School of Mathematical Sciences, Ministry of Education Key Laboratory of Mathematics and Engineering Applications & Shanghai Key Laboratory of PMMP, East China Normal University, Shanghai, 200241, China.
School of Science and Engineering, Chinese University of Hong Kong (Shenzhen), Shenzhen, 518172, Guangdong, China.
J Math Biol. 2023 Aug 8;87(3):39. doi: 10.1007/s00285-023-01970-0.
A consumer-resource reaction-diffusion model with a single consumer species was proposed and experimentally studied by Zhang et al.(Ecol Lett 20:1118-1128, 2017). Analytical study on its dynamics was further performed by He et al.(J Math Biol 78:1605-1636, 2019). In this work, we completely settle the conjecture proposed by He et al.(J Math Biol 78:1605-1636, 2019) about the global dynamics of the consumer-resource model for small yield rate. We then study a multi-species consumer-resource model where all the consumer species compete with each other through depression of the limited resources by consumption and there is no direct competition between them. We show that in this case, all consumer species persist uniformly, which implies that "competition exclusion" phenomenon will never happen. We also clarify its dynamics in both homogeneous and heterogeneous environments under various circumstances.
张等人提出并通过实验研究了一个具有单一消费物种的消费者-资源反应扩散模型(Ecol Lett 20:1118-1128, 2017)。何等人进一步对其动力学进行了分析研究(J Math Biol 78:1605-1636, 2019)。在这项工作中，我们彻底解决了何等人提出的关于小产量率的消费者-资源模型全局动力学的猜想(J Math Biol 78:1605-1636, 2019)。然后，我们研究了一个多物种消费者-资源模型，其中所有的消费者物种通过消耗有限资源来抑制彼此的生长，并且它们之间没有直接的竞争。我们表明，在这种情况下，所有的消费者物种都均匀地生存，这意味着“竞争排斥”现象永远不会发生。我们还澄清了在各种情况下同质和异质环境下的动力学。
