Mathematical description for nodule size distribution, and number, weight, and diameter of nodules deduced from a theoretical model of photosynthate competition among nodules

Abstract

To describe the nodule size distribution as well as the total number, weight, and diameter, and average weight and diameter of nodules using a set of input parameters, mathematical equations were derived from a model in which photosynthate allocation determined the nodule size after competition for photosynthates among nodules. This model contains four input parameters,jC, N, a, and b, representing the rate of photosynthate supply to the root system, distribution density of nodulation sites, a partition coefficient of photosynthates in the root system, and a threshold of photosynthate supply to maintain a visible nodule, respectively. However, the mathematical equations finally required only a set of three val- They were compared with the actual distribution and values to evaluate the accuracy of the equations. They showed a good consistency with the actual ones. Averages of relative differences between the calculated and measured values were 21.9, 17.2,43.2, 10.2, and 35.5% for the total number, diameter, and weight of the nodules, and average diameter and weight of a nodule, respectively. Simulation demonstrated the role of the parameters in the model and proved similarity between C and photosynthesis ability and between N and inoculation dose in their behaviour.

Distribution Pattern of Root Nodules in Relation to Root Architecture in Two Leading Cultivars of Peanut (Arachis hypogaeaL.) in Japan

“…Five plants of each cultivar were collected four times: 36, 66, 94, and 139 days after seeding (DAS) in 2003, and36, 65, 96, and134 DAS in 2004. At each growth stage, aboveground plant parts were harvested, dried at 80 o C for 72 h, and weighed.…”

“…In general, the distribution of nodule size varies with the plant growth stage. Tamura (1992) tried to describe the distribution of nodule size using Erlan's model, and Ikeda (2003) used four parameters including the partitioning of photosynthates in the root system to describe the distribution of nodule size in soybean. However, these modeling studies for soybean did not pay attention to the architecture of root system, and the distribution of nodule size is still unknown in other legumes.…”