Understanding why strains with different metabolic pathways that compete for a single limiting resource coexist is a challenging issue within a theoretical perspective. Previous investigations rely on mechanisms such as group or spatial structuring to achieve a stable coexistence between competing metabolic strategies. Nevertheless, coexistence has been experimentally reported even in situations where it cannot be attributed to spatial effects [Heredity {\bf 100}, 471 (2008)]. According to that study a toxin expelled by one of the strains can be responsible for the stable maintenance of the two strain types. We propose a resource-based model in which an efficient strain with a slow metabolic rate competes with a second strain type which presents a fast but inefficient metabolism. Moreover, the model assumes that the inefficient strain produces a toxin as a byproduct. This toxin affects the growth rate of both strains with different strength. Through an extensive exploration of the parameter space we determine the situations at which the coexistence of the two strains is possible. Interestingly, we observe that the resource influx rate plays a key role in the maintenance of the two strain types. In a scenario of resource scarcity the inefficient is favored, though as the resource influx rate is augmented the coexistence becomes possible and its domain is enlarged.
Neutral species facilitate coexistence among cyclically competing species under birth and death processes
School of Statistics and Mathematics, Yunnan University of Finance and Economics（云南财经大学统计与数学学院）；School of Mathematics and Statistics, Xidian University（西安电子科技大学数学与统计学院）；Department of Applied Mathematics, Colleage of Applied Sciences, Kyung Hee University（韩国庆熙大学应用科学学院应用数学系）；G-LAMP NEXUS Institute, Kyung Hee University（韩国庆熙大学G-LAMP NEXUS研究所）
A multiscale theory based on metabolic scaling connects forest dynamics to tree-size distributions
University of Padova（帕多瓦大学）；Department TESAF, University of Padova（帕多瓦大学TESAF系）；National Biodiversity Future Center（国家生物多样性未来中心）；Laboratory of Interdisciplinary Physics, Department of Physics and Astronomy “G. Galilei”, University of Padova（帕多瓦大学伽利略物理与天文学系跨学科物理实验室）；INFN, Sezione di Padova（意大利国家核物理研究所帕多瓦分部）；Department of Civil, Environmental and Architectural Engineering, University of Padova（帕多瓦大学土木、环境与建筑工程系）；CMCC Centro Euro-Mediterraneo sui Cambiamenti Climatici（欧洲地中海气候变化研究中心）
Coexistence versus extinction in the stochastic cyclic Lotka-Volterra model
物种的循环优势已被确定为维持生物多样性的一种潜在机制，见例如B。Kerr，M. a.莱利，M。W. Feldman和B. J. M. Bohannan [Nature {\bf 418}，171（2002）]和B. Kirkup和M. a. Riley [Nature {\bf 428}，412（2004）].通过数值模拟支持的分析方法，我们解决了这个问题，通过研究一个典型的非空间三种群随机系统，即"石头剪刀布"或循环洛特卡-沃尔泰拉模型的属性。虽然确定性的方法（速率方程）预测的物种的共存导致定期（但中性稳定）振荡的人口密度，我们表明，在系统中产生的波动与\emph{finite number of agents}大大改变了这一局面，并负责灭绝：经过足够长的时间后，三个物种中的两个灭绝。作为主要发现，我们提供了在给定时间的灭绝概率的解析估计和数值计算。我们还讨论了我们的研究结果的影响，一类广泛的竞争人口系统。
