Modeling ant warfare: a "chemical" approach.

The aim of our study is to develop an original approach to the modeling of battle dynamics among social animals. Although the model can be applied to any animal war, we focus on ant behavior, for a variety of reasons. Ants represent an important environmental actor, exhibit extraordinary strategies used to achieve their ecological success, and are sufficiently small and individually “simple” to be studied in laboratory. Moreover, modeling ant warfare has a direct application to the monitoring of invasive species. An invasive ant species become dominant through an extraordinary cooperative behavior, an aspect of which is represented by the strategies adopted during the wars against other species. Our studies focused on two species that share the same habitat but with different fighting strategies: the invasive Lasius neglectus and the autochthonous Lasius paralienus. We performed several in vitro experiments, with a small number of ants in a limited environment (Petri dish) due to observational limits. These experiments represent the validating framework of the models developed. We started by assuming the absence of any cognitive strategy, applying the classical “chemical modeling”, where all the interactions among members of the system are represented following the formalism used to represent chemical reactions. The proposed chemical model considers the ant individuals and fighting groups equivalent to atoms and molecules, respectively, since ant-fighting groups remain stable for a relatively long time. We identified a system of differential non-linear equations, taking into consideration the observed groups. Because this is essentially a mean-field description of the system, it cannot reproduce the stochastic fluctuations of the observed data. In order to generate realistic trajectories, we considered two agent-based stochastic models, with and without a spatial distribution. Assuming spatial homogeneity (supported by the limited extension of our battle field), we can accelerate the dynamics using an event-driven approach similar to the Gillespie algorithm, widely used in chemistry. We developed also a spatial version of the system in which agents vary randomly in the field, divided into compartments, and the Gillespie algorithm only determines the reactions inside a compartment. We obtained the parameters of our models by means of an optimization procedure with experimental data. With respect to other war models, our chemical model considers all phases of the battle and not only casualties. One more advantage of this approach is that all possible interactions can be outlined using a simple but biologically meaningful formalism, which provide a “microscopic” (i.e., at the individual level) description of the system, in contrast with the “macroscopic” population level description provided by classical models like Lanchester’s ones. Given a detailed model of an animal war, we can investigate the discrepancies between our model and the observed behaviour, aiming at distinguishing the collective effects (included in the model) from other effects due, for instance, to cognitive strategies or fatigue not included into the model. Finally, assuming that our model is a good description of the real interspecies interactions, and studying battles among more species, we can address the problem of deriving the chemical parameters from a smaller number of species-specific parameters (like aggressiveness, strength, cooperation, resistance, etc.). The possibility to have a scalable way of investigating animal fights (that may involve thousands of individuals) may have deep consequences in predicting the outcome of real combats, which may result to be an important tool in predicting the successfulness of invasive species.