  Neutron scattering results are presented for spin-wave excitations of three
ferromagnetic metallic $A_{1-x}A^{\prime}_{x}$MnO$_3$ manganites (where $A$ and
$A^\prime$ are rare- and alkaline-earth ions), which when combined with
previous work elucidate systematics of the interactions as a function of
carrier concentration $x$, on-site disorder, and strength of the lattice
distortion. The long wavelength spin dynamics show only a very weak dependence
across the series. The ratio of fourth to first neighbor exchange ($J_4/J_1$)
that controls the zone boundary magnon softening changes systematically with
$x$, but does not depend on the other parameters. None of the prevailing models
can account for these behaviors.
