increment associated with a given step in the simulation.

At each such step, we choose among the events: (1) creation attempt by an isolated individual, with probability $\lambda N_s \Delta t$; (2) creation attempt by an individual at a doubly occupied site, with probability $2 \lambda N_d \Delta t$; (3) death of an isolated individual, with probability $N_s \Delta t$; (4) death of an individual at a doubly occupied site, with probability $2 \mu N_d$ and (5) diffusion of an individual, with probability $D N_p \Delta t$.

Once the event type is selected a site $i$ is randomly chosen from the appropriate list. Creation occurs at a site $j$, a randomly chosen first-neighbor of site $i$, if $j$ is not already occupied by an individual of the species to be created. If site $i$ is doubly occupied, the species of the daughter (in a creation event) is chosen to be A or B with equal probability. Similarly, in an annihilation event at a doubly-occupied site, the species to be removed is chosen at random.

For the SCP with diffusion, we performed QS simulations [@qssim; @qssim2] for systems of linear sizes up to $L= 100$, with each run lasting $10^8$ time 