  The human gastrointestinal tract is an environment that hosts an ecosystem of
microorganisms essential to human health. Vital biological processes emerge
from fundamental inter- and intra-species molecular interactions that influence
the assembly and composition of the gut microbiota ecology. Here we quantify
the complexity of the ecological relationships within the human infant gut
microbiota ecosystem as a function of the information contained in the
nonlinear associations of a sequence of increasingly-specified maximum entropy
representations of the system. Our paradigm frames the ecological state, in
terms of the presence or absence of individual microbial ecological units that
are identified by amplicon sequence variants (ASV) in the gut microenvironment,
as a function of both the ecological states of its neighboring units and, in a
departure from standard graphical model representations, the associations among
the units within its neighborhood. We characterize the order of the system
based on the relative quantity of statistical information encoded by high-order
statistical associations of the infant gut microbiota.
