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Optimal foraging and the information theory of gambling

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Optimal foraging and the information theory of gambling. / Baddeley, Roland J.; Franks, Nigel R.; Hunt, Edmund R.

In: Journal of the Royal Society Interface, Vol. 16, No. 157, 20190162, 07.08.2019.

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Baddeley, Roland J. ; Franks, Nigel R. ; Hunt, Edmund R. / Optimal foraging and the information theory of gambling. In: Journal of the Royal Society Interface. 2019 ; Vol. 16, No. 157.

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@article{6e55577f08f24fbb9c3f425e79db2141,
title = "Optimal foraging and the information theory of gambling",
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 probability matching. 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 supplemented with momentum, i.e. a propensity to move in the same direction). This maps the problem of foraging (via the information theory of gambling, stochastic dynamics and techniques employed within Bayesian statistics to efficiently sample from probability distributions) to simple models of ant foraging behaviour. This identification has broad applicability, facilitates the application of information theory approaches to understanding movement ecology, and unifies insights from existing biomechanical, cognitive, random and optimality movement paradigms. At the cost of requiring ants to obtain (noisy) resource gradient information, we show that this model is both efficient, and matches a number of characteristics of real ant exploration.",
keywords = "Bayesian methods, Collective behaviour, L{\'e}vy foraging, Markov chain Monte Carlo, Movement ecology",
author = "Baddeley, {Roland J.} and Franks, {Nigel R.} and Hunt, {Edmund R.}",
year = "2019",
month = "8",
day = "7",
doi = "10.1101/497198",
language = "English",
volume = "16",
journal = "Journal of the Royal Society Interface",
issn = "1742-5689",
publisher = "The Royal Society",
number = "157",

}

RIS - suitable for import to EndNote

TY - JOUR

T1 - Optimal foraging and the information theory of gambling

AU - Baddeley, Roland J.

AU - Franks, Nigel R.

AU - Hunt, Edmund R.

PY - 2019/8/7

Y1 - 2019/8/7

N2 - 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 probability matching. 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 supplemented with momentum, i.e. a propensity to move in the same direction). This maps the problem of foraging (via the information theory of gambling, stochastic dynamics and techniques employed within Bayesian statistics to efficiently sample from probability distributions) to simple models of ant foraging behaviour. This identification has broad applicability, facilitates the application of information theory approaches to understanding movement ecology, and unifies insights from existing biomechanical, cognitive, random and optimality movement paradigms. At the cost of requiring ants to obtain (noisy) resource gradient information, we show that this model is both efficient, and matches a number of characteristics of real ant exploration.

AB - 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 probability matching. 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 supplemented with momentum, i.e. a propensity to move in the same direction). This maps the problem of foraging (via the information theory of gambling, stochastic dynamics and techniques employed within Bayesian statistics to efficiently sample from probability distributions) to simple models of ant foraging behaviour. This identification has broad applicability, facilitates the application of information theory approaches to understanding movement ecology, and unifies insights from existing biomechanical, cognitive, random and optimality movement paradigms. At the cost of requiring ants to obtain (noisy) resource gradient information, we show that this model is both efficient, and matches a number of characteristics of real ant exploration.

KW - Bayesian methods

KW - Collective behaviour

KW - Lévy foraging

KW - Markov chain Monte Carlo

KW - Movement ecology

UR - http://www.scopus.com/inward/record.url?scp=85071155569&partnerID=8YFLogxK

U2 - 10.1101/497198

DO - 10.1101/497198

M3 - Article

C2 - 31387483

AN - SCOPUS:85071155569

VL - 16

JO - Journal of the Royal Society Interface

JF - Journal of the Royal Society Interface

SN - 1742-5689

IS - 157

M1 - 20190162

ER -