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Modeling warfare in social animals: a "chemical" approach.

Santarlasci A, Martelloni G, Frizzi F, Santini G, Bagnoli F - PLoS ONE (2014)

Bottom Line: The main result that we obtained is a dominance phase diagram, that gives the average trajectory of a generic battle, for an arbitrary number of opponents.With respect to other war models (e.g., Lanchester's ones), our chemical model considers all phases of the battle and not only casualties.This allows a more detailed description of the battle (with a larger number of parameters), allowing the development of more sophisticated models (e.g., spatial ones), with the goal of distinguishing collective effects from the strategic ones.

View Article: PubMed Central - PubMed

Affiliation: Department of Information Engineering, University of Florence, Firenze, Italy; Center for the Study of Complex Dynamics (CSDC), University of Florence, Sesto Fiorentino (FI), Italy.

ABSTRACT
We present here a general method for modelling the dynamics of battles among social animals. The proposed method exploits the procedures widely used to model chemical reactions, but still uncommon in behavioural studies. We applied this methodology to the interpretation of experimental observations of battles between two species of ants (Lasius neglectus and Lasius paralienus), but this scheme may have a wider applicability and can be extended to other species as well. We performed two types of experiment labelled as interaction and mortality. The interaction experiments are designed to obtain information on the combat dynamics and lasted one hour. The mortality ones provide information on the casualty rates of the two species and lasted five hours. We modelled the interactions among ants using a chemical model which considers the single ant individuals and fighting groups analogously to atoms and molecules. The mean-field behaviour of the model is described by a set of non-linear differential equations. We also performed stochastic simulations of the corresponding agent-based model by means of the Gillespie event-driven integration scheme. By fitting the stochastic trajectories with the deterministic model, we obtained the probability distribution of the reaction parameters. The main result that we obtained is a dominance phase diagram, that gives the average trajectory of a generic battle, for an arbitrary number of opponents. This phase diagram was validated with some extra experiments. With respect to other war models (e.g., Lanchester's ones), our chemical model considers all phases of the battle and not only casualties. This allows a more detailed description of the battle (with a larger number of parameters), allowing the development of more sophisticated models (e.g., spatial ones), with the goal of distinguishing collective effects from the strategic ones.

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Distribution of the reaction coefficient.Coefficients  (A),  (B),  (C),  (D),  (E) and  (F), obtained with our stochastic procedure; the best fit is achieved by means of Log-normal distribution comparing the likelihoods.
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pone-0111310-g003: Distribution of the reaction coefficient.Coefficients (A), (B), (C), (D), (E) and (F), obtained with our stochastic procedure; the best fit is achieved by means of Log-normal distribution comparing the likelihoods.

Mentions: Some examples of the frequency distributions of parameter values estimated from the stochastic model are shown in Fig. 3. The best fit of their distribution is given by a Log-normal distribution (we test also Exponential and Weibull), using the likelihood method. We proceeded in this way: we divided the 100 Gillespie simulations in two sets of 50. We then evaluated the parameters of the Log-normal distribution (average and variance) for the first set and used them in the likelihood test for the following 50 samples. The same was done dividing the 20 experimental samples in two sets of 10. The results are reported in Table 4


Modeling warfare in social animals: a "chemical" approach.

Santarlasci A, Martelloni G, Frizzi F, Santini G, Bagnoli F - PLoS ONE (2014)

Distribution of the reaction coefficient.Coefficients  (A),  (B),  (C),  (D),  (E) and  (F), obtained with our stochastic procedure; the best fit is achieved by means of Log-normal distribution comparing the likelihoods.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4219847&req=5

pone-0111310-g003: Distribution of the reaction coefficient.Coefficients (A), (B), (C), (D), (E) and (F), obtained with our stochastic procedure; the best fit is achieved by means of Log-normal distribution comparing the likelihoods.
Mentions: Some examples of the frequency distributions of parameter values estimated from the stochastic model are shown in Fig. 3. The best fit of their distribution is given by a Log-normal distribution (we test also Exponential and Weibull), using the likelihood method. We proceeded in this way: we divided the 100 Gillespie simulations in two sets of 50. We then evaluated the parameters of the Log-normal distribution (average and variance) for the first set and used them in the likelihood test for the following 50 samples. The same was done dividing the 20 experimental samples in two sets of 10. The results are reported in Table 4

Bottom Line: The main result that we obtained is a dominance phase diagram, that gives the average trajectory of a generic battle, for an arbitrary number of opponents.With respect to other war models (e.g., Lanchester's ones), our chemical model considers all phases of the battle and not only casualties.This allows a more detailed description of the battle (with a larger number of parameters), allowing the development of more sophisticated models (e.g., spatial ones), with the goal of distinguishing collective effects from the strategic ones.

View Article: PubMed Central - PubMed

Affiliation: Department of Information Engineering, University of Florence, Firenze, Italy; Center for the Study of Complex Dynamics (CSDC), University of Florence, Sesto Fiorentino (FI), Italy.

ABSTRACT
We present here a general method for modelling the dynamics of battles among social animals. The proposed method exploits the procedures widely used to model chemical reactions, but still uncommon in behavioural studies. We applied this methodology to the interpretation of experimental observations of battles between two species of ants (Lasius neglectus and Lasius paralienus), but this scheme may have a wider applicability and can be extended to other species as well. We performed two types of experiment labelled as interaction and mortality. The interaction experiments are designed to obtain information on the combat dynamics and lasted one hour. The mortality ones provide information on the casualty rates of the two species and lasted five hours. We modelled the interactions among ants using a chemical model which considers the single ant individuals and fighting groups analogously to atoms and molecules. The mean-field behaviour of the model is described by a set of non-linear differential equations. We also performed stochastic simulations of the corresponding agent-based model by means of the Gillespie event-driven integration scheme. By fitting the stochastic trajectories with the deterministic model, we obtained the probability distribution of the reaction parameters. The main result that we obtained is a dominance phase diagram, that gives the average trajectory of a generic battle, for an arbitrary number of opponents. This phase diagram was validated with some extra experiments. With respect to other war models (e.g., Lanchester's ones), our chemical model considers all phases of the battle and not only casualties. This allows a more detailed description of the battle (with a larger number of parameters), allowing the development of more sophisticated models (e.g., spatial ones), with the goal of distinguishing collective effects from the strategic ones.

Show MeSH