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.Index terms: Phaseolus vulgaris, Rhizobium, symbiotic nitrogen fixation, inoculant, overdispersion, underdispersion. Abordagem de modelos lineares generalizados mistos para analisar nodulação em linhagens de feijoeiro-comumResumo -O objetivo deste trabalho foi comparar distribuições para a modelagem do número e da massa de matéria seca de nódulos (MSN) de Rhizobium de diferentes inoculantes em linhagens de feijoeiro-comum (Phaseolus vulgaris) submetidas a diferentes doses de nitrogênio, bem como identificar o melhor inoculante para essas linhagens. O experimento foi instalado em blocos completos ao acaso, arranjados em parcelas subsubdivididas, com três fatores -quatro linhagens, cinco doses de nitrogênio (0, 20, 40, 60 e 80 kg ha . A MSN com o inoculante CIAT 899 excedeu em 0,66 g a MSN com o UFLA 02-100, e em 0,95 g a MSN obtida sem inoculação (inoculação com turfa apenas). O uso das distribuições bionomial negativa e gama é uma maneira simples de controlar a superdispersão dos dados do número de nódulos e a subdispersão dos dados de MSN, respectivamente.Termos para indexação: Phaseolus vulgaris, Rhizobium, fixação simbiótica de nitrogênio, inoculantes, superdispersão, subdispersão.

The Use of the Generalized Linear Model to Assess the Speed and Uniformity of Germination of Corn and Soybean Seeds

“…These results demonstrate the importance of considering the choice of the correct link function, since the use of inaccurate models is potentially generating misleading conclusions [26,28]. Although the logit model is currently preferred in some areas-for example, in biometrics [22,29,30]-in this study, smaller deviances were obtained for most hybrid and/or cultivar studied; it is necessary to study this by comparing the link seeking functions that best describe the probability of interest [31].…”

“…The main consequences of these phenomena are the estimation of standard errors, which consequently can induce an inappropriate choice of models, potentially compromising the conclusions [26]. Even in the face of researchers' efforts to control experimental conditions, the occurrence of phenomena such as overdispersion is common for agricultural systems, as there is great variability [27,28].…”

“…The use of quasi-likelihood to correct estimated standard errors is recommended by [33] and has been adopted in seed germination studies [18,29], in entomology data [34,35], in the assessment of ecological data [26], and in the modeling of the number and dry matter mass of Rhizobium nodules in bean culture [28]. Therefore, there is a solid body of literature on the use of this methodology.…”