The robustness, link-species relationship and network properties of model food webs

•The Webworld eco-evolutionary model is reproduced and discussed in detail. We collect many properties of the food webs that it assembles (such as clustering coefficients) as time-series over the course of simulations, and obtain values averaged over multiple final ensembles for a selection of parameter choices.•We investigate the link-species relationship in the model food webs, finding that this model supports an intermediate scaling exponent and not constant link density or constant connectance.•Network stability in the form of community robustness is calculated for food webs generated by this model. We find evidence for positive correlation with connectance, and weaker negative correlation with diversity and link density.•We study the behaviour of the model over very long simulations, finding that the frequency distribution of extinctions events does not quite fit either a power law or an exponential law. New results are collected using the Webworld model which simulates evolutionary food web construction with population dynamics (Drossel et al., 2001 [1]). We show that it supports a link-species relationship of neither constant link-density nor constant connectance, and new properties for the food webs are calculated including clustering coefficients and stability in the sense of community robustness to species deletion. Time-series for more than 40 properties of the taxonomic and trophic webs are determined over the course of individual simulations. Robustness is found to be positively correlated with connectance, but negatively with diversity, and we study the long-term development of model webs including the distribution of extinction events in a simulation with 108 speciation events.