  Generalizing results of \cite{MC,S} and \cite{HSZ} for certain model
reaction-diffusion and reaction-convection-diffusion equations, we derive and
rigorously justify weakly nonlinear amplitude equations governing general
Turing bifurcation in the presence of conservation laws. In the nonconvective,
reaction-diffusion case, this is seen similarly as in \cite{MC,S} to be a real
Ginsburg-Landau equation coupled with a diffusion equation in a large-scale
mean-mode vector comprising variables associated with conservation laws. In the
general, convective case, by contrast, the amplitude equations as noted in
\cite{HSZ} consist of a complex Ginsburg-Landau equation coupled with a
singular convection-diffusion equation featuring rapidly-propagating modes with
speed $\sim 1/\eps$ where $\eps$ measures amplitude of the wave as a
disturbance from a background steady state. Different from the partially
coupled case considered in \cite{HSZ} in the context of B\'enard-Marangoni
convection/inclined flow, the Ginzburg Landau and mean-mode equations are here
fully coupled, leading to substantial new difficulties in the analysis.
Applications are to biological morphogenesis, in particular vasculogenesis, as
described by the Murray-Oster and other mechanochemical/hydrodynamical models
