  We consider the traveling wave speed for Fisher-KPP (FKPP) fronts under the
influence of repulsive chemotaxis and provide an almost complete picture of its
asymptotic dependence on parameters representing the strength and length-scale
of chemotaxis. Our study is based on the convergence to the porous medium FKPP
traveling wave and a hyperbolic FKPP-Keller-Segel traveling wave in certain
asymptotic regimes. In this way, it clarifies the relationship between three
equations that have each garnered intense interest on their own. Our proofs
involve a variety of techniques ranging from entropy methods and decay of
oscillations estimates to a general description of the qualitative behavior to
the hyperbolic FKPP-Keller-Segel equation. For this latter equation, we, as a
part of our limiting arguments, establish an explicit lower bound on the
minimal traveling wave speed and provide a new construction of traveling waves
that extends the known existence range to all parameter values.
