A fermion representation of the compact symplectic sp(4) algebra provides a natural description of the pairing interaction in nuclei. In the nondeformed and deformed cases the reduction chains to different realization of u(2) and u_q(2) are explored for multiple orbits. One of the realizations is associated with the SU(2) group of the valene isospin. The other reductions describe pairing between identical fermions or proton-neutron configuratrions. Microscopic nondeformed and deformed Hamiltonians are expressed in terms of the generators of sp(4) and sp_q(4). In both cases eigenvalues of the Hamiltonian are fit to experimental ground state energies which allows the role of the deformation to be investigated. The q-deformation parameter varies the pairing strength, thereby providing for a nonlinear expansion of the nuclear collective motion.