  Agent-based modeling and simulation is a useful method to study biological
phenomena in a wide range of fields, from molecular biology to ecology. Since
there is currently no agreed-upon standard way to specify such models it is not
always easy to use published models. Also, since model descriptions are not
usually given in mathematical terms, it is difficult to bring mathematical
analysis tools to bear, so that models are typically studied through
simulation. In order to address this issue, Grimm et al. proposed a protocol
for model specification, the so-called ODD protocol, which provides a standard
way to describe models. This paper proposes an addition to the ODD protocol
which allows the description of an agent-based model as a dynamical system,
which provides access to computational and theoretical tools for its analysis.
The mathematical framework is that of algebraic models, that is, time-discrete
dynamical systems with algebraic structure. It is shown by way of several
examples how this mathematical specification can help with model analysis.
