Scottish Crop Research Institute, Invergowrie, Dundee DD2 5DA, UK.
J Exp Bot. 2010 May;61(8):2131-43. doi: 10.1093/jxb/erp389. Epub 2010 Jan 27.
Models of root system growth emerged in the early 1970s, and were based on mathematical representations of root length distribution in soil. The last decade has seen the development of more complex architectural models and the use of computer-intensive approaches to study developmental and environmental processes in greater detail. There is a pressing need for predictive technologies that can integrate root system knowledge, scaling from molecular to ensembles of plants. This paper makes the case for more widespread use of simpler models of root systems based on continuous descriptions of their structure. A new theoretical framework is presented that describes the dynamics of root density distributions as a function of individual root developmental parameters such as rates of lateral root initiation, elongation, mortality, and gravitropsm. The simulations resulting from such equations can be performed most efficiently in discretized domains that deform as a result of growth, and that can be used to model the growth of many interacting root systems. The modelling principles described help to bridge the gap between continuum and architectural approaches, and enhance our understanding of the spatial development of root systems. Our simulations suggest that root systems develop in travelling wave patterns of meristems, revealing order in otherwise spatially complex and heterogeneous systems. Such knowledge should assist physiologists and geneticists to appreciate how meristem dynamics contribute to the pattern of growth and functioning of root systems in the field.
根系生长模型于 20 世纪 70 年代初出现，其基础是对土壤中根系长度分布的数学表述。过去十年，更复杂的结构模型得到了发展，并且采用了计算密集型方法来更详细地研究发育和环境过程。迫切需要能够整合根系知识的预测技术，从分子水平扩展到植物群体。本文提出了更广泛地使用基于根系结构连续描述的更简单的根系模型的理由。提出了一个新的理论框架，该框架将根密度分布的动态描述为个体根系发育参数（如侧根发生、伸长、死亡和向地性的速率）的函数。此类方程产生的模拟可以在生长导致变形的离散域中最有效地进行，并且可以用于模拟许多相互作用的根系的生长。所描述的建模原理有助于弥合连续体和结构方法之间的差距，并增强我们对根系空间发育的理解。我们的模拟表明，根系以分生组织的移动波模式发育，揭示了在其他情况下空间复杂和异质的系统中的有序性。这种知识应该有助于生理学家和遗传学家理解分生组织动态如何有助于根系在田间的生长和功能模式。
