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Modeling of the effect of temperature on developmental rate of common green lacewing, Chrysoperla carnea (Steph.) (Neuroptera: Chrysopidae)
Egyptian Journal of Biological Pest Control volume 30, Article number: 145 (2020)
Abstract
Background
The common green lacewing Chrysoperla carnea (Steph.) (Neuroptera: Chrysopidae) is a polyphagous and efficient predatory species commonly found in a wide range of agricultural habitats. It plays an important role in biological control of pests.
Main body
The effect of temperature on developmental rate of the predator C. carnea was studied at 7 constant temperatures, 15, 20, 25, 27, 30, 32, and 35 °C, 50 ± 10% RH, and a photoperiod of 16:8 h (L:D). Six nonlinear models were evaluated to determine the trend of developmental rate of the predator in examined temperatures and to estimate thermal thresholds of development. Nonlinear models were evaluated based on coefficient of determination (R^{2}), adjusted coefficient of determination (R^{2}_{adj}), residual sum of squares (RSS), and Akaike information criterion (AIC), beside biological significance of the estimated values for the model parameters. Among evaluated nonlinear models, Lactin2 for all immature stages was the bestfitted model on observations, considering statistical criteria and biological significance of the estimations. The values of the lower temperature threshold by using Lacin2 were 9.90, 10.90, 11.90, 11.40, 11.11, 11.61, and 11.30 °C for incubation period, 1st, 2nd, and 3rd larval instars, overall larval period, and pupal and total immature stages, respectively. The values of the upper temperature threshold for the mentioned developmental stages were 33.82, 37.66, 33.14, 34.04, 33.58, 32.14, and 32.18 °C, respectively. Estimated values for the optimal temperature for incubation period, 1st, 2nd, and 3rd larval instars, overall larval period, and pupal and total immature stages were 30.69, 30.22, 30.90, 30.34, 30.90, 31.75, and 31.72 °C, respectively.
Short conclusion
The results, in addition to determine thermal tolerance for the development of C. carnea, provided advantage information for better use of C. carnea in biological control programs.
Background
Increasing resistance of different insect species to commonly used insecticides, the tendency to use unauthorized food without residues of chemical pesticides, and the increasing concern about human health and the gradual reduction of conventional insecticide usage have allowed researchers to evaluate the possibility of using other forms of lowrisk pest control methods (Athanassiou et al. 2004). Meanwhile, the roles of predators have been approved practically as effective and efficient agents in biological control programs.
The common green lacewing Chrysoperla carnea Stephen (Neuroptera: Chrysopidae) widely preys on small arthropods with a soft body such as aphids, whiteflies, thrips, butterfly eggs and larvae, and mites (Rimoldi et al. 2008). It is a cosmopolitan polyphagous and efficient predator commonly found in a wide range of agricultural habitats (Varma and Shenhmar 1983). Many studies have been carried out on C. carnea regarding its geographical distribution, prey range, and adaptation potential. In addition, its relatively easy massrearing in the laboratory and the possibility of shortterm storage of eggs and longterm storage of adults (Ashfagh et al. 2002), large appetite, and high searching ability of the lacewing larvae justifies its release against pests such as aphids, mites, and bollworms (Ashfagh et al. 2007). Besides, some of the researchers have focused on improving its rearing on different laboratory and natural hosts (Khanzada et al. 2018).
Temperature is the most important abiotic factor in biological changes of arthropods. Its effect on survival, reproduction, and population growth can be demonstrated by special functions of the temperature and can be used to predict interaction effect of natural enemies and pests (Roy et al. 2002). Developmental rate, expressed as the reciprocal of time taken to develop from one stage to another (Cossins and Bowler 1987), is nil at the lower temperature threshold, increases with temperature before leveling off at the optimal temperature, and then decreases rapidly as the upper temperature threshold is approached (Roy et al. 2002). This relationship is curvilinear near the extremes but approximately linear at moderate temperatures (Wagner et al. 1984). To describe the developmental rate more realistically and over a wider temperature range, several nonlinear models have been applied (e.g., Logan et al. 1976, Lactin et al. 1995, Briere et al. 1999, Roy et al. 2002, Arbab et al. 2006, and Ranjbar Aghdam et al. 2009). These models provide value estimates of lower and upper temperature thresholds and optimal temperature for development of a given stage.
Previously conducted studies confirmed the effect of different preys on biological characters of C. carnea (Balakrishnan et al. 2005, Zeraati et al. 2009, Hesami et al. 2011, and Jokar and Zarabi 2012). Sharifi Fard and Mossadegh (2006) studied the effects of different aphid prey on developmental time of C. carnea. Despite studying developmental time of C. carnea at different temperatures by Mirabzadeh et al. (2000), Yadav and Pathak (2010), Nadeem et al. (2012), and Saljoqi et al. (2015), there was no enough information concerning thermal tolerance range and thermal indices of C. carnea developmental stages.
The aim of the present study was focused on determination of the best descriptive model for temperaturedependent developmental rate of C. carnea and precise estimation of its thermal indices, lower temperature threshold, optimum temperature, and upper temperature threshold.
Materials and methods
Insect culture
Adults of C. carnea were collected from alfalfa fields of Firoozkooh region located in Tehran province, Iran. Rearing of the predator was carried out in an insectary located in Iranian Research Institute of Plant Protection (IRIPP) at 27 ± 1 °C, 60 ± 10% RH, and a photoperiod of 16L: 8D h. The second laboratory generation (F_{2}) was used in the present study.
Laboratory rearing
Eggs of the flour moth Ephestia kuehniella Zeller (Lepidoptera: Pyralidae) were used for feeding C. carnea. The eggs were obtained from insectary culture of flour moth established in Biological Control Research Department (BCRD) of IRIPP. In order to prevent cannibalism, rearing of C. carnea larvae was carried out individually, using small rearing containers. These containers were transparent cubic with 1.5 × 1.5 × 1.5cm dimensions. After pupation and emergence of adults, lacewings were transferred daily to plastic cylindrical containers with 30cm height and 25cm diameter for mating and oviposition. Upper side of the adult containers was closed using a fine mesh. Moreover, paper sheets (2 × 10 cm) were placed inside the containers as ovipositional substrate. In order to supply water for the adults, a small moist sponge was provided during mating and oviposition inside each Petri dish. Complementary, adults were fed on a 4:7:10 diet of yeast: honey: water (Malkeshi et al. 2004). Adult lacewings from these colonies served as the parent stock for the experiments.
Developmental time
Developmental time of incubation period, larval instars, total larval period, pupal period, and total immature stages were recorded at the 7 constant temperatures: 15, 20, 25, 27, 30, 32 and 35 (± < 1)°C, 50 ± 10% RH, and a photoperiod of 16L:8D h. Inside the growth chamber, 100–400 newly laid eggs (< 24 h) were located under each abovementioned temperatures to determine the incubation period by checking hatched eggs every 24 h. Newly emerged larvae were placed individually in plastic containers (50mm diameter and 30mm height). To provide enough ventilation, upper side of the containers had a 20 × 20mm hole in the middle part of the opening side, covered with a piece of fine net (2mm mesh). Larvae fed on fresh eggs of E. kuehniella. Larvalrearing containers were examined once daily, and fresh eggs were added on them. Larval development to next instar was recorded by visiting larval head capsule until pupation. Pupae were checked daily until adult’s exclusion for recoding pupal period of individuals. In order to determine the effect of temperature on developmental time of each immature stage of C. carnea, data was analyzed according to completely randomized design, and mean comparison was carried out using Tukey range test.
Mathematical models
In order to find the best descriptive model for temperaturedependent development of the C. carnea, 6 nonlinear models, namely, Briere1, Briere2, Lactin2, Logan6, Logan10, and polynomial 3rd order, were evaluated (Table 1). Evaluation of the models for better describing temperaturedependent development of C. carnea was done according to the values of coefficient of determination (R^{2}), adjusted coefficient of determination (R^{2}_{adj}), Akaike information criterion (AIC), and residual sum of squares (RSS). Higher values of coefficient of determination and adjusted coefficient of determination and lower values of Akaike information criterion and residual sum of squares confirmed better fit.
Thermal indices
Lower temperature threshold (t _{min})
At the lower temperature threshold, or the zero development temperature, no measurable development was detected, or the rate of development was zero. The intersection point of regression line with temperature axis showed the lower temperature threshold of development (t_{min}). After calculation of this index, the standard error of t_{min} was calculated, using the following equation:
where S^{2} is the mean square residual, r^{2} is the developmental mean, and N is the number of samples (Kontodimas et al. 2004).
Optimal temperature (t _{opt})
At the optimal temperature (t_{opt}), the rate of development was the highest. It may be estimated directly from the equations of some nonlinear models or as the parameter value for which their first derivatives equal zero. The SE of t_{opt} was estimated from the nonlinear models (Kontodimas et al. 2004).
Upper temperature threshold (t _{max})
Upper temperature threshold is the highest temperature, at which the rate of development was zero, or life cannot be maintained for a long time. Most nonlinear models can estimate this temperature. The SE of t_{max} was estimated from nonlinear models (Kontodimas et al. 2004).
Model selection criteria
Model selection was carried out according to statistical criteria and biological indices (with biological significance).
Statistical criteria
Four statistical criteria were used to evaluate the fitness of models with the data derived from laboratory observations:

1
The coefficient of determination: coefficient of determination or R^{2} index was shown for the models. The higher the value of determination coefficient, the higher accuracy will increase. The highest value of determination coefficient was 1, so the closer the obtained value of coefficient to 1 was, the better fit of the data to the models.

2
The residual sum of squares: this index was shown by RSS. It showed the standard deviation of the data from the model, so the lower the value of RSS was, the better the fit of the data to the models.

3
The Akaike information criterion: this index was shown by AIC. The model with the lowest AIC was a model with the lowest amount of lost data (Akaike 1974; Burnham and Anderson 2002; Vucetich et al. 2002; Angilletta 2006). AIC was calculated by the following formula:
$$ \mathrm{AIC}=\mathrm{nln}\left(\frac{\mathrm{SSE}}{\mathrm{n}}\right)+2\uprho $$
where n is the number of observations (in this study, the number of examined temperatures), ρ is the number of model parameters also including intercept, and SSE is the sum of squared errors.

4
The adjusted coefficient of determination: this index is shown by R^{2}_{adj}. This index deducts the effect of parameter numbers from the value of determination coefficient, so higher values of R^{2}_{adj} shows the better fit of data with the model (Rezaei and Soltani 1998). R^{2}_{adj} and AIC are parameterindependent indices of evaluation, therefore are more accurate, but R^{2} and RSS are parameterdependent. R^{2}_{adj} is calculated by the following formula:
$$ {\mathrm{R}}_{\mathrm{adj}}^2=1\left(\frac{\mathrm{n}1}{\mathrm{n}\uprho}\right)\left(1{\mathrm{R}}^2\right) $$
where n is the number of observations, ρ is the number of model parameters, and R^{2} is determination coefficient.
All nonlinear models and parameter estimation was statistically analyzed using the SPSS.V.16.0 software.
Biological indices
A good model should be able to estimate t_{opt}, t_{max}, and t_{min}, or at least t_{opt} and t_{min}. Models, with better estimation of biological indices and their predicted values, closer to the values obtained in laboratory tests are more appropriate to predict insect development at different temperatures. In order to select the best describing model for temperature development of C. carnea, first, statistical parameters were calculated, and then, results were evaluated in terms of biological standards, considering that biological parameters are much more important.
Results and discussion
Developmental time
In this research, relationship between temperature and developmental rate of C. carnea was studied. Increasing temperature showed an inverse effect on developmental time of C. carnea, and increasing temperature led to decreasing its developmental time. Mean developmental times of the lacewing immature stages are shown in Table 2. Based on these findings, it was concluded that the total developmental time varied from a maximum of 79.71 days at 15 °C through a minimum of 15.73 days at 30 °C. Based on ANOVA, incubation period (F = 19,019.30, df = 5, P < 0.001), 1st instar larvae (F = 10,591.93, df = 5, P < 0.001), 2nd instar larvae (F = 9135.29, df = 5, P < 0.001), 3rd instar larvae (F = 6989.31, df = 5, P < 0.001), total larval period (F = 44,234.98, df = 5, P < 0.001), pupal period (F = 64,071.34, df = 5, P < 0.001), and total immature stages (F = 217,654.73, df = 5, P < 0.001) of C. carnea were significantly different among examined temperatures. Means were compared using Tukey range test at 5% probability level (Table 2).
Model evaluation
Maximum total developmental time (79.714 ± 0.052 days) was recorded at 15 °C, while the minimum (15.730 ± 0.057 days) was found at 30 °C. This relationship was not linear and accordingly nonlinear models could present better description for temperaturedependent developmental rate of C. carnea. Hence, nonlinear models were fitted well to the data (Table 3). Accordingly, these models all fitted and some measurable parameters were estimated from the regression, whereas some other measurable parameters were calculated because of the solution of the equations or their first derivatives. The values of fitted coefficients and measurable parameters of the model are presented in Table 4. In Table 5, there is a synoptic presentation of how each model met criteria of the evaluation.
Many references confirmed nonlinear relationship between temperature and developmental rate of different insect’s species, e.g., Kontodimas et al. (2004), Arbab et al. (2006), Ranjbar Aghdam et al. (2009), and Saljoqi et al. (2015). Based on Saljoqi et al. (2015), the total developmental times C. carnea fed on cabbage aphid, Brevicoryne brassicae (Linnaeus), were 26.5, 23.1, 21.4, and 19.8 days at temperatures 20, 24, 28, and 32 °C, respectively. Obtained results showed a little difference than Saljoqi et al. (2015) results. This difference may be due to using different hosts, environmental factors, and/or different populations (Gilbert and Raworth 1996, Roy et al. 2002 and Roy et al. 2003, and Kayahan et al. 2014). Maximum and minimum developmental times of all immature stages of C. carnea were recorded at 15 and 30 °C, respectively. In contrast, increasing temperature to 32 °C increased developmental time. This subject is more responsible for curvilinear relationship between temperature and developmental rate of C. carnea at higher temperatures. Butler and Ritchie (1970) previously suggested using prediction models, to show the rate of development in relation to temperature. Moreover, Nadeem et al. (2012) reported C. carnea larval duration of 20.4 ± 0.12, 12.9 ± 021, 11.0 ± 0.14, 10.2 ± 0.11, and 10.0 ± 0.10 (days) at 20, 28, 31, and 35 (± 1)°C, respectively.
Statistical criteria
All evaluated nonlinear models were fitted well to the data (Table 3). Nevertheless, crucial differences among them were observed, especially in the estimated values of t_{min}, t_{opt}, and t_{max}. Considering the values of statistical criteria, Lactin2 showed the best fit to data among evaluated models (Table 3). The best model for estimating lower and upper temperature thresholds of C. carnea development was Lactin2. As presented in Table 3, Lactin2 model compared to the others was the best model to estimate the lower and upper temperature thresholds in most cases due to having the highest value of adjusted determination coefficient and lowest value of Akaike information criterion. Lactin2 model was also used to estimate temperature indices of different stages of development because of better conditions than the other models regarding biological indices. Lower temperature threshold, the optimum temperature of development, and the upper temperature threshold were estimated by Lactin2 model (Tables 4 and 5, Fig. 1).
In the present study, Lactin2 showed the best fit on observations among evaluated nonlinear models, considering statistical criteria and biological significance. Similarly, Fantinou et al. (2003) estimated the lower temperature thresholds for developmental stages of egg, larva, and pupa of sugarcane stem borer, Sesamia nonagrioides Lefebvre, by using Lactin2 model. Moreover, Kontodimas et al. (2004) estimated the lower temperature thresholds of 2 species of ladybirds, Nephus Includens and N. bisignatus, by using Lactin2 nonlinear model. All of these references showed the abilities of Lactin2 for modeling of temperaturedependent developments of the insects and mites. Figueira et al. (2000) calculated the lower temperature threshold of the green lacewing, C. externa, for different immature stages using a linear model, which was close to the estimates of this study. Kazemi and Mehrnejad (2011) reported that the lower temperature thresholds of different immature stages of the lacewing, C. lucasina, using a conventional linear model, were very close to the estimates of the present study. Results of the experimental observations showed that the optimum temperature for development stages of C. carnea was around 30 to 32 °C (Table 5).
Conclusion
This study seemed to be the first attempt to determine the optimal temperature for development of C. carnea. The results showed that the predator could be used well for biological control aims within the mentioned thermal tolerance.
Availability of data and materials
All the material and supporting data are available.
Abbreviations
 R ^{2} :

Coefficient of determination
 R ^{2} _{adj} :

Adjusted coefficient of determination
 RSS:

Residual sum of squares
 AIC:

Akaike information criterion
 L:

Light
 D:

Dark
 SSE:

Sum of squared errors
 t _{min} :

Lower temperature threshold (here for development)
 t _{opt} :

Optimal temperature (here for development)
 t _{max} :

Upper temperature threshold (here for development)
References
Akaike H (1974) A new look at the statistical model identification. IEEE T Auto Contr 19:716–723
Angilletta MJ (2006) Estimating and comparing thermal performance curves. J Theor Biol 31:541–545
Arbab A, Kontodimas DC, Sahragard A (2006) Estimating development of Aphis pomi (DeGeer) (Homoptera: Aphididae) using linear and nonlinear models. Environ Entomol 35(5):1208–1215
Ashfagh M, Hassan M, Salman B, Salman W, Rana N (2007) Some studies on the efficiency of Chrysoperla carnea against aphid, Brevicoryne brassicae, infesting canola. Pak Entomol 29(1):125–131
Ashfagh M, Nasreen N, Cheema GM (2002) A new technique for mass rearing of green lacewing on commercial scale. Pakistan J Appl Sci 2(9):925–926
Athanassiou CG, Kavallieratos NG, Andris NS (2004) Insecticidal effects of three diatomaceous earth formulations against adults of Sitophilus oryzae (Col: Curculionidae) and Tribolium confusum (Col.: Tenebrionidae) on oat, rye, and tritical. J Econ Entomol 97:2160–2167
Balakrishnan N, Murali Baskaran RK, Mahadevan NR (2005) Development and predatory potential of green lacewing Chrysoperla carnea (Stephens) (Neuroptera: Chrysopidae) on different prey insects. Agric Sci Dig 25(3):194–197
Briere JF, Pracros P, Roux AY, Pierre JS (1999) A novel rate model of temperaturedependent development for arthropods. Environ Entomol 28:22–29
Burnham KP, Anderson DR (2002) Model selection and multimodel inference: a practical informationtheoretic approach. Springer, New York
Butler GD, Ritchie PL (1970) Development of Chrysopa carnea at constant and fluctuating temperatures. J Econ Entomol 63(3):1028–1030
Cossins AR, Bowler K (1987) Temperature biology of animals. Chapman & Hall, London
Fantinou AA, Perdikis DC, Chatzoglou CS (2003) Development of immature stages of Sesamia nonagrioides (Lepidoptera: Noctuidae) under alternating and constant temperatures. Environ Entomol 32(6):1337–1342
Figueira LK, Carvalho CF, Souza B (2000) Biology and thermal requirements of Chrysoperla externa (Hagen, 1861) (Neuroptera: Chrysopidae) fed on Alabama argillacea (Hübner) (Lepidoptera: Noctuidae) eggs. Cienc Agrotec 24:319–326
Gilbert N, Raworth DA (1996) Insects and temperature, a general theory. Can Entomol 128:1–13
Harcourt DC, Yee JM (1982) Polynomial algorithm for predicting the duration of insect life stages. Environ Entomol 11:581–584
Hesami Sh, Farahi S, Gheibi M (2011) Effect of different host plants of normal wheat aphid (Sitobion avenae) on the feeding and longevity of green lacewing (Chrysoperla carnea). Paper presented at International Conference on Asia Agriculture and Animal IPCBEE, Hong Kong.
Jokar M, Zarabi M (2012) Surveying effect kind of food on biological parameters on Chrysoperla carnea (Neuroptera: Chrysopidae) under laboratory conditions. Egypt. Acad. J Biol Sci 5(1):99–106
Kayahan A, Şimşek B, Özgökçe MS, Karaca I (2014) Development and survival of Chrysoperla carnea on two different preys. TURKJANS, Special Issue: 2, 19441948.
Kazemi F, Mehrnejad MR (2011) Seasonal occurrence and biological parameters of the common green lacewing predator of the common pistachio psylla, Agonoscena pistaciae (Hemiptera: Psylloidea). Eur J Entomol 108:63–70
Khanzada KK, Chandio RH, Nahiyoon RA, Siddiqui AA, Jat MI, Mastoi SM, Mastoi PM (2018) Rearing of Chrysoperla carnea (Stephens) against two laboratory hosts and one natural host. J Entomol Zool Stud 6(1):980–983
Kontodimas DC, Eliopoulos PA, Stathas GJ, Economou LP (2004) Comparative temperaturedependent development of Nephus includens (Kirsch) and Nephus bisignatus (Boheman) (Coleoptera: Coccinellidae) preying on Planococcus citri (Risso) (Homoptera: Pseudococcidae): evaluation of a linear and various nonlinear models using specific criteria. Environ Entomol 33:1–11
Lactin DJ, Holliday NJ, Johnson DL, Craigen R (1995) Improved rate model of temperaturedependent development by arthropods. Environ Entomol 24:68–75
Logan JA, Wollkind DJ, Hoyt SC, Tanigoshi LK (1976) An analytic model for description of temperature dependent rate phenomena in arthropods. Environ Entomol 5:1133–1140
Malkeshi H, Haidari H, Jouyande A (2004) Green lacewing: the predator of agricultural products pests. Agricultural Research Education and Extension Organizations (AREEO), Iran
Mirabzadeh A, Azma M, Kharrazi Pakdel A (2000) Evaluation of the effect of different temperatures on lacewing growth period. Proceedings of the 14th Iranian Plant Protection Congress, Isfahan, p. 326, University of Isfahan, Iran
Nadeem S, Hamed M, Nadeem MK, Hasnain M, Atta BM, Saeed NA, Ashfaq M (2012) Comparative study of developmental and reproductive characteristics of Chrysoperla carnea (Stephens) (Neuroptera: Chrysopidae) at different rearing temperatures. J Anim Plant Sci 22(2):399–402
Ranjbar Aghdam H, Fathipour Y, Radjabi G, Rezapanah M (2009) Temperature dependent development and temperature thresholds of codling moth (Lepidoptera: Tortricidae) in Iran. Environ Entomol 38(3):885–895
Rezaei A, Soltani A (1998) An introduction to applied regression analysis. University of Technology, Isfahan, Iran, Isfahan
Rimoldi F, Schneider MI, Ronco AE (2008) Susceptibility of Chrysoperla externa eggs (Neuroptera: Chrysopidae) to conventional and biorational insecticides. Environ Entomol 37(5):1252–1257
Roy M, Brodeur J, Cloutier C (2002) Relationship between temperature and development rate of Stethorus punctillum (Coleoptera: Coccinellidae) and itsprey Tetranychus mcdanieli (Acarina: Tetranychidae). Environ Entomol 31:177–187
Roy M, Brodeur J, Cloutier C (2003) Effect of temperature on intrinsic rate of natural increase (rm) of a coccinellid and its spider mite prey. Biol Control 48:57–72
Sharifi Fard M, Mossadegh MS (2006) The effect of temperature and prey on growth of green lacewing, Chrysoperla carnea Stephen (Neuroptera: Chrysopidae) and estimation of its thermal needs feeding of various species of aphid. In: Proceedings of the 17th Iranian Plant Protection Congress, Karaj, p. 280, University of Tehran, Iran
Sharifi Fard M, Mossadegh MS (2006) The effect of temperature and prey on growth of green lacewing, Chrysoperla carnea Stephen (Neuroptera: Chrysopidae) and estimation of its thermal needs feeding of various species of aphid. In: Proceedings of the 17^{th} Iranian Plant Protection Congress, Karaj, p. 280.
Varma GC, Shenhmar M (1983) Some observations on the biologyEffect of different host plants of normal wheat aphid (Sitobion avenae of Chrysoperla carnea (Stephens) (Chrysopidae: Neuroptera). J Res Punjab Agric Univ 20(2):222–223
Vucetich JA, Peterson RO, Schaefer CL (2002) The effect of prey and predator densities on wolf predation. Ecology 83:3003–3013
Wagner TL, Wu HI, Sharpe PJH, Schoolfield RM, Coulson RN (1984) Modeling insect development rates: a literature review and application of a biophysical model. Ann Entomol Soc Am 77:208–225
Yadav R, Pathak PH (2010) Effect of temperature on the consumption capacity of Chrysoperla carnea (Stephens) (Neuroptera: Chrysopidae) reared on four aphid species. Bioscan 5(2):271–274
Zeraati Sh, Shishebor P, Soleiman Nejadian E, Taghadosi MV, Heidary H (2009) Investigation on life history of Chrysoperla carnea (Stephen) (Neu. Chrysopidae) on three aphid species in laboratory conditions. Plant Protect (Scientific Journal of Agriculture) 32(1):15–22
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ZN conducted the study under the supervision of HRA. HRA supervised the work, analyzed the data, and prepared the manuscript. Both of the authors have read and approved the manuscript.
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Ranjbar Aghdam, H., Nemati, Z. Modeling of the effect of temperature on developmental rate of common green lacewing, Chrysoperla carnea (Steph.) (Neuroptera: Chrysopidae). Egypt J Biol Pest Control 30, 145 (2020). https://doi.org/10.1186/s4193802000341x
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DOI: https://doi.org/10.1186/s4193802000341x
Keywords
 Chrysoperla carnea
 Thermal index
 Developmental periods
 Model