is present permanently on tomato and other solanaceous fields, fungal isolates which can infect the pest under different agroecologies and remaining viable for an extended period would be more economical for smallholder farmers. Although these candidate biopesticides hold considerable promise, unpredictable weather conditions in the field could seriously undermine their performance leading to poor delivery. Therefore, the main challenge of predicting the spatial virulence of fungal pathogens lies in the high variability of the environmental factors for which temperature is not the only factor affecting the viability of biopesticides. Climatic factors like relative humidity (more specifically "vapor pressure deficit", VPD) which was not explored in this study have been shown to have great impacts on fungal growth and virulence. It is therefore important to assess the combined impact of temperature and relative humidity (VPD) in future studies. One of the primary prerequisites for a pathogen to be developed as a biopesticide is its ease for mass-production 26,48 . We found that M. anisopliae ICIPE 18 outperformed the other two isolates ICIPE 20 and ICIPE 665, as it produced the highest conidial yield, consumed less substrate and displayed high moisture content indicating that this isolate is capable of colonizing the rice substrate and yields high conidia. This high sporulation capacity is an interesting feature which would definitely contribute to fast-track the registration of ICIPE 18 when field validation trials are conclusive. Interestingly, we recorded conidia yield higher than 2 × 10 9 conidia/g of powder  Rice is considered as the most suitable substrate for fungal spores mass-production as it is locally available and provides a large surface area for sporulation 49 . Using rice as growth substrate, Barra et al. 50 also reported a high production of conidia per gram (2.1 × 10 9 ) for Purpureocillium lilacinum isolate JQ926212. Besides, we recorded a high level of moisture content (40%) for isolate ICIPE 18. Moisture plays a crucial role in conidial production of fungal isolates in solid-state fermentation as fungal spores require free moisture during the germination and host penetration process 51 .
In conclusion, M. anisopliae isolates ICIPE 18 and ICIPE 20 were found to be effective against adult T. absoluta and could be developed as biopesticides based on their efficacy across a broad range of temperature regimes (germination, growth and sporulation), speed of kill (LT 50 ) and virulence against the pest. In addition, both isolates can successfully be mass-produced on rice using a simple, fast and cost-effective mass-production technique (especially for private sector for business incubation) suitable for deployment in the field. However, the successful deployment of these two biopesticides requires field validation trials under different agroecological zones for which the decision-support tool has provided us with tangible information related to the suitable locations where the two candidate fungal isolates are expected to cause significant epizootics in T. absoluta populations. Adequate fungal strains selection and their accurate spatial prediction are therefore fundamental approach to optimize their efficacy prior to field deployment and could consequently guide decision-making for private sector, farmer-based organizations and policy in promoting effective use of candidate fungal pathogens against adult T. absoluta in East Africa and beyond.

Materials and methods
Insects. Source colony of T. absoluta was initially established from wild adults and larvae collected from infested tomato leaves and fruits in Mwea (0°36′31.3″S 037°22′29.7″E), Kirinyaga county, Kenya in June 2019. The moths were kept in ventilated, sleeved Perspex cages (40 × 40 × 45 cm) and fed ad libitum with 10% honey solution placed on the top side of each cage 19 . Four potted tomato plants (Solanum lycopersicum L. cv. "Money maker" grown from seeds obtained from Simlaw Seeds Company Ltd., Nairobi, Kenya) were placed in the cages for oviposition. The plants were removed 24 h post-exposure to female insects and transferred to separate wooden cages (50 × 50 × 60 cm) with ventilated openings on both its sides and top covered with netting material until the eggs hatched. Leaves with larvae were removed from these plants, three days after the larvae hatched and placed into clean sterile plastic containers (21 cm long × 15 cm wide × 8 cm high) lined with paper towel to absorb excess moisture and fine netting infused lid for ventilation. The larvae were supplied daily with fresh tomato leaves as food until pupation. The pupae were collected from the plastic containers using a fine camel hair-brush and placed inside a clean plastic container (21 cm long × 15 cm wide × 8 cm high) for adult emergence. The colony was rejuvenated every three months through infusion, with infested tomato leaves collected from the field to reduce inbreeding 18,19 . Insects were maintained under a rearing condition of 28 ± 2 °C, 48% relative humidity (RH) and 12:12 L:D photoperiod at the Animal Rearing and Quarantine Unit (ARQU) of icipe for five generations prior to bioassays 19 .

Fungal isolates and viability assessment. The three M. anisopliae fungal isolates (ICIPE 18, ICIPE 20
and ICIPE 665) used in this study were obtained from the International Centre of Insect Physiology and Ecology (icipe)'s Arthropod Pathology Unit Germplasm ( Table 4). The isolates were cultured on Sabouraud dextrose agar (SDA) (OXOID CM0041, Oxoid Ltd., Basingstoke, UK), and maintained at 25 ± 2 °C in complete darkness. Conidia were harvested by scraping the surface of two-to three-week-old sporulated cultures using a sterile spatula. The harvested conidia were then suspended in 10 ml sterile distilled water containing 0.05% (w/v) Triton X-100 (MERCK KGaA, Darmstadt, Germany) and vortexed for five min at about 700 rpm to break conidial clumps and ensure a homogenous suspension. Conidial concentrations were quantified using an improved Neubauer hemocytometer under a light microscope 52 . The conidial suspension was adjusted to a concentration of 3 × 10 6 conidia ml −1 through serial dilution.
Prior to commencement of the bioassays, spore viability was determined by plating evenly 0.1 ml of 3 × 10 6 conidia ml −1 onto 9-cm Petri dishes containing SDA. Three sterile microscope cover slips (2 × 2 cm) were placed randomly on the surface of each inoculated plate. Plates were sealed with Parafilm membrane and incubated in complete darkness at 25 ± 2 °C and were examined after 16-20 h 52 . The percentage germination of conidia was determined from 100 randomly selected conidia on the surface area covered by each cover slip under a light microscope (400 ×) using the method described by Goettel and Inglis 52 . Conidia were considered to have germinated when the length of the germ tube was at least twice the diameter of the conidium 52 . Four replicates were made for each isolate making a total of 12 plates for all isolates. www.nature.com/scientificreports/ Effect of temperature on spore germination of Metarhizium anisopliae fungal isolates. Aliquots (0.1 ml) of a 3 × 10 6 conidia/ml conidial suspension were spread with a sterile glass spreader over the surface of 9-cm Petri dishes containing SDA. Three sterile microscope cover slips were placed on each plate, and the plates securely sealed with Parafilm membrane as described above. The plates were then incubated in complete darkness at constant temperatures of 15, 20, 25, 30, 33 and 35 °C. At 18 h post-incubation, plates were flooded with lactophenol aniline cotton blue to halt germination and to stain the spores for easy visibility. Percentage germination of 400 conidia, as four randomly selected counts of 100 conidia, on each plate was assessed under the 400 × objective of a Leica DM500 light microscope (Leica Microsystems, Wetzlar, Germany) using the method described by Goettel and Inglis 52 . A conidium was considered to have germinated when the germ tube length was equal to or greater than the length of the conidia. Each plate served as a replicate with four replicates per fungal isolate making a total of 72 plates.
Effect of temperature on radial growth and sporulation. Conidial suspensions of the three isolates (ICIPE 18, ICIPE 20 and ICIPE 665) were prepared from two-week-old sporulated cultures and adjusted at a concentration of 1 × 10 7 conidia ml −1 prior to subculture. Aliquots (0.1 ml) were spread-plated on 9-cm Petri dishes containing SDA. Inoculated plates were then incubated in complete darkness at 25 °C for three days to obtain mycelial mats. Mycelial mats were cut from culture plates into round agar plugs using an eight-mm diameter cork-borer. Each agar plug (ca. five mm thick) was then transferred onto the center of a fresh SDA medium plate from which a similar size plug of media had been previously removed using the same cork-borer. The plates with implanted mycelial plugs were sealed with Parafilm membrane and incubated in complete darkness at 15, 20, 25, 30, 33 and 35 °C. Radial growth was recorded daily for 12 days using two cardinal diameters, through two orthogonal axes previously drawn on the bottom of each Petri dish to serve as a reference 53 . The experiment was replicated four times with each replicate originating from a different culture plate. Twelve days post-incubation, conidia were then harvested by scraping the surface of the sporulated cultures from each plate using a sterile spatula. The harvested conidia were then suspended in 10 ml sterile distilled water containing 0.05% Triton X-100 and vortexed for five min at about 700 rpm to break conidial clumps and ensure a homogenous suspension. Conidial concentrations were quantified using an improved Neubauer hemocytometer under a light microscope as described above 52 .
Effect of temperature on the virulence of Metarhizium anisopliae fungal isolates against adults of the tomato leafminer Tuta absoluta. Temperatures above 30 °C were fatal to the insect given that all the adults in the control completely died during the first two days following their introduction into the incubator. Therefore, the bioassay was conducted at 10, 15, 20, 25 and 30 °C which are the representatives temperature range at which the pest occurs in the field 54 . Twenty one-day-old virgin (unmated newly emerged moths) T. absoluta, male and female (at the ratio of 1:1) were inoculated with dry conidia of the M. anisopliae isolates using velvet-coated plastic jars (60 × 40 cm) following the method described by Migiro et al. 55 and Akutse et al. 18 . For each isolate, the device was contaminated with 0.3 g of dry conidia (equal to 0.15 × 10 9 conidia/g), after which moths were introduced into the device for three minutes for them to pick up fungal spores. Evidence of infection was confirmed through visual observation of fungal spores strongly attached to the body of the insects. Control insects were exposed to fungus-free velvet plastic jars. Three (3)  After which the substrate was allowed to cool to 28 °C and inoculated with 50 ml of a three-day-old culture of blastospores/mycelia under a laminar flow cabinet. The bag was sealed under aseptic condition and incubated for 21 days at ambient conditions (26 ± 1 °C and 60-70% RH), after which the contents were transferred into sterile plastic buckets (33 × 25 × 13 cm) to allow the culture to dry for seven days at 26 ± 1 °C. Conidia were harvested by sifting through a mesh sieve (295 µm mesh size). Six replicated production sets were run for each isolate. At harvest, conidial powder from each bag and isolate was taken to estimate the following mass-production parameters: (i) weight of conidia powder per kg of rice, (ii) number of conidia per gram of powder, (iii) number of conidia per kg of powder, (iv) percentage water content (based on weight loss of 1 g powder dried at 120 °C for 2 h), (v) percentage viability based on counts of germinated conidia, and (vi) percentage consumed substrate in each bag (based on the weight of the dry rice substrate before inoculation and that of the dry substrate residues immediately after harvesting the conidia) 26 . www.nature.com/scientificreports/ Modelling the effect of temperature on the radial growth rate. For temperature-dependent models, both linear and nonlinear models were fitted to the calculated radial growth data. A linear function was fitted to the data to determine the relationship between growth rate and temperature 43 . The linear model expressed as y (t) = a + bt was used to estimate the relationship between relevant temperatures and growth rate of fungal isolates, where y is the rate of growth, t is ambient temperature, and intercept (a) and slope (b) as the model parameters.
The minimum temperature threshold (T min ) and standard error (SE Tmin ) were calculated using Eqs. (1) and (2): where y m is the average value of the growth rate, b is estimated slope of fitted line, S 2 is the residual mean square of the linear model, and N is the sample size 56 . However, linear function cannot accurately capture the growth rate at extreme temperatures 43 . Many empirical nonlinear models such as Logan and Brière models are fitted to fungal growth rate 23,43 . This allowed determining the minimum temperature (T min ), optimum temperature (T opt ) and upper temperature (T max ) thresholds. Optimum temperature threshold (T opt ) is defined as the temperature when the fungal growth rate is observed to be maximal, while T max is referred to threshold temperatures above which growth does not occur 43 . Among the nonlinear models evaluated, the nonlinear regression model of Brière-1 (Eq. 3) was fitted to the data so as to describe the fungal radial growth rate at the various temperature thresholds, r(T) 57 .
where, r is considered as the radial growth rate, derived as a function of temperature T, n being an empirical constant, T min being the lower developmental temperature threshold and T max the upper temperature threshold. The optimum temperature (T opt ) of the fungal growth was estimated using Eq. (4): 57 where m is an empirical constant 57 .
Goodness of fit and selection criteria of the model. The best-fitted model is selected based on the residuals and comparing Akaike's Information Criterion (AIC) and the Model Selection Criterion (MSC). The accuracy of different linear models in fitting the data was determined by comparing the coefficients of determination (R 2 ). Goodness-of-fit of the model was assessed using the coefficient of determination (for linear model; R 2 ) or the coefficient for nonlinear regression (for nonlinear models; R 2 ) and the residual sum of squares (RSS). Higher values of R 2 and lower values for RSS suggest a better fit 58 . For the linear regression, the data points at 33 °C and 35 °C which deviated from the straight line through the other points were omitted for correct calculation of regression 23,43 . Modelling the effect of temperature on the virulence of fungal strains against adult Tuta absoluta. An open-source computer-aided tool built on R-codes and Java interface, the entomopathogenic fungi application (EPFA) software version 1.0 45 was used for modelling the virulence of the fungal strains (ICIPE 18 and ICIPE 20) against adult T. absoluta. The recorded mortality was plotted against the corresponding temperature values from which nonlinear models were fitted function to the observed data 45 . The model parameters were estimated by fitting equations to the recorded mortality and the corresponding temperature values. Eighty two (82) models were fitted to the data and the best-fitted models were selected based on their coefficient of determination R 2 , adjusted R 2 , Akaike's information criteria (AIC), the root-mean-squared error (RMSE) and residual sum of squares (RSS) 45 . In addition, nonlinear models allowed the assessment of the minimum temperature threshold (T min ) and the maximum temperature threshold (T max ). The Logan-4 model (Logan et al. 59 ) predicted well the effect of temperature on virulence of ICIPE 18 against adult T. absoluta while the Logan-1 model gave the best fit to the virulence of ICIPE 20 and ICIPE 665. The mathematical expressions of the models are presented in Table 5.

Spatial prediction of the virulence of the most potent fungal isolates. Metarhizium anisopliae
isolates (ICIPE 18 and ICIPE 20) were selected for the spatial prediction study based on germination/viability and growth patterns, the speed of kill (LT 50 value) and the mortality rates they caused to adult T. absoluta across all tested temperature ranges. To predict the spatial virulence of each fungal isolate, the temperature-dependent mathematical expression obtained during the modelling step was run at each grid of the raster files of Kenya, Tanzania and Uganda using the monthly minimum and maximum temperature datasets obtained from World-Clim (http:// www. world clim. org/). The gridded temperature datasets were loaded into EPFA software, simultaneously extracted from the database and then organized in matrix format using longitude as column and latitude as a row 45 . A point object picks the temperature-dependent mathematical expression of the virulence for the isolates and this is consecutively applied in each geographical coordinate of the grid. The results were converted (1) T min = −a b (2) SE T min = y m b 2mT max + (m + 1)T min + (4m 2 T 2 max + (m + 1) 2 T 2 min − 4m 2 T min T max 4m + 2 Scientific Reports | (2021) 11:23346 | https://doi.org/10.1038/s41598-021-02718-w www.nature.com/scientificreports/ into ASCII file format (.asc) and transferred into an open source software Q-GIS 60 for visualization 45 . The virulence map was produced for Kenya, Tanzania and Uganda after completing the fitting process.
Data analyses. Conidial germination data were analyzed with generalized linear model (GLM) assuming a binomial distribution with the log link function. Percent mortality was corrected for control mortality using Abbott's formula 61 . Mortality data were analyzed using logistic regression in a GLM for a binomial distribution using the logit link function. Time-mortality data were analyzed with GLM using the function "dose.p" from the MASS library, to generate LT 50 estimates, along with slopes of the regression curves. GLM analysis was run for each replication, and the resultant LT 50 values and their respective slopes were subjected to ANOVA to generate means. Additionally, data on sporulation (conidia production) and number of conidia per gram of powder were analyzed using GLM with negative binomial error distribution taking into account overdispersion. Data on weight of conidia powder per kg of rice were analyzed using GLM with gamma distribution. Percentage water content and percentage consumed substrate data were analyzed with beta regression. Whenever a significant difference was found, multiple means comparison was made using Tukey's HSD post-hoc test to assess pairwise comparison, adjustment for LS means with α = 0.05. All statistical analyses were performed using R (version 3.6.3) statistical software packages 62 and all statistical results were considered significant at the confidence interval of 95% (P < 0.05).
Ethics approval. The experimental research and field studies on plants, including the collection of plant material, complied with relevant institutional, national, and international guidelines and legislation. The appropriate permissions and/or licenses for collection of plant or seed specimens were obtained for the study. All insect rearing, handling and experiments were performed using standard operating procedures at the icipe Animal Rearing and Quarantine Unit as approved by the National Commission of Science, Technology and Innovations, Kenya (License No: NACOSTI/P/20/4253). This article does not contain any studies with human participants performed by any of the authors.

Data availability
The dataset generated during the current study are available from the corresponding author upon request.  Table 5. Mathematical equations describing the relationship between temperature and virulence of Metarhizium anisopliae fungal isolates. For Logan models α, Y, k, b, Dt, and v are the model parameters, T min the minimum temperature threshold and T max the upper temperature threshold (°C).

Model Equation References
Logan