  This paper investigates the existence of generalized transition fronts for
Fisher-KPP equations in one-dimensional, almost periodic media. Assuming that
the linearized elliptic operator near the unstable steady state admits an
almost periodic eigenfunction, we show that such fronts exist if and only if
their average speed is above an explicit threshold. This hypothesis is
satisfied in particular when the reaction term does not depend on x or (in some
cases) is small enough. Moreover, except for the threshold case, the fronts we
construct and their speeds are almost periodic, in a sense. When our hypothesis
is no longer satisfied, such generalized transition fronts still exist for an
interval of average speeds, with explicit bounds. Our proof relies on the
construction of sub and super solutions based on an accurate analysis of the
properties of the generalized principal eigenvalues.
