Alisa Santarlasci - Università degli Studi di Firenze #
"Chemical" Modelling ants battles from experimental data, by means of a modified Gillespie algorithm #
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 ant behavior as an interesting 
topic for the aptitude to propagate easily to new habitats. In 
order to predict the ecological evolution of invasive species and 
their relative fast spreading, a description of their successful 
strategies, also considering their competition with other ant 
species is necessary. In our work we want to describe the 
interactions between two groups of different ant species, with 
different war strategies, as observed in our experiments. The 
proposed chemical 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. This 
deterministic approach is valid when the number of individuals of 
each species is large in the considered unit, while in our 
experiments 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 description. The 
DE schematization is exploited to characterize the stochastic 
model. The set of reaction constants of chemical equations, 
obtained by means of a minimization algorithm between the DE and 
the experimental data, 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 therefore 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 observed ant fighting dynamics. With respect to other war 
models (e.g., Lanchester's ones), our chemical model 
considers all phases of the battle and not only casualties. 
Therefore, 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.