  Inferring microbial interaction networks from abundance patterns is an
important approach to advance our understanding of microbial communities in
general and the human microbiome in particular. Here we suggest discriminating
two levels of information contained in microbial abundance data: (1) the
quantitative abundance values and (2) the pattern of presences and absences of
microbial organisms. The latter allows for a binary view on microbiome data and
a novel interpretation of microbial data as attractors, or more precisely as
fixed points, of a Boolean network.
  Starting from these attractors, our aim is to infer an interaction network
between the species present in the microbiome samples. To accomplish this task,
we introduce a novel inference method that combines the previously published
ESABO (Entropy Shifts of Abundance vectors under Boolean Operations) method
with an evolutionary algorithm. The key idea of our approach is that the
inferred network should reproduce the original set of (observed) binary
abundance patterns as attractors.
  We study the accuracy and runtime properties of this evolutionary method, as
well as its behavior under incomplete knowledge of the attractor sets. Based on
this theoretical understanding of the method we then show an application to
empirical data.
