Ecologists seek to understand patterns of distribution and abundance of species. Studies of distribution often use occurrence data to build models of the environmental niche of a species. Environmental suitability (ES) derived from such models may be used to predict the potential distributions of species. The ability of such models to predict spatial patterns in abundance is unknown; we argue that there should be a positive relationship between ES and local abundance. This will be so if ES reflects how well the species' physiological and ecological requirements are met at a site and if those factors also determine local abundance. However, the presence of other factors may indicate that potential abundance is not attained at all sites. Therefore, ES should predict the upper limit of abundance, and the observed relationship with ES should be wedge shaped. We tested the relationship of ES with local abundance for 69 rain forest vertebrates in the Australian wet tropics. Ordinary least squares and quantile regressions revealed a positive relationship between ES and local abundance for most species (>84%). The relationships for these species were wedge shaped. We conclude that ES modeled from presence-only data provides useful information on spatial patterns of abundance, and we discuss implications of this in addressing important problems in ecology.