  The networks of predator-prey interactions in ecological systems are
remarkably complex, but nevertheless surprisingly stable in terms of long term
persistence of the system as a whole. In order to understand the mechanism
driving the complexity and stability of such food webs, we developed an
eco-evolutionary model in which new species emerge as modifications of existing
ones and dynamic ecological interactions determine which species are viable.
The food-web structure thereby emerges from the dynamical interplay between
speciation and trophic interactions. The proposed model is less abstract than
earlier evolutionary food web models in the sense that all three evolving
traits have a clear biological meaning, namely the average body mass of the
individuals, the preferred prey body mass, and the width of their potential
prey body mass spectrum. We observed networks with a wide range of sizes and
structures and high similarity to natural food webs. The model networks exhibit
a continuous species turnover, but massive extinction waves that affect more
than $50 \%$ of the network are not observed.
