  We study the two-species symbiotic contact process (2SCP), recently proposed
in [de Oliveira, Santos and Dickman, Phys. Rev. E {\bf 86}, 011121 (2012)] . In
this model, each site of a lattice may be vacant or host single individuals of
species A and/or B. Individuals at sites with both species present interact in
a symbiotic manner, having a reduced death rate, $\mu < 1$. Otherwise, the
dynamics follows the rules of the basic CP, with individuals reproducing to
vacant neighbor sites at rate $\lambda$ and dying at a rate of unity. We
determine the full phase diagram in the $\lambda-\mu$ plane in one and two
dimensions by means of exact numerical quasistationary distributions, cluster
approximations, and Monte Carlo simulations. We also study the effects of
asymmetric creation rates and diffusion of individuals. In two dimensions, for
sufficiently strong symbiosis (i.e., small $\mu$), the absorbing-state phase
transition becomes discontinuous for diffusion rates $D$ within a certain
range. We report preliminary results on the critical surface and tricritical
line in the $\lambda-\mu-D$ space. Our results raise the possibility that
strongly symbiotic associations of mobile species may be vulnerable to sudden
extinction under increasingly adverse conditions.
