  We present two main contributions which help us in leveraging the theory of
graphons for modeling evolutionary processes. We show a generative model for
digraphons using a finite basis of subgraphs, which is representative of
biological networks with evolution by duplication. We show a simple MAP
estimate on the Bayesian non parametric model using the Dirichlet Chinese
restaurant process representation, with the help of a Gibbs sampling algorithm
to infer the prior. Next we show an efficient implementation to do simulations
on finite basis segmentations of digraphons. This implementation is used for
developing fast evolutionary simulations with the help of an efficient 2-D
representation of the digraphon using dynamic segment-trees with the
square-root decomposition representation. We further show how this
representation is flexible enough to handle changing graph nodes and can be
used to also model dynamic digraphons with the help of an amortized update
representation to achieve an efficient time complexity of the update at
$O(\sqrt{|V|}\log{|V|})$.
