units. Averages are taken in the QS regime, after discarding an initial transient which depends on the system size and diffusion rate used.

![[]{data-label="scpD"}](scpD.eps){width="0.8\hsize"}

Figure \[scpD\] shows that with increasing diffusion rate, the critical creation rate $\lambda_c$ tends to unity, the value predicted by simple mean-field theory. (The increase in $\lambda_c$ in the small-$D$ regime reflects the elimination symbiotic A-B pairs due to diffusion.) In Fig. \[mu25d0\] we plot near-critical quasistationary probability distributions of single individuals, $\rho$, and of doubly occupied sites, $q$, for $\mu=0.25$ and $D=0$. The distributions are unimodal, showing that the transition is continuous. We verify that in the absence of diffusion, the absorbing phase transition is always continuous, regardless the value of $\mu$. For diffusion rates considerably in excess of unity, we observe a discontinuous transition for certain values of $\mu$. An example of bimodal QS probability distributions, signaling a discontinuous transition, is shown in Fig. \[mu25d5\], for $D=5.0$.\

![[]{data-label="mu25d0"}](mu25D0L100.eps){width="0.8\hsize"}

![[]{data-label="mu25d5"}](mu25D5L100.eps){width="0.8\hsize"}

![[]{data-label="mu01d.1"}](mu001D01L100.eps){width="0.8\hsize"}

![[]{data-label="rqd01"}](rqd01.eps){width="0.95\hsize"}

![[]{data-label="mu25d100"}](mu25D100L100.eps){width="0.8\hsize"}

The mechanism by which diffusion gives rise to a discontinuous transition can be understood as follows. Under strong symbiosis ($\mu$ close to zero), only doubly occupied sites are observed near the critical point, in the absence of diffusion. Since the transition is 