Spacing patterns of adult Proechimys semispinosus (Central American spiny rat) within five island populations in central Panamá were determined by live‐trapping over a one‐year period. Home ranges were described by minimum convex polygons for each individual that had a sufficient number of captures to allow accurate description. Home‐range size was calculated as the area of an individual's polygon. The total area of overlap of each individual's home range with every other consexual's home range was also calculated. Mean home‐range size and overlap were compared among islands and between sexes with two‐way analysis of variance and were related to mean density of adult males and females and island size with linear regression analysis. Home‐range size and overlap were also compared while controlling for density using analysis of covariance. Home‐range size varied between the sexes but not among islands, with males generally having larger home ranges than females. Home‐range size showed a negative relationship to density, and the difference in home‐range size between the sexes prevailed even after controlling for density. Home‐range overlap varied among islands but not between the sexes. There was no linear relationship between overlap and density, although individuals within two low‐density populations had nearly exclusive home ranges. The high degree of overlap among home ranges within some populations suggests that P. semispinosus do not maintain large exclusive territories. Such territories may be economically indefensible because of the spatial and temporal distribution of resources (i.e. primarily falling fruit). Although theory predicts that spatially patchy and poorly renewable resources promote territoriality, resources in tropical forests of the study area may be randomly or too patchily distributed or ephemeral to permit maintenance of territories that span a large portion of an animal's home range. More detailed study is necessary to reveal finer‐scale patterns of territoriality (e.g. defence of burrows or concentrations of fallen fruit).