How populations distribute in both space and time is one of the key issues in ecological systems, which can characterize the relationship between populations, space–time structure and evolution law. Consequently, pattern dynamics in ecosystems has been widely investigated including their causes and ecological functions. In order to systematically understand the interactions in ecosystems, we summarize the related results in pattern formation of ecological systems. Based on mathematical modeling and analysis, we show the mechanisms of different patterns including feedback, scale-dependent, phase separation, nonlocal effects, time delay and spatial heterogeneity. This work offers assistance for better understanding the complexity of ecosystems and provides new insights for self-organizations evolution and ecosystem protection. We hope that our results may be applied in other related fields such as epidemiology, medical science, atmospheric science and so on.

种群如何在时空上分布是生态系统中的关键问题之一，可以表征种群，时空结构和进化规律之间的关系。因此，生态系统中的模式动态已被广泛研究，包括其成因和生态功能。为了系统地理解生态系统中的相互作用，我们总结了生态系统模式形成中的相关结果。基于数学建模和分析，我们展示了不同模式的机制，包括反馈，比例依赖，相分离，非局部效应，时间延迟和空间异质性。这项工作为更好地了解生态系统的复杂性提供了帮助，并为自组织演化和生态系统保护提供了新的见解。