The Bayesian Superorganism: Collective Probability Estimation in Swarm Systems

Abstract

Superorganisms such as social insect colonies are very successful relative to their non-social counterparts. Powerful emergent information processing capabilities would seem to contribute to the abundance of such 'swarm' systems, as they effectively explore and exploit their environment collectively. We develop a Bayesian model of collective information processing in a decision-making task: choosing a nest site (a 'multi-armed bandit' problem). House-hunting Temnothorax ants are adept at discovering and choosing the best available nest site for their colony: we propose that this is possible via rapid, decentralised estimation of the probability that each choice is best. Viewed this way, their behavioural algorithm can be understood as a statistical method that anticipates recent advances in mathematics. Our model of their nest finding incorporates insights from approximate Bayesian computation as a model of colony-level behaviour; and particle filtering as a model of Temnothorax 'tandem running'. Our Bayesian framework suggests that the mechanisms of complex collective behaviour can sometimes be explained with reference to Bayesian inference. It facilitates the generation of quantitative hypotheses regarding individual and collective movement behaviours when collective decisions must be made. It also points to the potential for bio-inspired statistical techniques. Finally, it suggests simple mechanisms for collective decision-making in engineered swarm systems, such as robot swarms.

The Bayesian superorganism: externalized memories facilitate distributed sampling

“…Such a method was shown to significantly enhance the efficiency of the Metropolis-Hastings method [7,8] when sampling from sparse probability distributions, because the random walk-type behaviour of the method is reduced, but at little computational cost in comparison to more advanced momentum-based methods such as Hamiltonian Monte Carlo [9]. When the 'superorganism' [43] is examined using our Bayesian framework [5,38], behavioural mechanisms such as individual trail markers become better understood in an ultimate sense [72] in relation to their facilitation of adaptive collective information-processing capabilities.…”

“…We test this hypothesis of enhanced exploration efficiency in the following way. In nature the ants might benefit from sampling preferentially from surrounding regions of higher quality, in the sense of being more likely to contain valuable resources such as food [5] or a potential new nest site [38]; and would want to spend less time in 'empty' regions of the space that contain little of relevance to their reproductive fitness. High-quality regions are likely to be associated with cues that help the ants navigate toward them: for instance, a good potential nest site may be more likely to be located in brighter regions of space than darker regions, because it could benefit from warmer ambient temperatures.…”

“…In previous research [5,38], we have proposed that a central challenge that an ant colony confronts, that of trying to identify regions of value in an unknown surrounding environment, is analogous to the problem found in statistics, physics, etc., of efficiently sampling from complex probability distributions or computing numerical integrations. This is because in order to sample from a probability distribution efficiently, one must identify regions of high probability density, yet these are not known a priori but only after evaluating the probability density function at those locations.…”

The Bayesian Superorganism: externalised memories facilitate distributed sampling

“…Such a method was shown to significantly enhance the efficiency of the Metropolis–Hastings method (Metropolis et al 1953; Hastings 1970) when sampling from sparse probability distributions, because the random walk type behaviour of the method is reduced, but at little computational cost in comparison to more advanced momentum-based methods such as Hamiltonian Monte Carlo (Duane et al 1987). When the ‘superorganism’ (Hölldobler and Wilson 2009) is examined using our Bayesian framework (Baddeley et al 2018; Hunt et al 2018), behavioural mechanisms such as individual trail markers become better understood in an ultimate sense (Tinbergen 1963) in relation to their facilitation of adaptive collective information-processing capabilities.…”

Optimal foraging and the information theory of gambling

“…This is not included in the models here, although state-dependent behaviours such as tandem running [25] could be included by analogy with particle filtering (e.g. [55]), for instance [26]. Our use of the Markov assumption (movement being memoryless, depending only on the current position) is justifiable with respect both to the worker ant's individual cognitive capacity and its single-minded focus on serving the colony through discovering and exploiting resources.…”