Application of mathematical models to describe rice growth and nutrients uptake in the presence of plant growth promoting microorganisms

Two plant growth promoting microorganisms (PGPM) including Pantoea ananatis (KM977993) and Piriformospora indica were tested for their ability to improve rice (cv. 'Tarom Mahalli') growth and yield under field condition, which was arranged in a split-plot based on a randomized complete block design with three replications. The experimental soil was classified as Haplic Luvisols and Gleyic Cambisols according to WRB. Four levels of potassium sulfate fertilizer (PSF: zero, 60, 120 and 180 kg ha−1) were used as the main plot and four levels of inoculation (single inoculations with P. ananatis, P. indica, co-inoculation and control) served as the sub-plots. Based on our knowledge, this is the first study that use a range of mathematical models to describe the effect of PGPM on rice growth and yield. The results indicated that the tiller number hill−1 (TNH), leaf area index (LAI), biomass dry weight (BDW), grain yield (GY), harvest index (HI), uptake of potassium (UK) in the straw and grain, HI of K, uptake of nitrogen (UN) in the grain and protein content increased by 9.0-27.2%, 11.7-45.4%, 11.1-24.7%, 13.6-30.6%, 1.25-17.6%, 1.81-27.4%, 10.8-39.9%, 7.04-12.5%, 12.3-36.8% and 3.24-5.56%, respectively, compared with the control (depending on the PGPM and PSF). The co-inoculation with P. ananatis and P. indica as the best treatment, declining the use of PSF (∼40.5%) and enhancing GY (∼22.6%) compared to the control. Consequently, an increase in BDW, UN and UK can be related to increasing TNH, LAI, radiation interception capacity and photosynthesis efficiency. Our findings showed, for the first time, physiological aspects of the effects both PGPM and PSF on rice growth and also recommended that PGPM can be used as biofertilizer in sustainable rice production systems.