Bull Math Biol (2012) 74:491–508 DOI 10.1007/s11538-011-9705-x ORIGINAL ARTICLE Life Stages: Interactions and Spatial Patterns Suzanne L. Robertson · J.M. Cushing · R.F. Costantino Received: 7 June 2011 / Accepted: 4 November 2011 / Published online: 2 December 2011 © Society for Mathematical Biology 2011 Abstract In many stage-structured species, different life stages often occupy sepa- rate spatial niches in a heterogeneous environment. Life stages of the giant flour bee- tle Tribolium brevicornis (Leconte), in particular adults and pupae, occupy different locations in a homogeneous habitat. This unique spatial pattern does not occur in the well-studied stored grain pests T. castaneum (Herbst) and T. confusum (Duval). We propose density dependent dispersal as a causal mechanism for this spatial pattern. We model and explore the spatial dynamics of T. brevicornis with a set of four den- sity dependent integrodifference and difference equations. The spatial model exhibits multiple attractors: a spatially uniform attractor and a patchy attractor with pupae and adults spatially separated. The model attractors are consistent with experimental observations. Keywords Spatial distribution · Life stage interactions · Density dependent dispersal · Flour beetle · Integrodifference equations S.L. Robertson ( ) Interdisciplinary Program in Applied Mathematics, University of Arizona, Tucson, AZ 85721, USA e-mail: srobertson@mbi.osu.edu Present address: S.L. Robertson Mathematical Biosciences Institute, The Ohio State University, 1735 Neil Avenue, Columbus, OH 43210, USA J.M. Cushing Department of Mathematics, University of Arizona, Tucson, AZ 85721, USA R.F. Costantino Department of Ecology and Evolutionary Biology, University of Arizona, Tucson, AZ 85721, USA