Krone Stephen M, Guan Yongtao
Department of Mathematics, University of Idaho, Moscow, ID 83844-1103, USA.
J Theor Biol. 2006 Jul 7;241(1):14-25. doi: 10.1016/j.jtbi.2005.11.005. Epub 2005 Dec 19.
Biological communities are remarkable in their ability to form cooperative ensembles that lead to coexistence through various types of niche partitioning, usually intimately tied to spatial structure. This is especially true in microbial settings where differential expression and regulation of genes allows members of a given species to alter their lifestyle so as to fill a functional role within the community. The resulting species interactions can involve feedback, as in the case of some bacterial consortia that participate in the cooperative degradation of a given resource in a succession of steps and in such a way that certain "later" species provide catalytic support for the primary degrader. We seek to capture the essential features of such spatially extended biological systems by introducing a lattice-based stochastic spatial model (interacting particle system) with cyclic local dynamics. Here, a given site progresses through a sequence of resource and species states in a prescribed order. Furthermore, this succession of states (at a site) is assumed to form a cyclic pattern due to a natural feedback mechanism. We explore conditions under which all the species are able to coexist and consider the extent to which this coexistence requires the development of spatio-temporal patterns, including spiral waves. This self-organization, if it occurs, results when synchronization of the dynamics at the microscopic level leads to macroscopic patterns. These patterns result in consumer-driven resource fluctuations that generate a form of spatio-temporal niche partitioning. As with most models of this complexity, we employ a mixture of mathematical analysis and simulations to develop an understanding of the resulting dynamics.
生物群落形成合作集合体的能力非凡，通过各种类型的生态位划分实现共存，且通常与空间结构紧密相连。在微生物环境中尤其如此，基因的差异表达和调控使特定物种的成员能够改变其生活方式，从而在群落中发挥功能作用。由此产生的物种相互作用可能涉及反馈，例如一些细菌群落参与给定资源的逐步协同降解，某些“后来”的物种以这种方式为主要降解者提供催化支持。我们试图通过引入具有循环局部动力学的基于晶格的随机空间模型（相互作用粒子系统）来捕捉此类空间扩展生物系统的基本特征。在此模型中，给定的位点按规定顺序经历一系列资源和物种状态。此外，由于自然反馈机制，假定（位点处的）这种状态序列形成循环模式。我们探索所有物种能够共存的条件，并考虑这种共存需要发展时空模式（包括螺旋波）的程度。如果发生这种自组织，它是在微观层面的动力学同步导致宏观模式时产生的。这些模式导致消费者驱动的资源波动，从而产生一种时空生态位划分形式。与大多数这种复杂性的模型一样，我们采用数学分析和模拟相结合的方法来理解由此产生的动力学。
