Species interactions and abiotic factors are important determinants of abundance and distribution, but accounting for biotic interactions is complicated by the fact that interactions occur at the individual-level at unknown spatial scales. Ignoring individual-level interactions can yield incorrect conclusions about biotic interactions when analyzing aggregated count data or presence-absence data. We present a hierarchical species distribution model that includes a Markov point process in which an individual’s location is dependent upon both abiotic variables and the locations of individuals of another species. The model can be regarded as a thinned point process in which encounter probability is a function of the distance between individual activity centers and survey locations. We applied the model to spatial capture-recapture data on two ecologically similar songbird species – hooded warbler (Setophaga citrina) and black-throated blue warbler (Setophaga caerulescens) – that segregate over a climate gradient in the southern Appalachian Mountains, USA. In spite of coarse spatial segregation and many ecological similarities between the two species, we found minimal evidence of spatial competition. There were strong, and opposing effects of climate on spatial variation in population densities, but spatial competition did not influence their distributions. A small simulation study indicated that the model can identify the distinct effects of environmental variation and biotic interactions on co-occurring species distributions. Unlike previous statistical models that attempt to infer competition from species-level co-occurrence data, the framework proposed here can be used to investigate how population-level patterns emerge from individual-level processes, while also allowing for inference on the spatial scale of biotic interactions. Our finding of minimal spatial competition between black-throated blue warbler and hooded warbler adds to the growing body of literature suggesting that, contrary to early theory from biogeography, abiotic factors may be more important than competition at low-latitude range margins.