Non-random patterns of species segregation and aggregation within ecological communities are often interpreted as evidence for interspecific interactions. However, it is unclear whether theoretical models can predict such patterns and how environmental factors may modify the effects of species interactions on species co-occurrence. Here we extend a spatially explicit neutral model by including competitive effects on birth and death probabilities to assess whether competition alone is able to produce non-random patterns of species co-occurrence. We show that transitive and intransitive competitive hierarchies alone (in the absence of environmental heterogeneity) are indeed able to generate non-random patterns with commonly used metrics and null models. Moreover, even weak levels of intransitive competition can increase local species richness. However, there is no simple rule or consistent directional change towards aggregation or segregation caused by competitive interactions. Instead, the spatial pattern depends on both the type of species interaction and the strength of dispersal. We conclude that co-occurrence analysis alone may not able to identify the underlying processes that generate the patterns