This paper is concerned with the asymptotic propagations for a nonlocal dispersal population model with shifting habitats. In particular, we verify that the invading speed of the species is determined by the speed c of the shifting habitat edge and the behaviours near infinity of the species’ growth rate which is nondecreasing along the positive spatial direction. In the case where the species declines near the negative infinity, we conclude that extinction occurs if c > c*(∞), while c < c*(∞), spreading happens with a leftward speed min{−c, c*(∞)} and a rightward speed c*(∞), where c*(∞) is the minimum KPP travelling wave speed associated with the species’ growth rate at the positive infinity. The same scenario will play out for the case where the species’ growth rate is zero at negative infinity. In the case where the species still grows near negative infinity, we show that the species always survives ‘by moving’ with the rightward spreading speed being either c*(∞) or c*(−∞) and the leftward spreading speed being one of c*(∞), c*(−∞) and −c, where c*(−∞) is the minimum KPP travelling wave speed corresponding to the growth rate at the negative infinity. Finally, we give some numeric simulations and discussions to present and explain the theoretical results. Our results indicate that there may exists a solution like a two-layer wave with the propagation speeds analytically determined for such type of nonlocal dispersal equations.

本文关注具有变化的栖息地的非局部分散种群模型的渐近传播。特别是，我们验证了物种的入侵速度是由移动栖息地边缘的速度c和物种生长速率接近无穷大的行为决定的，该生长速率沿正空间方向不递减。在物种在负无穷附近下降的情况下，我们得出结论，如果c > c *(∞) 会发生灭绝，而c < c *(∞) 则以向左的速度 min{− c , c *(∞ )} 和向右的速度c *(∞)，其中c*(∞) 是与物种在正无穷远处的生长速率相关的最小 KPP 行波速度。在负无穷时物种的增长率为零的情况下也会出现同样的情况。在物种仍然在负无穷附近生长的情况下，我们证明物种总是“通过移动”生存，向右传播速度为c *(∞) 或c *(−∞)，向左传播速度为以下之一c *(∞)、c *(−∞) 和 − c，其中c*(−∞) 是负无穷大时与增长率相对应的最小 KPP 行波速度。最后，我们给出了一些数值模拟和讨论来展示和解释理论结果。我们的结果表明，对于这种类型的非局部色散方程，可能存在像两层波这样的传播速度解析确定的解。