The aim of our study is to describe the dynamics of ant battles, with reference to laboratory experiments, by means of a chemical stochastic model. We focus on ants behavior as an interesting topic in order to predict the ecological evolution of invasive species and their spreading. In our work we want to describe the interactions between two groups of different ant species with different war strategies. Our model considers the single ant individuals and fighting groups in a way similar to atoms and molecules, respectively, considering that ant fighting groups remain stable for a relative long time. Starting from a system of differential non-linear equations (DE), derived from the chemical reactions, we obtain a mean field description of the system. The DE approach is valid when the number of individuals of each species is large in the considered unit, while we consider battles of at most 10 vs. 10 individuals, due to the difficulties in following the individual behavior in a large assembly. Therefore, we also adapt a Gillespie algorithm to reproduce the fluctuations around the mean field. The DE scheme is exploited to characterize the stochastic model. The set of parameters of chemical equations, obtained using a minimization algorithm, are used by the Gillespie algorithm to generate the stochastic trajectories. We then fit the stochastic paths with the DE, in order to analyze the variability of the parameters and their variance. Finally, we estimate the goodness of the applied methodology and we confirm that the stochastic approach must be considered for a correct description of the ant fighting dynamics. With respect to other war models, our chemical one considers all phases of the battle and not only casualties. Thus, we can count on more experimental data, but we also have more parameters to fit. In any case, our model allows a much more detailed description of the fights.
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