The Bayesian superorganism: externalized memories facilitate distributed sampling

Abstract

A key challenge for any animal (or sampling technique) is to avoid wasting time by searching for resources (information) in places already found to be unprofitable. In biology, this challenge is particularly strong when the organism is a central place forager-returning to a nest between foraging bouts-because it is destined repeatedly to cover much the same ground. This problem will be particularly acute if many individuals forage from the same central place, as in social insects such as the ants. Foraging (sampling) performance may be greatly enhanced by coordinating movement trajectories such that each ant (walker) visits separate parts of the surrounding (unknown) space. We find experimental evidence for an externalized spatial memory in Temnothorax albipennis ants: chemical markers (either pheromones or cues such as cuticular hydrocarbon footprints) that are used by nest-mates to mark explored space. We show these markers could be used by the ants to scout the space surrounding their nest more efficiently through indirect coordination. We also develop a simple model of this marking behaviour that can be applied in the context of Markov chain Monte Carlo methods (Baddeley et al. 2019 J. R. Soc. Interface16, 20190162 (doi:10.1098/rsif.2019.0162)). This substantially enhances the performance of standard methods like the Metropolis-Hastings algorithm in sampling from sparse probability distributions (such as those confronted by the ants) with only a little additional computational cost. Our Bayesian framework for superorganismal behaviour motivates the evolution of exploratory mechanisms such as trail marking in terms of enhanced collective information processing.

Keywords: Markov chain Monte Carlo; exploration; extended cognition; spatial memory; superorganism; trail markers.

Figure 1.

The ants’ exploration trajectories for the two treatments and empirical target distribution P. All trajectories are shown in the top-left pane, marked by treatment, while trajectories are shown by treatment and ant order in the bottom panes (three ants for each order in the sequence).

Figure 2.

The ants in the no cleaning (NC) treatment converge most quickly toward the final distribution, indicating that they benefit from chemical information left by preceding nest-mates. The error bars indicate one standard error of the mean; a permutation test on ants 2–6 indicate that the cross-entropy is significantly lower in NC than C (p = 0.0161). The simulated ‘Markov ant’ converges slowest, because it benefits neither from the chemical markers (externalized spatial memory) nor internal memory about where it has already visited. The cross-entropy minimum is indicated by the dashed black line.

Figure 3.

The trail avoidance model converges much more quickly to the simulated sparse target distribution, while ‘cleaning’ (removing the externalized memory of the sampling trajectory) slows its progress somewhat. The target (cross-entropy minimum) is shown by the dashed black line.

Figure 4.

The trail avoidance model again converges more quickly to the target. The M–H model is more likely to get ‘stuck’ in higher probability regions and take longer to get to other important parts of the distribution. However, the performance gain is less obvious than in the preceding gamma distribution example.