Generalized mixed linear modeling approach to analyze nodulation in common bean inbred lines

Abstract

The objective of this work was to compare distributions for the modeling of the number and dry matter weight of nodules (DWN) of Rhizobium from different inoculants in common bean (Phaseolus vulgaris) inbred lines subjected to nitrogen doses, as well as to identify the best inoculant for those lines. The experiment was carried out in a randomized complete block design, arranged in split-split plots, with three factors - four inbred lines, five nitrogen doses (0, 20, 40, 60, and 80 kg ha(-1)), and three inoculants (CIAT 899, UFLA 02-100, and peat) - and four replicates. The number of nodules and their dry matter weight were analyzed with the generalized linear mixed modeling approach. The highest number of nodules was obtained with the CIAT 899 inoculant, at the dose of 20 kg ha(-1) N (260 nodules), followed by UFLA 02-100, at 80 kg ha(-1) (109 nodules), and peat alone at 20 kg ha(-1) (98 nodules). The DWN with CIAT 899 exceeded in 0.66 g the DWN with UFLA 02-100, and in 0.95 g the DWN obtained without inoculation (inoculated with peat alone). The use of the negative binomial distribution and of the gamma distribution is a simple way to control data overdispersion of the nodule number and data underdispersion of DWN, respectively.