Appendix A
Piecewise linear matching habitat choice
Because we have no a priori knowledge about the functional forms that might
describe imperfect matching habitat choice, even though we think expression (1) is
reasonable, it is useful to consider alternative formulations. Features of imperfect habitat
choice that emerge across a range of functional forms are more likely to be robustly
relevant to natural systems. An alternative function we used for habitat choice is
piecewise linear, with a dispersal probability that is pij for an individual that matched its
natal habitat’s phenotypic optimum and increases linearly with phenotype in the direction
of the opposite habitat (and decreased in the opposite direction). The function describing
the probability that an individual born in habitat i moves to habitat j is given by
pij  pij  mz ( z  zi ) / ( z j  zi )
(A1)
where z is again the individual’s phenotype, zi is the optimum phenotype in its habitat and
zj is the optimum phenotype in the other habitat. If the calculated value is less than 0, the
probability is set to 0, and if it is greater than 1, it is set to 1. Again pij is the dispersal
probability if dispersal is independent of phenotype. For one-way dispersal, eq. (A1) is
used only for source-to-sink movement (since the reverse movement flow is 0).
Again, if mz  0 , an individual is more likely to disperse if it has a phenotype
closer to the destination’s optimum. The probability of dispersal is pij if the individual is
at its habitat’s optimum and is pij + mz (or 1, if this is larger than 1) at the other habitat’s
optimum. If an individual is further from the putative destination’s optimum than its own
habitat’s optimum is, the probability of dispersal is lower than the nominal value pij .
Results with piecewise linear matching habitat choice, adult dispersal
The results in the main text are all for a logistic function describing the
probability an individual will move from one habitat to the other. Figs. A1 and A2 show
the probability of adaptation as a function of maladaptation for piecewise linear habitat
choice and adult movement, with and without the protocol of disperser replication,
respectively, and show similar patterns to those with logistic habitat choice, indicating
that our conclusions do not depend on the exact form of the habitat choice function. Note
that the dispersal rate without habitat choice for these figures is only 5% rather than the
10% used with logistic habitat choice. However, the linear habitat choice allows high
dispersal probabilities to be reached for lower deviations of the phenotype from the
originating habitat’s optimum. Therefore, the average dispersal rates with habitat choice
were similar with our parameters between the two forms of habitat choice. With
piecewise linear habitat choice without replication (as in Fig. A1), the average movement
rate is about 10.5% with moderate habitat choice and about 16% with strong habitat
choice. Without the shift in source genetics (as in Fig. A2), the numbers are 12% and
21%.
1
Figure A1. The probability of sink adaptation for different sink maladaptations and
strengths of linear habitat choice. pij = 0.05 (other parameters as in Fig. 2 in the main
text). Dashed lines and open symbols are for one-way dispersal; solid lines and filled
symbols are for two-way dispersal.
Probability of adaptation
1.0
0.8
0.6
mz
0.4
2
1
0
2
1
0
0.2
1-way
2-way
0.0
2.6
2.8
3.0
3.2
Sink maladaptation
2
3.4
Figure A2. The probability of sink adaptation for different sink maladaptations and
strengths of linear habitat choice. pij = 0.05 (other parameters as in Fig. 2 in the main
text). Dashed lines and open symbols are for one-way dispersal; solid lines and filled
symbols are for two-way dispersal. Dispersing individuals are replicated so each can
remain in their initial habitat as well as disperse.
Probability of adaptation
1.0
0.8
0.6
mz
0.4
2
1
0
2
1
0
0.2
1-way
2-way
0.0
2.6
2.8
3.0
3.2
3.4
3.6
Sink maladaptation
3
3.8
4.0