Biological parameters of Muscidifurax raptorellus (Hymenoptera: Pteromalidae) on Bactrocera oleae (Diptera: Tephritidae), the key pest of olives

ABSTRACT
 The olive fruit fly, Bactrocera oleae, is one of the main pests of this crop and its control requires the development of methods environmentally safer than those used mostly nowadays, being biological control a possible alternative. Accordingly, the capacity of parasitisation and the biological parameters of Muscidifurax raptorellus, a generalist parasitoid of dipteran pupae, were evaluated on B. oleae at 25°C, 80% RH and a 16:08 h light/dark photoperiod. In a development assay, the rates of parasitism ranged 60% to 72% and the duration of the preimaginal period was between 17.0 and 18.5 days. The total mean number of adult wasps produced per pair in a reproduction assay was 50.7, with a mean daily production of 7 individuals and a mean rate of parasitism of 32.6%. The moment of maximum offspring production was estimated at 2.6 days after the beginning of the oviposition. The intrinsic rate of natural increase of M. raptorellus on B. oleae was 0.147, what determines a population doubling time of 4.7 days. The functional response was type II and the maximum attack rate in 24 h was 19.6 pupae. At host densities ranging 20–80 pupae per female, the number of adult wasps produced was around 20–22. The results obtained show the potential of M. raptorellus to be used for the biological control of B. oleae.


Introduction
The olive fruit fly, Bactrocera oleae (Rossi) (Diptera: Tephritidae), is the key pest of this crop because it attacks olives in the main olive growing areas and requires control measures every year. The damages produced by this species are due to the feeding habits of larvae which develop and feed inside the fruit by digging galleries. This produces a premature fall of the fruits and, in addition, allows the development of moulds in the olives that reduces oil quality. Annual losses due to this insect worldwide have been estimated in $800 million . Traditionally, the control of B. oleae infestations in the Mediterranean countries has been based on the application of broad-spectrum chemical insecticides (González-Núñez et al., 2021). The organophosphate dimethoate was the most widely used insecticide for this purpose for decades but it was recently banned in the European Union and, although other insecticides such as pyrethroids, neonicotinoids and spinosad continue to be used, the development of other control strategies against this pest is urgent (Checchia et al., 2022). In addition, there is a growing need to reduce the use of this type of conventional insecticides due to the concern about the environmental pollution, contamination of olive oil and the negative effects that this substances produce on the populations of beneficial arthropods. Moreover, the development of resistance to insecticides in the B. oleae populations entails and additional problem Kampouraki et al., 2018;Skouras et al., 2007). Among the alternative control measures to conventional insecticides are mass trapping, sterile insect technique, particle film technology, selective insecticides and biological control Delrio & Lentini, 2018).
Of the olive tree pests, the olive fly is also the one in which the action of natural enemies is the poorest. Among the natural enemies that have been cited preying or parasitising B. oleae in the Mediterranean area, none exerts sufficient natural control of this pest. It seems that the most significant natural control of B. oleae is that exerted by generalist ground dwelling predators that feed on larvae and pupae (Morris et al., 1999) and it has been observed that soil management and landscape structure affect the action of these predators (Ortega et al., 2018). Few native parasitoids have been cited on B. oleae in European Mediterranean countries, all of them polyphagous, with very variable action and almost never significant (Neuenschwander et al., 1986;Wang et al., 2021). In contrast, in eastern and southern Africa, the place of origin of B. oleae, the action of specialised parasitoids is important, so, at the beginning of the twentieth century, to alleviate this lack of parasitism, small releases of almost all these African parasitoids were made, but without success in the establishment of any of them in the European Mediterranean countries. These failures may have been due to the small number of released individuals and the limited previous knowledge about the biology and ecology of the parasitoids . Also in the last century, great efforts were made to establish, in Spain and in other European Mediterranean countries, the parasitoid Psyttalia concolor (Szépligeti) (Hymenoptera: Braconidae), native from North Africa (Jiménez et al., 1969(Jiménez et al., , 1990. Despite the repeated releases, P. concolor has only been established in areas with warm winters and in those places its control of B. oleae seems very limited (Alexandrakis, 1986), although rates of important natural parasitism (23.4%) have been registered in organic olive groves of the Balearic Islands (Spain) (Miranda et al., 2008). Due to this limited success of classical biological control, inoculative and inundative releases of P. concolor have been carried out in several Mediterranean countries like Italy and Turkey (Delrio et al., 2005;Hepdurgun et al., 2009). In these cases, the release of high numbers of parasitoids per tree and year is needed, which is not always economically acceptable and the results are very variable.
With the establishment of B. oleae in California (USA) in 1998, a new interest in the biological control of this pest raised and new surveys of parasitoids were carried out in East Africa, Pakistan, India and South Africa Hoelmer et al., 2011). As a result, some parasitoid braconids that exert an important natural control on B. oleae in their place of origin (28-57% of parasitism) and with a certain degree of specificity were selected and studied in California as candidates for classical biological control programmes (Daane et al., , 2015, as well as some species of parasitoid braconids of other Tephritidae that have parasitised B. oleae, in laboratory . Psyttalia lounsburyi (Silvestri) and Psyttalia humilis (Silvestri) (Hymenoptera: Braconidae) were the first species selected to carry out biological control experiments of B. oleae in olive groves in California and have undergone field trials to study their adaptation to their environmental conditions and olive varieties Yokoyama et al., 2011). According to the latest data offered, there is no evidence that P. humilis has permanently established in California and P. lounsburyi is established only in the coastal areas, although parasitism ratios are very small (Daane et al., 2015). Releases of P. lounsburyi were also carried out in the south of France in 2008 and although a small number of parasitoids were recovered in the two years after the releases, none was recovered later (Borowiec et al., 2012). In the same way, P. lounsburyi and P. humilis were released in Israel, in 2008, but none of these parasitoids was found in the 2009 samplings (Argov et al., 2012). Some studies have shown that the efficacy of these larval parasitoids depends on the size of the fruit. Thus, its action would be very limited in cultivated olives, since they have coevolved with the smallest fruits of the wild olive trees and, in the large commercial fruits, the larva of B. oleae escapes more easily from the parasitoid Wang, Nadel, et al., 2009).
An additional possible candidate to be used as biological control agent of the olive fruit fly is Muscidifurax raptorellus Kogan & Legner (Hymenoptera: Pteromalidae). This parasitoid is a gregarious idiobiont ectoparasitoid of filth fly pupae that is currently commercialised for the augmentative biological control of flies usually found in livestock facilities (Bonneau et al., 2019). Muscidifurax raptorellus has a great range of potential dipteran hosts in a wide range of production systems and in different geographic areas (Geden & Moon, 2009;Legner, 1987;Petersen & Currey, 1996). Dipteran families of filth flies like Muscidae, Calliphoridae and Sarcophagidae have been shown to be parasitised by this wasp (Geden & Moon, 2009;). In addition, laboratory studies performed under controlled conditions have shown the capacity of this parasitoid to parasitise and develop on pupae of tephritid pests like Ceratitis capitata (Wiedemann) (de Pedro et al., 2020) and invasive pests like Drosophila suzukii (Matsumura) (Diptera: Drosophilidae) (Bonneau et al., 2019).
In this work, we present the results obtained in our laboratory regarding the capacity of parasitisation and the basic biological parameters of M. raptorellus using B. oleae as host to estimate the potential of this parasitoid to be used as biological control agent of one of the most important pest of olive tree. Concretely, we evaluate the rate of parasitoidism, the preimaginal developmental period, the reproductive capacity, the life table parameters and the functional and numerical responses.

Insects
A M. raptorellus population was established from parasitised pupae of C. capitata provided by the Unidad de Entomología del Centro de Protección Vegetal y Biotecnología del Instituto Valenciano de Investigaciones Agrarias (IVIA) (Spain). Voucher specimens of this population are preserved and stored in 70% ethanol at the Entomology laboratory (CSIC-INIA). In turn, the IVIA population was obtained as described in de Pedro et al. (2020). To maintain this population at the INIA facilities, a C. capitata population was also established from pupae provided by the Grupo de Manejo Integrado de Plagas de la Escuela Técnica Superior de Ingeniería Agronómica, Alimentaria y de Biosistemas (ETSIAAB) de la Universidad Politécnica de Madrid (Spain). The assays were performed using B. oleae pupae provided periodically by express courier by the International Atomic Energy Agency (IAEA) (Vienna, Austria) where this insect is reared on artificial diet to be used for the control strategy of sterile insect technique (Ahmad et al., 2014).
The mass rearing of M. raptorellus and C. capitata took place at 22°C, 70% RH and a 16:08 h light/dark photoperiod in an environmental chamber (IBERCEX, Spain). The mass rearing of C. capitata was done based on the procedures described in Jacas and Viñuela (1994). The parasitoid M. raptorellus was reared on C. capitata freeze-killed pupae, following a procedure similar to that described by de Pedro et al. (2020). In our case, 1300-1700 freeze-killed pupae were offered to 1000-2000 adult parasitoids in two petri dishes and kept in the adult parasitoid cage (40 × 30 × 30 cm) for 24 h. The experiments were performed at 25°C, 80% RH and a 16:08 h light/dark photoperiod in environmental chambers (Panasonic MLR-352H, Panasonic, Japan).

Experimental procedures
Previous research has shown that the biological parameters of M. raptorellus are not affected by the use of C. capitata freeze-killed pupae as host, what facilitates to carry out laboratory assays (de Pedro et al., 2020). Accordingly, it was determined first the effect of freezing of the olive fruit fly pupae on the capacity of parasitisation and the development of the immature stages of the parasitoid. Thus, the rate of parasitoidism (calculated as the number of pupae from which adult parasitoids emerged), the duration of the immature developmental period and the sex ratio of the adults produced were established on 5-6 day-old live pupae of B. oleae and on pupae of the same age killed by freezing for one hour at −20°C and stored at 4°C for at most one month before they were employed for the assays. To do that, 125 live pupae and 125 freeze-killed pupae were set inside two Petri dishes (5.4 cm diameter) without cover that were introduced within two ventilated methacrylate cylindrical cages (29 cm length × 16 cm diameter) together with two groups of 50 M. raptorellus females of the fourth day of emergence, following the proportion employed by Petersen and Currey (1996), and a food source. After 24 h, the pupae were individualised in glass tubes (5.5 cm height × 1.1 cm diameter) covered with cotton to allow ventilation and introduced in the environmental chamber where development occurred.
The experiments performed to determine the reproductive parameters and the functional and numerical responses were carried out in rearing units consisting of plastic tubes (15 cm height × 5.5 cm diameter) placed vertically in the upper half of a Petri dish (5.8 cm diameter) with the upper opening covered by a piece of translucent nylon cloth held in place by a rubber band, which provided ventilation for the rearing cell. Within this experimental unit, a round box (2 cm height × 4 cm diameter) was introduced containing the olive fruit fly pupae offered as hosts. A piece of folded filter paper (2 cm × 0.5 cm) impregnated with honey, some sugar grains and a small cotton ball soaked in water (which was moistened daily in the reproduction assay) were provided as food sources.
In the reproduction assay, 20 pairs of adults < 24 h old from emergence were employed. A pair was introduced within each experimental unit together with a round box containing ten B. oleae pupae killed by freezing as described before that were replaced daily. Each daily batch of pupae was afterwards introduced in glass tubes (4.9 cm height × 1.7 cm diameter), covered with cotton and transferred to the environmental chamber until the emergence of the new adults. Pairs were allowed to lay eggs for 10 days and when all the viable offspring had emerged, the percentage of fertile mating (proportion of pairs that were able to produce offspring), the number of days with egg laying out of the total days of the assay, the total number of adults produced per fertile mating, the number of adults produced per fertile mating and per day and the sex ratio of the progeny produced were established. In addition, curves of mean daily and cumulative production of offspring per fertile female were constructed.
The data obtained regarding the duration on the immature development and the adult survival and reproduction were used to calculate the life table parameters according to Birch (1948). The intrinsic rate of natural increase (r m ) represents the innate capacity of increase in idealised populations under idealised environments and was estimated according to the equation: where x is the age in days, l x the age-specific survival rate of females (probability at birth of being alive at age x), and m x the age-specific wasp production rate (mean number of female adult offspring produced in a unit of time by a female aged x). The net reproductive rate (R 0 ) is given by R 0 = l x m x ; the mean generation time (T ), expressed in days, is given by T = ln R 0 /r m ; the finite rate of natural increase (λ) is given by l = e r m ; and the population doubling time (PDT) is given by PDT = ln 2/r m . The programme r m 2.0 (Taberner et al., 1993) was used to calculate these parameters. This programme provides an estimate of the r m variance by means of a bootstrap resampling method. The minimum number of replicates used was 500 as recommended by Meyer et al. (1986). The sex ratio of the progeny obtained in the reproduction assay was employed for the calculation of the life table parameters (Lysyk, 2001).
The functional and numerical responses of M. raptorellus using olive fruit fly pupae killed by freezing were established. The functional response represents the increase in the number of hosts attacked by the parasitoid as a function of host density and the numerical response determines the influence of the host density on the total progeny produced. In our case, since dead pupae were used for the assays, the estimation of the functional response was made from the number of pupae from which adult parasitoids emerged. Pupae densities offered were 2, 5, 10, 20, 40 and 80 and the exposure period was 24 h. Ten replicates per density were used and a M. raptorellus female of the third day of emergence (2-3 day-old) was introduced in each replicate. Females were in contact with males and were exposed to B. oleae pupae from emergence, so they had parasitisation experience. After the 24 h period, the pupae were individualised in glass tubes (5.5 cm height × 1.1 cm diameter) covered with cotton and transferred to the environmental chamber where development occurred. After emergence of the new adults, the number of pupae from which adult parasitoids emerged, the total number of adults produced and the sex ratio were established.

Statistical analysis
For the development assay, the effect of the type of host offered (alive or killed by freezing) on the rate of parasitoidism and sex ratio obtained was analysed by Chi-squared tests with Yates' correction for 2-by-2 frequency tables. The effect of the type of host and sex on the duration of the developmental period was analysed by multifactor ANOVA. The interaction between these factors was also included in the model. In addition, since more than one parasitoid may emerge from each pupa, this factor was included in the analysis as a nested random factor within type of host. The effect of the type of host on the number of adult parasitoids produced per pupae was analysed by Generalised Linear Models (GzLM) (McCullagh & Nelder, 1989). The probability distribution of the response variable was considered Poisson and the link function was Log.
For the reproduction assay, a Chi-squared test was carried out to establish the deviation of the sex ratio obtained from the 1:1 ratio. In addition, a Maxima function (Richter & Söndgerath, 1990) was used to fit the offspring mean daily production per female. The equation is where f (t) represents the offspring mean daily production per female, α and τ are parameters, and t is time expressed in days after the start of oviposition, so that t = 1 is the first day of oviposition. Moreover, a Weibull-cumulative function selected from the Tablecurve 2D 5.01 equations library was used to fit the cumulative offspring production data. The equation is where f(t) represents the mean cumulative offspring production per female, a, b, c, d and e are parameters and t is time expressed in days after the start of oviposition. Models were fitted using Tablecurve 2D 5.01.
To establish which type of functional response described best the parasitisation data of M. raptorellus vs. B. oleae pupae, the frair test of the R software was used. This test performs a hypothesis test to determine if the functional response is type II (null hypothesis) or type III (alternative hypothesis) (Juliano, 2001). Once this was established, a model was fitted to describe the functional response. Since the assays were conducted without replenishment of parasitised pupae, the number of available non-parasitised pupae decreased during the 24 h period of the experiment (host depletion). To describe the functional response under these conditions and to estimate the attack rate and the handling time per host, the equation by Rogers (Rogers, 1972) for type II functional response was employed. The equation of the model is where N e represents the number of host killed, N 0 is the initial host density, a is the attack rate, T h is the handling time and T is the duration of the experiment in hours. To obtain the model, the Lambert W function was used by means of the R package frair. This function was used because it allows the estimation of the parameters of the model even when N e is in both sides of the equation. Finally, the effect of host density on the total number of adult offspring produced and the number of adult offspring produced per parasitised pupae was analysed by one-way ANOVA followed by the LSD test. When necessary, data were transformed by log(x) to meet the assumptions of parametric statistics. In addition, the effect of host density on the rates of parasitism was analysed by GzLM with Binomial distribution and Logit as link function followed by the LSD test for pairwise comparisons.
The level of significance employed was P < 0.05 in all cases. Except when indicated, analyses were done using SPSS 17.0 and Statgraphics® Centurion XVI statistical programmes.

Results
Muscidifurax raptorellus was able to parasitise both live and dead pupae in similar percentages, so no statistical differences were found in the rates of parasitoidism (72% in live pupae and 60% in dead pupae, χ 2 1 with Yates' correction = 3.494, P = 0.0616). The duration of the preimaginal period was not affected either by the type of host offered. With live pupae, development was completed in 17.0 ± 0.1 days (mean ± SE) for males and in 18.5 ± 0.1 days for females, while with dead pupae, duration was 17.1 ± 0.1 days for males and 18.4 ± 0.1 days for females (F 1, 163 = 0.64, P = 0.4259, multifactor ANOVA); however, differences between males and females were significant (F 1, 499 = 400.65, P < 0.0001, multifactor ANOVA), but no interaction effect was observed between both factors (F 1, 499 = 1.02, P = 0.3133, multifactor ANOVA). The number of adult wasps produced in the development assay with regard to the type of host offered was 351 (215 males and 136 females) with live pupae and 315 (182 males and 133 females) with dead pupae. Accordingly, the number of adult parasitoids produced per offered pupae was 2.81 ± 0.2 for live pupae and 2.52 ± 0.3 for dead pupae, being this difference not significant (χ 2 1 = 0.717, P = 0.397, GzLM with Poisson distribution). No differences were detected either for the sex ratio obtained with regard to the type of host offered (χ 2 1 with Yates' correction = 0.695, P = 0.4045). All pairs in the reproduction assay were able to produce adult offspring. Out of the ten days of duration of the assay, offspring production was observed for a mean of 7.4 ± 0.1 days and the total mean number of emerged wasps was 50.7 ± 3.3, with a mean daily production of 7.0 ± 0.4 adult parasitoids. The sex ratio of the progeny was 44.3% males and 55.7% females, being this difference statistically significant (χ 2 1 = 13.055, P < 0.001). The mean number of parasitised pupae per female was 30.7 ± 1.9 and the mean rate of parasitism was 32.6% ± 2.0. The mean number of adult wasps produced per parasitised pupa was 1.7 ± 0.1. Figure 1 shows the mean daily and cumulative curves of offspring production per female obtained after fitting the Maxima and Weibull models. The peak of maximum progeny production was estimated at 2.6 days after the beginning of the oviposition, with an estimated mean number of 8.1 wasps produced at that moment, although the maximum mean number obtained empirically was 10.1 wasps for the pupae offered the second day of oviposition. Moreover, the asymptote provided by the Weibull model showed that the maximum number of offspring produced per female under the experimental conditions would be 51.5 wasps, indicating that the oviposition period is not much longer than the ten days initially established for the assay.
The intrinsic rate of natural increase, r m , estimated for M. raptorellus at 25°C was 0.147 ± 0.003; the net reproductive rate, R 0 , 28.2; the mean generation time, T, 22.8 days; and the finite rate of natural increase, λ, 1.158. The population doubling time, PDT, determined by these population parameters was 4.7 days.

Discussion
The investigations concerning the implementation of biological control with parasitoids to fight against the olive fruit fly have focused so far in the development of classical biological control programmes. Thus, different species have been collected from the original distribution areas of this fly to test their suitability to parasitise and develop on this pest in order to be liberated to exert a natural control Yokoyama et al., 2010Yokoyama et al., , 2011. Most of the species tested are larval parasitoids that present short ovipositors adapted to attack olive fruit fly larvae in wild olive trees, whose fruits are small. Because of that, females of some of these species have difficulties to reach larvae of B. oleae in cultivated olives  since these prefer to feed deep inside the mesocarp of larger fruits (Wang, Nadel, et al., 2009), thus limiting their efficacy to control this fly. Other species tested were originally from Asia or Australia and had been proved useful for the control of other tephritids, but, when assayed against B. oleae, they have shown either low efficacy to parasitise and thrive on the olive fruit fly  or difficulty to become established .
As indicated before, M. raptorellus is a generalist parasitoid of pupae of Diptera that is successfully used for the control of filth flies in livestock production. It is easily produced and it is commercialised for that purpose (Floate & Spooner, 2002). As it parasitises pupae, it would not have the inconvenient of some larval parasitoids to find the hosts inside the olives because from mid-autumn onwards, most individuals of B. oleae leave the olives and pupate in the soil to overwinter (Dimou et al., 2003;Neuenschwander et al., 1986). Thus, at that moment pupae can be susceptible to predators and parasitoids, and this could be an appropriate moment to carry out inoculative or inundative liberations of M. raptorellus to reduce B. oleae populations. However, as a first step in that direction, we have determined first the capacity of this parasitoid to parasitise and develop on the olive fruit fly in the laboratory. Values are mean ± SE. Within each graph, different letters indicate significant differences (P < 0.0001, ANOVA followed by LSD test for A and B, and GzLM with Binomial distribution followed by LSD test for C).
The use of freeze-killed pupae of B. oleae did not affect the rates of parasitoidism, duration of the preimaginal period, number of adult parasitoids produced per offered pupae and sex ratio of the progeny, corroborating the findings by Petersen and Currey (1996) and de Pedro et al. (2020) on M. domestica and C. capitata, respectively. In general, the biological parameters evaluated for M. raptorellus on B. oleae showed a worse profile compared to their usual hosts in nature. Thus, the rates of parasitoidism obtained in the development assay for M. raptorellus using B. oleae as host are markedly lower than the values recorded on Musca domestica L. (Diptera: Muscidae), for which rates of 85% at 25°C have been obtained (Petersen & Currey, 1996). Nevertheless, the age of the females employed by these authors was 1-2 days after emergence, contrasting with the 3-4 day-old females employed here, what could have influenced the difference observed between the values obtained. Also, the developmental periods obtained were longer than those reported at 25°C on M. domestica and Stomoxys calcitrans (L.) (Diptera: Muscidae) Lysyk, 2001;Petersen & Currey, 1996). However, the M. domestica pupae employed by Petersen and Currey (1996) and  were 1-2 day-old, contrasting with the 5-6 day-old B. oleae pupae employed here. On the other hand, as with B. oleae, shorter preimaginal developmental periods have also been reported for males comparing to females when M. domestica and S. calcitrans were used as hosts Lysyk, 2001). Moreover, for the same parasitoid:host proportion used here, the total number of offspring produced per parasitised pupae of M. domestica obtained by Petersen and Currey (1996) were almost 5 wasps, a noticeably higher value, and Lysyk (2001) reported 9.4 and 6.9 adults/pupa at 25°C on M. domestica and S. calcitrans, respectively, although this author did not control the density of pupae offered per parasitoid. As indicated by Lysyk (2001), the production of more progeny per pupa could be related to the size of the pupae offered, which in general is greater for M. domestica (8 mm long) compared to S. calcitrans (4.5-6.0 mm long), and for these two species compared to B. oleae (3.5-4.5 mm long) (Kaufman et al., 2022;Neuenschwander et al., 1986;Sanchez-Arroyo & Capinera, 2020).
The sex ratio of the progeny obtained in the reproduction assay is similar to that obtained by Lysyk (2001) at 25°C on M. domestica and S. calcitrans when the progeny produced on both species were pooled (57% of females). Also, as in our case, Petersen and Currey (1996) and Lysyk (2001) obtained the maximum offspring production around the third oviposition day, although the number of adults produced was almost doubled (18-20 wasps). Similarly, when the total number of wasps produced per pair is considered, the value obtained in our assay (around 51 individuals) was much lower compared to those reported by other authors. Thus, Legner (1988), when crossing different south American strains of the parasitoid at 25°C, obtained values for non-virgin females ranging 85-177 offspring for 16 days using M. domestica as a host. Petersen and Currey (1996) obtained between 149 and 166 offspring with the same host and most of the wasps came from eggs laid in the first 14 days of the females' lifespan. In turn, Lysyk (2001) reported an offspring production of around 100 wasps, all of them obtained from the eggs laid for 11 days on M. domestica pupae. However, due to the limited availability of B. oleae pupae in our assay, only ten hosts were provided daily per pair. This might have limited offspring production because the functional response assay showed that maximum production was achieved with host densities over 20 pupae per pair. The number of M. domestica pupae provided by the authors cited previously ranged 10-25, and, as indicated before, the larger size of the pupae of this species may lead to producing more progeny per pupa. In any case, the offspring production obtained here is higher than that reported for larval parasitoids on B. oleae like P. concolor, for which 22-29 offspring per female have been obtained , Psyttalia ponerophaga (Silvestri) which produced around 19 offspring (Sime et al., 2007), P. lounsburyi, which produced around 10 offspring per female , Diachasmimorpha kraussii (Fullaway) and Diachasmimorpha longicaudata (Ashmead) (Hymenoptera: Braconidae), which produced around 23 offspring  or Bracon celer Szépligeti (Hymenoptera: Braconidae), for which less than 10 offspring were produced , although in all cases temperature was slightly lower (22°C). Similarly, the reproductive potential showed by M. raptorellus on B. oleae is much higher than that observed for Fopius arisanus (Sonan) (Hymenoptera: Braconidae), an egg and firstinstar larval parasitoid of tephritids that only produced 4.4 adult offspring per female at 23°C when tested on B. oleae .
The life table parameters obtained for M. raptorellus on B. oleae are smaller values than those reported on house flies, although they might be higher if optimal host densities could have been employed. Thus, the r m and R 0 values obtained at 25°C on M. domestica by Legner (1988) ranged 0.136-0.189 and 39.6-138.2, respectively. In turn, the r m reported by Lysyk (2001) on the same host and at the same temperature was 0.189, whereas the R 0 obtained was 42.3 and T was 18.7, what results in a PDT of 3.7 days. These results indicate again that this species is more suitable for the population increase of the parasitoid. However, the values obtained for r m and PDT of B. oleae at 27°C , a similar temperature to that employed here, were 0.078 and 8.9 days, respectively (Soroush et al., 2013). This indicates that M. raptorellus might have potential for the control of the olive fruit fly, since its populations would increment faster than those of the pest. In addition, the maximum attack rate predicted by the Rogers function is similar or even higher than the one estimated for different species of carabid beetles that are able to prey on B. oleae pupae and have been cited as potentially relevant for the natural control of this pest (Dinis et al., 2016;Lantero et al., 2019). Moreover, according to our results, M. raptorellus females diversify the egg laying in the highest possible number of available host pupae, what entails a lower number of offspring produced per parasitised pupae, but a greater global progeny production as host density increases. A similar result was obtained using M. domestica as a host (Petersen & Currey, 1996). This has good implications for its use for the biological control of B. oleae because maximises the number of pupae that the parasitoid can kill.
However, despite the good results obtained in general regarding the parasitism of M. raptorellus on B. oleae pupae in the laboratory, another important aspect that should be considered about the capacity of this parasitoid to control B. oleae in the field is its ability to locate the pupae buried in the soil. In this sense, it has been observed in laboratory experiments that for this species almost no parasitisation occurred at depths greater than 1 cm in large arenas (Floate & Spooner, 2002). This might be a limiting factor for the practical application of this parasitoid for the biological control of the olive fruit fly, because it has been reported, also from laboratory experiments, that the mean depth of B. oleae pupation is 1.16 cm, ranging between mean values of 0-3.2 cm depending on soil type and other abiotic factors such as moisture content and temperature (Dimou et al., 2003).
Another aspect that should be considered is the possible negative effects that the liberation of this generalist parasitoid for the control of the olive fruit fly could have on other non-target dipteran species, especially tephritids relevant for the control of weeds (Cobo et al., 2015;Nadel et al., 2009) or tachinids that could contribute in olive groves to the natural control of other pests (Tschorsnig et al., 2011). To evaluate this risk, it should be considered also the probability of temporal and spatial coincidence of the liberations of the parasitoid and the pupae of these possible hosts. Similarly, the introduction of a new parasitoid might also negatively affect the autochthonous natural enemies of target and non-target organisms (Van Lenteren et al., 2003.
In conclusion, although B. oleae is less suitable for M. raptorellus than other more usual hosts in the nature like S. calcitrans or M. domestica, we have shown that the olive fruit fly pupae are appropriate for the development of the populations of this parasitoid so it might have a good potential to be used as biological control agent of this pest by means of inoculative or inundative liberations. In any case, it would be necessary to assess such potential under the prevailing environmental conditions at the times of pupation of the overwintering generation of B. oleae and the risk of the massive introduction of this parasitoid for non-target dipteran species and other natural enemies.