Complex natural habitats such as tropical forests include a patchwork of microhabitats defined by spatially constrained biotic and physical factors. I modeled the interaction between stationary but patchy renewable resources, as exemplified by host plants, and a consumer that relies on these resource patches for growth and survival yet moves between them, as exemplified by a herbivorous insect. Qualitative analysis indicated that unstable models without patch heterogeneity could be stabilized by adding appropriate patchiness. I defined a patch as an area of habitat where consumers survive with a characteristic probability. Different patches have different survival rates that may be organized along a logarithmic axis. The biomass of host plant can then be plotted as a function of patch suitability. Using that plot, I modeled consumer/host plant interaction and found that, with 2 orders of magnitude heterogeneity along the plot's x axis, consumers and host plants came to equilibrium. The most suitable host plants to the right of the graph became defoliated, the least suitable host plants on the left of the graph grew to full size, and in between the plants were protected enough to survive yet vulnerable enough to support consumer survival and reproduction. Under a wide range of conditions, the "in-between" plants form a band on the graph about 2.5 log units wide and produce 80-90% of the successful consumers. Further analysis revealed a linear relationship between the off-plant death/birth ratio and the position of the marginal band along the x axis. I also modeled the effects of consumer choice on the system: consumers that were able to seek out the best host plant patches selectively defoliated the best plants, reducing the width of the marginal band and reducing their population numbers. I applied the model to a Heliconius butterfly/Passiflora host plant interaction for which we have field estimates, and the model predicted adult butterfly numbers (7/ha) close to actual observation (average = 8/ha). I also discussed implications for interspecific competition between consumers. Consumers that are vulnerable to the same predators or otherwise share the same marginal plants will compete strongly for those plants, while consumers that are susceptible to different predators or patch factors will depend upon a different set of patches and will not compete directly. I presented a possible example of this from herbivores sharing the same species of Passiflora vines.