Table 1.

For homogeneous landscapes, simulations were run for each value of K (ranging from 1 to 50) and the minimum K allowing for persistence is shown. This is compared with the K of the smallest inhabited patch on the environmental gradient for the equivalent parameter settings. Data shown are the mean of 30 replicates.

mutation effect size	standard deviation of dispersal kernel (emergent migration rate)	minimum K before more than 50% of replicates go extinct in homogeneous landscape	K of smallest inhabited patch on gradient
0.0	0.25 (0.05)	2	2
0.025	0.25 (0.05)	33	33
0.05	0.25 (0.05)	23	22
0.0	0.5 (0.32)	2	1
0.025	0.5 (0.32)	13	9
0.05	0.5 (0.32)	10	6
0.0	0.75 (0.5)	1	1
0.025	0.75 (0.5)	10	3
0.05	0.75 (0.5)	9	6
0.0	1.0 (0.62)	1	1
0.025	1.0 (0.62)	8	4
0.05	1.0 (0.62)	6	3