Non-stationary aging dynamics in ant societies

Abstract

In recent experiments by Richardson et al. (2010) [Richardson, T.O., Robinson, E.J.H., Christensen, K., Jensen, H.J., Franks, N.R., Sendova-Franks, A.B., 2010. PLoS ONE 5, e9621.] ant motion out of the nest is shown to be a non-stationary process intriguingly similar to the dynamics encountered in physical aging of glassy systems. Specifically, exit events can be described as a Poisson process in logarithmic time, or, for short, a log-Poisson process. Nouvellet et al. (2010) [Nouvellet, P., Bacon, J.P.,Waxman, D., 2010. J. Theor. Biol. 266, 573.] criticized these conclusions and performed new experiments where the exit process could more simply be described by standard Poisson statistics. In their reply Richardson et al. (2011b) [Richardson, T.O., Robinson, E.J.H., Christensen, K., Jensen, J.H., Christensen, K., Jensen, H.J., Franks, N.R., Sendova-Franks, A.B., 2011b. J. Theor. Biol. 269, 356-358.] stressed that the two sets of experiments were performed under very different conditions and claimed that this was the likely source of the discrepancy. Ignoring any technical issues which are part of the above discussion, the focal point of this work is to ascertain whether or not both log-Poisson and Poisson statistics are possible in an ant society under different external conditions. To this end, a model is introduced where interacting ants move in a stochastic fashion from one site to a neighboring site on a finite 2D lattice. The probability of each move is determined by the ensuing changes of a utility function which is a sum of pairwise interactions between ants, weighted by distance. Depending on how the interactions are defined and on a control parameter dubbed 'degree of stochasticity' (DS), the dynamics either quickly converges to a stationary state, where movements are a standard Poisson process, or may enter a non-stationary regime, where exits can be described as suggested by Richardson et al. Other aspects of the model behavior are also discussed, i.e. the time dependence of the average value of the utility function, and the statistics of spatial re-arrangements happening anywhere in the system. Finally, we discuss the role of record events and their statistics in the context of ant societies and suggest the possibility that a transition from non-stationary to stationary dynamics can be triggered experimentally.