Comparison of Frequentist and Bayesian Generalized Linear Models for Analyzing the Effects of Fungicide Treatments on the Growth and Mortality of Piper Nigrum

Foot rot disease poses a devastating threat to pepper agriculture. In Vietnam, conventionally, fungicides are the control methods used against the disease. However, the practical effectiveness of fungicide treatment has yet to be quantitatively assessed. To fill this gap a three-factorial experiment was conducted, the factors of which were fungicide application, soil type, and infection pathway, with plant mortality and plant growth as the target variables. Two of the most common fungicides were chosen, including Agrifos 400 (potassium phosphonate) and Aliette 800WG (fosetyl-Al). The two fungicides were used in multiple treatment plans, with soil drenching selected as the means of controlling foot rot disease on red basalt soil and red basalt soil added with organic matter in a greenhouse experiment. Three-month-old pepper (Piper nigrum) plants were treated with Agrifos (application interval of 10 and 20 days), Aliette (application interval of 30 and 60 days), and a combination of both fungicides at half doses. Pepper plants were infected with the fungus Pythium spp. from soil or by direct inoculation. To assess the effect of fungicides on foot rot mortality and the growth of pepper plants, multiple generalized linear models were set up using frequentist and Bayesian approaches. Generally, both procedures suggest the same conclusions for model selection in terms of the Akaike information criterion (AIC) and the deviance information criterion (DIC). Fungicide type was found to be the main factor that affected the survival of plants. Most of the treatments (except Aliette, with an interval of 60 days) effectively reduced the mortality. The usage of fungicides affected the growth of plants in interaction with soil types. Aliette suppressed the growth of plants, especially on red soil, while Agrifos had no effect on the growth of pepper plants. The combined application of Agrifos and Aliette with half doses proves to be a promising solution for balancing cost and effectiveness in protecting plants against foot rot pathogens without affecting their growth. In our case, under the inhomogeneity of variance and unbalanced samples, the Bayesian inference appeared to be the most useful because of its flexibility in terms of model structure.