Predator-prey models with a prey-dependent functional response have the property that the prey equilibrium value is determined only by predator characteristics. However, in observed natural systems (for instance, snail-periphyton interactions in streams) the equilibrium periphyton biomass has been shown experimentally to be influenced by both snail numbers and levels of available limiting nutrient in the water. Hypothesizing that the observed patchiness in periphyton in streams may be part of the explanation for the departure of behavior of the equilibrium biomasses from predictions of the prey-dependent response of the snail-periphyton system, we developed and analyzed a spatially-explicit model of periphyton in which snails were modeled as individuals in their movement and feeding, and periphyton was modeled as patches or spatial cells. Three different assumptions on snail movement were used: (1) random movement between spatial cells, (2) tracking by snails of local abundances of periphyton, and (3) delayed departure of snails from cells to reduce costs associated with movement. Of these assumptions, only the third strategy, based on an herbivore strategy of staying in one patch until local periphyton biomass concentration falls below a certain threshold amount, produced results in which both periphyton and snail biomass increased with nutrient input. Thus, if data are averaged spatially over the whole system, we expect that a ratio-dependent functional response may be observed if the herbivore behaves according to the third assumption. Both random movement and delayed cell departure had the result that spatial heterogeneity of periphyton increased with nutrient input.