Simple rules describe bottom-up and top-down control in food webs with alternative energy pathways.

Many human influences on the world's ecosystems have their largest direct impacts at either the top or the bottom of the food web. To predict their ecosystem-wide consequences we must understand how these impacts propagate. A long-standing, but so far elusive, problem in this endeavour is how to reduce food web complexity to a mathematically tractable, but empirically relevant system. Simplification to main energy channels linking primary producers to top consumers has been recently advocated. Following this approach, we propose a general framework for the analysis of bottom-up and top-down forcing of ecosystems by reducing food webs to two energy pathways originating from a limiting resource shared by competing guilds of primary producers (e.g. edible vs. defended plants). Exploring dynamical models of such webs we find that their equilibrium responses to nutrient enrichment and top consumer harvesting are determined by only two easily measurable topological properties: the lengths of the component food chains (odd-odd, odd-even, or even-even) and presence vs. absence of a generalist top consumer reconnecting the two pathways (yielding looped vs. branched webs). Many results generalise to other looped or branched web structures and the model can be easily adapted to include a detrital pathway.