In this paper we focus on three problems about the spreading speeds of nonlocal dispersal Fisher-KPP equations. First, we study the signs of spreading speeds and find that they are determined by the asymmetry level of the nonlocal dispersal and $f^{\prime }(0)$, where f is the reaction function. This indicates that asymmetric dispersal can influence the spatial dynamics in three aspects: it can determine the spatial propagation directions of solutions, influence the stability of equilibrium states, and affect the monotone property of solutions. Second, we give an improved proof of the spreading speed result by constructing new lower solutions and using the new “forward-backward spreading” method. Third, we investigate the relationship between spreading speed and exponentially decaying initial data. Our result demonstrates that when dispersal is symmetric, spreading speed decreases along with the increase of the exponential decay rate. In addition, the results on the signs of spreading speeds are applied to two special cases where we present more details on the influence of asymmetric dispersal.

在本文中，我们集中于关于非局部分散Fisher-KPP方程的扩散速度的三个问题。首先，我们研究传播速度的符号，发现它们是由非局部色散和$F^{\prime }（0）$，其中f是反应功能。这表明非对称扩散可以从三个方面影响空间动力学：它可以确定溶液的空间传播方向，影响平衡态的稳定性，并影响溶液的单调性质。其次，通过构造新的较低解并使用新的“向前-向后扩展”方法，可以更好地证明扩展速度的结果。第三，我们研究了扩展速度和指数衰减的初始数据之间的关系。我们的结果表明，当扩散是对称的时，扩散速度随着指数衰减率的增加而降低。另外，关于扩展速度的符号的结果被应用于两个特殊情况，其中我们给出了关于不对称分散影响的更多细节。