Two ants enter; one ant leaves. (Well, the numbers are actually somewhat larger than that.)
In the paper Modeling ant battles by means of a diffusion-limited Gillespie algorithm, biologist Giacomo Santini and his coauthors have proposed two modeling approaches for studying battles among ants.
When developing theories (for animal behavior and in other complex systems), a crucial scientific step — in addition to experiments and observations, of course — is to develop and analyze one or more models.
Indeed, scientists often pit models against each other. As Santini and coauthors write,
(…) This work is mainly motivated by the need to have realistic models to predict the interaction dynamics of invasive species. The two considered species exhibit different fighting strategies. In order to describe the observed battle dynamics, we start by building a chemical model considering the ants and the fighting groups (for instance two ants of a species and one of the other one) as a chemical species. From the chemical equations we deduce a system of differential equations, whose parameters are estimated by minimizing the difference between the experimental data and the model output. We model the fluctuations observed in the experiments by means of a standard Gillespie algorithm. In order to better reproduce the observed behavior, we adopt a spatial agent-based model, in which ants not engaged in fighting groups move randomly (diffusion) among compartments, and the Gillespie algorithm is used to model the reactions inside a compartment.
Bonus: One of the new paper’s citations is a 2009 preprint called Partial differential equations versus cellular automata for modelling combat, and the longstanding fight between PDE and cellular-automata approaches to modeling (of which that paper is but one tiny battle) rages to this day. If you believe Google Fight, it seems that PDEs win this battle. My fellow Oxford applied mathematicians will no doubt be happy about this result.