A dynamical model based on linearized D functions leads to a series of relations called the bootstrap algebras. Under specific conditions these algebras imply that the 1/2 + baryons must belong to a representation of the Lie algebra whose structure constants are given by the vector-meson coupling constants. If the u-channel forces admit of a static approximation, the algebras lead to consequences which are the same as those of the spin-internal-symmetry groups, while avoiding the usual difficulties encountered for the couplings in these groups. Several such systems leading to consequences of groups like SU (6), Sp(16), and the strong-coupling group are discussed. The results are shown to be applicable to meson-meson scattering even though the light pseudoscalars are exchanged in the u channel. It is found that the pseudoscalar-meson-vector-meson couplings in the SU (6) model and the strong-coupling model are in remarkable agreement with each other.