Abstract We consider a reaction-diffusion(-taxis) predator-prey system with group defense in the prey. Taxis-driven instability can occur if the group defense influences the taxis rate (Wang et al., 2017). We elaborate that this mechanism is indeed possible but biologically unlikely to be responsible for pattern formation in such a system. Conversely, we show that patterns in excitable media such as spatiotemporal Sierpinski gasket patterns occur in the reaction-diffusion model as well as in the reaction-diffusion-taxis model. If group defense leads to a dome-shaped functional response, these patterns can have a rescue effect on the predator population in an invasion scenario. Preytaxis with prey repulsion at high prey densities can intensify this mechanism leading to taxis-induced persistence. In particular, taxis can increase parameter regimes of successful invasions and decrease minimum introduction areas necessary for a successful invasion. Last, we consider the mean period of the irregular oscillations. As a result of the underlying mechanism of the patterns, this period is two orders of magnitude smaller than the period in the nonspatial system. Counter-intuitively, faster-moving predators lead to lower oscillation periods and eventually to extinction of the predator population. The study does not only provide valuable insights on theoretical spatially explicit predator-prey models with group defense but also comparisons of ecological data with model simulations.

中文翻译：

---

具有群体防御的捕食者-猎物模型中的出租车驱动模式形成

摘要 我们考虑在猎物中具有群体防御的反应-扩散（-趋向性）捕食者-猎物系统。如果群体防御影响出租车率，就会出现出租车驱动的不稳定（Wang et al., 2017）。我们详细说明这种机制确实是可能的，但在生物学上不太可能对这种系统中的模式形成负责。相反，我们表明可兴奋介质中的模式，例如时空谢尔宾斯基垫圈模式，出现在反应扩散模型以及反应扩散趋向模型中。如果群体防御导致圆顶形的功能反应，这些模式可以在入侵场景中对捕食者种群产生拯救作用。在高猎物密度下猎物排斥的捕食可以加强这种机制，导致出租车诱导的持久性。特别是，出租车可以增加成功入侵的参数范围并减少成功入侵所需的最小引入区域。最后，我们考虑不规则振荡的平均周期。由于模式的潜在机制，该周期比非空间系统中的周期小两个数量级。与直觉相反，快速移动的捕食者会导致较低的振荡周期，并最终导致捕食者种群的灭绝。该研究不仅为具有群体防御的理论空间显性捕食者-猎物模型提供了有价值的见解，而且还提供了生态数据与模型模拟的比较。由于模式的潜在机制，该周期比非空间系统中的周期小两个数量级。与直觉相反，快速移动的捕食者会导致较低的振荡周期，并最终导致捕食者种群的灭绝。该研究不仅为具有群体防御的理论空间显性捕食者-猎物模型提供了有价值的见解，而且还提供了生态数据与模型模拟的比较。由于模式的潜在机制，该周期比非空间系统中的周期小两个数量级。与直觉相反，快速移动的捕食者会导致较低的振荡周期，并最终导致捕食者种群的灭绝。该研究不仅为具有群体防御的理论空间显性捕食者-猎物模型提供了有价值的见解，而且还提供了生态数据与模型模拟的比较。