1. A short review of landscape genetics: A spatially-heterogeneous dispersal process: Paradox of fragmentation

2. References Landscape genetics Manel et al. (2003) Landscape genetics: combining landscape ecology and population genetics. Trends Ecol Evol 18:189–197 Special feature in Mol Ecol (2012) Manel et al. (2013) Ten years of landscape genetics. Trends Ecol Evol 28:614–621 Isolation by resistance and circuit theory Wright (1943) Isolation by distance. Genetics 28:114– 138 Slatkin (1993) Isolation by distance in equilibrium and nonequilibrium populations. Evolution 47:264–279 McRae (2006) Isolation by resistance. Evolution 60: 1551–1561

3. A spatially-heterogeneous dispersal process: Paradox of fragmentation Frequent, slow, and short dispersal in habitats Rare, fast, and long dispersal in a matrix

4. A heterogeneous dispersal process can be equal to a homogeneous pattern of an equilibrium flow Different capacity and velocity flow = capacity *velocity

6. A spatially-heterogeneous differentiation/migration pattern Populations in a landscape Pair-wise genetic distances Different intercepts and slopes in isolation-by- distance (IBD)

7. Three steps in landscape genetics Migration between populations in the habitats Resistances inferred from landscape elements Currents between habitats in a circuit GIS Niche modeling Circuit theory Least-cost path Test/ Model selection Population genetics

8. Can resistances in a circuit create local migration in habitats and global migration in a matrix? Local, distance- dependent migration in habitats Global, distance- independent migration in a matrix

9. IBD of local migration in habitats and global migration in a matrix Genetic distances in habitats and a matrix More gentle slopes and higher intercepts of IBD in the matrix than in the habitats

10. Distances and resistances along least-cost paths on a circuit IBD of distances and resistances along least- cost paths (LCPs) on the circuit A circuit with resistances (r = 1) and populations in a habitat

11. Habitats divided by a matrix zone: the matrix increases an intercept The matrix increases an intercept of LCPs through the matrix Habitats (r = 1) and a matrix (r = 2) parallel to each other in a linear shape

12. A corridor connecting habitats reduces an intercept The corridor reduces an intercept to LCPs in the habitats A corridor (r = 1) connects habitats

13. A highway connecting habitats more reduces an intercept The highway reduces an intercept less than LCPs in the habitats A highway (r = 1/2) connects habitats

14. A corridor and a highway reduce intercepts but do not reduce slopes Global migration with gentle slopes in a matrix cannot be created

15. A corridor parallel to habitats does not affect IBD The corridor does not affect IBD of LCPs A corridor (r = 1) parallel to habitats

16. A highway parallel to habitats reduces a slope The highway reduces slopes of LCPs through the matrix A highway (r = 1/2) parallel to habitats

17. Highways connecting habitats and parallel to them affect IBD differently A highway parallel to habitats creates global migration in a matrix

18. Does a highway parallel to habitats really exist in a matrix? Hetero- geneous resistances in a matrix A different dispersal process in a homo- geneous matrix

19. Resistances by circuit theory depend on positions in a circuit HabitatMatrixC. corridor C. highwayP. corridorP. highway Circles: within the same side; crosses: between different sides

20. Resistances by circuit theory decrease as circuit size increases Circles: within the same side; crosses: between different sides

21. Least-cost paths and circuit theory in landscape genetics may fail to express a spatially- heterogeneous dispersal process in a homogeneous matrix