1. Habitat loss, fragmentation and alteration of the landscape matrix are interdependent processes, collectively responsible for most recent species extinctions. Thus, determining the extent to which these landscape processes affect animals is critical for conservation. However, researchers have often assumed that interdependent effects are independently related to animals’ responses, underestimating the importance of one or several landscape processes in driving species declines. 2. We demonstrate how to disentangle the interdependent effects of habitat area, fragmentation, and edge context on population size by assessing abundance of a rapidly-declining grassland songbird species (Grasshopper Sparrow, Ammodramus savannarum) in eastern Kansas (USA). We conducted > 7,000 point-count bird surveys at > 2,000 sites over two breeding seasons, then modelled the direct, interactive, and indirect effects of landscape factors on abundance within spatial scales (200-, 400-, 800-, 1600-m radii) relevant to our focal species’ dispersal behavior. 3. Sparrow abundance correlated most strongly with landscape structure within 400-m radii, increasing non-linearly with grassland area and decreasing with the proportion of grassland near cropland or woody edges. Sparrows’ negative response to cropland edges was mostly an added, indirect consequence of reduced grassland area, whereas sparrows’ stronger negative response to woody edges was not attributable to variation in grassland area. Fragmentation and edge context mattered most in landscapes comprising ~ 50–80% grassland. 4. Synthesis and applications. Abundance of a threatened grassland songbird was influenced more by core grassland area (a function of total grassland area, fragmentation, and edge context) than total grassland area per se. Moreover, a local extinction threshold of ~ 50% grassland indicated that small amounts of habitat were unsuitable for our focal species regardless of habitat configuration or matrix type. Local extinction thresholds in response to habitat area provide clear baseline targets for land managers; above those thresholds, configuration and the matrix can be modified to increase abundance of edge-sensitive animals. Conflicting evidence in the literature regarding the importance of fragmentation and matrix features could be partially explained by species-level traits, or methodological issues such as defining landscapes at ecologically-arbitrary spatial scales, assessing landscape quality using species richness, and ignoring interactive and indirect effects.