  We propose a new mathematical model for the interaction of skin cell
populations with fibroblast growth factor and bone morphogenetic protein,
occurring within deformable porous media. The equations for feather primordia
pattering are based on the work by K.J. Painter et al. [J. Theoret. Biol., 437
(2018) 225--238]. We perform a linear stability analysis to identify relevant
parameters in the coupling mechanisms, focusing in the regime of infinitesimal
strains. We also extend the model to the case of nonlinear poroelasticity and
include solid growth by means of Lee decompositions of the deformation
gradient. We present a few illustrative computational examples in 2D and 3D,
and briefly discuss the design of tailored efficient solvers.
