Habitat fragmentation causes extinction of local animal populations by decreasing the amount of viable "core" habitat area and increasing edge effects. It is widely accepted that larger fragments make better nature reserves because core-dwelling species have a larger amount of suitable habitat. Nevertheless, fragments in real landscapes have complex, irregular shapes. We modeled the population sizes of species that have a representative range of preferences for or aversions to habitat edges at five spatial scales (within 10, 32, 100, 320, and 1000 m of an edge) in a nation-wide analysis of forest remnants in New Zealand. We hypothesized that the irregular shapes of fragments in real landscapes should generate statistically significant correlations between population density and fragment area, purely as a "geometric" effect of varying species responses to the distribution of edge habitat. Irregularly shaped fragments consistently reduced the population size of core-dwelling species by 10-100%, depending on the scale over which species responded to habitat edges. Moreover, core populations within individual fragments were spatially discontinuous, containing multiple, disjunct populations that inhabited small spatial areas and had reduced population size. The geometric effect was highly nonlinear and depended on the range of fragment sizes sampled and the scale at which species responded to habitat edges. Fragment shape played a strong role in determining population size in fragmented landscapes; thus, habitat restoration efforts may be more effective if they focus on connecting disjunct cores rather than isolated fragments.