BACKGROUND Natural habitats are typically structured, imposing constraints on inhabiting populations and their interactions. Which conditions are important for coexistence of diverse communities, and how cooperative interaction stabilizes in such populations, have been important ecological and evolutionary questions. RESULTS We investigate a minimal ecological framework of microbial population dynamics that exhibits crucial features to show coexistence: Populations repeatedly undergo cycles of separation into compartmentalized habitats and mixing with new resources. The characteristic time-scale is longer than that typical of individual growth. Using analytic approximations, averaging techniques and phase-plane methods of dynamical systems, we provide a framework for analyzing various types of microbial interactions. Population composition and population size are both dynamic variables of the model; they are found to be decoupled both in terms of time-scale and parameter dependence. We present specific results for two examples of cooperative interaction by public goods: collective antibiotics resistance, and enhanced iron-availability by pyoverdine. We find stable coexistence to be a likely outcome. CONCLUSIONS The two simple features of a long mixing time-scale and spatial compartmentalization are enough to enable coexisting strains. In particular, costly social traits are often stabilized in such an environment-and thus cooperation established.

中文翻译：

---

结构化栖息地的共存与合作。

背景技术自然栖息地通常是结构化的，对居住种群及其相互作用施加限制。哪些条件对不同群落的共存很重要，以及这些种群的合作互动如何稳定，一直是重要的生态和进化问题。结果 我们研究了微生物种群动态的最小生态框架，该框架表现出显示共存的关键特征：种群反复经历分离成分隔栖息地并与新资源混合的循环。典型的时间尺度比个体成长的典型时间尺度更长。我们使用动态系统的解析近似、平均技术和相平面方法，为分析各种类型的微生物相互作用提供了一个框架。人口构成和人口规模都是模型的动态变量；发现它们在时间尺度和参数依赖性方面都是解耦的。我们提出了公共产品合作互动的两个例子的具体结果：集体抗生素耐药性和 pyoverdine 增强的铁利用率。我们发现稳定的共存是一个可能的结果。结论 长混合时间尺度和空间划分这两个简单特征足以使菌株共存。特别是，代价高昂的社会特征通常在这样的环境中得到稳定——从而建立了合作。我们提出了公共产品合作互动的两个例子的具体结果：集体抗生素耐药性和 pyoverdine 增强的铁利用率。我们发现稳定的共存是一个可能的结果。结论 长混合时间尺度和空间划分这两个简单特征足以使菌株共存。特别是，代价高昂的社会特征通常在这样的环境中得到稳定——从而建立了合作。我们提出了公共产品合作互动的两个例子的具体结果：集体抗生素耐药性和 pyoverdine 增强的铁利用率。我们发现稳定的共存是一个可能的结果。结论 长混合时间尺度和空间划分这两个简单特征足以使菌株共存。特别是，代价高昂的社会特征通常在这样的环境中得到稳定——从而建立了合作。