Agent-Based Models and Optimal Control in Biology: A Discrete Approach - Mathematical Concepts and Methods in Modern Biology - page 143

status to each of the cells, then we can use this rule to evolve life on this grid by
updating the status of all the cells in discrete time steps. The result is a vast array of
different dynamics that can be observed, but is largely unpredictable from a particular
initialization. There is a rich literature on this topic and many websites with Game of
Life simulators. Before continuing, the reader is encouraged to try some of these and
explore the question of predicting dynamic behavior from particular initializations.
General agent-based models have many features similar to this set-up. There is
a collection of agents that are distributed across a spatial landscape. In the Game of
Life , the spatial landscape is the grid, and there is one agent per cell. Each agent can
be in one of a (typically finite) number of states, such as “dead” or “alive,” and has a
set of rules attached to it that it uses to determine its state, based on the state of those
other agents it interacts with at any given time. Beyond the Game of Life, in general
agent-based models, agents are able to move around in the spatial landscape, and
there are rules that determine the agents' movement patterns. Typically, the rules are
stochastic, rather than deterministic, and are governed by a collection of probabilities.
For instance, agents might be predisposed to follow a certain gradient, representing,
e.g., nutrient availability, but there is some chance that they might move in a different
direction. While there are many other variations and features in particular agent-based
models, these few basic features characterize the agent-based modeling framework.
These features are also sufficient to explain the basic differences between agent-
based models and equation-based models, such as ordinary differential equations.
Agent-based models lend themselves very well to a description of dynamical systems
that arise from local interactions of many parts/agents, based only on local rules rather
than on the configuration of the entire system at any given time. Also, it is very easy
to represent a rich heterogeneous spatial environment that the agents navigate. Thus,
the dynamics of the entire system, or its so-called global dynamics, “emerge” from
these local interactions by applying the local rules repeatedly. In contrast, a system
of differential equations, for instance, explicitly describes the global dynamics of the
system up front. Furthermore, all the specifications for an agent-based model are intu-
itive, in the sense that they are direct computational representations of recognizable
features in the actual system. This leads to models that are more faithful to the system
to be modeled and that are more accessible to domain experts. With existing software
for model building, they can even be built by domain experts directly, without the
intervention of a modeler or mathematician. But, as always, there are no free lunches.
These advantages come with some significant costs attached.
The reason that agent-based modeling became widespread only in the last 15 years
or so is due to the fact that larger models with more features require extensive com-
putational resources that were not available until recently. It is only now possible,
barely, to build and analyze models that might have hundreds of millions of agents
and tens of millions of spatial locations, with agents being very complex in terms
of the states they can take on and the rules they follow. Even moderately complex
models require high performance computing facilities for their analysis, which makes
it difficult for individual researchers to use them. High computational complexity is
compounded by the fact that there are very few mathematical tools available for the