Introduction
The two-spotted spider mite, Tetranychus urticae Koch (Acari: Tetranychidae), is a globally distributed agricultural pest that frequently inflicts substantial damage on both perennial and annual crops (Elsadany, Reference Elsadany2018; Taghizadeh and Chi, Reference Taghizadeh and Chi2022). Management of spider mite infestations has traditionally depended on acaricide applications (Hodek, Reference Hodek1987; Khanamani et al., Reference Khanamani, Fathipour, Hajiqanbar and Sedaratian2014), despite their well-documented disadvantages, including adverse impacts on natural enemies and the rapid development of resistance. Resistance to more than 80 acaricides has been documented in spider mite populations from over 60 countries (Khanamani et al., Reference Khanamani, Fathipour, Hajiqanbar and Sedaratian2014; Kim et al., Reference Kim, Lee, Kim and Kim2024), highlighting the urgent need to develop pesticides with novel modes of action (Devine et al., Reference Devine, Barber and Denholm2001) as well as effective non-chemical alternatives for pest management.
The use of natural enemies, including the predatory thrips Scolothrips longicornis Priesner (Thysanoptera: Thripidae), represents a promising strategy for reducing the risk of future pesticide resistance (Pakyari and Enkegaard, Reference Pakyari and Enkegaard2013), while supporting the growing emphasis on environmentally sustainable pest management. S. longicornis is indigenous to many countries (Priesner, Reference Priesner1950; Pakyari et al., Reference Pakyari, Fathipour and Enkegaard2011a, Reference Pakyari, Fathipour and Enkegaard2011b) and is commonly found on crops such as cucumber, eggplant, and bean (Pakyari et al., Reference Pakyari, Fathipour, Rezapanah and Kamali2009; Heidarian et al., Reference Heidarian, Fathipour and Kamali2012). This predator has been recognised as an effective biological control agent against several spider mite species (Abad-Moyano and Urbaneja, Reference Abad-Moyano and Urbaneja2009). It is well adapted to warm environments, with temperatures between 26°C and 35°C being optimal for its population growth, prey consumption, and reproduction (Pakyari et al., Reference Pakyari, Fathipour and Enkegaard2011a, Reference Pakyari, Fathipour and Enkegaard2011b; Pakyari and Enkegaard, Reference Pakyari and Enkegaard2012). Both larval and adult stages prey on spider mites at different developmental stages, with eggs representing an important food source (Pakyari et al., Reference Pakyari, Fathipour, Rezapanah and Kamali2009). Throughout their lifespan, adults consume approximately 200–300 spider mite eggs (Pakyari and Enkegaard, Reference Pakyari and Enkegaard2012) and exhibit a type II functional response, characterised by increased search efficiency and reduced handling time as temperature rises (Pakyari et al., Reference Pakyari, Fathipour, Rezapanah and Kamali2009).
Functional response analysis is among the most widely used approaches for evaluating the effectiveness of natural enemies in managing pest populations. Holling described three general categories of functional response curves (Holling, Reference Holling1959). In a type I functional response, the rate of prey consumption increases proportionally with prey density until it levels off at a maximum consumption rate, after which consumption remains constant. In contrast, a type II functional response is distinguished by a decelerating increase in prey consumption as prey density rises, ultimately approaching an asymptote. The type III functional response exhibits a sigmoidal pattern and is strongly influenced by experimental conditions and the predator’s previous feeding experience (Patel and Zhang, Reference Patel and Zhang2017). Although both type II and type III functional responses have been reported in arthropod predators, the type II pattern is the most frequently observed (Pakyari and Enkegaard, Reference Pakyari and Enkegaard2013; Han et al., Reference Han, Su, Zhang, Chen and Zhang2020; Yazdanpanah and Fathipour, Reference Yazdanpanah and Fathipour2023). Previous studies have likewise shown that other predatory thrips, including S. takahashii Priesner, also display a type II functional response (Ding-Xu et al., Reference Ding-Xu, Juan and Zuo-Rui2007).
The functional response describes the relationship between an individual predator’s rate of prey consumption and prey density (Pakyari et al., Reference Pakyari, Fathipour, Rezapanah and Kamali2009; Pakyari and Enkegaard, Reference Pakyari and Enkegaard2013; Han et al., Reference Han, Su, Zhang, Chen and Zhang2020). It also provides information on important components of predator–prey interactions, including searching efficiency, handling time, and predation capacity, which can be used to evaluate the predatory potential of natural enemies (Fathipour et al., Reference Fathipour, Karimi, Farazmand and Talebi2017). Consequently, functional response analysis can provide useful information for assessing the biological control potential of natural enemies against specific pest species (Jasin Rahman et al., Reference Jasin Rahman, Babu, Roobakkumar and Perumalsamy2012; Juliano, Reference Juliano2020).
Heat stress not only affects the development and growth of S. longicornis but may also alter its functional response. Previous research demonstrated that the predation rate of S. longicornis feeding on T. urticae eggs increased progressively between 15°C and 26°C before declining at 30°C (Pakyari and Enkegaard, Reference Pakyari and Enkegaard2012). However, the effects of short-term heat stress on the functional response of this predator have not yet been investigated. Therefore, the present research was conducted to examine how short-term heat stress affects the functional response of S. longicornis when preying on T. urticae. The associated functional response parameters, including attack rate (α) and handling time (Th), were calculated. The findings are expected to provide useful information for optimising the commercial mass rearing of this predatory thrips and improving its application in biological control programmes, particularly under high-temperature conditions encountered in greenhouses and during hot summer periods.
Material and methods
Prey and predator rearing
Adult spider mites and thrips were reared under laboratory conditions. A laboratory colony of T. urticae was established from individuals gathered from bean fields in Shahriar, Tehran Province, Iran (35.6588° N, 51.0578° E). The colony was reared on freshly excised bean leaves positioned abaxial side up on a layer of moistened cotton within 150-mm-diameter Petri dishes. Each Petri dish lid contained a 30-mm-diameter opening wrapped with fine nylon mesh to provide adequate ventilation. The colonies were maintained in an incubator (Binder KBWS 240, Germany) at 26 ± 1°C, 60 ± 10% relative humidity, and a 16:8 h (L:D) photoperiod. A colony of S. longicornis was similarly established using adults gathered from the same bean fields. For colony maintenance, fresh cucumber leaves collected from plants at the fourth- to fifth-leaf stage were placed in Petri dishes (180 mm diameter), and 40–50 adult female spider mites were introduced to oviposit for 48 h under the same environmental conditions, producing approximately 500–600 eggs. After the female mites were removed, five adult thrips were introduced into each Petri dish, and the colonies were maintained in a separate growth chamber under identical conditions. Adult female thrips were transferred to freshly infested bean leaves every 2 days. These rearing procedures were based on previously described methods for maintaining S. longicornis on T. urticae. The established colonies were used in the experiments after rearing periods of 2 months for S. longicornis and 3 months for T. urticae.
Test arena
Bean seedlings (Phaseolus calcaratus Roxb. cv. Goli) were grown in 20-cm-diameter pots containing a substrate composed of clay (33%), peat moss (34%), and sand (33%) until they reached the fourth- to fifth-leaf stage. Experimental arenas were prepared using excised bean leaf discs (30 mm in diameter) without major veins, positioned with the abaxial surface facing upward on moist cotton within 60-mm Petri dishes. Each dish lid contained a 15-mm-diameter ventilation opening covered with fine nylon mesh. To obtain spider mite eggs of uniform age, 5–20 adult female T. urticae were introduced onto each bean leaf disc and permitted to oviposit for 24 h. Subsequently, the adult females and any surplus eggs exceeding the required experimental density were carefully removed.
Experimental design
Newly emerged unmated females of S. longicornis were exposed to one of three elevated temperatures (38°C, 40°C, or 42°C) for 2, 4, or 6 h in the incubator (Binder KBWS 240, Tuttlingen, Germany). In the control treatment, one female per leaf disc was kept continuously at 25°C without exposure to heat stress. The temperature treatments and short-term heat-stress approach were selected based on previous studies of S. longicornis (Pakyari and Kakvan, Reference Pakyari and Kakvan2026). Following heat treatment, the females were deprived of food for 24 h. One-day-old T. urticae eggs were then introduced into the experimental arenas at seven prey densities (10, 20, 30, 40, 50, 60, and 70 individuals). Each heat-treated and subsequently starved S. longicornis female was then individually transferred to an arena containing the assigned prey density. Ten replicates were conducted for each treatment, and predation was assessed after a 24-h experimental period.
Data analyses
The functional response data were evaluated in a two-step procedure (Juliano, Reference Juliano2020). First, logistic regression was used to analyse the proportion of prey consumed (Na) as a function of the initial prey density (Nt) to determine the type of functional response.
\begin{equation}\frac{{N_a}}{{N_t}} = \ \frac{\exp ({P_0}+{P_1}{N_t}+\ {P_2}{N_t^2}+{P_3}{N_t^3})}{1+\exp ({P_0}+\ {P_1}{N_t}+\ {P_2}{N_t^2}+\ {P_3}{N_t^3})}\end{equation}The coefficients P₀, P₁, P₂, and P₃ are the maximum likelihood estimates for the intercept, linear, quadratic, and cubic terms, respectively. The functional response type is classified based on the sign of the linear coefficient (P₁): a negative value denotes a Type II response, whereas a positive value denotes a Type III response (Juliano Reference Juliano2001). Subsequently, the attack rate (a) and handling time (Th), defined as the total time required to pursue, kill, consume, and digest a prey item, are calculated using the random predator equation (Royama, Reference Royama1971; Rogers, Reference Rogers1972).
\begin{equation}{N_a} = {N_t}[1-\exp (a({T_h}{N_a}-T))]\end{equation}The equation incorporates the following parameters: the initial prey density (Nt), the number of prey consumed per predator (Na), the total available search time (T = 24 h), the attack rate (a, representing searching efficiency), and the handling time (Th). In the case of a Type III functional response, the attack rate is density-dependent, increasing with prey density according to the relationship defined by (Hassell et al., Reference Hassell, Lawton and Beddington1977).
\begin{equation}a = (d+b{N_t})/(1\ +\ \mathrm{c} {N_t})\end{equation}When neither d nor c was significantly different from zero, the model simplified to a = bNt, which was then substituted into Equation 2.
To characterise the functional responses, we employed iterative nonlinear least-squares regression. The random predator model was fitted to the data to estimate the parameters of the Type II functional response. Predatory efficiency of S. longicornis across treatments was assessed by comparing the maximum observed predation rate and the average number of prey consumed at the highest prey density (70 prey).
Estimating predation rate
The data were analysed with the SAS Generalised Linear Model procedure (version 9.1) to assess the main effects of prey density and temperature as well as their two-way interaction. Upon finding a significant interaction, a post-ANOVA slice analysis was employed to deconstruct the interaction by evaluating the influence of prey density within each temperature and duration. Pairwise comparisons were adjusted using Tukey’s HSD test. Additionally, a linear regression analysis was performed to quantify the relationship between the initial prey density and the predator’s prey consumption (Schabenberger et al., Reference Schabenberger, Gregoire and Kong2000).
The objective of this analysis was to examine separately how changes in prey density influence prey consumption at each predator age, and how changes in temperature and duration influence prey consumption at each prey density. Data were statistically analysed using Minitab (version 26) and SAS (version 9.1).
Results
Logistic regression analysis of the functional response of unmated S. longicornis females yielded negative P₁ values across all treatments (table 1), indicating that the predators exhibited a type II functional response under every temperature regime evaluated.
Maximum-likelihood estimates from logistic regressions of the proportion of prey consumed by Scolothrips longicornis females at different temperatures
Table 1 Long description
Logistic regression results are listed by treatment and parameter, with columns for estimate, SE, x2, and P-Value. Treatments are CK, 38 degrees C for 2 h, 4 h, and 6 h, and 40 degrees C for 2 h, 4 h, and 6 h; parameters are Intercept P0, Linear P1, Quadratic P2, and Cubic P3. For CK, estimates are 3.4484 for Intercept, minus 0.1353 for Linear, 0.00197 for Quadratic, and minus 0.00001 for Cubic, with P-Values less than 0.0001, 0.0097, 0.1155, and 0.2354. For 38 degrees C, Intercept estimates are 3.0321 at 2 h, 2.3118 at 4 h, and 1.6041 at 6 h; Linear estimates are minus 0.1128, minus 0.1013, and minus 0.0428, with P-Values 0.0218, 0.0225, and 0.3193. For 40 degrees C, Intercept estimates are 1.4817 at 2 h, 0.8173 at 4 h, and 0.7114 at 6 h; Linear estimates are minus 0.0354, minus 0.00920, and minus 0.0460, with P-Values 0.4073, 0.8226, and 0.2045. Quadratic estimates range from 0.00197 in CK down to minus 0.00078 at 40 degrees C for 4 h, with P-Values from 0.1155 to 0.7598 across treatments. Cubic estimates range from minus 0.00072 at 38 degrees C for 4 h to 0.00781 at 40 degrees C for 4 h, with P-Values from 0.2354 to 0.7933.
The estimated attack rate (a) and handling time (Th) are summarised in table 2. Overall, the attack rate of unmated S. longicornis females declined progressively with increasing temperature and longer durations of heat stress. In contrast, handling time (Th) gradually increased as the temperature rose from 38°C to 40°C.
Estimated values of attack rate and handling time for Scolothrips longicornis females at different temperatures
Table 2 Long description
Estimated attack rate, handling time, estimated maximum predation rate, observed maximum predation rate, and R2 are listed for CK and heat treatments at 38 degrees C and 40 degrees C for 2, 4, or 6 hours. CK reports attack rate 0.0506 plus or minus 0.00462 per hour with 95 percent confidence interval 0.0414 to 0.0598, handling time 0.4493 plus or minus 0.0382 hours with interval 0.3730 to 0.5256, T over Th 53.42 prey per day, OMPR 32.4 with 36 in parentheses, and R2 0.92. At 38 degrees C for 2 hours, attack rate is 0.0509 plus or minus 0.00489 with interval 0.0411 to 0.0606, handling time 0.6047 plus or minus 0.0421 with interval 0.5206 to 0.6888, T over Th 39.69, OMPR 28.4 with 35 in parentheses, and R2 0.91. At 38 degrees C for 4 hours, attack rate is 0.0491 plus or minus 00.639 with interval 0.0364 to 0.0619, handling time 0.7383 plus or minus 0.0608 with interval 0.6169 to 0.598, T over Th 32.51, OMPR 23.5 with 30 in parentheses, and R2 0.90. At 38 degrees C for 6 hours, attack rate is 0.0495 plus or minus 0.0070 with interval 0.0355 to 0.634, handling time 0.8410 plus or minus 0.0678 with interval 0.7058 to 0.9763, T over Th 93.53, OMPR 22.5 with 27 in parentheses, and R2 0.90. At 40 degrees C for 2 hours, attack rate is 0.0518 plus or minus 0.0064 with interval 0.0391 to 0.0645, handling time 0.8865 plus or minus 0.0573 with interval 0.7722 to 1.0009, T over Th 130.58, OMPR 20.2 with 25 in parentheses, and R2 0.89. At 40 degrees C for 4 hours, attack rate is 0.0469 plus or minus 0.0052 with interval 0.0365 to 0.0573, handling time is shown as 0.9406 to 0.0565 with interval 0.8278 to 1.0534, T over Th 133.78, OMPR 19.1 with 20 in parentheses, and R2 0.89. At 40 degrees C for 6 hours, attack rate is 0.0367 plus or minus 0.0051 with interval 0.0266 to 0.0469, handling time 1.1467 plus or minus 0.0894 with interval 0.9683 to 1.3251, T over Th 245.15, OMPR 15.2 with 20 in parentheses, and R2 0.90.
a, attack rate; Th, handling time; T/Th, estimated maximum predation rate; OMPR, observed maximum predation rate (in parentheses) and the average prey consumed at a density of 70 prey (outside parentheses); R 2=1 - (residual sum of squares/corrected total sum of squares).
Note: The values in parentheses represent 95% confidence intervals.
The lowest attack rate (0.0367 h−1) was recorded following exposure to 40°C for 6 h, whereas the highest value (0.0506 h−1) was observed in the control treatment. Conversely, the longest handling time (1.147 h) occurred at 40°C for 6 h, while the shortest handling time (0.449 h) was recorded in the control treatment (p = 0.029; p < 0.001; p = 0.0016).
Across all treatments, prey consumption by unmated predator females increased with increasing prey density. However, relative to the control, the number of prey consumed declined markedly as both temperature and the duration of heat stress increased (table 3).
Mean value ± SE of prey consumption per day by the female of Scolothrips longicornis at different temperatures
Table 3 Long description
Mean prey consumption per day is listed for treatments CK, 38 degrees C for 2, 4, or 6 hours, and 40 degrees C for 2, 4, or 6 hours, across columns labeled 10, 20, 30, 40, 50, 60, and 70. For 38 degrees C for 2 hours, values go from 8.9 plus or minus 0.35 at 10 to 28.4 plus or minus 1.20 at 70. For 38 degrees C for 4 hours, values go from 8.2 plus or minus 0.47 at 10 to 23.5 plus or minus 1.55 at 70, and for 38 degrees C for 6 hours, from 7.3 plus or minus 0.73 at 10 to 22.5 plus or minus 0.87 at 70. For 40 degrees C for 2 hours, values go from 7.3 plus or minus 0.67 at 10 to 20.2 plus or minus 1.30 at 70, for 40 degrees C for 4 hours from 6.6 plus or minus 0.85 at 10 to 19.1 plus or minus 0.62 at 70, and for 40 degrees C for 6 hours from 5.3 plus or minus 0.62 at 10 to 15.2 plus or minus 0.66 at 70. Each numeric cell includes a lower case letter after the mean and standard error. A row labeled, P value regression, reports P 0.001 at 10 and P less than 0.001 for columns 20 through 70, and a row labeled, r2, lists 0.297, 0.362, 0.450, 0.602, 0.764, 0.753, and 0.704 for columns 10 through 70.
Note: The means followed by different lowercase letters in each column are significantly different (p < 0.05; Tukey’s test). p-Values indicate the significance of the linear regression, and r 2 represents the coefficient of determination.
Under the experimental prey densities used, the minimum and maximum numbers of prey consumed in the control treatment were 8.9 and 32.4, respectively. Following exposure to 38°C and 40°C for 6 h, prey consumption decreased to 7.3 and 22.5, and to 5.3 and 15.2, respectively, representing significantly lower values than those recorded in the control. Furthermore, significant differences in both the minimum and maximum numbers of prey consumed were detected between the 38°C, 6 h and 40°C, 6 h treatments across all prey densities (p = 0.001; p = 0.0001) (table 3).
Discussion
The present study provides additional evidence supporting the value of functional response analysis as an effective approach for assessing the performance of biological control agents against economically important crop pests. Functional response analysis has long been used to evaluate predator performance because it describes the relationship between prey density and prey consumption by an individual predator (Holling, Reference Holling1959). In our previous study, exposure of S. longicornis to 42°C for 2, 4, and 6 h prevented egg hatching and severely impaired reproductive performance, demonstrating the pronounced detrimental effects of short-term heat stress on this predatory thrips (Pakyari and Kakvan, Reference Pakyari and Kakvan2026). Building upon those findings, the present study investigated the influence of short-term heat stress on the functional response of S. longicornis. The results demonstrated that exposure to different temperatures and durations of heat stress did not alter the functional response pattern, as female S. longicornis consistently exhibited a type II functional response when feeding on T. urticae eggs. These findings are consistent with those of Pakyari et al. (Reference Pakyari, Fathipour, Rezapanah and Kamali2009) and Pakyari and Enkegaard (Reference Pakyari and Enkegaard2013), who also reported a type II functional response for S. longicornis feeding on different densities of T. urticae eggs under various constant temperatures and following exposure to different pesticide doses.
The functional response of a predator is influenced by several factors, including the developmental stage of the prey (Jeschke et al., Reference Jeschke, Kopp and Tollrian2002), prey size (Rall et al., Reference Rall, Brose, Hartvig, Kalinkat, Schwarzmüller, Vucic-Pestic and Petchey2012), the host plant species on which predator–prey interactions occur (De Clercq et al., Reference De Clercq, Mohaghegh and Tirry2000), and environmental conditions (Pakyari et al., Reference Pakyari, Fathipour, Rezapanah and Kamali2009; Sentis et al., Reference Sentis, Hemptinne and Brodeur2012). A type II functional response has likewise been documented for other predatory thrips species and prey combinations, including S. takahashii feeding on T. viennensis Zacher (Li et al., Reference Li, Tian and Shen2006; Ding-Xu et al., Reference Ding-Xu, Juan and Zuo-Rui2007), S. longicornis preying on Schizotetranychus smirnovi Wainstein (Heidarian et al., Reference Heidarian, Fathipour and Kamali2012), and S. takahashii feeding on T. urticae (Gotoh et al., Reference Gotoh, Nozawa and Yamaguchi2004). Collectively, these studies suggest that the type II functional response is common among predatory thrips. The present findings further demonstrate that exposure to short-term heat stress does not modify the functional response type of S. longicornis.
Our results further confirmed that short-term heat stress markedly reduced the predation capacity of S. longicornis on the egg stage of T. urticae. Following heat exposure, prey consumption declined consistently, with the lowest consumption rates observed under the most severe heat stress treatments. These findings are consistent with previous reports describing the influence of temperature on the functional response parameters of predatory thrips (Gotoh et al., Reference Gotoh, Nozawa and Yamaguchi2004; Pakyari et al., Reference Pakyari, Fathipour, Rezapanah and Kamali2009).
The magnitude of a functional response is strongly influenced by the attack rate and handling time (Omkar and Pervez, Reference Omkar and Pervez2011). Among these parameters, handling time provides an important measure of predator efficiency because it reflects the time required to locate, capture, subdue, and consume prey (Pervez and Omkar, Reference Pervez and Omkar2005). In the present study, attack rate declined progressively with increasing heat stress, reaching its lowest value after exposure to 40°C for 6 h. In contrast, handling time increased with increasing temperature, a pattern consistent with previous studies (Li et al., Reference Li, Tian and Shen2006; Pakyari et al., Reference Pakyari, Fathipour, Rezapanah and Kamali2009).
Previous research has shown that elevated temperatures can accelerate respiration and metabolic activity (Andrew et al., Reference Andrew, Ghaedi and Groenewald2016), enhance locomotion and diffusion capacity (Auger et al., Reference Auger, Tixier, Kreiter and Fauvel1999; Kjærsgaard et al., Reference Kjærsgaard, Blanckenhorn, Pertoldi, Loeschcke, Kaufmann, Hald, Pagès and Bahrndorff2015), or ultimately result in mortality under extreme conditions (Coombs and Bale, Reference Coombs and Bale2014). Heat stress may also induce oxidative stress (Yang et al., Reference Yang, Tan, Fu, Feng and Zhang2010), leading to the upregulation of heat-shock protein expression (Chen et al., Reference Chen, Li, Zhang, Zhao, Wu and Zhang2015; King and MacRae, Reference King and MacRae2015). Although these physiological responses can enhance an organism’s ability to tolerate adverse environmental conditions, they may impose substantial energetic costs by increasing maintenance requirements and altering energy allocation, potentially constraining other fitness-related processes, including longevity, reproduction, growth, and feeding activity (Klepsatel et al., Reference Klepsatel, Gáliková, Xu and Kühnlein2016; Sokolova, Reference Sokolova2018). Consequently, heat stress can ultimately disrupt population growth and persistence (Zhang et al., Reference Zhang, Zhao, Hoffmann and Ma2013; Liu et al., Reference Liu, Feng, Yi, Zheng and Sun2025; Pakyari and Kakvan, Reference Pakyari and Kakvan2026). The results of increased handling time and decreased attack rate and prey consumption in this research were probably related to the long-term adaptation mechanism of S. longicornis to high temperature so as to win a better chance to survive.
Ongoing climate warming presents an increasing challenge to the successful biological control of insect pests (Eigenbrode et al., Reference Eigenbrode, Davis and Crowder2015), emphasising the importance of optimising the use of arthropod natural enemies in pest management programmes. The present findings demonstrate that short-term heat stress adversely affects both the functional response and prey consumption of S. longicornis. Nevertheless, additional field-based studies are required before definitive recommendations regarding its biological control performance can be made. As global climate change is projected to prolong extreme temperature events and increase their frequency (Stocker et al., Reference Stocker, Qin, Plattner, Alexander, Allen, Bindoff, Bréon, Church, Cubasch and Emori2013), further investigations examining the effects of heat stress across different developmental stages, temperature regimes, and exposure durations are essential for predicting the effectiveness of biological control in future climates. The findings of the present study indicate that exposure of S. longicornis to elevated temperatures should be minimised during both commercial transport and field release, even for relatively brief periods. To maximise the biocontrol efficacy of S. longicornis against two-spotted spider mite in both greenhouse and open-field production systems, releases should be avoided when ambient temperatures exceed 38°C.
Acknowledgements
The support of this research by the Islamic Azad University, Takestan Branch, Iran, is greatly appreciated. This manuscript has benefited from AI-based language enhancement tools to improve its English language quality.
Author contributions
H.P.: writing – original draft, software, methodology, investigation, data curation, and conceptualisation.
Data availability statement
The data that support the findings of this study are available from the corresponding author, upon reasonable request.
Competing interests
The authors have no conflicts of interest to declare.
