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.

Record dynamics of evolving metastable systems: theory and applications

“…Whether a similar mechanism involving social structures is at play in real ant nests remains of course to be seen. Let us finally note that the size of the barrier scaled during ant movement was not investigated in [77]. We are therefore unable to give a precise definition of quake and use nest exits as a proxy.…”

“…Importantly, the analysis of [76] is based on observational data and hence independent of modeling assumptions. A theoretical model of the same phenomenology [77] is also discussed below.…”

“…In the model proposed in [77], from which Figs. 10 and 11 are taken, ants of different types move in a stochastic fashion from one site to a neighboring site on a finite 2D lattice, similar to an ant's nest.…”

“…The initial configuration is in all cases obtained by randomly placing the ants on the grid. Figure taken from [77] lations starting from a random distribution of ants in the nest, ever larger ant clusters establish themselves on gradually fewer sites. This in turn creates continually growing dynamical barriers (e.g.…”

Coarse-graining complex dynamics: Continuous Time Random Walks vs. Record Dynamics

“…That thermal noise records have an impact in complex dynamics was proposed [9] in a model study of Charge Density Waves. Over the years the same idea, which we now refer to as Record Dynamics, has found applications in condensed matter physics [10][11][12][13], evolutionary biology [14] and the dynamics of ant societies [15]. The term 'record' in RD signals that overcoming a record-sized dynamical barrier elicits a jump -henceforth in this connection termed quake-which brings the system from one trap to a new and previously unexplored trap.…”