  We propose a model for evolution aiming to reproduce statistical features of
fossil data, in particular the distributions of extinction events, the
distribution of species per genus and the distribution of lifetimes, all of
which are known to be of power law type. The model incorporates both
species-species interactions and ancestral relationships. The main novelty of
this work is to show the feasibility of k-core percolation as a selection
mechanism. We give theoretical predictions for the observable distributions,
confirm their validity by computer simulation and report good agreement with
the fossil data. A key feature of the proposed model is a co-evolving fitness
landscape determined by the topology of the underlying species interactions,
ecological niches emerge naturally. The predicted distributions are independent
of the rate of speciation, i.e. whether one adopts an gradualist or punctuated
view of evolution.
