Grover James P, Hsu Sze-Bi, Wang Feng-Bin
Department of Biology and Program in Environmental and Earth Sciences, University of Texas at Arlington, P.O. Box 19498, Arlington, USA.
J Math Biol. 2012 Apr;64(5):713-43. doi: 10.1007/s00285-011-0426-4. Epub 2011 May 21.
Microbial populations compete for nutrient resources, and the simplest mathematical models of competition neglect differences in the nutrient content of individuals. The simplest models also assume a spatially uniform habitat. Here both of these assumptions are relaxed. Nutrient content of individuals is assumed proportional to cell size, which varies for populations that reproduce by division, and the habitat is taken to be an unstirred chemostat where organisms and nutrients move by simple diffusion. In a spatially uniform habitat, the size-structured model predicts competitive exclusion, such that only the species with lowest break-even concentration persists. In the unstirred chemostat, coexistence of two competitors is possible, if one has a lower break-even concentration and the other can grow more rapidly. In all habitats, the calculation of competitive outcomes depends on a principal eigenvalue that summarizes relationships among cell growth, cell division, and cell size.
微生物种群会争夺营养资源，而最简单的竞争数学模型忽略了个体营养含量的差异。最简单的模型还假定栖息地在空间上是均匀的。在此，这两个假设都被放宽。假定个体的营养含量与细胞大小成正比，对于通过分裂进行繁殖的种群，细胞大小会有所不同，并且将栖息地视为一个未搅拌的恒化器，其中生物体和营养物质通过简单扩散移动。在空间均匀的栖息地中，大小结构模型预测会发生竞争排斥，以至于只有具有最低盈亏平衡点浓度的物种能够存续。在未搅拌的恒化器中，如果一个竞争者的盈亏平衡点浓度较低而另一个生长得更快，则两个竞争者有可能共存。在所有栖息地中，竞争结果的计算都取决于一个主特征值，该特征值总结了细胞生长、细胞分裂和细胞大小之间的关系。
