Extreme Variability Modelling of Overdispersed Germination Count Experiments

Abstract

Germination tests are carried out for a wide variety of purposes in weed control. The variability in seed germination counts raises the overdispersion problem. The objective of this study is to compare different approaches used in solving overdispersion and to offer practical solutions to researchers. The data sets were created from seed germination counts, which examined the allelopathic effect of white cabbage (Brassica oleracea L. var. capitata L.) on the germination of some culture and weed seeds. Methanol and aqueous concentrations (30%, 40%, 50%) of dry and fresh white cabbage were used. Assuming the Poisson distribution in the generalized linear mixed model, overdispersion problem was determined in redroot pigweed (Amaranthus retroflexus L.), lamb's quarters (Chenopodium album L.) and sugar beet (Beta vulgaris L.) Equidispersion was determined in corn (Zea mays L.) and it was perfectly adapted to the Poisson distribution. In order to overcome the overdispersion problem, generalized Poisson distribution outperformed negative binomial distribution. The increase concentration in the generalized Poisson in weeds, fresh cabbage methanol and aqueous applications were very effective reducing germination (p < 0.05). The best results in weed seeds were obtained at 50%. Unlike weeds, 30% concentration of dry cabbage methanol and aqueous were considered as the upper limit in order not to adversely affect germination in Z. mays and B. vulgaris. Consequently, in germination tests, the problem of overdispersion is inevitable as a result of excessive variability. For germination count data, generalized Poisson distribution is viable option and powerful alternative to accurately describe mean-variance relationship.