DOI: 10.1101/497198Dec 17, 2018Paper

Optimal foraging and the information theory of gambling

BioRxiv : the Preprint Server for Biology
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 optimised by a strategy of betting in proportion to the probability of payoff. 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 generates predictions for 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 methods, specifically Hamiltonian Markov chain Monte Carlo (HMC). This can be done by the ants following a (noisy) local measurement of the (logarithm of) the resource probability gradient (possibly su...Continue Reading

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