Longitudinal Pattern of Aerenchyma Formation Using the Ti-Gompertz Model in Rice Adventitious Roots

The longitudinal pattern of root aerenchyma formation its relationship with the function of adventitious roots in rice remain unclear. In the present study, the percentage of the aerenchyma area to the cross-sectional area (aerenchyma percentage) was fit with four nonlinear models: W0-Gompertz, Ti-Gompertz, logistic and von Bertalanffy. Goodness-of-fit criteria such as the R2, the Akaike information criterion (AIC) and the Bayesian information criteria (BIC) were used to select the model. The bias of the parameters was evaluated using the difference between the ordinary least squares-based parameter estimates and the mean of 1,000 bootstrap-based parameter estimates and the symmetry of the distributions of these parameters. The results showed that the Ti-Gompertz model which had a high goodness-of-fit with an R2 close to one, lower AIC and BIC values, parameter estimates close to being unbiased and good linear approximation, provided the best fit for the longitude pattern of rice aerenchyma formation with different root length among the competing models. Using the second- and third- order derivatives according to the distance from the root apex, the critical points of Ti-Gompertz were calculated. The rapid stage for aerenchyma formation was from the maximum acceleration point (1.38–1.76 cm from the root apex) to the maximum deceleration point (3.13–4.19 cm from the root apex). In this stage the aerenchyma percentage increased by 5.3%–15.7% per cm, suggesting that the cortical cells tended to die rapidly for aerenchyma formation rather than for respiration cost during this stage. Meanwhile, the volume of the aerenchyma of the entire roots could be computed using the integral function of the Ti-Gompertz model. We proposed that the longitudinal pattern of root aerenchyma formation modelled by the Ti-Gompertz model helped to deeply understand the relationship among the anatomical traits and physiological function in rice adventitious roots.