Computational methods for population-size-dependent branching processes

分支过程是用来模拟随时间随机进化的种群的主要数学工具。该理论的大多数关键结果都是在个体相互独立繁殖和死亡的简化假设下得出的。然而，这种假设在大多数现实情况下都是不成立的，特别是在环境资源有限或栖息地容量有限的情况下。本项目旨在为一类具有依赖性的分支过程开发新颖有效的算法技术和统计方法。我们将利用这些结果来研究大洋洲濒危岛屿鸟类种群保护中的重大问题，并为其保护管理提供信息。

Branching processes are the primary mathematical tool used to model populations that evolve randomly in time. Most key results in the theory are derived under the simplifying assumption that individuals reproduce and die independently of each other. However, this assumption fails in most real-life situations, in particular when the environment has limited resources or when the habitat has a restricted capacity. This project aims to develop novel and effective algorithmic techniques and statistical methods for a class of branching processes with dependences. We will use these results to study significant problems in the conservation of endangered island bird populations in Oceania, and to help inform their conservation management.