Since 17981, one of the key questions in ecology has been how populations of animals and plants are regulated. From the 1930s to the 1990s several theories emerged, with as the two most important ones the density-dependent regulation of populations2 and population limitation by density-independent factors3. Heated debates took place at congresses and in the literature, which still continue. However, ecologists today are of the opinion that perfect density dependence does rarely or not occur, and that populations are regulated by interacting density-independent and density-dependent factors. For an extensive discussion of the population regulation debate see Turchin4. In several disciplines of applied ecology, population regulation theories are playing an important role, including nature conservation, restoration of biodiversity, ecology of reintroduction of locally extinct species to their previous habitats, invasive species biology and biological control. According to Bellows and Hassell5 “population equilibria and population regulation lie at the heart of biological control”. In biological control, an organism (a natural enemy) is used to reduce the population density of another organism (a pest)6, which contributes to manage native and exotic pests in natural and managed ecosystems. In this paper we discuss a new method for efficacy evaluation of candidate organisms for use in the reduction of populations of pests and apply this method to natural enemies of a serious, quickly spreading invasive pest over the world, the South American tomato moth Tuta absoluta (Meyrick) (Lepidoptera: Gelechiidae)7,8. Although the paper focuses on biological control of pests, the same method can be used, for example, to estimate population reduction effects of invasive organisms on native organisms in natural and agricultural ecosystems.

The need for biological control of Tuta absoluta

The distribution of T. absoluta was limited to South America until 2006, then the species was accidentally introduced into Spain and currently occurs on most continents and is still spreading at a high rate7,8. Without control methods, the pest may lead to a complete loss of yield. As the larvae of the pest spend most of their time within the leaf or in the fruit, chemical control is difficult and demands up to five sprays per week and 36 times per production cycle of 12 weeks to be effective and this results in quick development of resistance to pesticides, environmental pollution and human health risks9. One of the alternatives for controlling T. absoluta is to use biological control, but finding an effective natural enemy for a new, invasive pest is not an easy task as a pest often has tens to hundreds of species attacking it6. Tuta absolua is said to be associated with almost 200 species of predators and parasitoids in their native and newly invaded areas7,8. Currently, only four species of all pest associated natural enemies are commercially used: the egg parasitoids Trichogramma pretiosum Riley (Hymenoptera: Trichogrammatidae) and Trichogramma achaeae (Nagaraja and Nagarkatti) are applied on a very small scale, and the predatory mirids Nesidiocoris tenuis Reuter (Hemiptera: Miridae) and Macrolophus pygmaeus (Rambur) are used on a larger scale7,8. All four species were found fortuitously (e.g. the mirid N. tenuis was found preying on T. absoluta in Spain by Urbaneja10 a few days after the first T. absoluta individuals were found in a tomato crop in 2009), or as a result of testing organisms that are easily mass produced (e.g. the egg parasitoid T. pretiosum in Latin America11). However, all four are not optimal for T. absoluta control, because release of the predator N. tenuis can cause serious plant damage12, M. pygmaeus needs alternative food to be able to reproduce13, and the parasitoids T. pretiosum and T. achaeae have to be released frequently and in very large numbers14,15. Therefore, other, more effective natural enemies are acutely needed, as well as efficient methods to identify promising candidates from the multitude of pest associated species. We propose a three step approach: (1) a quick scan procedure to separate clearly ineffective or hazardous species, from potentially promising candidates based on available information, (2) a phase during which the pest reduction capacity of the candidates selected in step 1 is determined, and (3) a final stage where the performance of the most promising candidates is tested under commercial tomato production conditions.

Quick scan procedure to select promising candidates from the pool of pest associated species

We previously published a list of 15 evaluation criteria, ranging from issues as “climatic adaptation to area where natural enemy will be used” to “complexity of importation and registration procedures”, for a quick scan of all organisms said to be associated with T. absoluta16. Applying these criteria, 180 species may be removed from lists of potentially effective natural enemies of this pest mentioned in publications8,16. This is, among others, because either they (1) have not been shown to attack T. absoluta, (2) are very likely to cause unacceptable nontarget effects, (3) develop too slowly or not at all on the targeted prey, (4) are trapped by the glandular trichomes on tomato and die, (5) do not kill sufficient pest organisms, or (6) are too expensive to mass produce. An example related to the fourth cause is the predator Orius insidiosus (Say) (Hemiptera: Anthocoridae): although it may kill a considerable number of pest eggs, it is caught by the sticky hairs on the stems of tomato and dies within minutes after release on the plant. Too slow immature development, high immature mortality and very low predation rates on pest eggs by Geocoris punctipes (Say) (Hemiptera: Geocoridae) illustrate causes three and five. Slow immature development, high mortality and low parasitism rates also make the parasitoids Dineulophus phthorimaeae de Santis (Hymenoptera: Eulophidae) and, when not provided with alternative food, T. pretiosum unlikely successful candidates for control of the pest. The quick scan results in less than 20 species remaining on the list of potentially successful natural enemies16.

The pest kill rate as an aggregate parameter to estimate pest reduction capacity

To obtain an idea of the biological control potential of the remaining 20 species, van Lenteren et al.16 proposed to rank them by the pest kill rate as aggregate evaluation criterion. The pest kill rate is the weighted daily average of the lifetime killing of the host or prey due to actions (predation, parasitism and nonreproductive prey and host killing) of a natural enemy. Tommasini et al.17 used a preliminary version of the pest kill rate to compare species of the genus Orius as predator of thrips pests. Next, van Lenteren18 explained that the kill rate could be used not only to rank the potential control capacity of predators, but also of parasitoids. Then, Biondi et al.19 calculated the host kill rate of the parasitoid Bracon nigricans Szépligeti (Hymenoptera: Braconidae), which included both parasitism and host killing due to stinging and host feeding. The pest kill rate, km, they found (0.121) is much higher than the intrinsic rate of population increase, rm, of B. nigricans (0.052). Van Lenteren et al.16 explained why the rm, of predators is not a useful criterion for comparison of their biocontrol capacity: it only provides information on how quickly a predator population can grow and does not tell how many prey items it can kill. In parasitoids, the rm can be used for comparison of species that do not kill hosts by nonreproductive activities. However, many species do not only eventually kill the host as a result of parasitism, but additionally kill hosts by feeding or stinging them for host examination20,21. Therefore, also in parasitoids it is better to use the pest kill rate for comparison of their pest reduction capacity.

Use of the pest kill rate parameter to compare effectivity of predators and parasitoids of Tuta absoluta

During the past two years detailed life-table data for development, mortality, sex ratio, nymphal and adult predation, parasitism capacity, nonreproductive host killing and longevity for predators and parasitoids of T. absoluta have been collected by contacting researchers who might have these data and were willing to provide them for determination of pest kill rates. Such data are relatively rare as they need to include the above-mentioned details for each organism of the cohort that was studied, which is an expensive, time and space consuming effort. Sadly, these detailed data are often neither included in a publication, nor available in a data repository. Life-table data were obtained for six species of mirid predators, four species of parasitoids that only kill hosts by parasitism and three species of parasitoids that both kill hosts by parasitism and nonreproductive host killing (Table 1). These species would not all emerge as potential candidates for control of T. absoluta in classical and augmentative control programmes when evaluated with the criteria discussed in van Lenteren et al.16. However, by using the life-table data of these natural enemies it is possible to illustrate how the pest kill rate can be used in the future for comparison and ranking of the biological control capacity of predators and parasitoids.

Table 1 Natural enemies of Tuta absoluta used in this study.

In this paper, pest kill rates of 13 predators and parasitoids of T. absoluta are calculated and compared. Moreover, species characteristics other than their pest kill rates, as well as information on their current commercial application is used to speculate which of the evaluated species might be promising candidates for biological control of this pest.


Intrinsic rate of population increase, rm, of the pest, predators and parasitoids by the Birch and Lotka-Euler approaches

Published values of the rm of T. absoluta are summarized in supplementary material (Table S16), showing that most values are in the range of 0.13–0.19. For the natural enemies, the rm calculated by the Lotka-Euler approach is higher than the rm calculated by the Birch approach in all but one case (Table 2). The exception is T. pretiosum when offered no honey as food and this can be explained simply by the short life span of one day. Both for the predators and parasitoids, there is a strong and significant positive correlation between the rm values calculated by both approaches (P <  < 0.001; Fig. 1). From now on, only the Lotka-Euler rm values will be considered, because the Lotka-Euler approach results in a more precise estimate of rm than the Birch approximation.

Table 2 Life-table parameters for six predator species and seven parasitoid species.
Figure 1
figure 1

Correlation between values of rm calculated by the Birch (x-axis) and the Lotka-Euler (y-axis) approach for predators (a), parasitoids (b) and predators + parasitoids (c).

All the rm values of the predators are lower than the rm of the pest (Table 2 and Supplementary material Table S16) and, consequently, predator populations in the presence of ample T. absoluta eggs will be growing slower than the pest in the absence of natural enemies. The same reasoning holds for several parasitoid species. However, four out of the seven species of parasitoids have similar or higher rm values than that of the pest: N. tutae, P. dignus, T. pretiosum with provision of honey as additional food, and T. bactrae. All natural enemies, except for D. phthorimaeae and T. pretiosum without additional food, have an R0 larger than 1 and a positive rm, so their population size will increase when only T. absoluta eggs and/or larvae are available for predation or parasitism. Tomato plants do not produce (extra-) floral nectar, but in a tomato crop other pests may be present that produce honey which can be used as additional food for D. phthorimaeae and T. pretiosum, resulting in higher R0 and rm, values. With the exception of T. pretiosum (Supplementary material Table S11), no experiments have been performed in tomato without additional food. The dramatic negative effect on the lifespan of and parasitism by T. pretiosum when honey is not offered as food is shown in Table 2.

Pest kill rate, km, of predators and parasitoids by the Birch and Lotka-Euler approaches

In all cases, the km calculated by the Lotka-Euler approach is higher than the km estimated by the Birch approach (Table 3), with the exception of T. pretiosum without food which is explained by the short life span of one day only. For the predators, there is a weak, nonsignificant, positive correlation between the km values calculated by both approaches (P = 0.608, Fig. 2), while the correlation is strong and positive for the parasitoids (P <  < 0.001, Fig. 2). From now on, only the Lotka-Euler km values will be considered, for the same reason as given in the section above.

Table 3 Life-table parameters related to the pest kill rate of predators and parasitoids of Tuta absoluta.
Figure 2
figure 2

Correlation between values of km calculated by the Birch (x-axis) and the Lotka-Euler (y-axis) approach for predators (a) and parasitoids (b).

The rm and km values for predators show a weak, nonsignificant correlation (P = 0.79, Fig. 3a), while this correlation is strong for parasitoids (P <  < 0.001, Fig. 3b). The nonsignificant correlation found for predators can be explained by the fact that the total number of eggs killed has no linear relationship with the number of female offspring produced. This not only holds for M. pygmaeus and T. cucurbitaceus (high predation, very few offspring), but also for the other predators (high predation but varying numbers of offspring). Parasitoids that do not kill hosts by host feeding or stinging show, as expected, very small differences between rm and km values (Fig. 3c), while parasitoids that do kill hosts by feeding and stinging show larger differences between rm and km values, showing why it is important to calculate the pest kill rate km in order to estimate their total pest reduction capacity (Fig. 3d).

Figure 3
figure 3

Correlation between rm and km calculated by the Lotka-Euler approach for all predators (a), for all parasitoids (b), for parasitoids without nonreproductive host killing (c), and for parasitoids showing nonreproductive host killing (d).

The km values of the six predators are all higher than the rm of the pest (Table 3), which indicates that the predators may kill more eggs of T. absoluta than the latter can produce. The high kill rate, together with a considerable rate of population increase of the predators C. infumatus, E. varians, M. basicornis and N. tenuis is theoretically sufficient to reduce pest populations below the economic threshold density after a single or only a few releases. Two out of the seven species of parasitoids have similar km values as the rm of the pest (Table 3): P. dignus and T. pretiosum (with provision of honey as additional food). The km values of the parasitoids T. bactrae and N. tutae are higher than the rm value of the pest. This, together with these parasitoids’ high rm values, suggests that they may be able to reduce pest populations below the economic threshold density after a single release.

In Fig. 4, the survival rates (lx), the reproduction rates (mx) and the killing activity (kx) values over the lifetime of several T. absoluta natural enemies are presented. The supplementary material provides these figures for each species of predator and parasitoid. Macrolophus basicornis (Fig. 4a) is an example of a predator that lives, reproduces and preys during a long period of time; M. pygmaeus (Fig. 4b), is an example of a predator that lives, reproduces and preys during a short period of time. This translates to a very low rm for M. pygmaeus, but the km is similar to that of M. basicornis because the predation rate is high during the short adult lifespan of M. pygmaeus. Necremnus tutae (Fig. 4c), is an example of a larval parasitoid that kills hosts through parasitism and by nonreproductive activities like stinging and host feeding. This parasitoid has a long adult life, and high rm and km values. Trichogrammatoidea bactrae (Fig. 4d), is an example of an egg parasitoid that only parasitizes eggs, has a short adult life, but exhibits the highest rm and km values of all parasitoids. The life tables in the supplementary material (Tables S1S14) and the examples in Fig. 4 also show that predators, with the exception of M. pygmaeus, live longer (averages from about 50 to more than 90 days) and kill pest eggs over longer periods (averages from 40–80 days) than parasitoids (average lifespans from 11 to about 60 days, average parasitism/host kill periods from 1 to 15 days; with B. nigricans as the exception with a 64 days long maximal lifespan and a pest killing period of more than 50 days). Immature development times of predator and parasitoid species range from 10 to 28 days, and the average duration of a generation is longer for predators (from 40 to 60 days) than for parasitoids (from 11 to 37 days).

Figure 4
figure 4

Examples of survival rate (lx), the reproduction rate (mx) and predation/parasitism rate (kx) values over the lifetime of selected species of predators and parasitoids of Tuta absoluta.

Differences between Birch and Lotka-Euler approaches

The Birch approximation is easier to apply than the Lotka-Euler iteration, but it results in an underestimate of both the rm and km due to the approximation of T and Tk. The approximation results in higher values for Tk than for T, particularly in predators, because predation is spread over a much longer time (all nymphal stages and the adult stage) than reproduction. This translates to a higher underestimate for km than for rm and to the highest underestimate in absolute terms for km in predators. In parasitoids, the difference between the two values for rm and km calculated by both approaches is the smallest for those species that only kill hosts as a result of parasitism. The differences are larger for parasitoid species that do kill hosts by nonreproductive activities because this host killing is additional to killing by parasitism and takes place over a longer period than the parasitization activities. This leads to the choice to use rm and km values calculated by the Lotka-Euler approach, and is discussed in more detail in van Lenteren et al.16. Another illustration that the Lotka-Euler iteration results in better estimates of the pest kill rate is the weak correlation between the differently estimated km values for predators (Fig. 2a). This is because in the Birch approach the Tk is calculated as an average estimate concentrated at a single point in time, while predation occurs over a long period and during both the nymphal and adult stages.

Discussion and conclusions

The question of what would be the most effective natural enemy of T. absoluta is not easy to answer, as tomato production conditions and the pest spectra on tomato are widely varying across the world. A multitude of factors, including multitrophic and intraguild interactions, availability of alternative prey/hosts/sugar sources, host plant resistance, irrigation, fertilization, neighbouring crops7,22,23 will influence the control effect of a natural enemy. However, if only the pest kill rate is considered, the predators N. tenuis and T. cucurbitaceus would rank as potentially most effective, but all predators have a km higher than the rm of the pest. Successful control of T. absoluta has been confirmed in the case of N. tenuis15,24. In addition, C. infumatus and M. basicornis successfully established on T. absoluta infested tomato plants and significantly reduced pest numbers25. The low rm of T. cucurbitaceus and the very low rm of M. pygmaeus indicate that these predators may only be used in inundative release programmes or play a role in natural and conservation biological control. Trichogrammatoidea bactrae would rank as the potentially most effective parasitoid, with N. tutae, P. dignus, and T. pretiosum showing kill rates similar to or higher than the population growth rate of the pest. The control capacity of N. tutae is confirmed by results published by Calvo et al.26 who observed that N. tutae significantly reduced T. absoluta populations, although relatively high release rates were needed. Interestingly, N. tutae often spontaneously invade greenhouses and successfully controlled T. absoluta in Spain27. The other parasitoids discussed in this paper could play a role in inundative release programmes or in natural and conservation biological control. The least effective natural enemy would be D. phthorimaeae with a km far below the rm of the pest. We are now preparing a population dynamics model (to be presented elsewhere) to estimate the effect of the kill rate of the predator together with its population growth rate to be able to draw more precise conclusions about the potential role of the natural enemies in controlling T. absoluta. Also, not only the pest kill rate in combinatin with the population growth rate should be considered when answering the question about the best and worst natural enemy and this is discussed below.

As explained in the introduction, the main aim of using the pest kill rate parameter is to rank natural enemies after they have first been evaluated by the list of criteria given in van Lenteren et al.16. When these criteria are applied to the species discussed in this paper for use in seasonal inoculative (one or few releases when pest is observed or not yet present) or inundative (frequent releases of large numbers) programmes in a tomato crop with only T. absoluta as pest, B. nigricans, D. phthorimaeae, D. gelechiidivoris and T. pretiosum without provision of additional food would not be considered candidates for its control. Their population development is too slow and their capacity to parasitize and kill hosts too limited. The following species would be considered problematic as well: M. pygmaeus because it hardly reproduces on T. absoluta13 and N. tenuis because of its severe plant damaging effect due to phytophagy if its population density becomes too high12. The following candidates offer potential: the predators C. infumatus, E. varians, M. basicornis and T. cucurbitaceus, and the parasitoids P. dignus, N. tutae, T. pretiosum and T. bactrae. However, all parasitoids, with the exception of T. pretiosum without food, have been tested with provision of honey. It is not yet known how they would perform in a tomato crop with only T. absoluta as pest, where they have no access to nectar or honeydew. On the other hand, it is rather unrealistic to consider a situation with only T. absoluta as pest. In greenhouses in temperate climates occurrence of other pests such as whiteflies, aphids, lepidopterans and dipteran leafminers, thrips and spider mites is common28,29,30. As a result, honeydew is usually present, as well as alternative prey for the predators (e.g. see Fig. 2 in Biondi et al.7). In (sub)tropical greenhouses and in open field tomato production an even larger pest spectrum occurs22,23,31. If alternative prey is available, M. pygmaeus might still play a role as they kill large numbers of T. absoluta eggs and can reproduce on other prey. When honeydew is available the parasitoids T. pretiosum and T. bactrae might also be considered as candidates. This, then, results in all six species of predators (provided that N. tenuis populations are properly managed) and four species of parasitoids (N.tutae, P. dignus, T. pretiosum and T. bactrae) as candidates for seasonal inoculative or inundative release for control of the pest. Some of these species, when environmental risk assessments do not show serious nontarget effects, can be used also in classical biological control. The parasitoids that develop too slowly and/or kill too few hosts (B. nigricans, D. phthorimaeae and D. gelechiidivoris) might play a supportive role in conservation and classical biological control.

Part of the selection process for a natural enemy to be useful in commercial releases is its ease of mass rearing and whether the natural enemy is able to control other pests. Concerning the first issue, ease of mass rearing , economic mass-production methods have been developed earlier by commercial companies for mirid predators. The same holds for the parasitoids T. pretiosum and T. bactrae, but N. tutae is very difficult to mass rear32. The second issue, being able to control other pests, depends on the complexity of the pest situation in greenhouses. The pest spectrum in temperate greenhouses is much narrower than in the (sub)tropics, so both generalist predators or the more specific parasitoids could be used. In the (sub)tropics generalist mirid predators might be of greater value, as they not only kill a wide range of lepidopterans, but also whiteflies, aphids and even spider mites (V.H.P. Bueno, F.C. Montes and D. B. Silva, personal communication 2021,33). Bueno (personal communication 2020, and supplementary material (Table S17)) concluded that more than 15 different species of natural enemies would be needed for the control of more than 15 species of pests that occur on tomato in Brazil. With an effective Neotropical mirid predator, the number of species of natural enemies needed in tomato in Brazil might be reduced to less than five. A. Urbaneja (personal communication 2021) confirms that the same reasoning holds for the Paleotropic mirid N. tenuis with regard to control of a similar range of pests on tomato in the Mediterranean Basin.

An interesting characteristic of mirid predators besides their broad prey menu is that they are champions in dealing with the poisonous sticky hairs on tomato34,35. Yet another attractive characteristic is their capacity to induce defensive plant responses due to their phytophagous behaviour36. These defenses can activate the production of secondary metabolites and proteins that have toxic, repellent, and/or antifeedant effects on herbivores (direct defenses). Furthermore, the production and release of Herbivore-Induced Plant Volatiles can modify the behaviour of both phytophagous pests and their natural enemies (indirect defenses). Mirid-induced defenses may reduce the impact of pest herbivores on tomato plants, e.g. those induced by the N. tenuis might partly explain the success achieved by this predator in southeastern Mediterranean tomatoes36.

Eventually, only well-replicated experiments and/or well-documented experience under practical tomato growing situations will provide an answer to the suitability of these natural enemies for control of T. absoluta.

Concluding remarks

  1. 1.

    As pest kill rate (km) values are always higher than intrinsic rate of natural increase (rm) values, they provide better insight for estimating the potential of a natural enemy to control the pest. With the pest kill rates calculated in this paper, several species of natural enemies can be removed from the list of potential candidates for biological control of T. absoluta in seasonal inoculative or inundative release programmes. The few natural enemies that have shown to be able to control T. absoluta on tomato, in particular the predator N. tenuis and the parasitoid N. tutae, have km values that are considerably larger than the rm of the pest.

  2. 2.

    To evaluate the potential of natural enemies in controlling the pest during several generations, a model linking the intrinsic rate of natural increase and the pest kill rate needs to be developed. With this model, it would be possible to estimate whether a seasonal inoculative or an inundative biological control programme is required.

  3. 3.

    Authors stating that a certain organism might be a promising candidate for biological control should support such statements with a critical evaluation of natural enemy characteristics, provision of quantitative data such as the pest kill rate as presented in this paper, and with results of experiments performed under realistic crop production conditions to confirm laboratory findings. When using evaluation criteria and the pest kill rate parameter, it is, for example, possible to eliminate more than 180 of the 200 species that are currently listed as candidates for control of T. absoluta. Over the years, many authors speculated about the contribution to biological control by the organism they studied without presenting data that make it possible to substantiate and confirm their supposition. Other authors mentioning rm—and in a few cases km—values did not present the raw data as supplementary material or in a data repository, were not willing to provide the data upon request or, in some cases, the provided data indicated that the paper contained mistakes and that these raw data proved unsuitable to calculate the pest kill rate because they were incomplete. However, most requests for sending us detailed life-table data resulted in provision of these raw data. Thus, we petition for compulsory provision of raw data with the submission of a manuscript.

Material and methods

Predators of Tuta absoluta

In South America, more than 50 species of predators have been found in association with T. absoluta but less than 10 species might be sufficiently effective for its control8,24,25. Currently, the mirid Tupiocoris cucurbitaceus (Spinola) (Hemiptera: Miridae) is used for control of T. absoluta in Chile37 and for control of whitefly in Argentina and Uruguay (Carlos Silvestre, Brometan Biological System—Biobest Argentina, personal communication). Complete sets of life-table data are rare for predators, because the nymphal and adult stages consume many T. absoluta eggs per day (up to on average 70 eggs) and in their total lifetime (up to on average 1265 eggs). Comprehensive life tables have been published for three Neotropical mirids (Campyloneuropsis infumatus (Carvalho), Engyttatus varians (Distant) and Macrolphus basicornis (Stäl) (Hemiptera: Miridae))16, and sufficient predation data are available for the mirid T. cucurbitaceus to be able to reconstruct a life table38. Ten arthropod species, mainly hemipterans are known to prey on T. absoluta in Europe8. For two of these European mirid predators, M. pygmaeus and N. tenuis, detailed life-table data are available for predation by the nymphal stages13, and adult predation could be estimated based on partial daily predation data determined by Molla et al.13 and data earlier published10,39,40,41,42,43. A recent paper44 showed that the predation rates of nymphs and adults of the damsel bug Nabis pseudoferus Remane (Hemiptera: Nabidae) are similar to those of mirid predators, but the paper contained insufficient information to be able to calculate the pest kill rate.

Parasitoids of Tuta absoluta

More than 50 (morpho) species of egg, larval and pupal parasitoids are associated with T. absoluta in South America, but only 23 could be confirmed parasitizing this host45. Almost 50 species of parasitoids are supposed to parasitize T. absoluta in Europe8. Recently, stocktaking of parasitoids in Africa46 resulted in finding several new species. Of all these parasitoids, few species have been tested under (semi-)practical conditions: the egg parasitoids T. achaeae in France and Spain8, T. pretiosum in Brazil11, and the larval parasitoid Necremnus tutae (= N. artynes) Ribes and Bernardo (Hymenoptera: Eulophidae) in Spain26. Only Trichogramma and Trichogrammatoidea egg parasitoids are mass reared and augmentatively released on a small area in the southwestern Mediterranean basin7,8 and in Brazil, Chile, Colombia, Ecuador and Peru in Latin America45,47. Detailed life-table data could be obtained for T. pretiosum with14 and without food (Montes, personal communication 2020, supplementary material Table S11). A third set of complete life-table data exists for T. pretiosum48,49, as well as a set for T. achaeae (T. Cabello, University of Almeria, personal communication 2018), but the original data sets were not made available. A complete life table was provided for Trichogrammatoidea bactrae Nagaraja (Hymenoptera: Trichogrammatidae)50, an exotic species initially introduced into Argentina for control of Pectinophora gossypiella Saunders (Lepidoptera: Gelechiidae)45,50.

In South America, most studies on larval parasitoids of T. absoluta concern D. phthorimaea, Dolichogenidea (Apanteles) gelechiidivoris Marsh. (Hymenoptera: Braconidae) and Pseudapanteles dignus (Muesebeck) (Hymenoptera: Braconidae)45. In Europe, several larval parasitoids have been studied, including B. nigricans and N. tutae8. Recent studies in Africa concentrated on D. gelechiidivoris, which was imported from Peru into Kenya51, and on B. nigricans and Dolichogenidea appellator (Telenga) (Hymenoptera: Braconidae)46. The host kill rate of the Neochrysocharis formosa (Westwood) (Hymenoptera: Eulophidae) was recently published52, but important basic information to judge the quality of the data was lacking in the paper and contact with the authors did not result in the provision of the raw data used for calculation of the kill rate by us. Complete sets of life-table data could be obtained for the larval parasitoids B. nigricans19, D. gelechiidivoris51, N. tutae53, and P. dignus54. Partial life-table data for D. phthorimaeae55,56 combined with additional information provided by these authors, resulted in sufficient material to determine the pest kill rate for this species.

In total, we obtained life tables for 13 species of natural enemies: six predators and seven parasitoids (Table 1). All cohort-based life-table data for each species together with a reference to the original paper details on material and methods are provided as supplementary material (supplementary material Tables S1S14). Only life-table data have been used that were determined at temperatures between 24 and 26 °C. Although the experimental conditions differed with regard to humidity, photoperiod, light intensity, ventilation and size of the experimental arenas, we do not expect they strongly influenced the life-table data which is explained in supplementary material Text S15.

Research involving plants

The plants used in the experiments were commercially available cultivars and did not involve plant species at risk of extinction or species of the wild flora. Our research complied with local and national regulations—Formal ethical approval was not required.

Calculation of intrinsic rate of population increase (r m) and pest kill rate (k m)

Life-table parameters of predators and parasitoids were studied following the methodology explained by Birch57, where x denotes the pivotal age in days after an egg is laid (so, including immature stages for predators), lx the age-specific survival (including immature mortality), and mx the age-specific fertility (the number of females produced per female alive at age x). These were determined in order to calculate the derived quantities as defined in Table 4. The pest kill rate (km) of the predators and parasitoids was calculated using the same formula as rm, but the age-specific fertility (mx) was substituted with the age-specific predation (kx) both during the nymphal and the adult stages for predators and only the adult stage for parasitoids. The mean predation time Tk can be considered as the time required for a population to predate at a rate of K0. The net consumption rate K0 is the number of prey items killed during a generation of the predator, corrected by natural mortality of the predator. For parasitoids, mx was substituted by the age-specific parasitism, and, if parasitoids showed nonreproductive host killing due to stinging and/or host feeding, by the age-specific host killing. K0 for parasitoids is the number of hosts killed by parasitism and nonreproductive host killing, corrected by natural mortality of the parasitoid.

Table 4 Description and formulas for the data-based quantities.

When individual daily predation and parasitism data are available, pest kill rates values can also be calculated with the Euler-Lotka Eq. 58,59, which is a more accurate method than the Birch approach16. In that case rm can be assessed with Eq. (1) and km with Eq. (2). The values for rm and km are obtained by iteration, i.e. by updating rm and km values until the formula gives the required value of 1.

$$1 = \mathop \sum \limits_{x = 0}^{{x_{max} }} l_{x} m_{x} {\text{exp}}\left( { - r_{m} x} \right)$$
$$1 = \mathop \sum \limits_{x = 0}^{{x_{max} }} l_{x} k_{x} {\text{exp}}\left( { - k_{m} x} \right)$$

For all predators and parasitoids, the intrinsic rate of natural increase and the pest kill rate was calculated with both the Birch and Euler-Lotka approach as explained in van Lenteren et al.16. The rm and km calculations are provided as supplementary material (supplementary material Tables S1S14).


The Pearson’s product-moment correlation60 was used to calculate the correlations coefficients (PPMCC) between rm values, km values and the rmkm values.