The stress-gradient hypothesis (SGH) posits that the relative importance of facilitative interactions versus negative interactions increases as levels of abiotic stress increase. Originally formulated in empirical studies of plant populations, in recent years the SGH has been found to describe how interactions change in response to stress in a wide range of species including algae, mussels and moths. However, there has been little theory attempting to predict patterns from first principles in relation to different types of interactions. Here, we use mathematical models of microbial populations to investigate whether patterns consistent with the SGH arise when species interact through resource use and allelopathy. Evolution alters the degree to which competition for resource use versus facilitation (cross-feeding) occurs. Our results are consistent with the SGH; species interactions evolve to be more facilitative as average stress intensifies. This occurs because at greater stress the species evolve to become specialists on either of the two resources thereby decreasing overlap in resource use and increasing facilitation through cross-feeding. In addition, the production of toxic allelopathic compounds decreases as stress intensifies due to density-dependent effects. Our results suggest that the SGH could arise through fundamental interactions that are common to many organisms and therefore that the SGH could be a more widespread phenomenon than previously recognised.