A spatially-explicit count data regression for modeling the density of forest cockchafer ( Melolontha hippocastani ) larvae in the Hessian Ried (Germany)

Abstract

Background: In this paper, a regression model for predicting the spatial distribution of forest cockchafer larvae in the Hessian Ried region (Germany) is presented. The forest cockchafer, a native biotic pest, is a major cause of damage in forests in this region particularly during the regeneration phase. The model developed in this study is based on a systematic sample inventory of forest cockchafer larvae by excavation across the Hessian Ried. These forest cockchafer larvae data were characterized by excess zeros and overdispersion. Methods: Using specific generalized additive regression models, different discrete distributions, including the Poisson, negative binomial and zero-inflated Poisson distributions, were compared. The methodology employed allowed the simultaneous estimation of non-linear model effects of causal covariates and, to account for spatial autocorrelation, of a 2-dimensional spatial trend function. In the validation of the models, both the Akaike information criterion (AIC) and more detailed graphical procedures based on randomized quantile residuals were used. Results: The negative binomial distribution was superior to the Poisson and the zero-inflated Poisson distributions, providing a near perfect fit to the data, which was proven in an extensive validation process. The causal predictors found to affect the density of larvae significantly were distance to water table and percentage of pure clay layer in the soil to a depth of 1 m. Model predictions showed that larva density increased with an increase in distance to the water table up to almost 4 m, after which it remained constant, and with a reduction in the percentage of pure clay layer. However this latter correlation was weak and requires further investigation. The 2-dimensional trend function indicated a strong spatial effect, and thus explained by far the highest proportion of variation in larva density.

Applications of Generalized Additive and Bayesian Hierarchical Models for Areal Safety Analysis: Case Study of an Urban Multimodal Transportation System in Chicago, Illinois

“…The other study used GAM to incorporate interaction terms into crash modification factors, concluding that this approach adequately captured the interactions between geometric design and operational features (22). Other disciplines, such as ecology and epidemiology, have used GAMs in spatial analysis, taking advantage of the ability of smooth functions to account for random spatial effects and spatial correlation in the data (23,24).…”

“…If a smoothing function is used across the locations on spatially aggregated data, GAM may be used to represent spatial processes in the data and account for spatial variation. Although two previous applications of additive models in crash studies developed smoothing functions related to explanatory variables such as traffic volumes and geometric design (21,22), smoothing across locations has been used previously only in epidemiology and ecological studies (23,24). Ecology research uses GAMs to account for the effects of explanatory variables, as well as spatial autocorrelation by including a two-dimensional spatial trend function in the model (23).…”

“…Although two previous applications of additive models in crash studies developed smoothing functions related to explanatory variables such as traffic volumes and geometric design (21,22), smoothing across locations has been used previously only in epidemiology and ecological studies (23,24). Ecology research uses GAMs to account for the effects of explanatory variables, as well as spatial autocorrelation by including a two-dimensional spatial trend function in the model (23). The general form of the model with a spatial trend function is shown in Equation 4 (23,24):…”

“…Ecology research uses GAMs to account for the effects of explanatory variables, as well as spatial autocorrelation by including a two-dimensional spatial trend function in the model (23). The general form of the model with a spatial trend function is shown in Equation 4 (23,24):…”

“…The smoothing function f i used in this paper is estimated by minimizing the following penalized least square function: part of the model, similar to modeling a lag effect. The additive regression models were fitted with a two-dimensional smoothing function of the geographic location of each spatial unit of analysis, to capture the spatial autocorrelation and nonlinear effects that could not be captured by the observed explanatory variables (23,24). Whether this approach is appropriate for modeling the existing spatial autocorrelation in the data depends on the complexity of spatial dependence.…”