FIGURE 1.

All extant species in the metacommunity model cycle through (a) reproduction, (b) dispersal, and (d) competition before (e) the temperature changes stochastically, and the next time step repeats this process. The target species is also moved through (c) assisted migration during certain time steps

Symbol definitions: t, time; x, space; $T(x,t)$, temperature; $b_i[T(x,t)]$, per capita reproductive output; z_i , species’ thermal optimum;${\sigma }_i,$ thermal tolerance breadth; r_i , reproductive strength; ${\gamma }_i$, mean dispersal distance; $\eta$, low population threshold for assisted migration; $\alpha$, cooldown time before another relocation can happen; $\rho$, fraction of the population removed from original distribution and moved to a new location; $\mu$, fraction that survive relocation; $\beta$, when relocating the population, the number of patches ahead of the thermal optimum estimate to move the relocated population; F, target species; E, equatorward species; P, poleward species; K, carrying capacity; $p(x,t)$, individual survival probability; lower line in panel e, $t=0$; upper line in panel e, $t=100$; vertical dashed line, model changes from the initialization phase (average temperature change $\tau =0$) to the climate change phase ($\tau =0.04$). Climate change occurs only after a relatively stable metacommunity has been assembled (i.e., after 100 time steps with no extinctions)