Department of Environmental Science and Policy, University of California, Davis, CA 95616, USA.
J R Soc Interface. 2013 Jul 31;10(87):20130559. doi: 10.1098/rsif.2013.0559. Print 2013 Oct 6.
Critical population phase transitions, in which a persistent population becomes extinction-prone owing to environmental changes, are fundamentally important in ecology, and their determination is a key factor in successful ecosystem management. To persist, a species requires a suitable environment in a sufficiently large spatial region. However, even if this condition is met, the species does not necessarily persist, owing to stochastic fluctuations. Here, we develop a model that allows simultaneous investigation of extinction due to either stochastic or deterministic reasons. We find that even classic birth-death processes in spatially extended ecosystems exhibit phase transitions between extinction-prone and persistent populations. Sometimes these are first-order transitions, which means that environmental changes may result in irreversible population collapse. Moreover, we find that higher migration rates not only lead to higher robustness to stochastic fluctuations, but also result in lower sustainability in heterogeneous environments by preventing efficient selection for suitable habitats. This demonstrates that intermediate migration rates are optimal for survival. At low migration rates, the dynamics are reduced to metapopulation dynamics, whereas at high migration rates, the dynamics are reduced to a multi-type branching process. We focus on species persistence, but our results suggest a unique method for finding phase transitions in spatially extended stochastic systems in general.
关键种群相变，即由于环境变化，持续存在的种群变得容易灭绝，在生态学中具有重要意义，其确定是成功进行生态系统管理的关键因素。为了生存，一个物种需要在足够大的空间区域内具有适宜的环境。然而，即使满足了这个条件，由于随机波动，物种也不一定能够存活。在这里，我们开发了一个模型，可以同时研究由于随机或确定性原因导致的灭绝。我们发现，即使在空间扩展生态系统中的经典出生-死亡过程中，也会出现易灭绝和持续存在的种群之间的相变。有时这些是一级相变，这意味着环境变化可能导致种群不可逆转的崩溃。此外，我们发现较高的迁移率不仅会导致对随机波动的更高鲁棒性，而且由于阻止了对合适栖息地的有效选择，还会导致在异质环境中的可持续性降低。这表明中间迁移率对于生存是最优的。在低迁移率下，动力学简化为集合种群动力学，而在高迁移率下，动力学简化为多类型分支过程。我们关注的是物种的生存，但我们的结果表明，对于一般的空间扩展随机系统，存在一种独特的寻找相变的方法。
