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Optimal collective foraging by bee colonies

Dr Richard Mann (SoM), Dr Elizabeth Duncan (SoB)

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Understanding how eusocial insect colonies use information to explore and exploit resources is vital to managing our environmental resources. Bees, including bumblebees and honeybees, are crucial for their role in supporting global biodiversity and plant pollination. Insects pollinate 80% of crop plants in Europe and pollination services are estimated to contribute €22 billion to the European economy annually(Gallai et al., 2009).  Bee species, including managed pollinator species, are under increasing threat from intensive agricultural practices, diseases (McMenamin and Genersch, 2015), pesticides(Smith et al., 2013) and climate change (Pyke et al., 2016; Robbirt et al., 2014).

Understanding how information about the environment is gathered, processed and utilised by these species to contribute to collective decision making will allow us to predict how changes to the natural environment will affect the foraging behaviour of worker bees and what effect this will have on pollination of both wild and agricultural plants. 

Figure 1: Foraging bees must make individual decisions about where to forage given partial knowledge of food distributions and with limited communication between individuals. They must act to maximise the fitness of the colony through a decentralised foraging strategy without central coordination.


In this project we will apply mathematical theory, specifically set function theory, to understand the fundamental question of how bees make collective decisions to maximise foraging efficiency.  This will be the first time such an approach has been applied to biological problems and thus has the potential to provide novel insights into these commercially and ecologically important pollinator species.  

Set function optimisation requires the selection of a set of objects,  that maximises a specified set function f(S). This is a computationally challenging task, the full solution of which is not generally achievable. However, the field of machine learning has made substantial progress in creating algorithms that can identify near-optimal solutions in polynomial time (Krause, et al. 2006). These algorithms are to varying degrees decentralised; each element of the set is chosen without full consideration of the others. These results demonstrate that decentralised systems are capable of producing near optimal collective behaviour.  This has clear implications for the decentralised collective behaviour of animal groups, particularly insect colonies.  Particularly if, for example, the set S consists of a set of foraging sites, and the function f(S) is colony level fitness resulting from these foraging trips (see Figure 1).

However, these results have yet to be translated from the field of machine learning to biological problems. Doing so requires adapting algorithms to account for biological constraints and deriving results that can be tested empirically in real animals. Combining set function theory with our knowledge of bee biology and real-world field experiments to examine foraging strategies in bees is a powerful and unique approach that will yield novel insights into the biology of bees, collective decision making and, perhaps more importantly, will establish this mathematical approach for use in biological systems.


This project will investigate the use of information in bee colonies from both a mathematical and a biological perspective. Starting from results from machine-learning research regarding decentralised optimisation algorithms the student will work towards a mathematical theory of optimal foraging by a decentralised colony of agents representing a colony of bees. This theory will extend upon previous theoretical work in mathematics by imposing realistic biological constraints upon agents such as limited motility and communication abilities. It will extend on biological theory by rigorously treating the acquisition and exploitation of information from first principles of information theory. The ultimate goal of the project will be to make biological predictions about the behaviour of real bees that can be experimentally tested in the laboratory and/or field studies.


Applicants should have:

  • A genuine interest in animal behaviour and the influence of human activities on the natural environment.
  • A strong mathematical background: a degree in a mathematical subject (e.g. physics, computer science) or an excellent ‘A’ level grade in mathematics for biology graduates.
  • Experience with programming or computational modelling is not obligatory but the candidate must be willing to learn required computational techniques. Prior knowledge of R, Matlab or Python will be valuable.


The student will work under the supervision of Dr. Richard Mann in the School of Mathematics and Dr. Elizabeth Duncan within the School of Biology. Co-supervision will involve meetings between all participants and the co-supervisors will provide guidance on the overall direction of the project. The School of Biology has excellent resources for this project including an apiary on campus as well as a farm for larger field-based studies. This supervision team provides expertise in computational statistics, collective behaviour, environmental responsiveness and the evolution of eusociality.  The student will acquire a high level of specialist expertise in: (i) statistical decision theory; and (ii) collective behaviour and the study of eusociality in bees.  Combining modelling/statistical decision theory with problems of biological and ecological relevance will ensure that the student is trained in skills that are increasingly valuable in a burgeoning area of research.  This research also represents a fundamental step forward in our knowledge of pollinator species and will have applied outcomes for pollinator biology and potentially conservation. We anticipate this project generating several publications and papers regarding collective decision-making are often targeted to high impact journals. In addition the PhD student will be expected to present the outcomes of this project at both National and International conferences (i.e. International Congress of Entomology, International Union for the study of Social Insects conference, Neural Information Processing Systems (NIPS))


Krause, A.; Guestrin, C.; Gupta, A. & Kleinberg, J.  2006. Near-optimal sensor placements: Maximizing information while minimizing communication cost, Proceedings of the 5th international conference on Information processing in sensor networks,

Gallai, N., Salles, J.-M., Settele, J., et al., 2009. Economic valuation of the vulnerability of world agriculture confronted with pollinator decline. Ecol. Econ. 68, 810-821.

McMenamin, A.J., Genersch, E., 2015. Honey bee colony losses and associated viruses. Curr Opin Insect Sci 8, 121-129.

Pyke, G.H., Thomson, J.D., Inouye, D.W., et al., 2016. Effects of climate change on phenologies and distributions of bumble bees and the plants they visit. Ecosphere 7, e01267-n/a.

Robbirt, K.M., Roberts, D.L., Hutchings, M.J., et al., 2014. Potential disruption of pollination in a sexually deceptive orchid by climatic change. Curr Biol 24, 2845-2849.

Smith, K.M., Loh, E.H., Rostal, M.K., et al., 2013. Pathogens, Pests, and Economics: Drivers of Honey Bee Colony Declines and Losses. EcoHealth 10, 434-445.

Related undergraduate subjects:

  • Applied mathematics
  • Bioinformatics
  • Biology
  • Computer science
  • Computing
  • Economics
  • Geophysics
  • Mathematics
  • Mechanical engineering
  • Natural sciences
  • Physics
  • Statistics