  Probabilistic biological network growth models have been utilized for many
tasks including but not limited to capturing mechanism and dynamics of
biological growth activities, null model representation, capturing anomalies,
etc. Well-known examples of these probabilistic models are Kronecker model,
preferential attachment model, and duplication-based model. However, we should
frequently keep developing new models to better fit and explain the observed
network features while new networks are being observed. Additionally, it is
difficult to develop a growth model each time we study a new network. In this
paper, we propose BioCode, a framework to automatically discover novel
biological growth models matching user-specified graph attributes in directed
and undirected biological graphs. BioCode designs a basic set of instructions
which are common enough to model a number of well-known biological graph growth
models. We combine such instruction-wise representation with a genetic
algorithm based optimization procedure to encode models for various biological
networks. We mainly evaluate the performance of BioCode in discovering models
for biological collaboration networks, gene regulatory networks, metabolic
networks, and protein interaction networks which features such as
assortativity, clustering coefficient, degree distribution closely match with
the true ones in the corresponding real biological networks. As shown by the
tests on the simulated graphs, the variance of the distributions of biological
networks generated by BioCode is similar to the known models' variance for
these biological network types.
