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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 compare with 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.