Optimal foraging and the information theory of gambling

Journal of the Royal Society, Interface
Roland J BaddeleyEdmund R Hunt

Abstract

At a macroscopic level, part of the ant colony life cycle is simple: a colony collects resources; these resources are converted into more ants, and these ants in turn collect more resources. Because more ants collect more resources, this is a multiplicative process, and the expected logarithm of the amount of resources determines how successful the colony will be in the long run. Over 60 years ago, Kelly showed, using information theoretic techniques, that the rate of growth of resources for such a situation is optimized by a strategy of betting in proportion to the probability of pay-off. Thus, in the case of ants, the fraction of the colony foraging at a given location should be proportional to the probability that resources will be found there, a result widely applied in the mathematics of gambling. This theoretical optimum leads to predictions as to which collective ant movement strategies might have evolved. Here, we show how colony-level optimal foraging behaviour can be achieved by mapping movement to Markov chain Monte Carlo (MCMC) methods, specifically Hamiltonian Monte Carlo (HMC). This can be done by the ants following a (noisy) local measurement of the (logarithm of) resource probability gradient (possibly supplemen...Continue Reading

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Citations

Jan 26, 2020·Animals : an Open Access Journal From MDPI·Youssef ChebliJean-François Cabaraux
Jun 18, 2020·Journal of the Royal Society, Interface·Edmund R HuntRoland J Baddeley
Apr 22, 2021·Proceedings. Biological Sciences·Valentin LechevalElva J H Robinson
Jul 13, 2021·Frontiers in Behavioral Neuroscience·Daniel Ari FriedmanAxel Constant

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