Comparison of Statistical Models for Time- Dependent Repellency Using the Novel Pole-Dance Bioassay against Tetranychus urticae Koch

Comparison of Statistical Models for Time- Dependent Repellency Using the Novel Pole-Dance Bioassay against Tetranychus urticae Koch | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Comparison of Statistical Models for Time- Dependent Repellency Using the Novel Pole-Dance Bioassay against Tetranychus urticae Koch Junho Yoon This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6820848/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 21 Aug, 2025 Read the published version in Experimental and Applied Acarology → Version 1 posted You are reading this latest preprint version Abstract Evaluating the repellency of essential oils against Tetranychus urticae requires robust methodologies to detect time-dependent changes in their efficacy, due to differential efficacy, volatility, and sustained effectiveness. This study introduces the Pole-dance bioassay, a novel no-choice method optimized for high-throughput screening of time-dependent repellency, demonstrated through tests on twenty botanical volatiles against T. urticae . Four statistical models, probit, two-parameter Hill, four-parameter Hill, and Gaussian Process (GP) regression, were compared for analyzing time-response landing data, employing both experimental results and scenario-based synthetic datasets reflecting diverse curve shapes. GP regression often provided superior model fits, especially for complex or incomplete landing trajectories. While repellency rankings based on median effective time (ET 50 ) and area under the curve (AUC) were highly correlated within respective models, the choice of model significantly influenced parameter estimates. AUC proved essential for quantifying activity for highly potent compounds where ET 50 was inestimable (e.g., t-cinnamaldehyde, 1,8-cineole, (-)-terpinen-4-ol, thymol) and offered complementary insights into repellent effects. The Pole-dance bioassay combined with GP modeling establishes an optimized framework for statistically rigorous in vivo high-throughput screening against T. urticae . high-throughput repellent essential oils spider mite gaussian process Figures Figure 1 Figure 2 Figure 3 Figure 4 Introduction The two-spotted spider mite, Tetranychus urticae Koch, poses a significant threat to global agriculture due to its broad host range (Jakubowska et al. 2022 ; Razuvaeva et al. 2023 ). Management of this pest has traditionally depended heavily on chemical acaricides, yet this approach is increasingly challenged by environmental safety concerns and rapid development of acaricide resistance (Adesanya et al. 2021 ; Ilias et al. 2014 ). Consequently, pest management strategies are progressively incorporating behavioral manipulation tactics, with repellents derived from agricultural sources presenting a potential alternative to conventional chemical pesticides (Deletre et al. 2016 ; Isman 2006 ; Oliveira et al. 2018 ). Among these, plant-derived volatiles are notable candidates, although their effective utilization demands robust methodologies capable of accurately quantifying repellency over time, as their efficacy can diminish due to volatility, chemical degradation, or habituation by target pests (Deletre et al. 2016 ; Isman and Miresmailli 2011 ). To facilitate a rigorous evaluation of repellent efficacy, a novel no-choice bioassay named the Pole-dance method was developed, specifically optimized for high-throughput screening of repellents against small arthropods such as T. urticae . Many assay systems often keep the initial inoculation site accessible, allowing mites to move bidirectionally between treated and untreated surfaces. Such reversible movements can obscure clear interpretations of repellency (Dunn et al. 2019 ; Manu et al. 2021 ). The bridge assay was developed for this purpose, but no comparable no-choice test has previously been proposed (Dawood and Snyder 2020 ; Snyder et al. 2011 ; Tak and Isman 2017 ). Moreover, conventional assays often emphasize escape responses rather than measuring inhibition of initial host acceptance, a critical behavioral parameter in pest management contexts (Antonious and Snyder 2006 ; Faraone et al. 2020 ; Roh et al. 2012 ). Conventionally, dose-response or time-response repellency data have been analyzed using models such as probit, logistic, or the Hill equation, as in toxicological or pharmacological contexts (Badolo et al. 2004 ; Elamir et al. 2019 ; Jiang et al. 2019 ; Organization 2009 ). Nevertheless, uniformly applying a single model type without regard to observed response dynamics can introduce bias, potentially misrepresenting compound efficacy when actual responses deviate from the models (Elamir et al. 2019 ). The selection of models can critically influence parameter estimation, including key metrics such as median effective time (ET 50 ), commonly employed to indicate repellent activity, and the area under the curve (AUC), proposed herein as an additional metric. Both metrics can be used to summarize efficacy and rank the potency of candidate repellents. This study explores the impact of model selection on the interpretation of time-dependent repellency data generated using our novel Pole-dance bioassay with T. urticae , supplemented by synthetic simulation data. The performance of three distinct modeling frameworks, probit regression, Hill-type equations (two- and four-parameter variants), and non-parametric Bayesian Gaussian Process (GP) regression were compared. Using diverse curve-shape scenarios reflected in synthetic and experimental datasets, model fits through standard metrics (RMSE, MAE, R²) and how model choice affects derived ET 50 and AUC values, as well as subsequent rankings of compound repellency were assessed. The objective of this study was to provide empirical guidance on selecting appropriate statistical models for analyzing time-dependent repellency data from Pole-dance assay, a novel method to enhance both the methodological rigor and throughput of future repellency studies. Materials and Methods Chemicals Twenty botanical volatiles used in this study were selected based on previous reports identifying chemicals with repellent activities against T. urticae and other arthropods(An and Tak 2022 ; da Camara et al. 2015 ; Nerio et al. 2010 ; Wood et al. 2024 ; Wu et al. 2022 ; Yoon and Tak 2018 ). The selected chemicals included carvacrol (99%), β-caryophyllene (> 98%), (±)-citronellal (> 98.0%), eugenol (99%), geranic acid (> 98%), D-limonene (97%), linalool (> 97%), linalyl acetate (> 98%), α-pinene (98%), α-terpineol (90%), (-)-terpinen-4-ol (> 95.0%), t -cinnamaldehyde (99%), citral (> 95%), (+)-borneol (87%), camphor (96%), 1,8-cineole (99%), t -anethole (> 98%), thymol (> 98.5%), citronellol (> 98%), and L-menthol (99%). Carvacrol, eugenol, geranic acid, D-limonene, linalool, α-pinene, α-terpineol, (-)-terpinen-4-ol, (+)-borneol, camphor, 1,8-cineole, thymol, citronellol, and L-menthol were purchased from Sigma-Aldrich (St. Louis, MO, USA). β-Caryophyllene, (±)-citronellal, t -cinnamaldehyde, citral, linalyl acetate, and t -anethole were obtained from Tokyo Chemical Industry Co., Ltd. (Tokyo, Japan). Analytical grade ethanol (> 99.9%) was acquired from Duksan Pure Chemicals Co., Ltd. (Ansan, South Korea). Two-spotted spider mites The colony of T. urticae used in this study was maintained in an insectary at Seoul National University for over 10 years without exposure to any known pesticides. Kidney bean plants ( Phaseolus vulgaris var. humilis ) infested with mites were kept under controlled conditions of 25 ± 1 ℃, 70 ± 10% relative humidity, and a photoperiod of 16:8 h (L:D). Kidney beans were purchased from Sohwa Farm (Yecheon, South Korea), and the soil medium (68% coco peat, 15% peat moss, 7% perlite, 4% zeolite) was obtained from Seoul Bio (Eumseong, South Korea). Plants were grown in small plastic pots (Ø 85 × 70 mm), watered twice weekly, and replaced regularly to maintain colony health. Female adult mites less than two weeks old were selected for experimentation. Pole-dance assay Leaf discs (Ø 20 mm) were excised from kidney bean leaves and placed on a 2% (w/w) agar medium in Petri dishes (Ø 55 mm), with their abaxial surface facing upward (Fig. 1 A). The agar medium was hollowed out to create a recessed area, and water was filled into the surrounding space to form a “leaf island” that prevented mites from escaping. Test compounds were dissolved in ethanol and applied evenly to the abaxial surface of each leaf disc at a dosage of 1 mg per disc using 100 µL of test solution. Following evaporation of the solvent, a wooden toothpick (50 mm length) was vertically impaled at the center of the leaf disc, forming a pole for mite introduction. Twenty adult female mites were then gently placed at the top edge of the toothpick, allowing voluntary downward movement onto the treated leaf disc. This vertical arrangement ensured mites could not reverse their choice (once mites landed, they did not climb back up) nor escape downward using webs. Landing was defined as the moment a mite made sustained physical contact with the leaf disc, remaining continuously for at least 10 seconds without climbing back onto the pole. Brief or transient contacts shorter than 10 seconds without direct sustained body-leaf interaction were not counted as successful landings at that moment. The number of mites successfully landing on the leaf disc was recorded at 30-minute intervals over a period of 720 minutes post-introduction. Assay on each compound was replicated for ten times (Fig. 1 B). Time-response models Time-dependent landing data were analyzed using four modeling approaches: probit regression, two-parametric Hill equation (Hill2P), four-parametric Hill equation (Hill4P), and GP regression. Probit regression modeled the cumulative proportion of mites landed over time, assuming a linear relationship between the probit-transformed response to log time: $$\:{\varPhi\:}^{-1}(\left(p\left(t\right)\right)=\:{\beta\:}_{0}+\:{\beta\:}_{1}\text{l}\text{o}\text{g}(t)$$ where \(\:{\varPhi\:}^{-1}\) is the inverse cumulative distribution function of the standard normal distribution, and p(t) is the cumulative proportion of mites landed at time t, and β 0 and β 1 are coefficients.​ The Hill equation included two variants: a two-parametric version where the minimum and maximum of p(t) were fixed, and a four-parametric version where they were estimated from the data. The general form of the Hill equation is: $$\:p\left(t\right)=\:{E}_{min}+\:\frac{{E}_{max}-\:{E}_{min}}{1+{\left(\frac{{ET}_{50}}{t}\right)}^{h}}$$ where ET 50 is the time at which 50% of mites were landed, and h is the Hill slope parameter indicating the steepness of the curve. For two-parametric variant, E min was fixed to 0.0 and E max to 1.0, assuming that repellency fully inhibits and eventually fully permits landing over time. Fixing these values ensures that ET 50 corresponds to the time when 50% of mites have landed relative to the total number introduced, regardless of whether this assumption perfectly matches the observed data. In the four-parametric variant, E min , E max , h, and ET 50 were simultaneously estimated. Under this flexible fitting, ET 50 corresponds to the time point at which the cumulative landing reaches 50% of fitted E max -E min , rather than 50% of the total introduced mites. This allows the model to accommodate situations where complete landing does not occur by the end of the observation period but affects the interpretation of ET 50 in comparisons among compounds. Gaussian Process (GP) regression is a flexible, non-parametric Bayesian method useful when the exact form of the relationship between variables is unknown or complex. Unlike parametric models that assume a fixed functional form (e.g., probit or Hill equations), GP regression relies on the correlation between observed data points to smoothly interpolate predictions, effectively accommodating complex and irregular data trajectories $$\:p\left(t\right)\:\sim\:GP(m\left(t\right),\:k\left(t,\:{t}^{{\prime\:}}\right))$$ where m(t) is the mean function and k(t, t') is the covariance kernel function describing the correlation between landing proportion at two time points t and t'. A Matérn 5/2 kernel was adopted as the covariance function, defined as: $$\:k\left(t,{t}^{{\prime\:}}\right)=\:{\sigma\:}^{2}\:\left(1+\frac{\sqrt{5}\left|t-{t}^{{\prime\:}}\right|}{l}+\:\frac{5{\left(t-{t}^{{\prime\:}}\right)}^{2}}{3{l}^{2}}\right)\text{e}\text{x}\text{p}(-\frac{\sqrt{5}\left|t-{t}^{{\prime\:}}\right|}{l})$$ where l is the characteristic length-scale parameter controlling the smoothness of the curve. Synthetic simulation data To evaluate model performance across diverse repellency patterns, synthetic datasets were generated to represent four distinct curve types that can be observed in the repellency data, each reflecting combinations of landing completeness and shape complexity: Complete landing with sigmoid shape: mites gradually land over time, following a sigmoidal trajectory, and ultimately reach 100% cumulative landing. Incomplete landing with sigmoid shape: landing behavior follows a simple sigmoid curve but asymptotes below 100%, representing incomplete repellency decay even at the end of the observation period. Complete landing with complex shape: mites eventually achieve 100% landing, but the cumulative landing curve exhibits a complex pattern, such as fluctuations in landing rates over time. Incomplete landing with complex shape: mite landing behavior is both incomplete (final cumulative landing < 100%) and irregular The synthetic data were generated under the assumption that the underlying model parameters follow normal distributions. For each scenario, means and standard deviations for key parameters were predefined based on the desired curve characteristics. Individual replicate curves were then generated by randomly sampling parameter values from these normal distributions and computing the corresponding landing trajectories. Matching the structure of the experimental bioassays, ten independent replicate datasets were generated per hypothetical compound. Five hypothetical compounds were simulated for each scenario, resulting in a total of twenty synthetic compounds across the four scenarios. Model evaluation and repellency indicators Three model fit metrics were used to evaluate how accurately the fitted models matched observed data. Root Mean Square Error (RMSE) measures the average magnitude of prediction errors, penalizing larger errors more heavily due to squaring. Mean Absolute Error (MAE) provides a straightforward average of absolute errors, reflecting typical prediction accuracy without emphasizing large deviations. The coefficient of determination (R²) indicates the proportion of data variability explained by the model, with values closer to 1 indicating better fits. In addition to fit statistics, two repellency indicator parameters were extracted from each model: the ET 50 and the area under the curve (AUC). ET 50 was defined as the time point at which the cumulative proportion of landed mites reached 50%, reflecting the median timing of repellency decay and being particularly sensitive to early-to-mid phase landing dynamics. AUC was defined as the integral of the cumulative landing curve over the entire observation period, capturing the overall degree of repellency loss across time. Lower AUC values indicate slower landing progression and thus stronger sustained repellency throughout the tested period. These two metrics were compared across models and compounds to evaluate how model selection influences the interpretation of repellent activity. To evaluate how model selection influenced repellency interpretation, rankings of compounds based on ET 50 and AUC were compared across models. Spearman rank correlation coefficients were calculated to assess the consistency between ET 50 -based and AUC-based rankings within synthetic and experimental datasets. In addition, the degree of ranking diversification across different models was analyzed for ET 50 and AUC, respectively, to show how model choice affected the perceived potency of candidate repellents. Software Data generation, model fitting, and statistical analyses were performed using R version 4.2.2 (R Core Team, 2022). The package GauPro (version 0.2.5) was used for fitting Gaussian Process regression models. boot (version 1.3–28) was used for bootstrapping to estimate parameter distributions and confidence intervals. pracma (version 2.3.8) was used for numerical integration to calculate the AUC. For synthetic data generation, MASS (version 7.3–58.1) was used for multivariate normal sampling, and splines (version 4.2.2) was used for spline generation in complex curve shapes. Results Model fitting on experimental data To evaluate the performance of the four modeling approaches (Probit, Hill2P, Hill4P, and GP) on experimental Pole-dance assay data, model fit statistics including RMSE, MAE, and R² across twenty botanical volatiles and a solvent control were analyzed (Supplementary Table S1 ). The experimental cumulative landing curves exhibited diversity, including incomplete landing (final cumulative landing < 1.0), non-sigmoidal trajectories with complex landing trajectories. Fitted curves for each compound are presented in Supplementary Fig. S1 –S21. During model fitting, several compounds failed to converge under specific models, particularly in Hill2P and Hill4P. Hill2P fitting failed for Estragole, Linalool, and (-)-Terpinen-4-ol, while Hill4P fitting failed for Bornyl acetate, Estragole, Thymol, and (-)-Terpinen-4-ol. In contrast, Probit and GP models successfully generated fits for all compounds without convergence failures. Multiple-comparison analysis revealed no significant differences among the four models for RMSE (ANOVA, F 3,71 = 1.676, P = 0.180), MAE (ANOVA, F 3,71 = 1.251, P = 0.298), or R² (Kruskal–Wallis, H 3 = 4.022, P = 0.259) when fitting the experimental time-dependent landing data (Table 1 ). Table 1 For experimental data and each synthetic data scenario, RMSE, MAE, and R² were compared across Probit, Hill2P, Hill4P, and GP. Following normality check with Shapiro-Wilk test, Overall differences were tested with one-way ANOVA (parametric) or Kruskal-Wallis (non-parametric). Multiple comparisons were made by Tukey's test (parametric) or Dunn's test (non-parametric) at α of 0.05. Data source Data group Metric Test used Test statistics (df) P Pairwise comparison Probit Hill2P Hill4P GP Experimental All compounds RMSE ANOVA 1.6761 ( F 3,71 ) 0.1799 A a A A A Experimental All compounds MAE ANOVA 1.2505 ( F 3,71 ) 0.298 A A A A Experimental All compounds R 2 Kruskal-Wallis 4.0219 ( H 3 ) 0.2591 A A A A Synthetic Scenario A RMSE ANOVA 0.4043 ( F 3,16 ) 0.7519 A A A A Synthetic Scenario A MAE ANOVA 0.1706 ( F 3,16 ) 0.9147 A A A A Synthetic Scenario A R 2 ANOVA 0.5087 ( F 3,16 ) 0.6819 A A A A Synthetic Scenario B RMSE ANOVA 3.6738 ( F 3,15 ) 0.0364 A A A A Synthetic Scenario B MAE ANOVA 2.0067 ( F 3,15 ) 0.1563 A A A A Synthetic Scenario B R 2 Kruskal-Wallis 7.2695 ( H 3 ) 0.0638 A A A A Synthetic Scenario C RMSE ANOVA 8.6213 ( F 3,16 ) 0.0012 B B B A Synthetic Scenario C MAE ANOVA 8.4579 ( F 3,16 ) 0.0014 B B B A Synthetic Scenario C R 2 ANOVA 3.4608 ( F 3,16 ) 0.0414 A B A A Synthetic Scenario D RMSE Kruskal-Wallis 6.0857 ( H 3 ) 0.1075 A A A A Synthetic Scenario D MAE Kruskal-Wallis 5.3086 ( H 3 ) 0.1505 A A A A Synthetic Scenario D R 2 ANOVA 0.9196 ( F 3,16 ) 0.4537 A A A A Synthetic Scenario A + B + C + D RMSE ANOVA 6.1238 ( F 3,75 ) 0.0009 B B A A Synthetic Scenario A + B + C + D MAE ANOVA 4.0312 ( F 3,75 ) 0.0103 B A A A Synthetic Scenario A + B + C + D R 2 Kruskal-Wallis 8.9843 ( F 3,75 ) 0.0295 B A A A a Within each row, models assigned different letters in the pair-wise comparison column differ significantly at α = 0.05 (Nemenyi post-hoc) Model fitting on synthetic data To systematically evaluate model performance, Probit, Hill2P, Hill4P, and GP models were applied to synthetic datasets simulating four distinct repellency curve types. These scenarios included complete landing with a sigmoidal shape (Scenario A), incomplete landing with a sigmoidal shape (Scenario B), complete landing with a complex shape (Scenario C), and incomplete landing with a complex shape (Scenario D). Model fitting results revealed scenario-specific differences in model performance (Table 1 , Supplementary Table S2 & Fig. S22-S31). In Scenarios A, B, and D, no statistical differences were observed among the four models based on RMSE, MAE, or R² values. In Scenario C, however, GP achieved significantly better fits compared to Probit, Hill2P, and Hill4P. Specifically, for RMSE in Scenario C, ANOVA detected a significant difference among models (F 3,16 = 6.542, P = 0.0042), and Tukey's post-hoc indicated that GP had significantly lower RMSE compared to Probit (P = 0.016), Hill2P (P = 0.009), and Hill4P (P = 0.007). For MAE, ANOVA similarly revealed a significant difference (F 3,16 = 7.103, P = 0.0031), with GP outperforming Probit (P = 0.012), Hill2P (P = 0.008), and Hill4P (P = 0.006) in post-hoc comparisons. For R², a significant difference was found by Kruskal-Wallis analysis (H 3 = 9.204, P = 0.0268), and Dunn's post-hoc tests showed that GP achieved significantly higher R² values compared to Probit (P = 0.034), Hill2P (P = 0.022), and Hill4P (P = 0.019). When all dataset from four synthetic scenarios were aggregated, significant differences among models for RMSE (ANOVA, F 3,75 = 6.124, P = 0.0009), MAE (ANOVA, F 3,75 = 4.031, P = 0.010), and R² (Kruskal–Wallis, H 3 = 8.984, P = 0.030) were detected. Tukey’s HSD was applied for RMSE and MAE, and Dunn’s test for R². For RMSE, Hill4P and GP performed significantly better (P < 0.05). For MAE, Probit performed significantly poorer than Hill2P, Hill4P, and GP. For R², same trend was observed to MAE, where Probit's performance significantly poorer than others. These results indicate that Probit consistently underperformed when multiple landing trajectory scenarios presence together. Ranking concordance across repellency metrices To assess the consistency of compound rankings based on different repellency indices, rankings derived from ET 50 and AUC values for each model using Spearman rank correlation analysis were compared. Across synthetic datasets, all four models exhibited strong and statistically significant concordance between ET 50 - and AUC-based rankings. Spearman correlation coefficients were 0.989 for Probit (P < 0.001), 0.989 for Hill2P (P < 0.001), 0.821 for Hill4P (P = 0.0001), and 0.844 for GP (P < 0.001) (Fig. 2 A). In experimental datasets, a similarly high degree of concordance was observed across all models. Spearman correlation coefficients were 0.986 for Probit (P < 0.001), 0.985 for Hill2P (P < 0.001), 0.974 for Hill4P (P < 0.001), and 0.962 for GP (P < 0.001) (Fig. 2 B). These results indicate that ET 50 - and AUC-based rankings were highly consistent regardless of the modeling approach, with particularly strong alignment across all models in both synthetic and experimental datasets. Repellent activity in synthetic data and ranking concordance across models To compare the estimated repellent activity across different modeling approaches, the ET 50 and AUC values obtained from synthetic datasets were analyzed. In ET 50 -based comparisons, Friedman test revealed statistically significant differences among models (χ 2 = 11.6526, P = 0.0087). Post-hoc Nemenyi tests indicated that Hill2P differed significantly from Probit (P = 0.0047) and Hill4P also differed significantly from Probit (P = 0.0272), whereas no significant differences were observed between GP and the other models (Fig. 3 A). Similarly, AUC-based comparisons demonstrated significant differences across models (Friedman test, χ 2 = 14.0526, P = 0.0028). Post-hoc analyses revealed that Hill2P differed significantly from both Probit (P = 0.0118) and Hill4P (P = 0.0272), while GP showed a significant difference from Probit (P = 0.0272) (Fig. 3 B). Repellent activity in experimental data and ranking concordance across models To compare the estimated repellent activity across different modeling approaches, the ET 50 and AUC values obtained from experimental datasets were analyzed. In ET 50 -based comparisons, Friedman test revealed statistically significant differences among models (χ² = 7.9714, P = 0.0466). Post-hoc Nemenyi tests indicated that Hill4P differed significantly from Probit (P = 0.0175), whereas no significant differences were observed among the other model pairs (Fig. 4 A). Similarly, AUC-based comparisons demonstrated significant differences across models (Friedman test, χ² = 12.2571, P = 0.0066). Post-hoc analyses revealed that Hill2P differed significantly from Probit ( P = 0.0020), and GP also differed significantly from Probit (P = 0.0438) (Fig. 4 B). Comparative repellent activities of botanical volatiles These comparisons relied exclusively on the Gaussian-process (GP) model because (i) it can generate a reliable curve for every compound unless the end-point landing proportion remains below 50% (in which case ET 50 is, by definition, inestimable) and (ii) across the experimental dataset the GP model yielded the lowest RMSE and MAE and the highest R², outperforming Probit, Hill2P, and Hill4P (Supplementary Table S1 &S2). For ET 50 values, the solvent control landed earliest, with an ET50 of 54.5 (95% CI, 47.1–63.7) min. Its 95% CI overlapped that of (+)-borneol, indicating no detectable repellent activity. In contrast, five compounds, 1,8-cineole, t-cinnamaldehyde, L-menthol, (-)-terpinen-4-ol, and thymol, never reached 50% cumulative landing, so ET 50 could not be calculated. These were considered as the strongest repellents, although no comparison among them was available. Among volatiles with calculable ET 50s , t-anethole was the most potent, with an ET 50 of 669.5 (628.8–708.0) min. Its 95% CI overlapped that of eugenol, which had an ET 50 of 650.7 (629.1–667.2) min, marking these two as the strongest repellents among the compounds with quantified ET 50 s. For AUC, the control produced the largest value, 653.5 (631.8–655.0) as expected. Unlike when compared based on ET 50 s, (+)-Borneol showed significant repellency with an AUC of 589.1 (568.2–589.2), whose interval did not overlap that of the control. Unlike ET 50 , AUCs were calculated for every compound regardless of end-point landing proportion. The smallest AUC, and therefore strongest protection, was recorded for t-cinnamaldehyde at 5.8 (5.0–5.8), followed by 1,8-cineole at 10.9 (9.4–10.9) and (-)-terpinen-4-ol at 10.9 (9.4–10.9). Discussion This study introduced the Pole-dance bioassay, a novel no-choice method for assessing time-dependent repellent effects against T. urticae . The performance of four distinct statistical models, probit, Hill2P, Hill4P, and GP for analyzing the resulting time-response data were compared. Our findings demonstrate that while all models can capture basic repellent dynamics, GP regression offers superior flexibility and fit, particularly for experimental data exhibiting complex trajectory shapes or incomplete landing at the end-point. Furthermore, ET 50 and AUC values were used as indicators for repellent activities. The Pole-dance bioassay was developed to address limitations inherent in existing repellency testing methodologies. Many conventional assays, including choice tests, can be confounded by factors such as mite indecision or reversible movements between treated and untreated zones, complicating the interpretation of true repellency (Dunn et al. 2019 ; Manu et al. 2021 ). While no-choice assays like the bridge assay exist, our Pole-dance method might offer an advantage by preventing mites from returning to the introduction point or escaping via webbing, ensuring that observed movement onto the treated surface directly reflects the decay of repellency over time (Dawood and Snyder 2020 ; Snyder et al. 2011 ; Tak and Isman 2017 ). This setup specifically measures the inhibition of host acceptance rather than escape responses, a potential factor in evaluating practical pest management potential. Accurate quantification of time-dependent repellency relies on appropriate statistical modeling. Traditional models like probit and Hill equations, assume specific curve shapes (Elamir et al. 2019 ). However, biological responses, especially behavioral ones can deviate significantly from these curves, potentially leading to biased parameter estimates and misinterpretation of compound efficacy if models are applied rigidly. Our results highlight this challenge: while probit and Hill models performed adequately in simple sigmoidal scenarios, they struggled to fit complex landing patterns observed experimentally and in synthetic Scenario C, sometimes failing to converge. Furthermore, while the Hill4P offers flexibility by estimating the minimum (E min ) and maximum (E max ) landing proportions, its ET 50 parameter represents the time to reach 50% of the fitted range (E max −E min ), not necessarily 50% of the total mites landed. Caution must therefore be exercised when comparing Hill4P-derived ET 50 values, especially if E max ​ is substantially below 1.0, as it reflects a different conceptual point than the ET 50 from models assuming a 0.0–1.0 range (Jiang et al. 2019 ). In contrast, the GP demonstrated flexibility, accommodating diverse curve shapes, including incomplete landing and fluctuations in landing rates. As well as assessing for fit statistics, Two key metrics were used to quantify repellency, ET 50 and AUC. ET 50 provides an intuitive measure of the median-based tendency of repellency decay, sensitive to early-to-mid phase dynamics. AUC, conversely, captures the overall repellency effect across the entire observation period, with lower values indicating stronger, more sustained repellency. However, our analysis revealed a strong, significant positive correlation between rankings derived from ET 50 and AUC across all models for both synthetic and experimental data. This high concordance may suggests that, for this dataset, both metrics generally identify the same compounds as more or less repellent relative to each other. Nevertheless, the choice of metric could influence conclusions about whether a compound exhibits statistically significant repellent activity compared to the control, based on 95% CI overlap. For instance, although (+)-Borneol ranked among the least potent compounds by both metrics, its 95% CI for ET 50 overlapped with that of the solvent control, suggesting no significant repellency based on this metric. In contrast, its AUC value's 95% CI did not overlap with the control's, indicating significant repellency when assessed over the entire time course. This exemplifies how ET 50 and AUC can provide complementary information for screening potential repellents, in spite of their ranking concordances. ​ A key advantage of using AUC is its universal applicability across all compounds tested. Unlike ET 50 , which is not able to be defined if fewer than 50% of mites landed during the observation period, AUC provides a quantifiable measure of repellency regardless of the ultimate landing percentage. This proved essential in our study for evaluating and ranking the most potent repellents, such as t-cinnamaldehyde, 1,8-cineole, (-)-terpinen-4-ol, and thymol, for which ET 50 values could not be determined due to their strong effects. While this study advocates the utility of the Pole-dance bioassay and GP fittings, there are certain limitations when interpreting the findings. The experiments were conducted under stable laboratory conditions, which may not fully represent the variable environmental factors encountered in agricultural fields that can affect volatile persistence and mite behavior. Additionally, T. urticae colony used has been maintained in the laboratory for over 10 years without pesticide exposure, thereby responses might differ in field populations with different genetic backgrounds or histories of chemical exposure. Another limitation is that repellency was assessed using only a single dosage for the screening purpose. Furthermore, potential habituation or desensitization to repellents over time was not evaluated beyond the 720-minute observation period (Jeon and Tak 2024 ; Stockton et al. 2021 ). Future research should prioritize validating the repellent effects of the most promising compounds identified (e.g., t-cinnamaldehyde, 1,8-cineole, (-)-terpinen-4-ol ) under semi-field or field conditions as well as mite strains. Studies investigating the persistence of these specific volatiles on plant surfaces are also crucial for assessing their practical applicability. Additionally, as the volatiles often occurs simultaneously to make mixtures, exploring potential synergistic effects by testing blends of the top-performing volatiles identified in this study could lead to more effective repellent formulations (An and Tak 2022 ; Masoumi et al. 2016 ). In conclusion, utilizing the novel Pole-dance bioassay, GP regression proved superior for analyzing complex time-dependent repellency, demonstrating flexibility regardless of the final landing proportion or curve shape. In terms of repellency indices, ET 50 - and AUC-based rankings correlated well, but AUC also provided complementary insights into repellency dynamics above 50% landing and offered quantifiable metrics even when ET 50 could not be calculated due to strong repellent effects. This study is expected to establish a robust screening system for repellents against spider mites, combining a high-throughput bioassay with statistically rigorous analysis for effective comparison among candidate compounds. Corresponding Author Correspondence to Junho Yoon Abbreviations Median effective time ET 50 Area under curve AUC Two-parametric Hill equation Hill2P Four-parametric Hill equation Hill4P Gaussian process GP Root Mean Squared Error RMSE Mean Absolute Error MAE Declarations Competing interests The author declare no competing interests. Funding Sources Not applicable Author Contribution Not applicable (single author) Data Availability The summary of synthetic/experimental data is described in the figures and tables in within the manuscript. The raw data is available upon reasonable request. References Adesanya, A.W., M.D. Lavine, T.W. Moural, L.C. Lavine, F. Zhu, D.B. Walsh (2021) Mechanisms and management of acaricide resistance for Tetranychus urticae in agroecosystems. Journal of Pest Science 94, 639–663 An, H., J.-H. Tak (2022) Miticidal and repellent activity of thirty essential oils and their synergistic interaction with vanillin against Tetranychus urticae koch (acari: Tetranychidae). Industrial Crops and Products 182, 114872 Antonious, G.F., J.C. Snyder (2006) Natural products: Repellency and toxicity of wild tomato leaf extracts to the two-spotted spider mite, Tetranychus urticae koch. Journal of Environmental Science and Health Part B 41, 43–55 Badolo, A., E. Ilboudo‐Sanogo, A.P. Ouédraogo, C. Costantini (2004) Evaluation of the sensitivity of aedes aegypti and anopheles gambiae complex mosquitoes to two insect repellents: Deet and kbr 3023. Tropical Medicine & International Health 9, 330–334 da Camara, C.A., Y. Akhtar, M.B. Isman, R.C. Seffrin, F.S. Born (2015) Repellent activity of essential oils from two species of citrus against Tetranychus urticae in the laboratory and greenhouse. Crop Protection 74, 110–115 Dawood, M.H., J.C. Snyder (2020) The alcohol and epoxy alcohol of zingiberene, produced in trichomes of wild tomato, are more repellent to spider mites than zingiberene. Frontiers in Plant Science 11, 35 Deletre, E., B. Schatz, D. Bourguet, F. Chandre, L. Williams, A. Ratnadass, T. Martin (2016) Prospects for repellent in pest control: Current developments and future challenges. Chemoecology 26, 127–142 Dunn, J., J. Prickett, D. Collins, R. Macarthur, R. Weaver (2019) Choice test to determine potential attractants and repellents for the sheep scab mite, Psoroptes ovis (acari: Psoroptidae). Experimental and Applied Acarology 79, 187–194 Elamir, E.E., A.A. Almadiy, G.E. Nenaah, A.A. Alabas, H.S. Alsaqri (2019) Comparing six mathematical link function models of the antifeedant activity of lesser grain borer exposed to sub-lethal concentrations of some extracts from Calotropis procera . Bioengineered 10, 292–305 Faraone, N., R. Evans, J. LeBlanc, N.K. Hillier (2020) Soil and foliar application of rock dust as natural control agent for two-spotted spider mites on tomato plants. Scientific reports 10, 12108 Ilias, A., J. Vontas, A. Tsagkarakou (2014) Global distribution and origin of target site insecticide resistance mutations in Tetranychus urticae . Insect biochemistry and molecular biology 48, 17–28 Isman, M.B. (2006) Botanical insecticides, deterrents, and repellents in modern agriculture and an increasingly regulated world. Annual review of entomology 51, 45–66 Isman, M.B., S. Miresmailli (2011) Plant essential oils as repellents and deterrents to agricultural pests Recent developments in invertebrate repellents.(pp67–77). ACS Publications Jakubowska, M., R. Dobosz, D. Zawada, J. Kowalska (2022) A review of crop protection methods against the twospotted spider mite— Tetranychus urticae koch (acari: Tetranychidae)—with special reference to alternative methods. Agriculture 12, 898 Jeon, H., J.-H. Tak (2024) Gustatory habituation to essential oil induces reduced feeding deterrence and neuronal desensitization in Spodoptera litura . Journal of Pest Science, 1–16 Jiang, S., L. Yang, J.R. Bloomquist (2019) High‐throughput screening method for evaluating spatial repellency and vapour toxicity to mosquitoes. Medical and Veterinary Entomology 33, 388–396 Manu, N., M.W. Schilling, T.W. Phillips (2021) Natural and synthetic repellents for pest management of the storage mite Tyrophagus putrescentiae (schrank)(sarcoptiformes: Acaridae). Insects 12, 711 Masoumi, F., M.R. Youssefi, M.A. Tabari (2016) Combination of carvacrol and thymol against the poultry red mite ( Dermanyssus gallinae ). Parasitology research 115, 4239–4243 Nerio, L.S., J. Olivero-Verbel, E. Stashenko (2010) Repellent activity of essential oils: A review. Bioresource technology 101, 372–378 Oliveira, J.L.d., E.V. Campos, A.E. Pereira, T. Pasquoto, R. Lima, R. Grillo, D.J.d. Andrade, F.A.d. Santos, L.F. Fraceto (2018) Zein nanoparticles as eco-friendly carrier systems for botanical repellents aiming sustainable agriculture. Journal of agricultural and food chemistry 66, 1330–1340 Organization, W.H. (2009) Guidelines for efficacy testing of mosquito repellents for human skin Guidelines for efficacy testing of mosquito repellents for human skin. Razuvaeva, A., E. Ulyanova, E. Skolotneva, I. Andreeva (2023) Species identification of spider mites (tetranychidae: Tetranychinae): A review of methods. Vavilov Journal of Genetics and Breeding 27, 240 Roh, H.S., K.C. Park, C.G. Park (2012) Repellent effect of santalol from sandalwood oil against Tetranychus urticae (acari: Tetranychidae). Journal of economic entomology 105, 379–385 Snyder, J.C., G.F. Antonious, R. Thacker (2011) A sensitive bioassay for spider mite ( Tetranychus urticae ) repellency: A double bond makes a difference. Experimental and Applied Acarology 55, 215–224 Stockton, D.G., D.H. Cha, G.M. Loeb (2021) Does habituation affect the efficacy of semiochemical oviposition repellents developed against Drosophila suzukii ? Environmental Entomology 50, 1322–1331 Tak, J.-H., M.B. Isman (2017) Acaricidal and repellent activity of plant essential oil-derived terpenes and the effect of binary mixtures against Tetranychus urticae koch (acari: Tetranychidae). Industrial Crops and Products 108, 786–792 Wood, M.J., J.C. Bull, K. Kanagachandran, T.M. Butt (2024) Development and laboratory validation of a plant-derived repellent blend, effective against Aedes aegypti [diptera: Culicidae], Anopheles gambiae [diptera: Culicidae] and Culex quinquefasciatus [diptera: Culicidae]. Plos one 19, e0299144 Wu, W., Y. Yang, Y. Feng, X. Ren, Y. Li, W. Li, J. Huang, L. Kong, X. Chen, Z. Lin (2022) Study of the repellent activity of 60 essential oils and their main constituents against Aedes albopictus , and nano-formulation development. Insects 13, 1077 Yoon, J., J.-H. Tak (2018) Toxicity and repellent activity of plant essential oils and their blending effects against two spotted spider mites, Tetranychus urticae koch. Korean Journal of Applied Entomology 57, 199–207 Additional Declarations No competing interests reported. Supplementary Files JYExpAppAcaSupplementary.docx Cite Share Download PDF Status: Published Journal Publication published 21 Aug, 2025 Read the published version in Experimental and Applied Acarology → Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6820848","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":470602095,"identity":"159b02c4-e0f6-4ef0-92e4-4b8598f0f553","order_by":0,"name":"Junho Yoon","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA4klEQVRIiWNgGAWjYHACNiCWgDA/QIUYG/DqYAZrAethnEGCFog1zDzEaNFt7z/24G2bRR2/2OFnj23+3ElsYD/8gHHmHtxazM4cZjec2yYhITk7zdw4t+1ZYgNPmgHjhmd4tNxIZpPmBWoxuJ1gJp3bcDixgSGHgfHBAaK0pH+TtvgD1ML/hmgtOWbSDGxALRJAWzbg03LmsJnknHMSkjNn55RJ9rYdNm6TeGZwcAY+Lccbn0m8Kavj55dO3ybx489h2X7+5IcPe/BoAQMeZA4omghpQNMyCkbBKBgFowAdAACyYE8J0161iAAAAABJRU5ErkJggg==","orcid":"","institution":"Seoul National University","correspondingAuthor":true,"prefix":"","firstName":"Junho","middleName":"","lastName":"Yoon","suffix":""}],"badges":[],"createdAt":"2025-06-04 13:08:31","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6820848/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6820848/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s10493-025-01058-y","type":"published","date":"2025-08-21T16:29:36+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":84702716,"identity":"ea8886a8-e02f-4626-9e3d-4a453940660f","added_by":"auto","created_at":"2025-06-16 11:52:00","extension":"jpeg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":178319,"visible":true,"origin":"","legend":"\u003cp\u003e(\u003cstrong\u003eA) \u003c/strong\u003eSchematic diagram of the Pole Dance method used to assess time-series repellency behavior in spider mites. (\u003cstrong\u003eB) \u003c/strong\u003eRepresentative landing trajectories of mites over time under solvent control and D-limonene treated conditions.\u003c/p\u003e","description":"","filename":"image1.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-6820848/v1/37d47b922a4475cbed99c1f9.jpeg"},{"id":84702717,"identity":"f2a47fd6-e006-4996-bcf0-40d95f95c25f","added_by":"auto","created_at":"2025-06-16 11:52:00","extension":"jpeg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":159534,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of repellency rankings derived from ET\u003csub\u003e50\u003c/sub\u003e and AUC metrics. Spearman rank correlations were calculated for synthetic data (\u003cstrong\u003eA\u003c/strong\u003e) and experimental data (\u003cstrong\u003eB\u003c/strong\u003e), assessing the consistency between the two indices.\u003c/p\u003e","description":"","filename":"image2.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-6820848/v1/33c24edbdeb79f1b81070fa3.jpeg"},{"id":84702731,"identity":"201e8802-29a9-4955-8315-098280df44ff","added_by":"auto","created_at":"2025-06-16 11:52:01","extension":"jpeg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":233031,"visible":true,"origin":"","legend":"\u003cp\u003eModel-dependent diversification of compound rankings in synthetic data based on ET\u003csub\u003e50\u003c/sub\u003e (A) and AUC (B) based on Friedman's test (α = 0.05), followed by Nemenyi's post-hoc analysis (α = 0.05). Statistically different models are indicated by different letters in parentheses beneath each model label.\u003c/p\u003e","description":"","filename":"image3.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-6820848/v1/7a90a8a86b681612fa5e582f.jpeg"},{"id":84702721,"identity":"339286d9-3a3d-4519-b67d-983e6c159c46","added_by":"auto","created_at":"2025-06-16 11:52:00","extension":"jpeg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":256846,"visible":true,"origin":"","legend":"\u003cp\u003eModel-dependent diversification of compound rankings in experimental data based on ET\u003csub\u003e50\u003c/sub\u003e (A) and AUC (B) based on Friedman's test (α = 0.05), followed by Nemenyi's post-hoc analysis (α = 0.05). Statistically different models are indicated by different letters in parentheses beneath each model label.\u003c/p\u003e","description":"","filename":"image4.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-6820848/v1/c48308005720b5ada2309552.jpeg"},{"id":89847809,"identity":"9b263915-1ddb-4464-9227-e8753e71bb3b","added_by":"auto","created_at":"2025-08-25 16:44:19","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1809252,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6820848/v1/ba071087-89c8-4540-98ea-b5e00bd95147.pdf"},{"id":84702734,"identity":"5aca1c2f-8db3-4d65-838e-81b1a1862655","added_by":"auto","created_at":"2025-06-16 11:52:03","extension":"docx","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":5814670,"visible":true,"origin":"","legend":"","description":"","filename":"JYExpAppAcaSupplementary.docx","url":"https://assets-eu.researchsquare.com/files/rs-6820848/v1/e0013903c1f431b96440d375.docx"}],"financialInterests":"No competing interests reported.","formattedTitle":"Comparison of Statistical Models for Time- Dependent Repellency Using the Novel Pole-Dance Bioassay against Tetranychus urticae Koch","fulltext":[{"header":"Introduction","content":"\u003cp\u003eThe two-spotted spider mite, \u003cem\u003eTetranychus urticae\u003c/em\u003e Koch, poses a significant threat to global agriculture due to its broad host range (Jakubowska et al. \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Razuvaeva et al. \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). Management of this pest has traditionally depended heavily on chemical acaricides, yet this approach is increasingly challenged by environmental safety concerns and rapid development of acaricide resistance (Adesanya et al. \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Ilias et al. \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2014\u003c/span\u003e). Consequently, pest management strategies are progressively incorporating behavioral manipulation tactics, with repellents derived from agricultural sources presenting a potential alternative to conventional chemical pesticides (Deletre et al. \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2016\u003c/span\u003e; Isman \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2006\u003c/span\u003e; Oliveira et al. \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). Among these, plant-derived volatiles are notable candidates, although their effective utilization demands robust methodologies capable of accurately quantifying repellency over time, as their efficacy can diminish due to volatility, chemical degradation, or habituation by target pests (Deletre et al. \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2016\u003c/span\u003e; Isman and Miresmailli \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2011\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eTo facilitate a rigorous evaluation of repellent efficacy, a novel no-choice bioassay named the Pole-dance method was developed, specifically optimized for high-throughput screening of repellents against small arthropods such as \u003cem\u003eT. urticae\u003c/em\u003e. Many assay systems often keep the initial inoculation site accessible, allowing mites to move bidirectionally between treated and untreated surfaces. Such reversible movements can obscure clear interpretations of repellency (Dunn et al. \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Manu et al. \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). The bridge assay was developed for this purpose, but no comparable no-choice test has previously been proposed (Dawood and Snyder \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Snyder et al. \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2011\u003c/span\u003e; Tak and Isman \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2017\u003c/span\u003e). Moreover, conventional assays often emphasize escape responses rather than measuring inhibition of initial host acceptance, a critical behavioral parameter in pest management contexts (Antonious and Snyder \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2006\u003c/span\u003e; Faraone et al. \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Roh et al. \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2012\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eConventionally, dose-response or time-response repellency data have been analyzed using models such as probit, logistic, or the Hill equation, as in toxicological or pharmacological contexts (Badolo et al. \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2004\u003c/span\u003e; Elamir et al. \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Jiang et al. \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Organization \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2009\u003c/span\u003e). Nevertheless, uniformly applying a single model type without regard to observed response dynamics can introduce bias, potentially misrepresenting compound efficacy when actual responses deviate from the models (Elamir et al. \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). The selection of models can critically influence parameter estimation, including key metrics such as median effective time (ET\u003csub\u003e50\u003c/sub\u003e), commonly employed to indicate repellent activity, and the area under the curve (AUC), proposed herein as an additional metric. Both metrics can be used to summarize efficacy and rank the potency of candidate repellents.\u003c/p\u003e \u003cp\u003eThis study explores the impact of model selection on the interpretation of time-dependent repellency data generated using our novel Pole-dance bioassay with \u003cem\u003eT. urticae\u003c/em\u003e, supplemented by synthetic simulation data. The performance of three distinct modeling frameworks, probit regression, Hill-type equations (two- and four-parameter variants), and non-parametric Bayesian Gaussian Process (GP) regression were compared. Using diverse curve-shape scenarios reflected in synthetic and experimental datasets, model fits through standard metrics (RMSE, MAE, R\u0026sup2;) and how model choice affects derived ET\u003csub\u003e50\u003c/sub\u003e and AUC values, as well as subsequent rankings of compound repellency were assessed. The objective of this study was to provide empirical guidance on selecting appropriate statistical models for analyzing time-dependent repellency data from Pole-dance assay, a novel method to enhance both the methodological rigor and throughput of future repellency studies.\u003c/p\u003e"},{"header":"Materials and Methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003eChemicals\u003c/h2\u003e \u003cp\u003eTwenty botanical volatiles used in this study were selected based on previous reports identifying chemicals with repellent activities against \u003cem\u003eT. urticae\u003c/em\u003e and other arthropods(An and Tak \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; da Camara et al. \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2015\u003c/span\u003e; Nerio et al. \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2010\u003c/span\u003e; Wood et al. \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Wu et al. \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Yoon and Tak \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). The selected chemicals included carvacrol (99%), β-caryophyllene (\u0026gt;\u0026thinsp;98%), (\u0026plusmn;)-citronellal (\u0026gt;\u0026thinsp;98.0%), eugenol (99%), geranic acid (\u0026gt;\u0026thinsp;98%), D-limonene (97%), linalool (\u0026gt;\u0026thinsp;97%), linalyl acetate (\u0026gt;\u0026thinsp;98%), α-pinene (98%), α-terpineol (90%), (-)-terpinen-4-ol (\u0026gt;\u0026thinsp;95.0%), \u003cem\u003et\u003c/em\u003e-cinnamaldehyde (99%), citral (\u0026gt;\u0026thinsp;95%), (+)-borneol (87%), camphor (96%), 1,8-cineole (99%), \u003cem\u003et\u003c/em\u003e-anethole (\u0026gt;\u0026thinsp;98%), thymol (\u0026gt;\u0026thinsp;98.5%), citronellol (\u0026gt;\u0026thinsp;98%), and L-menthol (99%).\u003c/p\u003e \u003cp\u003eCarvacrol, eugenol, geranic acid, D-limonene, linalool, α-pinene, α-terpineol, (-)-terpinen-4-ol, (+)-borneol, camphor, 1,8-cineole, thymol, citronellol, and L-menthol were purchased from Sigma-Aldrich (St. Louis, MO, USA). β-Caryophyllene, (\u0026plusmn;)-citronellal, \u003cem\u003et\u003c/em\u003e-cinnamaldehyde, citral, linalyl acetate, and \u003cem\u003et\u003c/em\u003e-anethole were obtained from Tokyo Chemical Industry Co., Ltd. (Tokyo, Japan). Analytical grade ethanol (\u0026gt;\u0026thinsp;99.9%) was acquired from Duksan Pure Chemicals Co., Ltd. (Ansan, South Korea).\u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eTwo-spotted spider mites\u003c/h3\u003e\n\u003cp\u003eThe colony of \u003cem\u003eT. urticae\u003c/em\u003e used in this study was maintained in an insectary at Seoul National University for over 10 years without exposure to any known pesticides. Kidney bean plants (\u003cem\u003ePhaseolus vulgaris\u003c/em\u003e var. \u003cem\u003ehumilis\u003c/em\u003e) infested with mites were kept under controlled conditions of 25\u0026thinsp;\u0026plusmn;\u0026thinsp;1 ℃, 70\u0026thinsp;\u0026plusmn;\u0026thinsp;10% relative humidity, and a photoperiod of 16:8 h (L:D). Kidney beans were purchased from Sohwa Farm (Yecheon, South Korea), and the soil medium (68% coco peat, 15% peat moss, 7% perlite, 4% zeolite) was obtained from Seoul Bio (Eumseong, South Korea). Plants were grown in small plastic pots (\u0026Oslash; 85 \u0026times; 70 mm), watered twice weekly, and replaced regularly to maintain colony health. Female adult mites less than two weeks old were selected for experimentation.\u003c/p\u003e\n\u003ch3\u003ePole-dance assay\u003c/h3\u003e\n\u003cp\u003eLeaf discs (\u0026Oslash; 20 mm) were excised from kidney bean leaves and placed on a 2% (w/w) agar medium in Petri dishes (\u0026Oslash; 55 mm), with their abaxial surface facing upward (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eA). The agar medium was hollowed out to create a recessed area, and water was filled into the surrounding space to form a \u0026ldquo;leaf island\u0026rdquo; that prevented mites from escaping. Test compounds were dissolved in ethanol and applied evenly to the abaxial surface of each leaf disc at a dosage of 1 mg per disc using 100 \u0026micro;L of test solution. Following evaporation of the solvent, a wooden toothpick (50 mm length) was vertically impaled at the center of the leaf disc, forming a pole for mite introduction. Twenty adult female mites were then gently placed at the top edge of the toothpick, allowing voluntary downward movement onto the treated leaf disc. This vertical arrangement ensured mites could not reverse their choice (once mites landed, they did not climb back up) nor escape downward using webs. Landing was defined as the moment a mite made sustained physical contact with the leaf disc, remaining continuously for at least 10 seconds without climbing back onto the pole. Brief or transient contacts shorter than 10 seconds without direct sustained body-leaf interaction were not counted as successful landings at that moment. The number of mites successfully landing on the leaf disc was recorded at 30-minute intervals over a period of 720 minutes post-introduction. Assay on each compound was replicated for ten times (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eB).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e\n\u003ch3\u003eTime-response models\u003c/h3\u003e\n\u003cp\u003eTime-dependent landing data were analyzed using four modeling approaches: probit regression, two-parametric Hill equation (Hill2P), four-parametric Hill equation (Hill4P), and GP regression.\u003c/p\u003e \u003cp\u003eProbit regression modeled the cumulative proportion of mites landed over time, assuming a linear relationship between the probit-transformed response to log time:\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$\\:{\\varPhi\\:}^{-1}(\\left(p\\left(t\\right)\\right)=\\:{\\beta\\:}_{0}+\\:{\\beta\\:}_{1}\\text{l}\\text{o}\\text{g}(t)$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varPhi\\:}^{-1}\\)\u003c/span\u003e\u003c/span\u003e is the inverse cumulative distribution function of the standard normal distribution, and \u003cem\u003ep(t)\u003c/em\u003e is the cumulative proportion of mites landed at time t, and \u003cem\u003eβ\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eβ\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e are coefficients.​\u003c/p\u003e \u003cp\u003eThe Hill equation included two variants: a two-parametric version where the minimum and maximum of \u003cem\u003ep(t)\u003c/em\u003e were fixed, and a four-parametric version where they were estimated from the data. The general form of the Hill equation is:\u003cdiv id=\"Equb\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equb\" name=\"EquationSource\"\u003e\n$$\\:p\\left(t\\right)=\\:{E}_{min}+\\:\\frac{{E}_{max}-\\:{E}_{min}}{1+{\\left(\\frac{{ET}_{50}}{t}\\right)}^{h}}$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cem\u003eET\u003c/em\u003e\u003csub\u003e\u003cem\u003e50\u003c/em\u003e\u003c/sub\u003e is the time at which 50% of mites were landed, and \u003cem\u003eh\u003c/em\u003e is the Hill slope parameter indicating the steepness of the curve. For two-parametric variant, \u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003emin\u003c/em\u003e\u003c/sub\u003e was fixed to 0.0 and \u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003emax\u003c/em\u003e\u003c/sub\u003e to 1.0, assuming that repellency fully inhibits and eventually fully permits landing over time. Fixing these values ensures that \u003cem\u003eET\u003c/em\u003e\u003csub\u003e\u003cem\u003e50\u003c/em\u003e\u003c/sub\u003e corresponds to the time when 50% of mites have landed relative to the total number introduced, regardless of whether this assumption perfectly matches the observed data.\u003c/p\u003e \u003cp\u003eIn the four-parametric variant, \u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003emin\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003emax\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003eh, and ET\u003c/em\u003e\u003csub\u003e\u003cem\u003e50\u003c/em\u003e\u003c/sub\u003e were simultaneously estimated. Under this flexible fitting, ET\u003csub\u003e50\u003c/sub\u003e corresponds to the time point at which the cumulative landing reaches 50% of fitted E\u003csub\u003emax\u003c/sub\u003e-E\u003csub\u003emin\u003c/sub\u003e, rather than 50% of the total introduced mites. This allows the model to accommodate situations where complete landing does not occur by the end of the observation period but affects the interpretation of ET\u003csub\u003e50\u003c/sub\u003e in comparisons among compounds.\u003c/p\u003e \u003cp\u003eGaussian Process (GP) regression is a flexible, non-parametric Bayesian method useful when the exact form of the relationship between variables is unknown or complex. Unlike parametric models that assume a fixed functional form (e.g., probit or Hill equations), GP regression relies on the correlation between observed data points to smoothly interpolate predictions, effectively accommodating complex and irregular data trajectories\u003cdiv id=\"Equc\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equc\" name=\"EquationSource\"\u003e\n$$\\:p\\left(t\\right)\\:\\sim\\:GP(m\\left(t\\right),\\:k\\left(t,\\:{t}^{{\\prime\\:}}\\right))$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere m(t) is the mean function and k(t, t') is the covariance kernel function describing the correlation between landing proportion at two time points t and t'. A Mat\u0026eacute;rn 5/2 kernel was adopted as the covariance function, defined as:\u003cdiv id=\"Equd\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equd\" name=\"EquationSource\"\u003e\n$$\\:k\\left(t,{t}^{{\\prime\\:}}\\right)=\\:{\\sigma\\:}^{2}\\:\\left(1+\\frac{\\sqrt{5}\\left|t-{t}^{{\\prime\\:}}\\right|}{l}+\\:\\frac{5{\\left(t-{t}^{{\\prime\\:}}\\right)}^{2}}{3{l}^{2}}\\right)\\text{e}\\text{x}\\text{p}(-\\frac{\\sqrt{5}\\left|t-{t}^{{\\prime\\:}}\\right|}{l})$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cem\u003el\u003c/em\u003e is the characteristic length-scale parameter controlling the smoothness of the curve.\u003c/p\u003e\n\u003ch3\u003eSynthetic simulation data\u003c/h3\u003e\n\u003cp\u003eTo evaluate model performance across diverse repellency patterns, synthetic datasets were generated to represent four distinct curve types that can be observed in the repellency data, each reflecting combinations of landing completeness and shape complexity:\u003c/p\u003e \u003cp\u003e \u003col\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eComplete landing with sigmoid shape: mites gradually land over time, following a sigmoidal trajectory, and ultimately reach 100% cumulative landing.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eIncomplete landing with sigmoid shape: landing behavior follows a simple sigmoid curve but asymptotes below 100%, representing incomplete repellency decay even at the end of the observation period.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eComplete landing with complex shape: mites eventually achieve 100% landing, but the cumulative landing curve exhibits a complex pattern, such as fluctuations in landing rates over time.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eIncomplete landing with complex shape: mite landing behavior is both incomplete (final cumulative landing\u0026thinsp;\u0026lt;\u0026thinsp;100%) and irregular\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003c/ol\u003e \u003c/p\u003e \u003cp\u003eThe synthetic data were generated under the assumption that the underlying model parameters follow normal distributions. For each scenario, means and standard deviations for key parameters were predefined based on the desired curve characteristics. Individual replicate curves were then generated by randomly sampling parameter values from these normal distributions and computing the corresponding landing trajectories. Matching the structure of the experimental bioassays, ten independent replicate datasets were generated per hypothetical compound. Five hypothetical compounds were simulated for each scenario, resulting in a total of twenty synthetic compounds across the four scenarios.\u003c/p\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003eModel evaluation and repellency indicators\u003c/h2\u003e \u003cp\u003eThree model fit metrics were used to evaluate how accurately the fitted models matched observed data. Root Mean Square Error (RMSE) measures the average magnitude of prediction errors, penalizing larger errors more heavily due to squaring. Mean Absolute Error (MAE) provides a straightforward average of absolute errors, reflecting typical prediction accuracy without emphasizing large deviations. The coefficient of determination (R\u0026sup2;) indicates the proportion of data variability explained by the model, with values closer to 1 indicating better fits.\u003c/p\u003e \u003cp\u003eIn addition to fit statistics, two repellency indicator parameters were extracted from each model: the ET\u003csub\u003e50\u003c/sub\u003e and the area under the curve (AUC). ET\u003csub\u003e50\u003c/sub\u003e was defined as the time point at which the cumulative proportion of landed mites reached 50%, reflecting the median timing of repellency decay and being particularly sensitive to early-to-mid phase landing dynamics. AUC was defined as the integral of the cumulative landing curve over the entire observation period, capturing the overall degree of repellency loss across time. Lower AUC values indicate slower landing progression and thus stronger sustained repellency throughout the tested period. These two metrics were compared across models and compounds to evaluate how model selection influences the interpretation of repellent activity.\u003c/p\u003e \u003cp\u003eTo evaluate how model selection influenced repellency interpretation, rankings of compounds based on ET\u003csub\u003e50\u003c/sub\u003e and AUC were compared across models. Spearman rank correlation coefficients were calculated to assess the consistency between ET\u003csub\u003e50\u003c/sub\u003e-based and AUC-based rankings within synthetic and experimental datasets. In addition, the degree of ranking diversification across different models was analyzed for ET\u003csub\u003e50\u003c/sub\u003e and AUC, respectively, to show how model choice affected the perceived potency of candidate repellents.\u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eSoftware\u003c/h3\u003e\n\u003cp\u003eData generation, model fitting, and statistical analyses were performed using R version 4.2.2 (R Core Team, 2022). The package \u003cem\u003eGauPro\u003c/em\u003e (version 0.2.5) was used for fitting Gaussian Process regression models. \u003cem\u003eboot\u003c/em\u003e (version 1.3\u0026ndash;28) was used for bootstrapping to estimate parameter distributions and confidence intervals. \u003cem\u003epracma\u003c/em\u003e (version 2.3.8) was used for numerical integration to calculate the AUC. For synthetic data generation, \u003cem\u003eMASS\u003c/em\u003e (version 7.3\u0026ndash;58.1) was used for multivariate normal sampling, and \u003cem\u003esplines\u003c/em\u003e (version 4.2.2) was used for spline generation in complex curve shapes.\u003c/p\u003e"},{"header":"Results","content":"\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003eModel fitting on experimental data\u003c/h2\u003e \u003cp\u003eTo evaluate the performance of the four modeling approaches (Probit, Hill2P, Hill4P, and GP) on experimental Pole-dance assay data, model fit statistics including RMSE, MAE, and R\u0026sup2; across twenty botanical volatiles and a solvent control were analyzed (Supplementary Table \u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003e). The experimental cumulative landing curves exhibited diversity, including incomplete landing (final cumulative landing\u0026thinsp;\u0026lt;\u0026thinsp;1.0), non-sigmoidal trajectories with complex landing trajectories.\u003c/p\u003e \u003cp\u003eFitted curves for each compound are presented in Supplementary Fig. \u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003e\u0026ndash;S21. During model fitting, several compounds failed to converge under specific models, particularly in Hill2P and Hill4P. Hill2P fitting failed for Estragole, Linalool, and (-)-Terpinen-4-ol, while Hill4P fitting failed for Bornyl acetate, Estragole, Thymol, and (-)-Terpinen-4-ol. In contrast, Probit and GP models successfully generated fits for all compounds without convergence failures.\u003c/p\u003e \u003cp\u003eMultiple-comparison analysis revealed no significant differences among the four models for RMSE (ANOVA, F\u003csub\u003e3,71\u003c/sub\u003e = 1.676, P\u0026thinsp;=\u0026thinsp;0.180), MAE (ANOVA, F\u003csub\u003e3,71\u003c/sub\u003e = 1.251, P\u0026thinsp;=\u0026thinsp;0.298), or R\u0026sup2; (Kruskal\u0026ndash;Wallis, H\u003csub\u003e3\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;4.022, P\u0026thinsp;=\u0026thinsp;0.259) when fitting the experimental time-dependent landing data (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eFor experimental data and each synthetic data scenario, RMSE, MAE, and R\u0026sup2; were compared across Probit, Hill2P, Hill4P, and GP. Following normality check with Shapiro-Wilk test, Overall differences were tested with one-way ANOVA (parametric) or Kruskal-Wallis (non-parametric). Multiple comparisons were made by Tukey's test (parametric) or Dunn's test (non-parametric) at α of 0.05.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"11\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c11\" colnum=\"11\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eData source\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eData group\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eMetric\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eTest used\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" morerows=\"1\" nameend=\"c6\" namest=\"c5\" rowspan=\"2\"\u003e \u003cp\u003eTest statistics (df)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e\u003cem\u003eP\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"4\" nameend=\"c11\" namest=\"c8\"\u003e \u003cp\u003ePairwise comparison\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eProbit\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003eHill2P\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c10\"\u003e \u003cp\u003eHill4P\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c11\"\u003e \u003cp\u003eGP\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eExperimental\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAll\u003c/p\u003e \u003cp\u003ecompounds\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eRMSE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eANOVA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1.6761\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e(\u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003e3,71\u003c/em\u003e\u003c/sub\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.1799\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eA\u003csup\u003ea\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003eA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003eA\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eExperimental\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAll\u003c/p\u003e \u003cp\u003ecompounds\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMAE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eANOVA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1.2505\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e(\u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003e3,71\u003c/em\u003e\u003c/sub\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.298\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003eA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003eA\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eExperimental\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAll\u003c/p\u003e \u003cp\u003ecompounds\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eR\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eKruskal-Wallis\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e4.0219\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e(\u003cem\u003eH\u003c/em\u003e\u003csub\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sub\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.2591\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003eA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003eA\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSynthetic\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eScenario A\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eRMSE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eANOVA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.4043\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e(\u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003e3,16\u003c/em\u003e\u003c/sub\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.7519\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003eA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003eA\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSynthetic\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eScenario A\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMAE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eANOVA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.1706\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e(\u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003e3,16\u003c/em\u003e\u003c/sub\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.9147\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003eA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003eA\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSynthetic\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eScenario A\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eR\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eANOVA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.5087\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e(\u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003e3,16\u003c/em\u003e\u003c/sub\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.6819\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003eA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003eA\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSynthetic\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eScenario B\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eRMSE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eANOVA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e3.6738\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e(\u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003e3,15\u003c/em\u003e\u003c/sub\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.0364\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003eA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003eA\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSynthetic\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eScenario B\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMAE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eANOVA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e2.0067\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e(\u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003e3,15\u003c/em\u003e\u003c/sub\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.1563\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003eA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003eA\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSynthetic\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eScenario B\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eR\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eKruskal-Wallis\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e7.2695\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e(\u003cem\u003eH\u003c/em\u003e\u003csub\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sub\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.0638\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003eA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003eA\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSynthetic\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eScenario C\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eRMSE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eANOVA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e8.6213\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e(\u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003e3,16\u003c/em\u003e\u003c/sub\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.0012\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eB\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eB\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003eB\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003eA\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSynthetic\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eScenario C\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMAE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eANOVA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e8.4579\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e(\u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003e3,16\u003c/em\u003e\u003c/sub\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.0014\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eB\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eB\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003eB\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003eA\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSynthetic\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eScenario C\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eR\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eANOVA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e3.4608\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e(\u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003e3,16\u003c/em\u003e\u003c/sub\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.0414\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eB\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003eA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003eA\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSynthetic\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eScenario D\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eRMSE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eKruskal-Wallis\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e6.0857\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e(\u003cem\u003eH\u003c/em\u003e\u003csub\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sub\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.1075\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003eA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003eA\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSynthetic\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eScenario D\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMAE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eKruskal-Wallis\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e5.3086\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e(\u003cem\u003eH\u003c/em\u003e\u003csub\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sub\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.1505\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003eA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003eA\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSynthetic\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eScenario D\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eR\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eANOVA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.9196\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e(\u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003e3,16\u003c/em\u003e\u003c/sub\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.4537\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003eA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003eA\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSynthetic\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eScenario\u003c/p\u003e \u003cp\u003eA\u0026thinsp;+\u0026thinsp;B\u0026thinsp;+\u0026thinsp;C\u0026thinsp;+\u0026thinsp;D\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eRMSE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eANOVA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e6.1238\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e(\u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003e3,75\u003c/em\u003e\u003c/sub\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.0009\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eB\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eB\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003eA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003eA\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSynthetic\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eScenario\u003c/p\u003e \u003cp\u003eA\u0026thinsp;+\u0026thinsp;B\u0026thinsp;+\u0026thinsp;C\u0026thinsp;+\u0026thinsp;D\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMAE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eANOVA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e4.0312\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e(\u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003e3,75\u003c/em\u003e\u003c/sub\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.0103\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eB\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003eA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003eA\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSynthetic\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eScenario\u003c/p\u003e \u003cp\u003eA\u0026thinsp;+\u0026thinsp;B\u0026thinsp;+\u0026thinsp;C\u0026thinsp;+\u0026thinsp;D\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eR\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eKruskal-Wallis\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e8.9843\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e(\u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003e3,75\u003c/em\u003e\u003c/sub\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.0295\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eB\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003eA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003eA\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"11\"\u003e\u003csup\u003ea\u003c/sup\u003e Within each row, models assigned different letters in the pair-wise comparison column differ significantly at α\u0026thinsp;=\u0026thinsp;0.05 (Nemenyi post-hoc)\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003eModel fitting on synthetic data\u003c/h2\u003e \u003cp\u003eTo systematically evaluate model performance, Probit, Hill2P, Hill4P, and GP models were applied to synthetic datasets simulating four distinct repellency curve types. These scenarios included complete landing with a sigmoidal shape (Scenario A), incomplete landing with a sigmoidal shape (Scenario B), complete landing with a complex shape (Scenario C), and incomplete landing with a complex shape (Scenario D).\u003c/p\u003e \u003cp\u003eModel fitting results revealed scenario-specific differences in model performance (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, Supplementary Table S2 \u0026amp; Fig. S22-S31). In Scenarios A, B, and D, no statistical differences were observed among the four models based on RMSE, MAE, or R\u0026sup2; values. In Scenario C, however, GP achieved significantly better fits compared to Probit, Hill2P, and Hill4P. Specifically, for RMSE in Scenario C, ANOVA detected a significant difference among models (F\u003csub\u003e3,16\u003c/sub\u003e = 6.542, P\u0026thinsp;=\u0026thinsp;0.0042), and Tukey's post-hoc indicated that GP had significantly lower RMSE compared to Probit (P\u0026thinsp;=\u0026thinsp;0.016), Hill2P (P\u0026thinsp;=\u0026thinsp;0.009), and Hill4P (P\u0026thinsp;=\u0026thinsp;0.007). For MAE, ANOVA similarly revealed a significant difference (F\u003csub\u003e3,16\u003c/sub\u003e = 7.103, P\u0026thinsp;=\u0026thinsp;0.0031), with GP outperforming Probit (P\u0026thinsp;=\u0026thinsp;0.012), Hill2P (P\u0026thinsp;=\u0026thinsp;0.008), and Hill4P (P\u0026thinsp;=\u0026thinsp;0.006) in post-hoc comparisons. For R\u0026sup2;, a significant difference was found by Kruskal-Wallis analysis (H\u003csub\u003e3\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;9.204, P\u0026thinsp;=\u0026thinsp;0.0268), and Dunn's post-hoc tests showed that GP achieved significantly higher R\u0026sup2; values compared to Probit (P\u0026thinsp;=\u0026thinsp;0.034), Hill2P (P\u0026thinsp;=\u0026thinsp;0.022), and Hill4P (P\u0026thinsp;=\u0026thinsp;0.019).\u003c/p\u003e \u003cp\u003eWhen all dataset from four synthetic scenarios were aggregated, significant differences among models for RMSE (ANOVA, F\u003csub\u003e3,75\u003c/sub\u003e = 6.124, P\u0026thinsp;=\u0026thinsp;0.0009), MAE (ANOVA, F\u003csub\u003e3,75\u003c/sub\u003e = 4.031, P\u0026thinsp;=\u0026thinsp;0.010), and R\u0026sup2; (Kruskal\u0026ndash;Wallis, H\u003csub\u003e3\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;8.984, P\u0026thinsp;=\u0026thinsp;0.030) were detected. Tukey\u0026rsquo;s HSD was applied for RMSE and MAE, and Dunn\u0026rsquo;s test for R\u0026sup2;. For RMSE, Hill4P and GP performed significantly better (P\u0026thinsp;\u0026lt;\u0026thinsp;0.05). For MAE, Probit performed significantly poorer than Hill2P, Hill4P, and GP. For R\u0026sup2;, same trend was observed to MAE, where Probit's performance significantly poorer than others. These results indicate that Probit consistently underperformed when multiple landing trajectory scenarios presence together.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec13\" class=\"Section2\"\u003e \u003ch2\u003eRanking concordance across repellency metrices\u003c/h2\u003e \u003cp\u003eTo assess the consistency of compound rankings based on different repellency indices, rankings derived from ET\u003csub\u003e50\u003c/sub\u003e and AUC values for each model using Spearman rank correlation analysis were compared. Across synthetic datasets, all four models exhibited strong and statistically significant concordance between ET\u003csub\u003e50\u003c/sub\u003e- and AUC-based rankings. Spearman correlation coefficients were 0.989 for Probit (P\u0026thinsp;\u0026lt;\u0026thinsp;0.001), 0.989 for Hill2P (P\u0026thinsp;\u0026lt;\u0026thinsp;0.001), 0.821 for Hill4P (P\u0026thinsp;=\u0026thinsp;0.0001), and 0.844 for GP (P\u0026thinsp;\u0026lt;\u0026thinsp;0.001) (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eA).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIn experimental datasets, a similarly high degree of concordance was observed across all models. Spearman correlation coefficients were 0.986 for Probit (P\u0026thinsp;\u0026lt;\u0026thinsp;0.001), 0.985 for Hill2P (P\u0026thinsp;\u0026lt;\u0026thinsp;0.001), 0.974 for Hill4P (P\u0026thinsp;\u0026lt;\u0026thinsp;0.001), and 0.962 for GP (P\u0026thinsp;\u0026lt;\u0026thinsp;0.001) (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eB). These results indicate that ET\u003csub\u003e50\u003c/sub\u003e- and AUC-based rankings were highly consistent regardless of the modeling approach, with particularly strong alignment across all models in both synthetic and experimental datasets.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec14\" class=\"Section2\"\u003e \u003ch2\u003eRepellent activity in synthetic data and ranking concordance across models\u003c/h2\u003e \u003cp\u003eTo compare the estimated repellent activity across different modeling approaches, the ET\u003csub\u003e50\u003c/sub\u003e and AUC values obtained from synthetic datasets were analyzed. In ET\u003csub\u003e50\u003c/sub\u003e-based comparisons, Friedman test revealed statistically significant differences among models (χ\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;11.6526, P\u0026thinsp;=\u0026thinsp;0.0087). Post-hoc Nemenyi tests indicated that Hill2P differed significantly from Probit (P\u0026thinsp;=\u0026thinsp;0.0047) and Hill4P also differed significantly from Probit (P\u0026thinsp;=\u0026thinsp;0.0272), whereas no significant differences were observed between GP and the other models (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eA).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eSimilarly, AUC-based comparisons demonstrated significant differences across models (Friedman test, χ\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;14.0526, P\u0026thinsp;=\u0026thinsp;0.0028). Post-hoc analyses revealed that Hill2P differed significantly from both Probit (P\u0026thinsp;=\u0026thinsp;0.0118) and Hill4P (P\u0026thinsp;=\u0026thinsp;0.0272), while GP showed a significant difference from Probit (P\u0026thinsp;=\u0026thinsp;0.0272) (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eB).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec15\" class=\"Section2\"\u003e \u003ch2\u003eRepellent activity in experimental data and ranking concordance across models\u003c/h2\u003e \u003cp\u003eTo compare the estimated repellent activity across different modeling approaches, the ET\u003csub\u003e50\u003c/sub\u003e and AUC values obtained from experimental datasets were analyzed. In ET\u003csub\u003e50\u003c/sub\u003e-based comparisons, Friedman test revealed statistically significant differences among models (χ\u0026sup2; = 7.9714, \u003cem\u003eP\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.0466). Post-hoc Nemenyi tests indicated that Hill4P differed significantly from Probit (P\u0026thinsp;=\u0026thinsp;0.0175), whereas no significant differences were observed among the other model pairs (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eA).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eSimilarly, AUC-based comparisons demonstrated significant differences across models (Friedman test, χ\u0026sup2; = 12.2571, P\u0026thinsp;=\u0026thinsp;0.0066). Post-hoc analyses revealed that Hill2P differed significantly from Probit (\u003cem\u003eP\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.0020), and GP also differed significantly from Probit (P\u0026thinsp;=\u0026thinsp;0.0438) (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eB).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec16\" class=\"Section2\"\u003e \u003ch2\u003eComparative repellent activities of botanical volatiles\u003c/h2\u003e \u003cp\u003eThese comparisons relied exclusively on the Gaussian-process (GP) model because (i) it can generate a reliable curve for every compound unless the end-point landing proportion remains below 50% (in which case ET\u003csub\u003e50\u003c/sub\u003e is, by definition, inestimable) and (ii) across the experimental dataset the GP model yielded the lowest RMSE and MAE and the highest R\u0026sup2;, outperforming Probit, Hill2P, and Hill4P (Supplementary Table \u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003e\u0026amp;S2).\u003c/p\u003e \u003cp\u003eFor ET\u003csub\u003e50\u003c/sub\u003e values, the solvent control landed earliest, with an ET50 of 54.5 (95% CI, 47.1\u0026ndash;63.7) min. Its 95% CI overlapped that of (+)-borneol, indicating no detectable repellent activity. In contrast, five compounds, 1,8-cineole, t-cinnamaldehyde, L-menthol, (-)-terpinen-4-ol, and thymol, never reached 50% cumulative landing, so ET\u003csub\u003e50\u003c/sub\u003e could not be calculated. These were considered as the strongest repellents, although no comparison among them was available.\u003c/p\u003e \u003cp\u003eAmong volatiles with calculable ET\u003csub\u003e50s\u003c/sub\u003e, t-anethole was the most potent, with an ET\u003csub\u003e50\u003c/sub\u003e of 669.5 (628.8\u0026ndash;708.0) min. Its 95% CI overlapped that of eugenol, which had an ET\u003csub\u003e50\u003c/sub\u003e of 650.7 (629.1\u0026ndash;667.2) min, marking these two as the strongest repellents among the compounds with quantified ET\u003csub\u003e50\u003c/sub\u003es.\u003c/p\u003e \u003cp\u003eFor AUC, the control produced the largest value, 653.5 (631.8\u0026ndash;655.0) as expected. Unlike when compared based on ET\u003csub\u003e50\u003c/sub\u003es, (+)-Borneol showed significant repellency with an AUC of 589.1 (568.2\u0026ndash;589.2), whose interval did not overlap that of the control. Unlike ET\u003csub\u003e50\u003c/sub\u003e, AUCs were calculated for every compound regardless of end-point landing proportion. The smallest AUC, and therefore strongest protection, was recorded for t-cinnamaldehyde at 5.8 (5.0\u0026ndash;5.8), followed by 1,8-cineole at 10.9 (9.4\u0026ndash;10.9) and (-)-terpinen-4-ol at 10.9 (9.4\u0026ndash;10.9).\u003c/p\u003e \u003c/div\u003e"},{"header":"Discussion","content":"\u003cp\u003eThis study introduced the Pole-dance bioassay, a novel no-choice method for assessing time-dependent repellent effects against \u003cem\u003eT. urticae\u003c/em\u003e. The performance of four distinct statistical models, probit, Hill2P, Hill4P, and GP for analyzing the resulting time-response data were compared. Our findings demonstrate that while all models can capture basic repellent dynamics, GP regression offers superior flexibility and fit, particularly for experimental data exhibiting complex trajectory shapes or incomplete landing at the end-point. Furthermore, ET\u003csub\u003e50\u003c/sub\u003e and AUC values were used as indicators for repellent activities.\u003c/p\u003e \u003cp\u003eThe Pole-dance bioassay was developed to address limitations inherent in existing repellency testing methodologies. Many conventional assays, including choice tests, can be confounded by factors such as mite indecision or reversible movements between treated and untreated zones, complicating the interpretation of true repellency (Dunn et al. \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Manu et al. \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). While no-choice assays like the bridge assay exist, our Pole-dance method might offer an advantage by preventing mites from returning to the introduction point or escaping via webbing, ensuring that observed movement onto the treated surface directly reflects the decay of repellency over time (Dawood and Snyder \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Snyder et al. \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2011\u003c/span\u003e; Tak and Isman \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2017\u003c/span\u003e). This setup specifically measures the inhibition of host acceptance rather than escape responses, a potential factor in evaluating practical pest management potential.\u003c/p\u003e \u003cp\u003eAccurate quantification of time-dependent repellency relies on appropriate statistical modeling. Traditional models like probit and Hill equations, assume specific curve shapes (Elamir et al. \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). However, biological responses, especially behavioral ones can deviate significantly from these curves, potentially leading to biased parameter estimates and misinterpretation of compound efficacy if models are applied rigidly. Our results highlight this challenge: while probit and Hill models performed adequately in simple sigmoidal scenarios, they struggled to fit complex landing patterns observed experimentally and in synthetic Scenario C, sometimes failing to converge. Furthermore, while the Hill4P offers flexibility by estimating the minimum (E\u003csub\u003emin\u003c/sub\u003e) and maximum (E\u003csub\u003emax\u003c/sub\u003e) landing proportions, its ET\u003csub\u003e50\u003c/sub\u003e parameter represents the time to reach 50% of the fitted range (E\u003csub\u003emax\u003c/sub\u003e \u0026minus;E\u003csub\u003emin\u003c/sub\u003e), not necessarily 50% of the total mites landed. Caution must therefore be exercised when comparing Hill4P-derived ET\u003csub\u003e50\u003c/sub\u003e values, especially if E\u003csub\u003emax\u003c/sub\u003e​ is substantially below 1.0, as it reflects a different conceptual point than the ET\u003csub\u003e50\u003c/sub\u003e from models assuming a 0.0\u0026ndash;1.0 range (Jiang et al. \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). In contrast, the GP demonstrated flexibility, accommodating diverse curve shapes, including incomplete landing and fluctuations in landing rates.\u003c/p\u003e \u003cp\u003eAs well as assessing for fit statistics, Two key metrics were used to quantify repellency, ET\u003csub\u003e50\u003c/sub\u003e and AUC. ET\u003csub\u003e50\u003c/sub\u003e provides an intuitive measure of the median-based tendency of repellency decay, sensitive to early-to-mid phase dynamics. AUC, conversely, captures the overall repellency effect across the entire observation period, with lower values indicating stronger, more sustained repellency. However, our analysis revealed a strong, significant positive correlation between rankings derived from ET\u003csub\u003e50\u003c/sub\u003e and AUC across all models for both synthetic and experimental data. This high concordance may suggests that, for this dataset, both metrics generally identify the same compounds as more or less repellent relative to each other.\u003c/p\u003e \u003cp\u003eNevertheless, the choice of metric could influence conclusions about whether a compound exhibits statistically significant repellent activity compared to the control, based on 95% CI overlap. For instance, although (+)-Borneol ranked among the least potent compounds by both metrics, its 95% CI for ET\u003csub\u003e50\u003c/sub\u003e overlapped with that of the solvent control, suggesting no significant repellency based on this metric. In contrast, its AUC value's 95% CI did not overlap with the control's, indicating significant repellency when assessed over the entire time course. This exemplifies how ET\u003csub\u003e50\u003c/sub\u003e and AUC can provide complementary information for screening potential repellents, in spite of their ranking concordances.\u003c/p\u003e \u003cp\u003e​ A key advantage of using AUC is its universal applicability across all compounds tested. Unlike ET\u003csub\u003e50\u003c/sub\u003e, which is not able to be defined if fewer than 50% of mites landed during the observation period, AUC provides a quantifiable measure of repellency regardless of the ultimate landing percentage. This proved essential in our study for evaluating and ranking the most potent repellents, such as t-cinnamaldehyde, 1,8-cineole, (-)-terpinen-4-ol, and thymol, for which ET\u003csub\u003e50\u003c/sub\u003e values could not be determined due to their strong effects.\u003c/p\u003e \u003cp\u003eWhile this study advocates the utility of the Pole-dance bioassay and GP fittings, there are certain limitations when interpreting the findings. The experiments were conducted under stable laboratory conditions, which may not fully represent the variable environmental factors encountered in agricultural fields that can affect volatile persistence and mite behavior. Additionally, \u003cem\u003eT. urticae\u003c/em\u003e colony used has been maintained in the laboratory for over 10 years without pesticide exposure, thereby responses might differ in field populations with different genetic backgrounds or histories of chemical exposure. Another limitation is that repellency was assessed using only a single dosage for the screening purpose. Furthermore, potential habituation or desensitization to repellents over time was not evaluated beyond the 720-minute observation period (Jeon and Tak \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Stockton et al. \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). Future research should prioritize validating the repellent effects of the most promising compounds identified (e.g., t-cinnamaldehyde, 1,8-cineole, (-)-terpinen-4-ol ) under semi-field or field conditions as well as mite strains. Studies investigating the persistence of these specific volatiles on plant surfaces are also crucial for assessing their practical applicability. Additionally, as the volatiles often occurs simultaneously to make mixtures, exploring potential synergistic effects by testing blends of the top-performing volatiles identified in this study could lead to more effective repellent formulations (An and Tak \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Masoumi et al. \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2016\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eIn conclusion, utilizing the novel Pole-dance bioassay, GP regression proved superior for analyzing complex time-dependent repellency, demonstrating flexibility regardless of the final landing proportion or curve shape. In terms of repellency indices, ET\u003csub\u003e50\u003c/sub\u003e- and AUC-based rankings correlated well, but AUC also provided complementary insights into repellency dynamics above 50% landing and offered quantifiable metrics even when ET\u003csub\u003e50\u003c/sub\u003e could not be calculated due to strong repellent effects. This study is expected to establish a robust screening system for repellents against spider mites, combining a high-throughput bioassay with statistically rigorous analysis for effective comparison among candidate compounds.\u003c/p\u003e \u003cp\u003e \u003cb\u003eCorresponding Author\u003c/b\u003e \u003c/p\u003e \u003cp\u003eCorrespondence to Junho Yoon\u003c/p\u003e"},{"header":"Abbreviations","content":"\u003cdiv class=\"DefinitionList\"\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eMedian effective time\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eET\u003csub\u003e50\u003c/sub\u003e\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eArea under curve\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eAUC\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eTwo-parametric Hill equation\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eHill2P\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eFour-parametric Hill equation\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eHill4P\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eGaussian process\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eGP\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eRoot Mean Squared Error\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eRMSE\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eMean Absolute Error\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eMAE\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003c/div\u003e"},{"header":"Declarations","content":"\u003ch2\u003eCompeting interests\u003c/h2\u003e \u003cp\u003eThe author declare no competing interests.\u003c/p\u003e \u003ch2\u003eFunding Sources\u003c/h2\u003e \u003cp\u003eNot applicable\u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eNot applicable (single author)\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e\u003cp\u003eThe summary of synthetic/experimental data is described in the figures and tables in within the manuscript. The raw data is available upon reasonable request.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n \u003cli\u003eAdesanya, A.W., M.D. Lavine, T.W. Moural, L.C. Lavine, F. Zhu, D.B. Walsh (2021) Mechanisms and management of acaricide resistance for \u003cem\u003eTetranychus urticae\u003c/em\u003e in agroecosystems. Journal of Pest Science 94, 639\u0026ndash;663\u003c/li\u003e\n \u003cli\u003eAn, H., J.-H. Tak (2022) Miticidal and repellent activity of thirty essential oils and their synergistic interaction with vanillin against \u003cem\u003eTetranychus urticae\u003c/em\u003e koch (acari: Tetranychidae). Industrial Crops and Products 182, 114872\u003c/li\u003e\n \u003cli\u003eAntonious, G.F., J.C. Snyder (2006) Natural products: Repellency and toxicity of wild tomato leaf extracts to the two-spotted spider mite, \u003cem\u003eTetranychus urticae\u003c/em\u003e koch. Journal of Environmental Science and Health Part B 41, 43\u0026ndash;55\u003c/li\u003e\n \u003cli\u003eBadolo, A., E. Ilboudo‐Sanogo, A.P. Ou\u0026eacute;draogo, C. Costantini (2004) Evaluation of the sensitivity of aedes aegypti and anopheles gambiae complex mosquitoes to two insect repellents: Deet and kbr 3023. Tropical Medicine \u0026amp; International Health 9, 330\u0026ndash;334\u003c/li\u003e\n \u003cli\u003eda Camara, C.A., Y. Akhtar, M.B. Isman, R.C. Seffrin, F.S. Born (2015) Repellent activity of essential oils from two species of citrus against \u003cem\u003eTetranychus urticae\u003c/em\u003e in the laboratory and greenhouse. Crop Protection 74, 110\u0026ndash;115\u003c/li\u003e\n \u003cli\u003eDawood, M.H., J.C. Snyder (2020) The alcohol and epoxy alcohol of zingiberene, produced in trichomes of wild tomato, are more repellent to spider mites than zingiberene. Frontiers in Plant Science 11, 35\u003c/li\u003e\n \u003cli\u003eDeletre, E., B. Schatz, D. Bourguet, F. Chandre, L. Williams, A. Ratnadass, T. Martin (2016) Prospects for repellent in pest control: Current developments and future challenges. Chemoecology 26, 127\u0026ndash;142\u003c/li\u003e\n \u003cli\u003eDunn, J., J. Prickett, D. Collins, R. Macarthur, R. Weaver (2019) Choice test to determine potential attractants and repellents for the sheep scab mite, \u003cem\u003ePsoroptes ovis\u003c/em\u003e (acari: Psoroptidae). Experimental and Applied Acarology 79, 187\u0026ndash;194\u003c/li\u003e\n \u003cli\u003eElamir, E.E., A.A. Almadiy, G.E. Nenaah, A.A. Alabas, H.S. Alsaqri (2019) Comparing six mathematical link function models of the antifeedant activity of lesser grain borer exposed to sub-lethal concentrations of some extracts from \u003cem\u003eCalotropis procera\u003c/em\u003e. Bioengineered 10, 292\u0026ndash;305\u003c/li\u003e\n \u003cli\u003eFaraone, N., R. Evans, J. LeBlanc, N.K. Hillier (2020) Soil and foliar application of rock dust as natural control agent for two-spotted spider mites on tomato plants. Scientific reports 10, 12108\u003c/li\u003e\n \u003cli\u003eIlias, A., J. Vontas, A. Tsagkarakou (2014) Global distribution and origin of target site insecticide resistance mutations in \u003cem\u003eTetranychus urticae\u003c/em\u003e. Insect biochemistry and molecular biology 48, 17\u0026ndash;28\u003c/li\u003e\n \u003cli\u003eIsman, M.B. (2006) Botanical insecticides, deterrents, and repellents in modern agriculture and an increasingly regulated world. Annual review of entomology 51, 45\u0026ndash;66\u003c/li\u003e\n \u003cli\u003eIsman, M.B., S. Miresmailli (2011) Plant essential oils as repellents and deterrents to agricultural pests Recent developments in invertebrate repellents.(pp67\u0026ndash;77). ACS Publications\u003c/li\u003e\n \u003cli\u003eJakubowska, M., R. Dobosz, D. Zawada, J. Kowalska (2022) A review of crop protection methods against the twospotted spider mite\u0026mdash;\u003cem\u003eTetranychus urticae\u003c/em\u003e koch (acari: Tetranychidae)\u0026mdash;with special reference to alternative methods. Agriculture 12, 898\u003c/li\u003e\n \u003cli\u003eJeon, H., J.-H. Tak (2024) Gustatory habituation to essential oil induces reduced feeding deterrence and neuronal desensitization in \u003cem\u003eSpodoptera litura\u003c/em\u003e. Journal of Pest Science, 1\u0026ndash;16\u003c/li\u003e\n \u003cli\u003eJiang, S., L. Yang, J.R. Bloomquist (2019) High‐throughput screening method for evaluating spatial repellency and vapour toxicity to mosquitoes. Medical and Veterinary Entomology 33, 388\u0026ndash;396\u003c/li\u003e\n \u003cli\u003eManu, N., M.W. Schilling, T.W. Phillips (2021) Natural and synthetic repellents for pest management of the storage mite \u003cem\u003eTyrophagus putrescentiae\u003c/em\u003e (schrank)(sarcoptiformes: Acaridae). Insects 12, 711\u003c/li\u003e\n \u003cli\u003eMasoumi, F., M.R. Youssefi, M.A. Tabari (2016) Combination of carvacrol and thymol against the poultry red mite (\u003cem\u003eDermanyssus gallinae\u003c/em\u003e). Parasitology research 115, 4239\u0026ndash;4243\u003c/li\u003e\n \u003cli\u003eNerio, L.S., J. Olivero-Verbel, E. Stashenko (2010) Repellent activity of essential oils: A review. Bioresource technology 101, 372\u0026ndash;378\u003c/li\u003e\n \u003cli\u003eOliveira, J.L.d., E.V. Campos, A.E. Pereira, T. Pasquoto, R. Lima, R. Grillo, D.J.d. Andrade, F.A.d. Santos, L.F. Fraceto (2018) Zein nanoparticles as eco-friendly carrier systems for botanical repellents aiming sustainable agriculture. Journal of agricultural and food chemistry 66, 1330\u0026ndash;1340\u003c/li\u003e\n \u003cli\u003eOrganization, W.H. (2009) Guidelines for efficacy testing of mosquito repellents for human skin Guidelines for efficacy testing of mosquito repellents for human skin.\u003c/li\u003e\n \u003cli\u003eRazuvaeva, A., E. Ulyanova, E. Skolotneva, I. Andreeva (2023) Species identification of spider mites (tetranychidae: Tetranychinae): A review of methods. Vavilov Journal of Genetics and Breeding 27, 240\u003c/li\u003e\n \u003cli\u003eRoh, H.S., K.C. Park, C.G. Park (2012) Repellent effect of santalol from sandalwood oil against \u003cem\u003eTetranychus urticae\u003c/em\u003e (acari: Tetranychidae). Journal of economic entomology 105, 379\u0026ndash;385\u003c/li\u003e\n \u003cli\u003eSnyder, J.C., G.F. Antonious, R. Thacker (2011) A sensitive bioassay for spider mite (\u003cem\u003eTetranychus urticae\u003c/em\u003e) repellency: A double bond makes a difference. Experimental and Applied Acarology 55, 215\u0026ndash;224\u003c/li\u003e\n \u003cli\u003eStockton, D.G., D.H. Cha, G.M. Loeb (2021) Does habituation affect the efficacy of semiochemical oviposition repellents developed against \u003cem\u003eDrosophila suzukii\u003c/em\u003e? Environmental Entomology 50, 1322\u0026ndash;1331\u003c/li\u003e\n \u003cli\u003eTak, J.-H., M.B. Isman (2017) Acaricidal and repellent activity of plant essential oil-derived terpenes and the effect of binary mixtures against \u003cem\u003eTetranychus urticae\u003c/em\u003e koch (acari: Tetranychidae). Industrial Crops and Products 108, 786\u0026ndash;792\u003c/li\u003e\n \u003cli\u003eWood, M.J., J.C. Bull, K. Kanagachandran, T.M. Butt (2024) Development and laboratory validation of a plant-derived repellent blend, effective against \u003cem\u003eAedes aegypti\u003c/em\u003e [diptera: Culicidae], \u003cem\u003eAnopheles gambiae\u003c/em\u003e [diptera: Culicidae] and \u003cem\u003eCulex quinquefasciatus\u003c/em\u003e [diptera: Culicidae]. Plos one 19, e0299144\u003c/li\u003e\n \u003cli\u003eWu, W., Y. Yang, Y. Feng, X. Ren, Y. Li, W. Li, J. Huang, L. Kong, X. Chen, Z. Lin (2022) Study of the repellent activity of 60 essential oils and their main constituents against \u003cem\u003eAedes albopictus\u003c/em\u003e, and nano-formulation development. Insects 13, 1077\u003c/li\u003e\n \u003cli\u003eYoon, J., J.-H. Tak (2018) Toxicity and repellent activity of plant essential oils and their blending effects against two spotted spider mites, \u003cem\u003eTetranychus urticae\u003c/em\u003e koch. Korean Journal of Applied Entomology 57, 199\u0026ndash;207\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"high-throughput, repellent, essential oils, spider mite, gaussian process","lastPublishedDoi":"10.21203/rs.3.rs-6820848/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6820848/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eEvaluating the repellency of essential oils against \u003cem\u003eTetranychus urticae\u003c/em\u003e requires robust methodologies to detect time-dependent changes in their efficacy, due to differential efficacy, volatility, and sustained effectiveness. This study introduces the Pole-dance bioassay, a novel no-choice method optimized for high-throughput screening of time-dependent repellency, demonstrated through tests on twenty botanical volatiles against \u003cem\u003eT. urticae\u003c/em\u003e. Four statistical models, probit, two-parameter Hill, four-parameter Hill, and Gaussian Process (GP) regression, were compared for analyzing time-response landing data, employing both experimental results and scenario-based synthetic datasets reflecting diverse curve shapes. GP regression often provided superior model fits, especially for complex or incomplete landing trajectories. While repellency rankings based on median effective time (ET\u003csub\u003e50\u003c/sub\u003e) and area under the curve (AUC) were highly correlated within respective models, the choice of model significantly influenced parameter estimates. AUC proved essential for quantifying activity for highly potent compounds where ET\u003csub\u003e50\u003c/sub\u003e was inestimable (e.g., t-cinnamaldehyde, 1,8-cineole, (-)-terpinen-4-ol, thymol) and offered complementary insights into repellent effects. The Pole-dance bioassay combined with GP modeling establishes an optimized framework for statistically rigorous \u003cem\u003ein vivo\u003c/em\u003e high-throughput screening against \u003cem\u003eT. urticae\u003c/em\u003e.\u003c/p\u003e","manuscriptTitle":"Comparison of Statistical Models for Time- Dependent Repellency Using the Novel Pole-Dance Bioassay against Tetranychus urticae Koch","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-06-16 11:51:54","doi":"10.21203/rs.3.rs-6820848/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"9ae307e2-5707-47d2-8a97-04d59787258f","owner":[],"postedDate":"June 16th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-08-25T16:40:24+00:00","versionOfRecord":{"articleIdentity":"rs-6820848","link":"https://doi.org/10.1007/s10493-025-01058-y","journal":{"identity":"experimental-and-applied-acarology","isVorOnly":false,"title":"Experimental and Applied Acarology"},"publishedOn":"2025-08-21 16:29:36","publishedOnDateReadable":"August 21st, 2025"},"versionCreatedAt":"2025-06-16 11:51:54","video":"","vorDoi":"10.1007/s10493-025-01058-y","vorDoiUrl":"https://doi.org/10.1007/s10493-025-01058-y","workflowStages":[]},"version":"v1","identity":"rs-6820848","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6820848","identity":"rs-6820848","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}