AI 中文总结
研究微生物群落利用资源生长的问题，基于新的微生物消费者-资源模型（MiCRM），用快慢近似法研究其持久性、可行性和稳定性，得出如M小于S时群落不持久等结论，还提出随机快慢模型并研究灭绝事件。
AI 中文摘要
微生物群落广泛存在，但人们对其如何利用可用资源生长了解不足。群落是包含数千个通过资源竞争相互作用的微生物物种的复杂系统。经典的麦克阿瑟消费者-资源模型低估了群落生物量。新的微生物消费者-资源模型（MiCRM）考虑了代谢物交换介导的种间相互作用。本文在一些简化假设下，用快慢近似法研究了MiCRM的持久性、可行性和稳定性。比如，当资源物种数量M小于消费者物种数量S时，微生物群落不持久；当幸存者数量S小于M时，慢稳态通常是稳定的。最后提出了具有快速泊松稳态的随机快慢模型并研究相关灭绝事件。
英文摘要
Microbial communities are ubiquitous in nature but how they grow on available resources is still poorly understood. Communities are complex systems harboring thousands of microbial species that interact through resource competition. The classical MacArthur consumer-resource model has been shown to underestimate formed community biomass. A recent new microbial consumer-resource model (MiCRM) considers the inclusion of inter-specific interactions mediated by metabolite exchange (cross-feeding) where the various bacterial growth byproducts can be reused by other species for their own growth. We study persistence, feasibility and stability for MiCRM under some simplifying assumptions using slow-fast approximation. We show e.g. the non-persistence of the microbial community when the number of resource species M is smaller than the number of consumer species S. We then study the stability of the slow steady state when the number or survivors S is smaller than M, and show that such equilibria are generically stable. We finally propose a stochastic slow-fast version of the model having fast Poisson steady state and study related extinction events.
