Multiplicative models for cultivar by location interaction in testing sugar beets for resistance to beet necrotic yellow vein virus

Summary Sugar beet cultivars were evaluated for resistance to beet necrotic yellow vein virus (BNYVV) on various locations in two consecutive years. Resistance levels of cultivars were measured by virus assays of plants from the field and the greenhouse. Infection levels in the fields were characterised by sampling plants of a susceptible indicator cultivar. For each year, statistical analyses were performed on two-way tables of cultivar by location for yield and quality parameters. In analysis of variance (ANOVA) significant main effects and significant cultivar by location interaction were found for all parameters (P<0.05). Interactions were further investigated by multiplicative models. In the Additive Main effects and Multiplicative Interaction effects (AMMI) model, interaction was written as the product of a cultivar score and a location score. Cultivar interaction scores were highly correlated to virus concentrations of the cultivars, and location interaction scores to virus concentrations of the susceptible indicator cultivar. Main effects of cultivars and locations were less clearly related to virus concentrations than interaction effects. In general, virus concentrations of plants from a greenhouse test gave higher correlations than virus concentrations of plants from the field. In the factorial regression model, virus concentrations were incorporated in the model. The model can be understood as a two-way ANOVA, with greenhouse virus concentrations and virus concentration of the indicator cultivar as concomitant variables on the cultivar and location factor. Results of analyses with both multiplicative interaction models showed that interactions of all yield and quality parameters can be described in terms of virus concentrations. Therefore, the relative performance of susceptible and partially resistant cultivars in infested fields can be estimated by means of three independent parameters, (i) the level of resistance determined in a greenhouse experiment, (ii) the yield and quality in non-infested fields, and (iii) the level of infection in the field.Abbreviations AMMI model Additive Main effects and Multiplicative Interaction effects model - ANOVA analysis of variance - BNYVV beet necrotic yellow vein virus - ELISA enzyme-linked immunosorbent assay - -amino N -amino nitrogen - K Kalium (potassium) - Na Natrium (sodium)