Ecosystems engineers are species that can substantially alter their abiotic environment and thereby enhance their population growth. The net growth rate of obligate engineers is even negative unless they modify the environment. We derive and analyze a model for the spread and invasion of such species. Prior to engineering, the landscape consists of unsuitable habitat; after engineering, the habitat is suitable. The boundary between the two types of habitat is moved by the species through their engineering activity. Our model is a novel type of a reaction-diffusion free boundary problem. We prove the existence of traveling waves and give upper and lower bounds for their speeds. We illustrate how the speed depends on individual movement and engineering behavior near the boundary.

中文翻译：

---

突破边界：生态系统工程师空间传播模型

生态系统工程师是能够显着改变其非生物环境从而促进其人口增长的物种。除非他们改变环境，否则专职工程师的净增长率甚至为负。我们推导出并分析了此类物种的传播和入侵模型。在工程之前，景观由不合适的栖息地组成；工程后，栖息地适宜。两种栖息地之间的边界由物种通过其工程活动移动。我们的模型是一种新型的反应扩散自由边界问题。我们证明了行波的存在并给出了它们速度的上限和下限。我们说明了速度如何取决于边界附近的个人运动和工程行为。