  Why are large, complex ecosystems stable? Both theory and simulations of
current models predict the onset of instability with growing size and
complexity, so for decades it has been conjectured that ecosystems must have
some unidentified structural property exempting them from this outcome. We show
that 'trophic coherence' -- a hitherto ignored feature of food webs which
current structural models fail to reproduce -- is a better statistical
predictor of linear stability than size or complexity. Furthermore, we prove
that a maximally coherent network with constant interaction strengths will
always be linearly stable. We also propose a simple model which, by correctly
capturing the trophic coherence of food webs, accurately reproduces their
stability and other basic structural features. Most remarkably, our model shows
that stability can increase with size and complexity. This suggests a key to
May's Paradox, and a range of opportunities and concerns for biodiversity
conservation.
