  We investigate the influence of a general non-local advection term of the
form K * u to propagation in the one-dimensional Fisher-KPP equation. This
model is a generalization of the Keller-Segel-Fisher system. When K $\in$ L 1
(R), we obtain explicit upper and lower bounds on the propagation speed which
are asymptotically sharp and more precise than previous works. When K $\in$ L p
(R) with p > 1 and is non-increasing in (--$\infty$, 0) and in (0, +$\infty$),
we show that the position of the "front" is of order O(t 1/p) if p < $\infty$
and O(e $\lambda$t) for some $\lambda$ > 0 if p = $\infty$ and K(+$\infty$) >
0. We use a wide range of techniques in our proofs.
