Dispersal success on fractal landscapes: a consequence of lacunarity thresholds

Habitat fragmentation is expected to disrupt dispersal, and thus we explore d how patch metrics of landscape structure, such as percolation thresholds used to define landscape connectivity, corresponded with dispersal success on neutral landscapes. We simulated dispersal as either a purely random pro cess (random direction and random step lengths) or as an area-limited rando m walk (random direction, but movement limited to an adjacent cell at each dispersal step) and quantified dispersal success for 1000 individuals on ra ndom and fractal landscape maps across a range of habitat abundance and fra gmentation. Dispersal success increased with the number of cells a disperse r could search (m), but poor dispersers (m < 5) searching via area-limited dispersal on fractal landscapes were more successful at locating suitable h abitat than random dispersers on either random or fractal landscapes. Dispe rsal success was enhanced on fractal landscapes relative to random ones bec ause of the greater spatial contagion of habitat. Dispersal success decreas ed proportionate to habitat loss for poor dispersers (In = 1) on random lan dscapes, but exhibited an abrupt threshold at low levels of habitat abundan ce (p < 0.1) for area-limited dispersers (m ( 10) on fractal landscapes. Co nventional metrics of patch structure, including percolation, did not exhib it threshold behavior in the region of the dispersal threshold. A lacunarit y analysis of the gap structure of landscape patterns, however, revealed a strong threshold in the variability of gap sizes at low levels of habitat a bundance (p < 0.1) in fractal landscapes, the same region in which abrupt d eclines in dispersal success were observed. The interpatch distances or gap s across which dispersers must move in search of suitable habitat should in fluence dispersal success, and our results suggest that there is a critical gap-size structure to fractal landscapes that interferes with the ability of dispersers to locate suitable habitat when habitat is rare. We suggest t hat the gap structure of landscapes is a more important determinant of disp ersal than patch structure, although both are ultimately required to predic t the ecological consequences of habitat fragmentation.