Abstract
In this paper, we study the minimal wave speed for a class of population models with density-dependent migration speed and the Allee effect. We first give the exact expression for the minimal wave speed for the case of linear migration speed. This in turn specifies a critical curve in the parameter plane of the migration speed and the Allee effect which separates a region of the linear determinacy of the minimal wave speed from a region of the nonlinear determinacy of the minimal wave speed. Next, for a class of nonlinear migration speed, the corresponding minimal wave speed is shown to enjoy similar qualitative properties as depicted in the case of linear migration speed.
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