Two interacting ants.

Abstract

<p>The ants follow dynamics of <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0193049#pone.0193049.e026" target="_blank">Eq (10)</a> where the stochastic switching between the states follows transition rates with and the same as for the single ant in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0193049#pone.0193049.g004" target="_blank">Fig 4</a> and the interaction strength . The interaction with a kernel <i>ψ</i>(<i>d</i>) = <i>e</i>^{−<i>d</i>²} modulates the rates multiplicatively by a factor which increases all transition rates when ants are close to each other and leaves them unchanged when they are sufficiently distant. <b>(A)</b> Short stochastic simulation of two interacting ants, showing also the instantaneous transition rates from the current state. The interaction modulating factor exp(0.5<i>ψ</i>(<i>d</i>)) is shown together with other transition rates (green) using the same axis. <b>(B)</b> The first and the second rows show the inferred transition rates (dots) for the parameters <i>α</i>⁽¹⁾ and <i>α</i>⁽²⁾, respectively, compared with the exact rates (solid curves). The inference is based on 500 simulated trajectories, each for <i>T</i> ∈ [0, 500]. We used the tiling functions in the <i>z</i> and Δ<i>z</i> = <i>z</i>_<i>n</i> − <i>z</i>_<i>n</i>′ space and a penalization function of the form to enforce vanishing interaction outside of the range |Δ<i>z</i>| > 2. Penalization term also avoids a degeneracy of the rates, ensuring existence of a unique solution of the inference problem.</p

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