Spatial patterns are commonly observed among dispersing populations in nature. When stored in a homogenous flour medium, the larval and adult stages of the flour beetle Tribolium brevicornis will spatially segregate. In this talk we explore stage-structured integro-difference equation models with density-dependent dispersal kernels through mathematical analysis. We will also use computer simulations to investigate the mathematical mechanisms that lead to spatial patterns such as those observed in T. brevicornis.