Two‐Dimensional Segmented Regression Model for Aluminum and Manganese Toxicity and Their Interaction in Soybean

Abstract

The toxicity of Al and Mn frequently occurs together to limit crop growth in tropical acid soils. There is need to develop a quantitative mechanistic model to describe the toxicity of Al and Mn individually as well as their interaction. A two‐dimensional segmented regression model was developed to describe the plant's tolerance, linear response, and saturation effect of Al and Mn individually as a plateau‐linear‐plateau trend. The model also included the interaction between Al and Mn defined as the multiplication of their linear responses. Two published data sets to demonstrate the model were from a field liming experiment (soybean [Glycine max (L.) Merr.] grain yield changed with soil extractable Al and Mn) and a solution culture experiment (soybean root and shoot growth changed with solution Al and Mn). Results showed that the model fitted well the two data sets. Soybean yield and growth in both experiments were reduced by individual Al and Mn. In the liming experiment, the interaction between Al and Mn was not significant. In the solution culture experiment, there were significant interactions in amelioration of toxicity to both root and shoot growth. Besides the estimates of tolerant levels and saturation levels of Al and Mn in solution, two other criteria derived from the mathematical model were critical levels at 90% relative yield and characteristic levels when soybean responded to Al only and Mn only. The model and the derived criteria can be used for optimal soil liming to reduce Al and Mn toxicity and accurate screening of Al‐ and Mn‐tolerant genotypes. A new segmented regression model can quantify Al and Mn toxicity and interaction. Al and Mn interaction based on the model was more accurate than conventional ANOVA. Critical Al and Mn levels depended on each other as mathematical functions. Soybean did not respond to Al in solution culture when Mn was 50.741 μmol L−1.