论文标题
大小不同的联盟之间的竞争
Competition among alliances of different sizes
论文作者
论文摘要
为了了解生态系统的生物多样性，不能通过仅分析竞争物种的一对关系来理解。取而代之的是，我们应该考虑多点相互作用，因为第三方的存在可以显着改变原始的微观结果。通过这种方式，联盟可能会出现，否则可能存在偏见的物种可以互相保护彼此免受外部入侵者的侵害。这样的联盟可以由两个，三个甚至更多的物种形成。通过引入最小模型，其中六个物种争夺空间，我们在这里研究联盟的大小如何决定形成的生命力。我们表明，在大多数参数空间中，最小尺寸和其他解决方案的组只能在有限的参数范围内观察到。这些阶段是通过不连续的相变隔开的，这些相位只能通过严重的有限尺寸效应和长松弛过程来通过密集的数值努力来识别。
To understand the biodiversity of an ecosystem cannot be understood by solely analyzing the pair relations of competing species. Instead, we should consider multi-point interactions because the presence of a third party could change the original microscopic outcome significantly. In this way an alliance may emerge where species, who may have biased relations otherwise, can protect each other from an external invader. Such an alliance can be formed by two, three or even more species. By introducing a minimal model where six species compete for space we here study how the size of an alliance determines the vitality of a formation. We show that in the majority of parameter space the group of the smallest size prevails and other solutions can only be observed in a limited parameter range. These phases are separated by discontinuous phase transitions which can only be identified by intensive numerical efforts due to serious finite size effects and long relaxation processes.
