Welcome to the Collective Behavior group

Who are we and what do we do?

We are a research group led by David Sumpter and based in the mathematics department of Uppsala University. Our research is about understanding collective behaviour in biological and social systems.

What is research in collective behaviour?

Research in collective behaviour is about linking together the way we understand systems at different levels. Take a bird flock as an example. Here we see many individuals moving in unison, but there is no clear leader or global controller. The question is how the bird's interactions link together to produce the overall motion of the flock. Similar questions arise when we look at ant and bee colonies, cellular interactions, and the human economy. How do individual behaviours integrate to produce global dynamics?

Why is understanding collective behaviour important?

We live in a data rich world. We can use image analysis to track the motion of fish and GPS to track birds. There are vast databases of information about the social welfare and economic development of humans. We can measure the flow of nutrients within a microorganism. But the question is how we understand this data? How is all this individual behaviour, be it of animals, humans or cells, integrated to produce dynamics at the level of the group? These are unanswered and general questions which research on collective behaviour addresses.

What has this got to do with mathematics?

Mathematics is a rigorous way of reasoning about the world. It is also a way of reasoning which allows us to draw powerful analogies between different systems. We use a range of statistical, mathematical and computer simulation tools to quantify and then model the behaviour of groups. These tools include differential equations, stochastic models, self-propelled particle models and individual-based models.



We are a strongly interdisciplinary team: Mathematicians, biologists, computer scientists, chemists, physicists, image analysts and sociologists. We use a wide range of tools including experimental techniques, nonlinear dynamics, stochastic processes and Monte Carlo type simulations. Currently, we are focusing on four research topics :

!-- Rules of motion start -->

Rules of motion and group decision-making

Tracking and analysing fish movements
Simple rules leading to complex motion (Strömbom, 2011).
David Sumpter talking about this research in York, 2009.

Moving fish schools and bird flocks provide stunning examples of complex collective motion (King & Sumpter, 2012; Sumpter 2006). But how do individuals interact to produce these dynamics? Our research in this area started by looking at global features of moving locust swarms (Buhl et al., 2006), bird flocks (Biro et al. 2006; Sumpter et al., 2008) and fish schools. We have looked in detail at how fish make decisons about where to go and how to avoid being eaten by predators (2011).

More recently the focus has been on detailed individual interactions between animals within moving groups. We are developping methods for quantifying these interactions (Mann, 2011), and have employed these methods on fish (Herbert-Read et al., 2011), ants, prawns and pigeons. This work is part of a large grant from the European Research Council on understanding Individual Differences in Collective Animal Behaviour.

As well as work linked directly to experiments we have developed mathematical models to help explain general properties of collective motion and decision-making. For example, we have shown how directed collective motion can be generated purely by attraction between individuals (Strömbom, 2011). Another unifying theme is the use of quorum thresholds, whereby individuals wait until a threshold number of others have committed to an option before they themselves commit to it (Sumpter et al., 2008; Ward et al., 2008; Pratt & Sumpter, 2006). We have used mathematical models to show that these quorum responses allow animals to filter out poor choices and make better decisions (Sumpter & Pratt, 2009, Nicolis et al., 2011).

Several popular science articles have been written about our recent research. See, for example, ABC, Discovery, Australian Geographic, Science News, Nature and SVT (Swedish) .

Researchers involved :

  • Arianna Botinelli.

  • Richard Mann.

  • Andrea Perna.

  • Daniel Strömbom.

Collaborators :

Problem solving by biological systems

image Ants, slime moulds and bifurcations

How biological systems solve problems? For example, how do ants choose between multiple food sources when no single ant knows which one is best? For many ant species, the answer is that they lay pheromones to tell each other where to go. In one study we showed that Argentine ants can solve a maze which encodes the Towers of Hanoi problem (Reid et al., 2011). You can see a short film about this work on the science programme Catalyst, and read what both Nature and a HFSP feature | creationist make of our results.

Ant species differ in the way their colonies solve problems. Big headed ants, use multiple pheromones, which decay at different rates, to allow them to track changes in the quality and location of food (Dussutour et al., 2009). In a long term project together with Stephen Pratt in Arizona we have disected the rules through which Temnothorax ants choose a new nest (Pratt & Sumpter, 2005, 2006). Comparisons between different systems using common models has allowed us to explain why these systems sometimes appear to make 'irrational' decisions (Nicolis et al., 2011).

Current reinforced random walk solves Towers of Hanoi.

Another impressive example by problem solving by ants is the construction of networks. We have studied the structure and dynamics of networks linking different nests together (Latty et al., 2011) and those which link a central nest to many different food sources (Buhl et al., 2008). These studies led us to draw parallels between ants and acellular slime mold, an organism which builds networks of tubes linking food sources (Ito et al., 2010). From these models we have been working on models of current reinforced random walks as a general explanation of these phenomena.

Since our approach involves determining the algortihms which biological systems use to solve problems, we can then use these algorithms to design better computer systems. This idea has been the focus of an interdisciplinary project financed by the Human Frontiers Science Programme. The final report from our project can be downloaded here.

Researchers involved :

  • Anders Johansson.

  • Qi Ma.

  • Stamatios Nicolis.

  • Natalia Zabzina.

Collaborators :

Social Dynamics and Development

What is exactly development space ...

All social structures are complicated. Be it the workplace, schooling, family life, or world economics, all of these structures are characterised by complex social interactions between large numbers of individuals. When faced with tough questions about our future,such as “How do we promote economic development in the poorest parts of the world?” or “How do we promote equality and prevent social exclusion?” we can’t limit our thinking to just one or two factors. We always have to be aware of the bigger picture and how the maze of social interactions can lead us in different directions.

Our research goal is to find statistical and mathematical tools for breaking through this complexity to provide clear explanations of how social systems work.We study social interactions in everyday activities, such as gaze following (Gallup et al., 2012), clapping after a seminar (Mann et al., in prep) and answering trivia questions as a group (Granovskiy et al., in prep.), as well as in instutionalised settings, such as share trading (Nicolis & Sumpter, 2011) and political negotiations (Saam & Sumpter, 2008). In a recent project, we call Development Space,we look at how we can model human development and social well-being as a dynamical system.

Researchers involved :

  • Betty Nannyonga.

  • Shyam Ranangathan.

  • Mario Romero.

  • Stamatios Nicolis.

  • Boris Granovsky.

Collaborators :

Ecology and evolution

image Spatial population dynamics

Our most recent work in evolution has concentrated on explaining why animals form and maintain groups (Sumpter & Brännström, 2008 Cornforth et al., 2012). Detailed empirical and modelling studies of house sparrows allowed us to suggest a simple model for characterising animal group size distributions (Griesser 2011; Ma et al. 2011).

A central problem in ecology and evolution is relating the behavioural interactions of individuals, described in terms of competition, predation, interference etc., to the dynamics of the populations of these individuals, in terms of change in numbers of individuals over time (Brännström & Sumpter 2005a; 2005b; 2006). We have derived a whole range of models of population dynamics, determining how they arose from spatial distribution and competition between individuals. These derivations allow us to make a more rigorous prescription for model choice when fitting to particular data-sets .

Researchers involved :

  • Anders Johansson.

  • Qi Ma.

Collaborators :

Publications (2008 - present)

for papers before 2007, see individual pages

  • Farine, DR, Aplin, LM, Garroway CJ, Mann RP and Sheldon BC (2014).Individuals use similar interaction rules for conspecifics and heterospecifics in mixed-species flocks. Animal Behaviour (accepted)

  • Forsman J, Mann RP, Linder C and Van den Bogaard M(2014). Sandbox University: Estimating influence of institutional action. PLoS ONE (accepted)

  • Aplin, LM, Farine, DR, Mann RP and Sheldon BC (2014). Individual-level personality influences social foraging and collective behaviour in wild birds. Proc Roy Soc B (accepted)

  • Spaiser V, Ranganathan S, Mann RP and Sumpter DJT (2014). The dynamics of democracy, development and cultural values. PLoS ONE

  • Arganda S, Nicolis SC, Perochain A, Pechabadens C, Latil G, and Dussutour A (2014). Collective choice in ants: The role of protein and carbohydrates ratios. Journal of insect physiology

  • Domenici P, Wilson ADM, Kurvers R, Marras S, Herbert-Read JE, Fleng Steffensen J, Krause S, Viblanc PE Couillaud P and Krause J (2014). How sailfish use their bills to capture schooling prey. Proc Roy Soc B

  • Mann RP, Armstrong C, Meade J, Freeman R, Biro D and Guilford T (2014). Landscape complexity influences route-memory formation in navigating pigeons. Biology Letters
    Media: ITV News, SVT, Discover MagazineDaily Mail, Daily Telegraph, Irish Independent

  • Ranganathan S, Spaiser V, Mann RP, and Sumpter DJT (2014). Bayesian Dynamical Systems Modelling in the Social Sciences. PLoS ONE

  • Strömbom D (2012). Attraction based models of collecive motion. Phd thesis, Uppsala University.

  • Mann RP, Herbert-Read JE, Ma Q, Jordan LA, Sumpter DJT and Ward AJW (2013). A model comparison reveals dynamic social information drives the movements of humbug damselfish (Dascyllus aruanus) . Journal of the Royal Society Interface

  • Petit, B, Perna A, Biro D, and Sumpter DJT (2013). Interaction rules underlying group decisions in homing pigeons. J R Soc Interface

  • Sasaki T, Granovskiy B , Mann RP , Sumpter DJT and Pratt SC (2013). Ant colonies outperform individuals when a sensory discrimination task is difficult but not when it is easy. Proceedings of the National Academy of Sciences.
    Media : NatureNational Geographic, The Atlantic, LA Times

  • Jordan LA, Herbert-Read JE and Ward AJW (2013). Rising costs of care make spiny chromis discerning parents. Behavioral Ecology and Sociobiology 67 (3), 449-455.

  • Ward AJW, Herbert-Read JE , Jordan LA, James R, Krause J, Ma Q, Rubenstein DI, Sumpter DJT and Morrell LJ (2013). Initiators, Leaders, and Recruitment Mechanisms in the Collective Movements of Damselfish. The American Naturalist 181 (6), 748-760.

  • Herbert-Read JE , Krause S, Morrell LJ, Schaerf TM, Krause J and Ward AJW (2013).The role of individuality in collective group movement. Proceedings of the Royal Society B: Biological Sciences 280 (1752).

  • Mann RP , Faria J, Sumpter DJT and Krause J (2013). The dynamics of audience applause. Journal of The Royal Society Interface 10 (85).
    Media : BBC Radio 4, NPR, Scientific American, Radio New Zealand, RTS 1ère (en Français), NRK (på Norsk/Svenska), Science MagazineBBC NewsThe Times,The GuardianDaily MailSlate, Wissenschaft, SvD

  • Nicolis SC , FernÃndez J, PÃrez-Penichet C, Noda C, Tejera F, Ramos O, Sumpter DJT and Altshuler E (2013). Foraging at the edge of chaos: Internal clock versus external forcing. Physcial Review Letters, 110, 268104.
    Media : PRL editor's choice, Highlights in

  • Dussutour A and Nicolis SC (2013). Flexibility in collective decision-making by ant colonies: Tracking food across space and time (2013). Chaos, Solitons and Fractals, 50: 32-38.

  • Mann RP. , Perna A , Strömbom D , Garnett R, Herbert-Read JE , Sumpter DJT and Ward, AJW (2013). Multi-scale inference of interaction rules in animal groups using Bayesian model selection. PLoS computational biology 9 (3), e1002961.

  • Ma Q , Johansson A , Tero A, Nakagaki T and Sumpter DJT (2013). Current-reinforced random walks for biological problem solving, Royal Society Interface, 10, 2012086.

  • Viana M. P., Fourcassié V, Perna A , da Fontoura Costa L. and Jost C (2013). Accessibility in networks: a useful measure for understanding social insect nest architecture. Chaos, Solitons & Fractals, 46, 38-45.

  • Ma Q (2013). Reinforcement in Biology: Stochastic models of group formation and network construction. Phd thesis, Uppsala University.

  • Granovskiy B (2012). Modeling Collective Decision-Making in Animal Groups. Phd thesis, Uppsala University.

  • Sumpter DJT (2012). David Sumpter. Current Biology, 22(17): R666–R667.

  • Kolm N, Amcoff M, Mann RP and Arnqvist G 20102. Diversification of a food-mimicking male ornament via sensory drive. Current Biology 22, 1440–1443.

  • Sumpter DJT , Mann RP , Perna A (2012). "The modelling cycle for collective animal behaviour", Royal Society Interface.
    doi: 10.1098/​rsfs.(2012).0031

  • Perna A, Granovskiy B , Garnier S, Nicolis SC Labédan M, Theraulaz G, Fourcassié V and Sumpter DJT (2012) Individual rules for trail pattern formation in Argentine ants (Linepithema humile) PLoS Computational Biology, 8(7): e1002592.

  • Gallup AC, Hale JJ, Sumpter DJT , Garnier S, Kacelnik A, Krebs J and Couzin ID (2012) "Visual attention and information transfer in human crowds", Proceedings of the National Academy of Sciences 109 (19), 7245-7250.

  • King A and Sumpter DJT (2012). “Murmurations” Current Biology Volume 22, Issue 4, Pages R112-R114.

  • Granovskiy B , Latty T, Duncan M, Sumpter DJT and Beekman M (2012). "How dancing honey bees keep track of changes: the role of inspector bees." Behavioral Ecology, in press.

  • Nannyonga B , Sumpter DJT , Joseph YT Mugisha, Livingstone S Luboobi (2012). "The Dynamics, Causes and Possible Prevention of Hepatitis E Outbreaks", PloS One 7 (7), e41135

  • Ward AJW, Krause J and Sumpter DJT (2012) Quorum Decision-Making in Foraging Fish Shoals, PloS One 7 (3), e32411

  • Johansson A , Ramsch K, Middendorf M and Sumpter DJT (2012) Tuning positive feedback for signal detection in noisy dynamic environments, Journal of Theoretical Biology, in press.

  • Sumpter DJT , Zabzina N and Nicolis SC (2012) Six predictions about the Decision Making of Animal and Human Groups, Managerial and Decision Economics, 33, 295-309.

  • Cornforth D, Sumpter DJT , Brown S and Brännström A (2012) Synergy and group size in microbial cooperation, American Naturalist, 180, 296-305.

  • 2011
    • Latty T, Ramsch K, Ito K, Nakagaki T, Sumpter DJT , Middendorf M and Beekman M. (2011). “Structure and Formation of Ant Transportation Networks.” Journal of the Royal Society, Interface.

    • Mann RP. (2011). “Bayesian Inference for Identifying Interaction Rules in Moving Animal Groups..” PLoS ONE 6 (8): e22827–.

    • Mann RP , Freeman R, Osborne M, Garnett R, Armstrong C, Meade J, Biro D, Guilford T and Roberts S (2011). “Objectively Identifying Landmark Use and Predicting Flight Trajectories of the Homing Pigeon Using Gaussian Processes.” Journal of the Royal Society, Interface 8 (55): 210–219.

    • Ward AJW, Herbert-Read JE, Sumpter DJT and Krause J (2011). “Fast and Accurate Decisions Through Collective Vigilance in Fish Shoals.” Proceedings of the National Academy of Sciences of the United States of America 108 (6) : 2312–2315.

    • Ma Q , Anders J and Sumpter DJT (2011). “A First Principles Derivation of Animal Group Size Distributions..” Journal of Theoretical Biology 283 (1) (August 21): 35–43.

    • Griesser M, Qi M , Webber S, Bowgen K and Sumpter DJT (2011). “Understanding Animal Group-Size Distributions..” PLoS ONE 6 (8): e23438–.

    • Herbert-Read, James E, Perna A , Richard P. Mann , Timothy M Schaerf, Sumpter DJT and Ashley J W Ward (2011). “Inferring the Rules of Interaction of Shoaling Fish.” Proceedings of the National Academy of Sciences 108 (46): 18726–18731.

    • Bousquet CAH, Sumpter DJT and Manser MB (2011). “Moving Calls: a Vocal Mechanism Underlying Quorum Decisions in Cohesive Groups.” Proceedings of the Royal Society B-Biological Sciences 278 (1711): 1482–1488.

    • Reid CR, Sumpter DJT and Beekman M. (2011). “Optimisation in a Natural System: Argentine Ants Solve the Towers of Hanoi.” The Journal of Experimental Biology 214 (Pt 1): 50–58.

    • Strömbom D (2011). “Collective Motion From Local Attraction.” Journal of Theoretical Biology 283 (1): 145–151.

    • Freeman R, Mann RP , Guilford T and Biro D (2011). “Group Decisions and Individual Differences: Route Fidelity Predicts Flight Leadership in Homing Pigeons (Columba Livia).” Biology Letters 7 (1): 63–66.

    • Nicolis SC. and Dussutour A (2011). “Resource Exploitation Strategies in the Presence of Traffic Between Food Sources.” Bio Systems 103 (1): 73–78.

    • Nicolis SC. and Sumpter DJT . (2011). “A Dynamical Approach to Stock Market Fluctuations.” International Journal of Bifurcation and Chaos 21 (12):3557.

    • Nicolis SC. (2011). “Information Flow and Information Production in a Population System.” Physical Review E (Statistical, Nonlinear, and Soft Matter Physics) 84 (1): 011110.

    • Nicolis SC. , Zabzina N, Latty T and Sumpter DJT (2011). “Collective Irrationality and Positive Feedback.” PLoS ONE 6 (4): e18901.

    • Ito K, Sumpter DJT and Nakagaki T (2010). “Risk Management in Spatio-Temporally Varying Field by True Slime Mold.” Nonlinear Theory and Its Applications, IEICE 1 (1): 26–36.

    • Nicolis H and Nicolis SC (2010). “The Selfish to Egalitarian Transition in Young Children: Developmental Processes Versus Cooperative Transitions.” Nonlinear Dynamics, Psychology and Life Science 14 (3): 257–264.

    • Sumpter DJT (2009). “Group Behaviour: Leadership by Those in Need.” Current Biology 19 (8) : R325–R327.

    • Sumpter DJT , and Pratt SC (2009). “Quorum Responses and Consensus Decision Making.” Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences 364 (1518): 743–753.

    • Buhl J, Hicks K, Miller ER, Persey S, Alinvi O, and Sumpter DJT (2009). “Shape and Efficiency of Wood Ant Foraging Networks.” Behavioral Ecology and Sociobiology 63 (3): 451–460.

    • Yates CA, Erban R, Escudero C, Couzin ID, Buhl J, Kevrekidis IG, Maini PK, and Sumpter DJT (2009). “Inherent Noise Can Facilitate Coherence in Collective Swarm Motion.” Proceedings of the National Academy of Sciences of the United States of America 106 (14) 5464–5469.
      doi:10.1073/pnas.0811195106 .

    • Nicolis C and Nicolis SC (2009). “Propagation of Extremes in Space.” Physical Review E (Statistical, Nonlinear, and Soft Matter Physics) 80 (2): 26201.

    • Dussutour A, Beekman M, Nicolis SC and Bernd Meyer (2009). “Noise Improves Collective Decision-Making by Ants in Dynamic Environments.” Proceedings of the Royal Society of London Series B-Biological Sciences 276 (1677): 4353–4361.

    • Dussutour A, Nicolis SC , G Shephard, Beekman M and Sumpter DJT (2009). “The Role of Multiple Pheromones in Food Recruitment by Ants.” Journal of Experimental Biology 212 (15): 2337–2348.

    • Sumpter DJT , Jens Krause, James R, Couzin ID and Ward AJW (2008). “Consensus Decision Making by Fish.” Current Biology 18 (22): 1773–1777.

    • Sumpter DJT , Buhl J, Biro D, and Couzin ID (2008). “Information Transfer in Moving Animal Groups.” Theory in Biosciences 127 (2): 177–186.

    • Ward AJW, Sumpter DJT , Couzin ID, Hart PJB and Krause J (2008). “Quorum Decision-Making Facilitates Information Transfer in Fish Shoals.” Proceedings of the National Academy of Sciences of the United States of America 105 (19): 6948–6953.

    • Dussutour A, Nicolis SC , Despland E and Stephen J Simpson (2008). “Individual Differences Influence Collective Behaviour in Social Caterpillars.” Animal Behaviour 76: 5–16.

    • Nicolis SC. and Dussutour A (2008). “Self-Organization, Collective Decision Making and Resource Exploitation Strategies in Social Insects.” European Physical Journal B 65 (3): 379–385.

    • Nicolis SC. and Nicolis C (2008). “Extreme Events in Bimodal Systems.” Physical Review E (Statistical, Nonlinear, and Soft Matter Physics) 78 (3): 036222.

    • Nicolis SC. , Despland E and Dussutour A (2008). “Collective Decision-Making and Behavioral Polymorphism in Group Living Organisms.” Journal of Theoretical Biology 254 (3): 580–586.

A new summer school will be planned in a near future.

Summer school in collective behaviour

Uppsala, Sweden, August 19th to 25th, 2012.

This week-long intensive summer school will introduce PhD students to the techniques and tools used in understanding the collective behaviour of animals and humans. We will introduce key concepts in the study of group behavior and provide numerous case studies on bird flocks, fish schools, social insects and human society. Most importantly we will concentrate on presenting methods for data collection and analysis; for mathematical modeling and for computer simulation in a way which accessible for students of all backgrounds and disciplines.

Each day will start with a lecture by David Sumpter based on his book Collective Animal Behaviour. A long lunch will allow for discussion. Then the afternoon session will go in to details of how techniques are applied in this field by other members of the collective behaviour group. The week will be structured as follows.




9:30 - 10:45 Models in collective animal behaviour (chapters 1, 2 and 10)
11:00 - 12:15 Information transfer and synergy (chapter 3 and 10)
12:15 - 14:00 Discussion and lunch.
14:00 - 18:00 Tutorial: Differential equation models. (Stam Nicolis)


9:30 - 10:45 Collective decision-making (chapter 4)
11:00 - 12:15 Collective motion (chapter 5).
12:15 - 14:00 Discussion and lunch.
14:00 - 18:00 Tutorial: Self-propelled particle models. (Daniel Strömbom)


9:30 - 10:45 Guest lecture: Peter Hedström (Institute for Future Studies, Stockholm)
11:00 - 12:15 Guest lecture: Jens Krause (Humbolt University, Berlin)
12:30 - Lunch and Free afternoon.


9:30 - 10:45 Quantifying individuals' interactions.
11:00 - 12:15 Collective structures (chapter 7).
12:15 - 14:00 Discussion and lunch.
14:00 - 18:00 Tutorial session: Automated data analysis and tracking. (Andrea Perna)


9:30 - 10:45 Negative feedback and regulation (chapter 8).
11:00 - 12:15 Individual complexity and Agent-based models (chapter 9).
12:00 - 14:00 Discussion and lunch.
14:00 - 18:00 Tutorial: Model fitting. (Richard Mann)
19:00 - End of summer school party.



The summer school will take place outside of Uppsala at Björkdala conference centre .

The summer school is free to all accepted participants. Accommodation is provided in shared rooms at the conference centre and tasty home cooked food is provided throughout your stay.

List of participants

Michael Anreiter (Barcelona), Zahedeh Bashardanesh (Uppsala), Hjalmar Eriksson (Perimeter Instiute), Josh Kirby (Delaware), Jennifer Miller (Delaware), Catherine E. Offord (Princeton), Yu Sun (Delaware), Roy Harpaz (Weizmann Institute), Klara Wanelik (Oxford), Damien Farine (Oxford), Giovanni Giusti (Barcelona) , David Wheatcroft (Chicago), Johannes Himmelreich (London School of Economics), Juta Kawalerowicz (Oxford), Quan-Xing Liu (Royal Netherlands Institute for Sea Research), Claudia Lopes (London School of Economics), Andres Quinones Paredes (Groningen), Takao Sasaki (Arizona), Arianna Bottinelli (Uppsala), Shyam ranganathan (Uppsala), Natalia Zabzina (Uppsala), James Herbert-Read (Sydney/Uppsala)