Ecologically, the evolutionary advantage of farmers over hunter-gatherers has led to their worldwide spreading. In this paper, we study a free boundary problem of a farmers and hunter-gatherers model featuring a type of prey-predator dynamics. The nonlinear diffusion of farmers is determined by the density of farmers in a way that higher population density accelerates the migration. We establish a spreading-vanishing dichotomy and provide some sufficient conditions in a heterogeneous environment. Moreover, in a homogeneous environment, we achieve exact asymptotic convergence to the constant equilibrium. Thereby, we verify that a strong sedentary lifestyle of farmers is advantageous for the spreading of farmers.

从生态上讲，农民相对于狩猎采集者的进化优势已导致其在全球范围内的传播。在本文中，我们研究了具有猎物-捕食者动力学类型的农民和猎人-采集者模型的自由边界问题。农民的非线性扩散是由农民的密度决定的，其方式是较高的人口密度会加速迁移。我们建立了一个消失的二分法，并在异构环境中提供了一些充分的条件。此外，在均匀环境中，我们实现了精确渐近收敛到恒定平衡。因此，我们证实了农民久坐不动的生活方式有利于农民的传播。