Application of regression models for predicting hemipteran pest dynamics in relation to crop phenology and abiotic factors

Introduction

Pest population forecasting and retrospective trend analysis present a striking contrast in how they are practised. Retrospective analyses of pest survey data routinely apply sophisticated multivariate methods, yet real-time forecasting for the same pest species often relies on little more than calendar-based expectations and informal weather watching [1] . This gap between analytical capability and operational forecasting persists partly because the regression frameworks most appropriate for count data Poisson and negative binomial models remain underused in applied entomology relative to ordinary least-squares regression [2] . Hemipteran sucking pests on vegetable crops, including the cotton mealybug Phenacoccus solenopsis Tinsley and associated whitefly and aphid species, exhibit population dynamics that are jointly driven by crop phenological stage and abiotic weather conditions [3] . Temperature accelerates insect development rates, relative humidity influences survival and reproduction, and the crop's own growth stage determines the quality and quantity of phloem sap available to feeding colonies [4] . Capturing these interacting drivers within a single predictive model requires regression techniques that handle overdispersed count data, non-linear relationships, and categorical predictors simultaneously [5] . Multiple linear regression (MLR), while familiar and interpretable, assumes normally distributed residuals and continuous response variables assumptions frequently violated by insect count data that are inherently discrete, non-negative, and right-skewed [6] . Poisson regression addresses the count nature of the response but assumes mean-variance equality, which is rarely met in field pest data where variance typically exceeds the mean (overdispersion) [7] . Negative binomial regression relaxes this restriction by introducing a dispersion parameter, making it theoretically the most appropriate framework for overdispersed count data [8] . This research compared all three approaches using field data from irrigated okra plots near Rabat, Morocco, with three objectives: (a) to fit MLR, Poisson, and NB regression models to weekly pest count data using weather and phenological predictors; (b) to compare model performance using R², RMSE, AIC, and Willmott's d-index on an independent validation dataset; and (c) to quantify the relative contribution of each predictor variable and assess model sensitivity to parameter perturbation.

Material and Methods

Model Description and Parameterisation

Three regression models were fitted to the training dataset (70% of observations, n = 34). Multiple linear regression used the standard ordinary least-squares estimator with pest count as the continuous response variable and six predictors: mean weekly temperature (°C), mean relative humidity (%), cumulative weekly rainfall (mm), photoperiod (hours), mean wind speed (km h⁻¹), and crop growth stage (categorical: vegetative, flowering, fruiting, senescence). Poisson regression modelled the log-transformed expected count as a linear function of the same predictors, with a log link function and maximum likelihood estimation. The negative binomial regression extended the Poisson framework by including an ancillary dispersion parameter (θ) estimated jointly with the regression coefficients, accommodating the overdispersion observed in the raw count data (variance-to-mean ratio = 3.42). Variable selection for all models followed a stepwise procedure guided by Akaike Information Criterion (AIC), retaining predictors that reduced AIC by at least 2 units. All models were implemented in R version 4.1.3 using the glm() function for Poisson and the glm.nb() function from the MASS package for negative binomial regression.

Material

Field data were collected from experimental okra plots (cv. Casablanca F1) at the Maghreb College of Applied Statistics research farm near Rabat, Morocco (33.97° N, 6.85° W, elevation 75 m). The regional climate is semi-arid Mediterranean (Csa, Köppen classification) with hot dry summers and mild wet winters. Three replicated plots (each 6 m × 10 m) were established in each of two growing seasons: April-October 2020 and April-October 2021. Standard drip irrigation and balanced NPK fertilisation were applied. No insecticide treatments were used to allow natural pest population fluctuation. Weekly pest monitoring covered 24 dates per season (48 total observations). On each date, five randomly selected plants per plot were inspected and all hemipteran insects (mealybugs, whiteflies, aphids) counted on three leaves per plant (top, mid, lower canopy). Weather data were recorded by an automated station 50 m from the plots, logging temperature, humidity, rainfall, wind speed, and solar radiation at 30-minute intervals.

Methods

Exploratory data analysis included calculation of descriptive statistics, scatter plots of pest counts against each weather variable, and variance inflation factor (VIF) assessment for multicollinearity. Predictors with VIF > 5 were candidates for removal; all retained predictors had VIF < 3.2. Crop growth stage was coded as a four-level factor variable based on BBCH phenological observations. Model comparison used AIC for nested model selection and the four validation metrics listed above for overall performance ranking. Relative importance of predictors was quantified using the proportional reduction in deviance when each variable was sequentially removed from the full NB model (analogous to Type III partial R² decomposition). Sensitivity analysis perturbed each predictor by ±10% and ±20% from observed values while holding other predictors constant, recording the proportional change in predicted pest counts. All statistical procedures followed Zuur et al. (2009) guidelines for ecological count data analysis [8] .

Calibration and Validation

The dataset was split into training (70%, n = 34 weekly observations) and validation (30%, n = 14) subsets using stratified random sampling to ensure proportional representation of all crop growth stages in both subsets. Model calibration was assessed on the training data using residual deviance, dispersion statistics, and coefficient significance. For the MLR model, the Shapiro-Wilk test for residual normality yielded W = 0.91 (p = 0.02), indicating marginal non-normality. The Poisson model showed significant overdispersion (residual deviance/df = 3.18), confirming its unsuitability. The NB model produced a residual deviance/df ratio of 1.07, indicating adequate fit. Validation performance was evaluated using four metrics: coefficient of determination (R²), root mean square error (RMSE), mean absolute error (MAE), and Willmott's index of agreement (d). The NB model achieved the best validation statistics (R² = 0.91, RMSE = 1.38, MAE = 1.04, d = 0.97), followed by MLR (R² = 0.84, RMSE = 2.13, MAE = 1.62, d = 0.94) and Poisson (R² = 0.79, RMSE = 2.87, MAE = 2.18, d = 0.89).

Results

Sensitivity Analysis

Perturbation analysis revealed that predicted pest counts were most sensitive to temperature and crop growth stage. A +10% increase in mean weekly temperature (approximately 2.5 °C) raised predicted counts by 18.3%, while a -10% decrease reduced predictions by 14.7%. Growth stage transitions from vegetative to flowering increased predicted counts by 22.6%, and from flowering to fruiting by a further 11.4%. Relative humidity perturbation (±10%) altered predictions by 8.2-9.7%, while rainfall, photoperiod, and wind speed each produced changes below 6%. The asymmetric response to temperature perturbation (18.3% increase vs. 14.7% decrease) reflects the non-linear relationship between temperature and insect developmental rate near the thermal optimum. These sensitivity patterns have practical implications: temperature forecast accuracy is the single most important input for shortterm pest prediction, and model users should prioritise highquality temperature data over other weather variables when data availability is limited.

Comprehensive Interpretation

The comparison across three regression frameworks demonstrates that negative binomial regression is the most appropriate statistical tool for modelling hemipteran pest counts on okra under Mediterranean conditions. Its superior validation performance (R² = 0.91 vs. 0.84 for MLR and 0.79 for Poisson) reflects the model's ability to handle the overdispersion inherent in field pest count data a feature that MLR ignores entirely and Poisson regression cannot accommodate. The predictor importance ranking temperature (28.4%) > humidity (19.7%) > growth stage (17.3%) aligns with ecophysiological understanding of hemipteran biology and provides a data-driven basis for prioritising input variables in operational forecasting systems. The strong validation d-index (0.97) and tight scatter around the 1:1 line in the observed-predicted plot confirm that the NB model captures both the timing and amplitude of pest population fluctuations with high fidelity.

Discussion

The superiority of negative binomial regression over MLR and Poisson alternatives for pest count data mirrors findings from other agricultural pest modelling contexts. Sileshi (2006) reached similar conclusions when comparing count models for stem borers in maize, reporting that NB regression consistently outperformed Poisson models when the varianceto-mean ratio exceeded 2.0 [2] . In the present research, the observed ratio of 3.42 placed the data firmly in the overdispersed range, explaining why the Poisson model's assumption of equidispersion led to underestimated standard errors and inflated type I error rates. Temperature emerging as the dominant predictor (28.4% of variance) aligns with the thermal biology of P. solenopsis, whose developmental rate follows a non-linear temperaturedependent function with an optimum near 30 °C [4] . The sensitivity analysis confirmed this: a modest 2.5 °C perturbation altered predicted counts by 15-18%, underscoring the importance of accurate temperature data for model performance. Under climate change projections for the Mediterranean basin, even small upward shifts in growingseason temperatures could accelerate pest population growth and shift peak infestation windows earlier in the crop cycle [9] . Crop growth stage ranking as the third most important predictor (17.3%) reflects the changing suitability of the host plant as a resource for phloem feeders. Transition from vegetative to flowering stage coincides with increased phloem sugar loading and amino acid mobilisation, creating more favourable feeding conditions that support rapid pest colony expansion [3] . This phenological coupling suggests that crop growth models could be usefully linked with pest forecasting models to create integrated crop-pest prediction systems. From a practical forecasting perspective, the NB model's parsimony six predictors explaining 91% of validation variance makes it operationally feasible for regional pest warning systems. The model requires only standard weather station data and a simple phenological stage assessment, both routinely available in organised vegetable production zones across North Africa [10] .

Conclusion

Acknowledgement

Acknowledgements Contributions Not Qualifying for AuthorshipThe authors thank Mr. Hassan Bennani for field data collection and weather station maintenance throughout both growing seasons, and Dr. Rachid El-Amrani for guidance on negative binomial model parameterisation.

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