Department of Physics, Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, MA, United States.
J Theor Biol. 2012 Apr 21;299:31-41. doi: 10.1016/j.jtbi.2011.03.008. Epub 2011 Mar 21.
The field of microbial cooperation has grown enormously over the last decade, leading to improved experimental techniques and a growing awareness of collective behavior in microbes. Unfortunately, many of our theoretical tools and concepts for understanding cooperation fail to take into account the peculiarities of the microbial world, namely strong selection strengths, unique population structure, and non-linear dynamics. Worse yet, common verbal arguments are often far removed from the math involved, leading to confusion and mistakes. Here, we review the general mathematical forms of Price's equation, Hamilton's rule, and multilevel selection as they are applied to microbes and provide some intuition on these otherwise abstract formulas. However, these sometimes overly general equations can lack specificity and predictive power, ultimately forcing us to advocate for more direct modeling techniques.
过去十年中，微生物合作领域发展迅速，这导致了实验技术的改进和对微生物群体行为的认识不断提高。不幸的是，我们用于理解合作的许多理论工具和概念都没有考虑到微生物世界的特殊性，即强大的选择强度、独特的种群结构和非线性动力学。更糟糕的是，常见的口头争论往往与所涉及的数学内容相去甚远，导致混淆和错误。在这里，我们回顾了 Price 方程、Hamilton 规则和多层次选择的一般数学形式，以及它们在微生物中的应用，并对这些原本抽象的公式提供了一些直观的理解。然而，这些有时过于笼统的方程可能缺乏特异性和预测能力，最终迫使我们提倡更多直接的建模技术。
