We study the dependence of macroscopic polarization on composition and stra
in in wurtzite III-V nitride ternary alloys using ab initio density-functio
nal techniques. The spontaneous polarization is characterized by a large bo
wing, strongly dependent on the alloy microscopic structure. The bowing is
due to the different response of the bulk binaries to hydrostatic pressure
and to internal strain effects (bond alternation). Disorder effects are ins
tead minor. Deviations from parabolicity (simple bowing) are of order 10% i
n the most extreme case of AlInN alloys, much less at all other composition
s. Piezoelectric polarization is also strongly nonlinear. At variance with
the spontaneous component, this behavior is independent of microscopic allo
y structure or disorder effects, and due entirely to the nonlinear strain d
ependence of the bulk piezoelectric response. It is thus possible to predic
t the piezoelectric polarization for any alloy composition using the piezoe
lectricity of the parent binaries.