Legumes produce root nodules containing symbiotic rhizobial bacteria that convert atmospheric molecular nitrogen into ammonia or related nitrogenous compounds. The host plant supplies photosynthetic products to root nodules forming a mutualistic system. Legumes have physiological mechanisms for regulating nodule production with chemical signals produced in leaves, called the autoregulation of nodulation. In this paper, we discuss the optimal number of root nodules that maximizes the performance of the host plant. Here, we study two models. In the stationary plant model, the acquired photosynthetic products minus cost and loss are used for reproduction. In the growing plant model, the excess material is invested to produce leaves, roots, and root nodules, resulting in the exponential growth of the whole plant. The analysis shows that having root nodules is beneficial to the plant for a high leaf nitrogen content, faster plant growth rate, a short leaf longevity, a low root/shoot ratio, and low soil nutrient concentration. We discuss the long-distance control of nodulation-autoregulation and dependence on the environmental conditions of terrestrial plants considering these results.

豆类产生根瘤，根瘤中含有共生的根瘤菌，将大气中的分子氮转化为氨或相关的含氮化合物。寄主植物向根瘤提供光合产物，形成互惠系统。豆类具有通过叶片中产生的化学信号调节根瘤产生的生理机制，称为根瘤的自动调节。在本文中，我们讨论了根瘤的最佳数量，该数量可使寄主植物的性能最大化。在这里，我们研究两个模型。在固定植物模型中，所获得的光合产物减去成本和损失后将用于繁殖。在植物生长模型中，将多余的材料投入到叶片，根和根瘤的生产中，从而使整个植物呈指数增长。分析表明，具有根瘤对于高的叶片氮含量，更快的植物生长速度，短的叶片寿命，低的根/茎比和低的土壤养分浓度对植物都是有益的。考虑到这些结果，我们讨论了结瘤自动调节的远程控制以及对陆地植物环境条件的依赖性。