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  • 1.
    Bali Swain, Ranjula
    et al.
    Södertörn Univ, Sch Social Sci, Huddinge, Sweden; Stockholm School of Economics, Mistra Ctr Sustainable Markets, Stockholm, Sweden.
    Blomqvist, Björn Rune Helmer
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Sumpter, David J. T.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Last night in Sweden?: Using Gaussian processes to study changing demographics at the level of municipalities2020In: European Journal of Crime, Criminal Law and Criminal Justice, ISSN 0928-9569, E-ISSN 1571-8174, Vol. 28, no 1, p. 46-75Article in journal (Refereed)
    Abstract [en]

    The increased immigration in Western Europe has been linked by some political parties to increased criminality rates. We study the statistical relationship between the proportion of foreign-born to three types of reported criminality - rapes, burglary, and assault. The analysis is based on Swedish municipality level data for 2002-2014, years with significant immigration. Using non-parametric Gaussian processes models, we find that while reported rape rates have increased, they are likely best explained by changes in reporting. The reported burglary rates have decreased, while reported assault rates are positively correlated to the proportion of foreign-born residents in the municipality.

  • 2. Birhane, Abeba
    et al.
    Sumpter, David J. T.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Artificial Intelligence.
    The games we play: critical complexity improves machine learning2022In: HHAI2022: Augmenting Human Intellect / [ed] Stefan Schlobach; María Pérez-Ortiz; Myrthe Tielman, 2022, p. 3-16Conference paper (Refereed)
    Abstract [en]

    When mathematical modelling is applied to capture a complex system, multiple models are often created that characterise different aspects of that system. Often, a model at one level will produce a prediction which is contradictory at another level but both models are accepted because they are both useful. Rather than aiming to build a single unified model of a complex system, the modeller acknowledges the infinity of ways of capturing the system of interest, while offering their own specific insight. We refer to this pragmatic applied approach to complex systems — one which acknowledges that they are incompressible, dynamic, nonlinear, historical, contextual, and value-laden — as Open Machine Learning (Open ML). In this paper we define Open ML and contrast it with some of the grand narratives of ML of two forms: 1) Closed ML, ML which emphasizes learning with minimal human input (e.g. Google’s Alpha Zero) and 2) Partially Open ML, ML which is used to parameterize existing models. To achieve this, we use theories of critical complexity to both evaluate these grand narratives and contrast them with the Open ML approach. Specifically, we deconstruct grand ML ‘theories’ by identifying thirteen ‘games’ played in the ML community. These games lend false legitimacy to models, contribute to over-promise and hype about the capabilities of artificial intelligence, reduce wider participation in the subject, lead to models that exacerbate inequality and cause discrimination and ultimately stifle creativity in research. We argue that best practice in ML should be more consistent with critical complexity perspectives than with rationalist, grand narratives.

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  • 3.
    Blomqvist, Björn R. H.
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Mann, Richard P.
    Univ Leeds, Sch Math, Leeds, W Yorkshire, England.
    Sumpter, David J. T.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Using Bayesian dynamical systems, model averaging and neural networks to determine interactions between socio-economic indicators2018In: PLOS ONE, E-ISSN 1932-6203, Vol. 13, no 5, article id e0196355Article in journal (Refereed)
    Abstract [en]

    Social and economic systems produce complex and nonlinear relationships in the indicator variables that describe them. We present a Bayesian methodology to analyze the dynamical relationships between indicator variables by identifying the nonlinear functions that best describe their interactions. We search for the 'best' explicit functions by fitting data using Bayesian linear regression on a vast number of models and then comparing their Bayes factors. The model with the highest Bayes factor, having the best trade-off between explanatory power and interpretability, is chosen as the 'best' model. To be able to compare a vast number of models, we use conjugate priors, resulting in fast computation times. We check the robustness of our approach by comparison with more prediction oriented approaches such as model averaging and neural networks. Our modelling approach is illustrated using the classical example of how democracy and economic growth relate to each other. We find that the best dynamical model for democracy suggests that long term democratic increase is only possible if the economic situation gets better. No robust model explaining economic development using these two variables was found.

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  • 4.
    Blomqvist, Björn R. H.
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Sumpter, David J. T.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Mann, Richard P.
    Univ Leeds, Sch Math, Dept Stat, Leeds, W Yorkshire, England;Alan Turing Inst, London, England.
    Inferring the dynamics of rising radical right-wing party support using Gaussian processes2019In: Philosophical Transactions. Series A: Mathematical, physical, and engineering science, ISSN 1364-503X, E-ISSN 1471-2962, Vol. 377, no 2160, article id 20190145Article in journal (Refereed)
    Abstract [en]

    The use of classical regression techniques in social science can prevent the discovery of complex, nonlinear mechanisms and often relies too heavily on both the expertise and prior expectations of the data analyst. In this paper, we present a regression methodology that combines the interpretability of traditional, well used, statistical methods with the full predictability and flexibility of Bayesian statistics techniques. Our modelling approach allows us to find and explain the mechanisms behind the rise of Radical Right-wing Populist parties (RRPs) that we would have been unable to find using traditional methods. Using Swedish municipality-level data (2002-2018), we find no evidence that the proportion of foreign-born residents is predictive of increases in RRP support. Instead, education levels and population density are the significant variables that impact the change in support for the RRP, in addition to spatial and temporal control variables. We argue that our methodology, which produces models with considerably better fit of the complexity and nonlinearities often found in social systems, provides a better tool for hypothesis testing and exploration of theories about RRPs and other social movements. This article is part of the theme issue 'Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences'.

  • 5.
    Bottinelli, Arianna
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Sumpter, David
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Silverberg, Jesse
    Wyss Institute for Biologically Inspired Engineering, Harvard University.
    Emergent Structural Mechanisms for High-Density Collective Motion Inspired by Human Crowds2016In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 117, no 22, article id 228301Article in journal (Refereed)
    Abstract [en]

    Collective motion of large human crowds often depends on their density. In extreme cases like heavy metal concerts and black Friday sales events, motion is dominated by physical interactions instead of conventional social norms. Here, we study an active matter model inspired by situations when large groups of people gather at a point of common interest. Our analysis takes an approach developed for jammed granular media and identifies Goldstone modes, soft spots, and stochastic resonance as structurally driven mechanisms for potentially dangerous emergent collective motion.

  • 6.
    Bottinelli, Arianna
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    van Wilgenburg, E.
    Fordham Univ, Dept Biol Sci, Bronx, NY 10458 USA..
    Sumpter, David J. T.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Latty, T.
    Univ Sydney, Sch Biol Sci, Sydney, NSW 2006, Australia..
    Local cost minimization in ant transport networks: from small-scale data to large-scale trade-offs2015In: Journal of the Royal Society Interface, ISSN 1742-5689, E-ISSN 1742-5662, Vol. 12, no 112, article id 20150780Article in journal (Refereed)
    Abstract [en]

    Transport networks distribute resources and information in many human and biological systems. Their construction requires optimization and balance of conflicting criteria such as robustness against disruptions, transport efficiency and building cost. The colonies of the polydomous Australian meat ant Iridomyrmex purpureus are a striking example of such a decentralized network, consisting of trails that connect spatially separated nests. Here we study the rules that underlie network construction in these ants. We find that a simple model of network growth, which we call the minimum linking model (MLM), is sufficient to explain the growth of real ant colonies. For larger networks, the MLM shows a qualitative similarity with a Euclidean minimum spanning tree, prioritizing cost and efficiency over robustness. We introduce a variant of our model to show that a balance between cost, efficiency and robustness can be also reproduced at larger scales than ant colonies. Remarkably, such a balance is influenced by a parameter reflecting the specific features of the modelled transport system. The extended MLM could thus be a suitable source of inspiration for the construction of cheap and efficient transport networks with non-zero robustness, suggesting possible applications in the design of human-made networks.

  • 7. Cornforth, Daniel M.
    et al.
    Sumpter, David J. T.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Brown, Sam P.
    Brannstrom, Ake
    Synergy and Group Size in Microbial Cooperation2012In: American Naturalist, ISSN 0003-0147, E-ISSN 1537-5323, Vol. 180, no 3, p. 296-305Article in journal (Refereed)
    Abstract [en]

    Microbes produce many molecules that are important for their growth and development, and the exploitation of these secretions by nonproducers has recently become an important paradigm in microbial social evolution. Although the production of these public-goods molecules has been studied intensely, little is known of how the benefits accrued and the costs incurred depend on the quantity of public-goods molecules produced. We focus here on the relationship between the shape of the benefit curve and cellular density, using a model assuming three types of benefit functions: diminishing, accelerating, and sigmoidal (accelerating and then diminishing). We classify the latter two as being synergistic and argue that sigmoidal curves are common in microbial systems. Synergistic benefit curves interact with group sizes to give very different expected evolutionary dynamics. In particular, we show that whether and to what extent microbes evolve to produce public goods depends strongly on group size. We show that synergy can create an "evolutionary trap" that can stymie the establishment and maintenance of cooperation. By allowing density-dependent regulation of production (quorum sensing), we show how this trap may be avoided. We discuss the implications of our results on experimental design.

  • 8. Dublon, Ian A. N.
    et al.
    Sumpter, David J. T.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Flying insect swarms2014In: Current Biology, ISSN 0960-9822, E-ISSN 1879-0445, Vol. 24, no 18, p. R828-R830Article in journal (Other academic)
  • 9. Dussutour, A.
    et al.
    Nicolis, S. C.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Shephard, G.
    Beekman, M.
    Sumpter, David J. T.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    The role of multiple pheromones in food recruitment by ants2009In: Journal of Experimental Biology, ISSN 0022-0949, E-ISSN 1477-9145, Vol. 212, no 15, p. 2337-2348Article in journal (Refereed)
    Abstract [en]

    In this paper we investigate the foraging activity of an invasive ant species, the big headed ant Pheidole megacephala. We establish that the ants' behavior is consistent with the use of two different pheromone signals, both of which recruit nestmates. Our experiments suggest that during exploration the ants deposit a long-lasting pheromone that elicits a weak recruitment of nestmates, while when exploiting food the ants deposit a shorter lasting pheromone eliciting a much stronger recruitment. We further investigate experimentally the role of these pheromones under both static and dynamic conditions and develop a mathematical model based on the hypothesis that exploration locally enhances exploitation, while exploitation locally suppresses exploration. The model and the experiments indicate that exploratory pheromone allows the colony to more quickly mobilize foragers when food is discovered. Furthermore, the combination of two pheromones allows colonies to track changing foraging conditions more effectively than would a single pheromone. In addition to the already known causes for the ecological success of invasive ant species, our study suggests that their opportunistic strategy of rapid food discovery and ability to react to changes in the environment may have strongly contributed to their dominance over native species.

  • 10.
    Dussutour, Audrey
    et al.
    Toulouse Univ, CNRS, Res Ctr Anim Cognit CRCA, Ctr Integrat Biol CBI,UPS, F-31062 Toulouse, France.
    Ma, Qi
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Sumpter, David J. T.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Phenotypic variability predicts decision accuracy in unicellular organisms2019In: Proceedings of the Royal Society of London. Biological Sciences, ISSN 0962-8452, E-ISSN 1471-2954, Vol. 286, no 1896, article id 20182825Article in journal (Refereed)
    Abstract [en]

    When deciding between different options, animals including humans face the dilemma that fast decisions tend to be erroneous, whereas accurate decisions tend to be relatively slow. Recently, it has been suggested that differences in the efficacy with which animals make a decision relate closely to individual behavioural differences. In this paper, we tested this hypothesis in a unique unicellular organism, the slime mould Physarum polycephalum. We first confirmed that slime moulds differed consistently in their exploratory behaviour from 'fast' to 'slow' explorers. Second, we showed that slow explorers made more accurate decisions than fast explorers. Third, we demonstrated that slime moulds integrated food cues in time and achieved higher accuracy when sampling time was longer. Lastly, we showed that in a competition context, fast explorers excelled when a single food source was offered, while slow explorers excelled when two food sources varying in quality were offered. Our results revealed that individual differences in accuracy were partly driven by differences in exploratory behaviour. These findings support the hypothesis that decision-making abilities are associated with behavioural types, even in unicellular organisms.

  • 11. Gallup, Andrew C.
    et al.
    Hale, Joseph J.
    Sumpter, David J. T.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Garnier, Simon
    Kacelnik, Alex
    Krebs, John R.
    Couzin, Iain D.
    Visual attention and the acquisition of information in human crowds2012In: Proceedings of the National Academy of Sciences of the United States of America, ISSN 0027-8424, E-ISSN 1091-6490, Vol. 109, no 19, p. 7245-7250Article in journal (Refereed)
    Abstract [en]

    Pedestrian crowds can form the substrate of important socially contagious behaviors, including propagation of visual attention, violence, opinions, and emotional state. However, relating individual to collective behavior is often difficult, and quantitative studies have largely used laboratory experimentation. We present two studies in which we tracked the motion and head direction of 3,325 pedestrians in natural crowds to quantify the extent, influence, and context dependence of socially transmitted visual attention. In our first study, we instructed stimulus groups of confederates within a crowd to gaze up to a single point atop of a building. Analysis of passersby shows that visual attention spreads unevenly in space and that the probability of pedestrians adopting this behavior increases as a function of stimulus group size before saturating for larger groups. We develop a model that predicts that this gaze response will lead to the transfer of visual attention between crowd members, but it is not sufficiently strong to produce a tipping point or critical mass of gaze-following that has previously been predicted for crowd dynamics. A second experiment, in which passersby were presented with two stimulus confederates performing suspicious/irregular activity, supports the predictions of our model. This experiment reveals that visual interactions between pedestrians occur primarily within a 2-m range and that gaze-copying, although relatively weak, can facilitate response to relevant stimuli. Although the above aspects of gaze-following response are reproduced robustly between experimental setups, the overall tendency to respond to a stimulus is dependent on spatial features, social context, and sex of the passerby.

  • 12.
    Granovskiy, Boris
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Gold, Jason M.
    Sumpter, David J. T.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Goldstone, Robert L.
    Integration of Social Information by Human Groups2015In: Topics in Cognitive Science, ISSN 1756-8757, E-ISSN 1756-8765, Vol. 7, no 3, p. 469-493Article in journal (Refereed)
    Abstract [en]

    We consider a situation in which individuals search for accurate decisions without direct feedback on their accuracy, but with information about the decisions made by peers in their group. The wisdom of crowds hypothesis states that the average judgment of many individuals can give a good estimate of, for example, the outcomes of sporting events and the answers to trivia questions. Two conditions for the application of wisdom of crowds are that estimates should be independent and unbiased. Here, we study how individuals integrate social information when answering trivia questions with answers that range between 0% and 100% (e.g., What percentage of Americans are left-handed?). We find that, consistent with the wisdom of crowds hypothesis, average performance improves with group size. However, individuals show a consistent bias to produce estimates that are insufficiently extreme. We find that social information provides significant, albeit small, improvement to group performance. Outliers with answers far from the correct answer move toward the position of the group mean. Given that these outliers also tend to be nearer to 50% than do the answers of other group members, this move creates group polarization away from 50%. By looking at individual performance over different questions we find that some people are more likely to be affected by social influence than others. There is also evidence that people differ in their competence in answering questions, but lack of competence is not significantly correlated with willingness to change guesses. We develop a mathematical model based on these results that postulates a cognitive process in which people first decide whether to take into account peer guesses, and if so, to move in the direction of these guesses. The size of the move is proportional to the distance between their own guess and the average guess of the group. This model closely approximates the distribution of guess movements and shows how outlying incorrect opinions can be systematically removed from a group resulting, in some situations, in improved group performance. However, improvement is only predicted for cases in which the initial guesses of individuals in the group are biased.

  • 13.
    Granovskiy, Boris
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Latty, Tanya
    Duncan, Michael
    Sumpter, David J. T.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Beekman, Madeleine
    How dancing honey bees keep track of changes: the role of inspector bees2012In: Behavioral Ecology, ISSN 1045-2249, E-ISSN 1465-7279, Vol. 23, no 3, p. 588-596Article in journal (Refereed)
    Abstract [en]

    How do honey bees track changes in their foraging environment? Previously, 2 complementary mechanisms have been identified by which bees can effectively switch between food sources when their relative quality changes. First, an increase in profitability of a food source elicits an increase in waggle dances (the bees' recruitment mechanism) for that source. Second, bees that have retired from foraging at a food source make occasional inspection visits to that food source and resume foraging if its quality improves. Here, we investigate, using both field experiments and a mathematical model, the relative importance of these 2 mechanisms. By manipulating dance information available to the bees, we find that when food sources change quality frequently, inspector bees provide a rapid response to changes, whereas the waggle dance contributes to a response over a longer time period. The bees' ability to switch feeders without dance language information was found to be robust with respect to the spatial configuration of the feeders. Our results show that individual memory, in the form of inspector bees, and collective communication can interact to allow an insect colony to adapt to changes on both short and long timescales.

  • 14.
    Gyllingberg, Linnéa
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Birhane, Abeba
    Mozilla Fdn, 2 Harrison St,Suite 175, San Francisco, CA 94105 USA..
    Sumpter, David J. T.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology.
    The lost art of mathematical modelling2023In: Mathematical Biosciences, ISSN 0025-5564, E-ISSN 1879-3134, Vol. 362, article id 109033Article in journal (Refereed)
    Abstract [en]

    We provide a critique of mathematical biology in light of rapid developments in modern machine learning. We argue that out of the three modelling activities - (1) formulating models; (2) analysing models; and (3) fitting or comparing models to data - inherent to mathematical biology, researchers currently focus too much on activity (2) at the cost of (1). This trend, we propose, can be reversed by realising that any given biological phenomenon can be modelled in an infinite number of different ways, through the adoption of a pluralistic approach, where we view a system from multiple, different points of view. We explain this pluralistic approach using fish locomotion as a case study and illustrate some of the pitfalls - universalism, creating models of models, etc. - that hinder mathematical biology. We then ask how we might rediscover a lost art: that of creative mathematical modelling.

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  • 15.
    Gyllingberg, Linnéa
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Sumpter, David J. T.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology.
    Brännström, Åke
    Finding analytical approximations for discrete, stochastic, individual-based models of ecology2023In: Mathematical Biosciences, ISSN 0025-5564, E-ISSN 1879-3134, Vol. 365Article in journal (Refereed)
    Abstract [en]

    Discrete time, spatially extended models play an important role in ecology, modelling population dynamics of species ranging from micro-organisms to birds. An important question is how ’bottom up’, individual-based models can be approximated by ’top down’ models of dynamics. Here, we study a class of spatially explicit individual-based models with contest competition: where species compete for space in local cells and then disperse to nearby cells. We start by describing simulations of the model, which exhibit large-scale discrete oscillations and characterize these oscillations by measuring spatial correlations. We then develop two new approximate descriptions of the resulting spatial population dynamics. The first is based on local interactions of the individuals and allows us to give a difference equation approximation of the system over small dispersal distances. The second approximates the long-range interactions of the individual-based model. These approximations capture demographic stochasticity from the individual-based model and show that dispersal stabilizes population dynamics. We calculate extinction probability for the individual-based model and show convergence between the local approximation and the non-spatial global approximation of the individual-based model as dispersal distance and population size simultaneously tend to infinity. Our results provide new approximate analytical descriptions of a complex bottom-up model and deepen understanding of spatial population dynamics.

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  • 16.
    Gyllingberg, Linnéa
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Szorkovszky, Alex
    Univ Oslo, RITMO Ctr Interdisciplinary Studies Rhythm Time &, Oslo, Norway..
    Sumpter, David J. T.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology.
    Using neuronal models to capture burst-and-glide motion and leadership in fish2023In: Journal of the Royal Society Interface, ISSN 1742-5689, E-ISSN 1742-5662, Vol. 20, no 204Article in journal (Refereed)
    Abstract [en]

    While mathematical models, in particular self-propelled particle models, capture many properties of large fish schools, they do not always capture the interactions of smaller shoals. Nor do these models tend to account for the use of intermittent locomotion, often referred to as burst-and-glide, by many species. In this paper, we propose a model of social burst-and-glide motion by combining a well-studied model of neuronal dynamics, the FitzHugh-Nagumo model, with a model of fish motion. We first show that our model can capture the motion of a single fish swimming down a channel. Extending to a two-fish model, where visual stimulus of a neighbour affects the internal burst or glide state of the fish, we observe a rich set of dynamics found in many species. These include: leader-follower behaviour; periodic changes in leadership; apparently random (i.e. chaotic) leadership change; and tit-for-tat turn taking. Moreover, unlike previous studies where a randomness is required for leadership switching to occur, we show that this can instead be the result of deterministic interactions. We give several empirically testable predictions for how bursting fish interact and discuss our results in light of recently established correlations between fish locomotion and brain activity.

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  • 17.
    Gyllingberg, Linnéa
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Tian, Yu
    Sumpter, David J. T.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Artificial Intelligence. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control.
    A minimal model of cognition based on oscillatory and reinforcement processesManuscript (preprint) (Other academic)
    Abstract [en]

    Building mathematical models of brains is difficult because of the sheer complexity of the problem. One potential approach is to start by identifying models of basal cognition, which give an abstract representation of a range organisms without central nervous systems, including fungi, slime moulds and bacteria. We propose one such model, demonstrating how a combination of oscillatory and current-based reinforcement processes can be used to couple resources in an efficient manner. We first show that our model connects resources in an efficient manner when the environment is constant. We then show that in an oscillatory environment our model builds efficient solutions, provided the environmental oscillations are sufficiently out of phase. We show that amplitude differences can promote efficient solutions and that the system is robust to frequency differences. We identify connections between our model and basal cognition in biological systems and slime moulds, in particular, showing how oscillatory and problem-solving properties of these systems are captured by our model.

  • 18.
    Herbert-Read, James E.
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Buhl, Jerome
    Univ Sydney, Sch Biol Sci, Sydney, NSW 2006, Australia.;Univ Sydney, Charles Perkins Ctr, Sydney, NSW 2006, Australia.;Univ Adelaide, Sch Agr, Adelaide, SA 5005, Australia..
    Hu, Feng
    Chongqing Normal Univ, Coll Phys & Elect Engn, Chongqing 400047, Peoples R China..
    Ward, Ashley J. W.
    Univ Sydney, Sch Biol Sci, Sydney, NSW 2006, Australia..
    Sumpter, David J. T.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Initiation and spread of escape waves within animal groups2015In: ROYAL SOCIETY OPEN SCIENCE, ISSN 2054-5703, Vol. 2, no 4, article id 140355Article in journal (Refereed)
    Abstract [en]

    The exceptional reactivity of animal collectives to predatory attacks is thought to be owing to rapid, but local, transfer of information between group members. These groups turn together in unison and produce escape waves. However, it is not clear how escape waves are created from local interactions, nor is it understood how these patterns are shaped by natural selection. By startling schools of fish with a simulated attack in an experimental arena, we demonstrate that changes in the direction and speed by a small percentage of individuals that detect the danger initiate an escape wave. This escape wave consists of a densely packed band of individuals that causes other school members to change direction. In the majority of cases, this wave passes through the entire group. We use a simulation model to demonstrate that this mechanism can, through local interactions alone, produce arbitrarily large escape waves. In the model, when we set the group density to that seen in real fish schools, we find that the risk to the members at the edge of the group is roughly equal to the risk of those within the group. Our experiments and modelling results provide a plausible explanation for how escape waves propagate in nature without centralized control.

  • 19. Herbert-Read, James E.
    et al.
    Perna, Andrea
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Mann, Richard P.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Schaerf, Timothy M.
    Sumpter, David J. T.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Ward, Ashley J. W.
    Inferring the rules of interaction of shoaling fish2011In: Proceedings of the National Academy of Sciences of the United States of America, ISSN 0027-8424, E-ISSN 1091-6490, Vol. 108, no 46, p. 18726-18731Article in journal (Refereed)
    Abstract [en]

    Collective motion, where large numbers of individuals move synchronously together, is achieved when individuals adopt interaction rules that determine how they respond to their neighbors' movements and positions. These rules determine how group-living animals move, make decisions, and transmit information between individuals. Nonetheless, few studies have explicitly determined these interaction rules in moving groups, and very little is known about the interaction rules of fish. Here, we identify three key rules for the social interactions of mosquitofish (Gambusia holbrooki): (i) Attraction forces are important in maintaining group cohesion, while we find only weak evidence that fish align with their neighbor's orientation; (ii) repulsion is mediated principally by changes in speed; (iii) although the positions and directions of all shoal members are highly correlated, individuals only respond to their single nearest neighbor. The last two of these rules are different from the classical models of collective animal motion, raising new questions about how fish and other animals self-organize on the move.

  • 20.
    Herbert-Read, James E.
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Romenskyy, Maxym
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Sumpter, David J. T.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    A Turing test for collective motion2015In: Biology Letters, ISSN 1744-9561, E-ISSN 1744-957X, Vol. 11, no 12, article id 20150674Article in journal (Refereed)
    Abstract [en]

    A widespread problem in biological research is assessing whether a model adequately describes some real-world data. But even if a model captures the large-scale statistical properties of the data, should we be satisfied with it? We developed a method, inspired by Alan Turing, to assess the effectiveness of model fitting. We first built a self-propelled particle model whose properties (order and cohesion) statistically matched those of real fish schools. We then asked members of the public to play an online game (a modified Turing test) in which they attempted to distinguish between the movements of real fish schools or those generated by the model. Even though the statistical properties of the real data and the model were consistent with each other, the public could still distinguish between the two, highlighting the need for model refinement. Our results demonstrate that we can use 'citizen science' to cross-validate and improve model fitting not only in the field of collective behaviour, but also across a broad range of biological systems.

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  • 21.
    Herbert-Read, James E.
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics. Stockholm University, Department of Zoology.
    Rosén, Emil
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Szorkovszky, Alex
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Ioannou, Christos C.
    University of Bristol, School of Biological Science.
    Rogell, Björn
    Stockholm University, Department of Zoology.
    Perna, Andrea
    Roehampton University, Department of Life Sciences.
    Ramnarine, Indar W.
    The University of the West Indies, Department of Life Science.
    Kotrschal, Alexander
    Stockholm University, Department of Zoology.
    Kolm, Niclas
    Stockholm University, Department of Zoology.
    Krause, Jens
    Humboldt-University zu Berlin, Albrecht Daniel Thaer-Institut, Faculty of Life Science; Leibniz-Institute of Freshwater Ecology and Inland Fisheries, Department of Biology and Ecology of Fishes.
    Sumpter, David J. T.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    How predation shapes the social interaction rules of shoaling fish2017In: Proceedings of the Royal Society of London. Biological Sciences, ISSN 0962-8452, E-ISSN 1471-2954, Vol. 284, no 1861, article id 20171126Article in journal (Refereed)
    Abstract [en]

    Predation is thought to shape the macroscopic properties of animal groups, making moving groups more cohesive and coordinated. Precisely how predation has shaped individuals' fine-scale social interactions in natural populations, however, is unknown. Using high-resolution tracking data of shoaling fish (Poecilia reticulata) from populations differing in natural predation pressure, we show how predation adapts individuals' social interaction rules. Fish originating from high predation environments formed larger, more cohesive, but not more polarized groups than fish from low predation environments. Using a new approach to detect the discrete points in time when individuals decide to update their movements based on the available social cues, we determine how these collective properties emerge from individuals' microscopic social interactions. We first confirm predictions that predation shapes the attraction-repulsion dynamic of these fish, reducing the critical distance at which neighbours move apart, or come back together. While we find strong evidence that fish align with their near neighbours, we do not find that predation shapes the strength or likelihood of these alignment tendencies. We also find that predation sharpens individuals' acceleration and deceleration responses, implying key perceptual and energetic differences associated with how individuals move in different predation regimes. Our results reveal how predation can shape the social interactions of individuals in groups, ultimately driving differences in groups' collective behaviour.

  • 22.
    Herbert-Read, James E.
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics. Stockholm Univ, Dept Zool, S-10691 Stockholm, Sweden.
    Ward, A. J. W.
    Univ Sydney, Sch Life & Environm Sci, Sydney, NSW 2006, Australia.
    Sumpter, David J. T.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Mann, R. P.
    Univ Leeds, Sch Math, Dept Stat, Leeds LS2 9JT, W Yorkshire, England.
    Escape path complexity and its context dependency in Pacific blue-eyes (Pseudomugil signifer)2017In: Journal of Experimental Biology, ISSN 0022-0949, E-ISSN 1477-9145, Vol. 220, no 11, p. 2076-2081Article in journal (Refereed)
    Abstract [en]

    The escape paths prey animals take following a predatory attack appear to be highly unpredictable - a property that has been described as 'protean behaviour'. Here, we present a method of quantifying the escape paths of individual animals using a path complexity approach. When individual fish (Pseudomugil signifer) were attacked, we found that a fish's movement path rapidly increased in complexity following the attack. This path complexity remained elevated (indicating a more unpredictable path) for a sustained period (at least 10 s) after the attack. The complexity of the path was context dependent: paths were more complex when attacks were made closer to the fish, suggesting that these responses are tailored to the perceived level of threat. We separated out the components of speed and turning rate changes to determine which of these components contributed to the overall increase in path complexity following an attack. We found that both speed and turning rate measures contributed similarly to an individual's path complexity in absolute terms. Overall, our work highlights the context-dependent escape responses that animals use to avoid predators, and also provides a method for quantifying the escape paths of animals.

  • 23.
    Isdory, Augustino
    et al.
    Univ Dar Es Salaam, Dept Math, Dar Es Salaam, Tanzania..
    Mureithi, Eunice W.
    Univ Dar Es Salaam, Dept Math, Dar Es Salaam, Tanzania..
    Sumpter, David J. T.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    The Impact of Human Mobility on HIV Transmission in Kenya2015In: PLOS ONE, E-ISSN 1932-6203, Vol. 10, no 11, article id e0142805Article in journal (Refereed)
    Abstract [en]

    Disease spreads as a result of people moving and coming in contact with each other. Thus the mobility patterns of individuals are crucial in understanding disease dynamics. Here we study the impact of human mobility on HIV transmission in different parts of Kenya. We build an SIR metapopulation model that incorporates the different regions within the country. We parameterise the model using census data, HIV data and mobile phone data adopted to track human mobility. We found that movement between different regions appears to have a relatively small overall effect on the total increase in HIV cases in Kenya. However, the most important consequence of movement patterns was transmission of the disease from high infection to low prevalence areas. Mobility slightly increases HIV incidence rates in regions with initially low HIV prevalences and slightly decreases incidences in regions with initially high HIV prevalence. We discuss how regional HIV models could be used in public-health planning. This paper is a first attempt to model spread of HIV using mobile phone data, and we also discuss limitations to the approach.

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  • 24.
    Johansson, Anders
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Ramsch, Kai
    Middendorf, Martin
    Sumpter, David J. T.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Tuning positive feedback for signal detection in noisy dynamic environments2012In: Journal of Theoretical Biology, ISSN 0022-5193, E-ISSN 1095-8541, Vol. 309, p. 88-95Article in journal (Refereed)
    Abstract [en]

    Learning from previous actions is a key feature of decision-making. Diverse biological systems, from neuronal assemblies to insect societies, use a combination of positive feedback and forgetting of stored memories to process and respond to input signals. Here we look how these systems deal with a dynamic two-armed bandit problem of detecting a very weak signal in the presence of a high degree of noise. We show that by tuning the form of positive feedback and the decay rate to appropriate values, a single tracking variable can effectively detect dynamic inputs even in the presence of a large degree of noise. In particular, we show that when tuned appropriately a simple positive feedback algorithm is Fisher efficient, in that it can track changes in a signal on a time of order L(h)= (vertical bar h vertical bar/sigma)(-2), where vertical bar h vertical bar is the magnitude of the signal and sigma the magnitude of the noise.

  • 25.
    Kotrschal, Alexander
    et al.
    Stockholm Univ, Dept Zool Ethol, Stockholm, Sweden.;Wageningen Univ, Behav Ecol, Wageningen, Netherlands..
    Szorkovszky, Alexander
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics. Stockholm Univ, Dept Zool Ethol, Stockholm, Sweden..
    Herbert-Read, James
    UniversityofCambridge, Dept Zool, Cambridge, England.;Lund Univ, Aquat Ecol, Lund, Sweden..
    Bloch, Natasha, I
    Univ Los Andes, Dept Biomed Engn, Bogota, Colombia..
    Romenskyy, Maksym
    Imperial Coll London, Dept Life Sci, London, England..
    Buechel, Severine Denise
    Stockholm Univ, Dept Zool Ethol, Stockholm, Sweden..
    Eslava, Ada Fontrodona
    Stockholm Univ, Dept Zool Ethol, Stockholm, Sweden.;Univ St Andrews, Ctr Biol Divers, St Andrews, Fife, Scotland..
    Alos, Laura Sanchez
    Stockholm Univ, Dept Zool Ethol, Stockholm, Sweden..
    Zeng, Hongli
    Nanjing Univ Posts & Telecommmunicat, Sch Sci, Nanjing, Peoples R China..
    Le Foll, Audrey
    Stockholm Univ, Dept Zool Ethol, Stockholm, Sweden..
    Braux, Ganael
    Stockholm Univ, Dept Zool Ethol, Stockholm, Sweden..
    Pelckmans, Kristiaan
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control.
    Mank, Judith E.
    UCL, London, England.;Univ British Columbia, Dept Zool, Vancouver, BC, Canada..
    Sumpter, David J. T.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Kolm, Niclas
    Stockholm Univ, Dept Zool Ethol, Stockholm, Sweden..
    Rapid evolution of coordinated and collective movement in response to artificial selection2020In: Science Advances, E-ISSN 2375-2548, Vol. 6, no 49, article id eaba3148Article in journal (Refereed)
    Abstract [en]

    Collective motion occurs when individuals use social interaction rules to respond to the movements and positions of their neighbors. How readily these social decisions are shaped by selection remains unknown. Through artificial selection on fish (guppies, Poecilia reticulata) for increased group polarization, we demonstrate rapid evolution in how individuals use social interaction rules. Within only three generations, groups of polarization-selected females showed a 15% increase in polarization, coupled with increased cohesiveness, compared to fish from control lines. Although lines did not differ in their physical swimming ability or exploratory behavior, polarization-selected fish adopted faster speeds, particularly in social contexts, and showed stronger alignment and attraction responses to multiple neighbors. Our results reveal the social interaction rules that change when collective behavior evolves.

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  • 26.
    Kotrschal, Alexander
    et al.
    Stockholm Univ, Dept Zool, SE-10691 Stockholm, Sweden.
    Szorkovszky, Alexander
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Romenskyy, Maksym
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Perna, Andrea
    Department of Life Sciences, University of Roehampton, London, United Kingdom.
    Buechel, Severine D.
    Stockholm Univ, Dept Zool, SE-10691 Stockholm, Sweden.
    Zeng, Hong-Li
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Pelckmans, Kristiaan
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Sumpter, David J. T.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Kolm, Niclas
    Stockholm Univ, Dept Zool, SE-10691 Stockholm, Sweden.
    Brain size does not impact shoaling dynamics in unfamiliar groups of guppies (Poecilia reticulata)2018In: Behavioural Processes, ISSN 0376-6357, E-ISSN 1872-8308, Vol. 147, p. 13-20Article in journal (Refereed)
    Abstract [en]

    Collective movement is achieved when individuals adopt local rules to interact with their neighbours. How the brain processes information about neighbours' positions and movements may affect how individuals interact in groups. As brain size can determine such information processing it should impact collective animal movement. Here we investigate whether brain size affects the structure and organisation of newly forming fish shoals by quantifying the collective movement of guppies (Poecilia reticulata) from large- and small-brained selection lines, with known differences in learning and memory. We used automated tracking software to determine shoaling behaviour of single-sex groups of eight or two fish and found no evidence that brain size affected the speed, group size, or spatial and directional organisation of fish shoals. Our results suggest that brain size does not play an important role in how fish interact with each other in these types of moving groups of unfamiliar individuals. Based on these results, we propose that shoal dynamics are likely to be governed by relatively basic cognitive processes that do not differ in these brain size selected lines of guppies.

  • 27.
    Levens, Watson
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Univ Dar es Salaam, Dept Math, Dar Es Salaam, Tanzania..
    Szorkovszky, Alex
    Univ Oslo, Dept Informat, Oslo, Norway.;Univ Oslo, RITMO, Oslo, Norway..
    Sumpter, David J. T.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control.
    Friend of a friend models of network growth2022In: Royal Society Open Science, E-ISSN 2054-5703, Vol. 9, no 10, article id 221200Article in journal (Refereed)
    Abstract [en]

    One of the best-known models in network science is preferential attachment. In this model, the probability of attaching to a node depends on the degree of all nodes in the population, and thus depends on global information. In many biological, physical and social systems, however, interactions between individuals depend only on local information. Here, we investigate a truly local model of network formation-based on the idea of a friend of a friend-with the following rule: individuals choose one node at random and link to it with probability p, then they choose a neighbour of that node and link with probability q. Our model produces power-laws with empirical exponents ranging from 1.5 upwards and clustering coefficients ranging from 0 up to 0.5 (consistent with many real networks). For small p and q = 1, the model produces super-hub networks, and we prove that for p = 0 and q = 1, the proportion of non-hubs tends to 1 as the network grows. We show that power-law degree distributions, small world clustering and super-hub networks are all outcomes of this, more general, yet conceptually simple model.

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  • 28.
    Lihoreau, Mathieu
    et al.
    Univ Sydney, Charles Perkins Ctr, Sydney, NSW 2006, Australia.;CNRS, Ctr Rech Cognit Anim, F-31062 Toulouse, France.;UPS, Ctr Rech Cognit Anim, F-31062 Toulouse, France..
    Clarke, Ireni M.
    Univ Sydney, Charles Perkins Ctr, Sydney, NSW 2006, Australia..
    Buhl, Jerome
    Univ Sydney, Charles Perkins Ctr, Sydney, NSW 2006, Australia.;Univ Adelaide, Sch Agr Food & Wine, Adelaide, SA 5005, Australia..
    Sumpter, David J. T.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Simpson, Stephen J.
    Univ Sydney, Charles Perkins Ctr, Sydney, NSW 2006, Australia..
    Collective selection of food patches in Drosophila2016In: Journal of Experimental Biology, ISSN 0022-0949, E-ISSN 1477-9145, Vol. 219, no 5, p. 668-675Article in journal (Refereed)
    Abstract [en]

    The fruit fly Drosophila melanogaster has emerged as a model organism for research on social interactions. Although recent studies have described how individuals interact on foods for nutrition and reproduction, the complex dynamics by which groups initially develop and disperse have received little attention. Here we investigated the dynamics of collective foraging decisions by D. melanogaster and their variation with group size and composition. Groups of adults and larvae facing a choice between two identical, nutritionally balanced food patches distributed themselves asymmetrically, thereby exploiting one patch more than the other. The speed of the collective decisions increased with group size, as a result of flies joining foods faster. However, smaller groups exhibited more pronounced distribution asymmetries than larger ones. Using computer simulations, we show how these non-linear phenomena can emerge from social attraction towards occupied food patches, whose effects add up or compete depending on group size. Our results open new opportunities for exploring complex dynamics of nutrient selection in simple and genetically tractable groups.

  • 29.
    Lindholm, Andreas
    et al.
    Annotell, Göteborg, Sweden.
    Wahlström, Niklas
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Artificial Intelligence.
    Lindsten, Fredrik
    Linköpings universitet, Sweden.
    Schön, Thomas B.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Artificial Intelligence.
    Machine learning: a first course for engineers and scientists2022Book (Other academic)
    Abstract [en]

    This book introduces machine learning for readers with some background in basic linear algebra, statistics, probability, and programming. In a coherent statistical framework it covers a selection of supervised machine learning methods, from the most fundamental (k-NN, decision trees, linear and logistic regression) to more advanced methods (deep neural networks, support vector machines, Gaussian processes, random forests and boosting), plus commonly-used unsupervised methods (generative modeling, k-means, PCA, autoencoders and generative adversarial networks). Careful explanations and pseudo-code are presented for all methods. The authors maintain a focus on the fundamentals by drawing connections between methods and discussing general concepts such as loss functions, maximum likelihood, the bias-variance decomposition, ensemble averaging, kernels and the Bayesian approach along with generally useful tools such as regularization, cross validation, evaluation metrics and optimization methods. The final chapters offer practical advice for solving real-world supervised machine learning problems and on ethical aspects of modern machine learning

  • 30.
    Liu, Yu
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Sumpter, David
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Insights into resource consumption, cross-feeding, system collapse, stability and biodiversity from an artificial ecosystem2017In: Journal of the Royal Society Interface, ISSN 1742-5689, E-ISSN 1742-5662, Vol. 14, no 126, article id 20160816Article in journal (Refereed)
    Abstract [en]

    Community ecosystems at very different levels of biological organization often have similar properties. Coexistence of multiple species, cross-feeding, biodiversity and fluctuating population dynamics are just a few of the properties that arise in a range of ecological settings. Here we develop a bottom-up model of consumer-resource interactions, in the form of an artificial ecosystem ``number soup'', that reflects basic properties of many bacterial and other community ecologies. We demonstrate four key properties of the number soup model: (1) Communities self-organise so that all available resources are fully consumed; (2) Reciprocal cross-feeding is a common evolutionary outcome, which evolves in a number of stages, and many transitional species are involved; (3) The evolved ecosystems are often ``robust yet fragile'', with keystone species required to prevent the whole system from collapsing; (4) Non-equilibrium dynamics and chaotic patterns are general properties, readily generating rich biodiversity. These properties have been observed in empirical ecosystems, ranging from bacteria to rainforests. Establishing similar properties in an evolutionary model as simple as the number soup suggests that these four properties are ubiquitous features of all community ecosystems, and raises questions about how we interpret ecosystem structure in the context of natural selection.

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    Liu and Sumpter 2017
  • 31.
    Liu, Yu
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Sumpter, David J. T.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Is the golden ratio a universal constant for self-replication?2018In: PLOS ONE, E-ISSN 1932-6203, Vol. 13, no 7, article id e0200601Article in journal (Other academic)
    Abstract [en]

    The golden ratio, ϕ = 1.61803..., has often been found in connection with biological phenomena, ranging from spirals in sunflowers to gene frequency. One example where the golden ratio often arises is in self-replication, having its mathematical origins in Fibonacci's sequence for "rabbit reproduction". Recently, it has been claimed that ϕ determines the ratio between the number of different nucleobases in human genome. Such empirical examples continue to give credence to the idea that the golden ratio is a universal constant, not only in mathematics but also for biology. In this paper, we employ a general framework for chemically realistic self-replicating reaction systems and investigate whether the ratio of chemical species population follows "universal constants". We find that many self-replicating systems can be characterised by an algebraic number, which, in some cases, is the golden ratio. However, many other algebraic numbers arise from these systems, and some of them—such as and 1.22074... which is also known as the 3rd lower golden ratio—arise more frequently in self-replicating systems than the golden ratio. The "universal constants" in these systems arise as roots of a limited number of distinct characteristic equations. In addition, these "universal constants" are transient behaviours of self-replicating systems, corresponding to the scenario that the resource inside the system is infinite, which is not always the case in practice. Therefore, we argue that the golden ratio should not be considered as a special universal constant in self-replicating systems, and that the ratios between different chemical species only go to certain numbers under some idealised scenarios.

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  • 32.
    Liu, Yu
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Sumpter, David J. T.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Mathematical modeling reveals spontaneous emergence of self-replication in chemical reaction systems2018In: Journal of Biological Chemistry, ISSN 0021-9258, E-ISSN 1083-351X, Vol. 293, no 49, p. 18854-18863Article in journal (Refereed)
    Abstract [en]

    Explaining the origin of life requires us to elucidate how self-replication arises. To be specific, how can a self-replicating entity develop spontaneously from a chemical reaction system in which no reaction is self-replicating? Previously proposed mathematical models either supply an explicit framework for a minimal living system or consider only catalyzed reactions, and thus fail to provide a comprehensive theory. Here, we set up a general mathematical model for chemical reaction systems that properly accounts for energetics, kinetics, and the conservation law. We found that 1) some systems are collectively catalytic, a mode whereby reactants are transformed into end products with the assistance of intermediates (as in the citric acid cycle), whereas some others are self-replicating, that is, different parts replicate each other and the system self-replicates as a whole (as in the formose reaction, in which sugar is replicated from form-aldehyde); 2) side reactions do not always inhibit such systems; 3) randomly chosen chemical universes (namely random artificial chemistries) often contain one or more such systems; 4) it is possible to construct a self-replicating system in which the entropy of some parts spontaneously decreases, in a manner similar to that discussed by Schrodinger; and 5) complex self-replicating molecules can emerge spontaneously and relatively easily from simple chemical reaction systems through a sequence of transitions. Together, these results start to explain the origins of prebiotic evolution.

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  • 33.
    Lo, Tiffany Y. Y.
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Probability Theory and Combinatorics.
    Levens, Watson
    University of Dar es Salaam, Tanzania.
    Sumpter, David J. T.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Artificial Intelligence.
    Properties of the 'friend of a friend' model for network generationManuscript (preprint) (Other academic)
  • 34.
    Ma, Qi
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Johansson, Anders
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Sumpter, David J. T.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    A first principles derivation of animal group size distributions2011In: Journal of Theoretical Biology, ISSN 0022-5193, E-ISSN 1095-8541, Vol. 283, no 1, p. 35-43Article in journal (Refereed)
    Abstract [en]

    Several empirical studies have shown that the animal group size distribution of many species can be well fit by power laws with exponential truncation. A striking empirical result due to Niwa is that the exponent in these power laws is one and the truncation is determined by the average group size experienced by an individual. This distribution is known as the logarithmic distribution. In this paper we provide first principles derivation of the logarithmic distribution and other truncated power laws using a site-based merge and split framework. In particular, we investigate two such models. Firstly, we look at a model in which groups merge whenever they meet but split with a constant probability per time step. This generates a distribution similar, but not identical to the logarithmic distribution. Secondly, we propose a model, based on preferential attachment, that produces the logarithmic distribution exactly. Our derivation helps explain why logarithmic distributions are so widely observed in nature. The derivation also allows us to link splitting and joining behavior to the exponent and truncation parameters in power laws.

  • 35.
    Ma, Qi
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Johansson, Anders
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Tero, Atsushi
    Nakagaki, Toshiyuki
    Sumpter, David
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Current-reinforced random walks for constructing transport networks2013In: Journal of the Royal Society Interface, ISSN 1742-5689, E-ISSN 1742-5662, Vol. 10, no 80, p. 20120864-Article in journal (Refereed)
    Abstract [en]

    Biological systems that build transport networks, such as trail-laying ants and the slime mould Physarum, can be described in terms of reinforced random walks. In a reinforced random walk, the route taken by 'walking' particles depends on the previous routes of other particles. Here, we present a novel form of random walk in which the flow of particles provides this reinforcement. Starting from an analogy between electrical networks and random walks, we show how to include current reinforcement. We demonstrate that current-reinforcement results in particles converging on the optimal solution of shortest path transport problems, and avoids the self-reinforcing loops seen in standard density-based reinforcement models. We further develop a variant of the model that is biologically realistic, in the sense that the particles can be identified as ants and their measured density corresponds to those observed in maze-solving experiments on Argentine ants. For network formation, we identify the importance of nonlinear current reinforcement in producing networks that optimize both network maintenance and travel times. Other than ant trail formation, these random walks are also closely related to other biological systems, such as blood vessels and neuronal networks, which involve the transport of materials or information. We argue that current reinforcement is likely to be a common mechanism in a range of systems where network construction is observed.

  • 36.
    Mann, R. P.
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Herbert-Read, James E.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics. Uppsala University, Disciplinary Domain of Science and Technology, Biology, Department of Ecology and Genetics, Animal ecology.
    Ma, Q.
    Jordan, L. A.
    Sumpter, David J. T.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Ward, A. J. W.
    A model comparison reveals dynamic social information drives the movements of humbug damselfish (Dascyllus aruanus)2014In: Journal of the Royal Society Interface, ISSN 1742-5689, E-ISSN 1742-5662, Vol. 11, no 90, p. 20130794-Article in journal (Refereed)
    Abstract [en]

    Animals make use a range of social information to inform their movement decisions. One common movement rule, found across many different species, is that the probability that an individual moves to an area increases with the number of conspecifics there. However, in many cases, it remains unclear what social cues produce this and other similar movement rules. Here, we investigate what cues are used by damselfish (Dascyllus aruanus) when repeatedly crossing back and forth between two coral patches in an experimental arena. We find that an individual's decision to move is best predicted by the recent movements of conspecifics either to or from that individual's current habitat. Rather than actively seeking attachment to a larger group, individuals are instead prioritizing highly local and dynamic information with very limited spatial and temporal ranges. By reanalysing data in which the same species crossed for the first time to a new coral patch, we show that the individuals use static cues in this case. This suggests that these fish alter their information usage according to the structure and familiarity of their environment by using stable information when moving to a novel area and localized dynamic information when moving between familiar areas.

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  • 37.
    Mann, Richard P.
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Faria, Jolyon
    Sumpter, David J. T.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Krause, Jens
    The dynamics of audience applause2013In: Journal of the Royal Society Interface, ISSN 1742-5689, E-ISSN 1742-5662, Vol. 10, no 85, p. 20130466-Article in journal (Refereed)
    Abstract [en]

    The study of social identity and crowd psychology looks at how and why individual people change their behaviour in response to others. Within a group, a new behaviour can emerge first in a few individuals before it spreads rapidly to all other members. A number of mathematical models have been hypothesized to describe these social contagion phenomena, but these models remain largely untested against empirical data. We used Bayesian model selection to test between various hypotheses about the spread of a simple social behaviour, applause after an academic presentation. Individuals' probability of starting clapping increased in proportion to the number of other audience members already 'infected' by this social contagion, regardless of their spatial proximity. The cessation of applause is similarly socially mediated, but is to a lesser degree controlled by the reluctance of individuals to clap too many times. We also found consistent differences between individuals in their willingness to start and stop clapping. The social contagion model arising from our analysis predicts that the time the audience spends clapping can vary considerably, even in the absence of any differences in the quality of the presentations they have heard.

  • 38.
    Mann, Richard P.
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Perna, Andrea
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Strömbom, Daniel
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Garnett, Roman
    Herbert-Read, James E.
    Sumpter, David J. T.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Ward, Ashley J. W.
    Multi-scale Inference of Interaction Rules in Animal Groups Using Bayesian Model Selection2012In: PloS Computational Biology, ISSN 1553-734X, E-ISSN 1553-7358, Vol. 8, no 1, p. e1002308-Article in journal (Refereed)
    Abstract [en]

    Inference of interaction rules of animals moving in groups usually relies on an analysis of large scale system behaviour. Models are tuned through repeated simulation until they match the observed behaviour. More recent work has used the fine scale motions of animals to validate and fit the rules of interaction of animals in groups. Here, we use a Bayesian methodology to compare a variety of models to the collective motion of glass prawns (Paratya australiensis). We show that these exhibit a stereotypical 'phase transition', whereby an increase in density leads to the onset of collective motion in one direction. We fit models to this data, which range from: a mean-field model where all prawns interact globally; to a spatial Markovian model where prawns are self-propelled particles influenced only by the current positions and directions of their neighbours; up to non-Markovian models where prawns have 'memory' of previous interactions, integrating their experiences over time when deciding to change behaviour. We show that the mean-field model fits the large scale behaviour of the system, but does not capture fine scale rules of interaction, which are primarily mediated by physical contact. Conversely, the Markovian self-propelled particle model captures the fine scale rules of interaction but fails to reproduce global dynamics. The most sophisticated model, the non-Markovian model, provides a good match to the data at both the fine scale and in terms of reproducing global dynamics. We conclude that prawns' movements are influenced by not just the current direction of nearby conspecifics, but also those encountered in the recent past. Given the simplicity of prawns as a study system our research suggests that self-propelled particle models of collective motion should, if they are to be realistic at multiple biological scales, include memory of previous interactions and other non-Markovian effects.

  • 39.
    Mann, Richard P.
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Perna, Andrea
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Strömbom, Daniel
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Garnett, Roman
    Herbert-Read, James E.
    Sumpter, David J. T.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Ward, Ashley J. W.
    Multi-scale Inference of Interaction Rules in Animal Groups Using Bayesian Model Selection2013In: PloS Computational Biology, ISSN 1553-734X, E-ISSN 1553-7358, Vol. 9, no 3, article id e1002961Article in journal (Refereed)
    Abstract [en]

    Inference of interaction rules of animals moving in groups usually relies on an analysis of large scale system behaviour. Models are tuned through repeated simulation until they match the observed behaviour. More recent work has used the fine scale motions of animals to validate and fit the rules of interaction of animals in groups. Here, we use a Bayesian methodology to compare a variety of models to the collective motion of glass prawns (Paratya australiensis). We show that these exhibit a stereotypical 'phase transition', whereby an increase in density leads to the onset of collective motion in one direction. We fit models to this data, which range from: a mean-field model where all prawns interact globally; to a spatial Markovian model where prawns are self-propelled particles influenced only by the current positions and directions of their neighbours; up to non-Markovian models where prawns have 'memory' of previous interactions, integrating their experiences over time when deciding to change behaviour. We show that the mean-field model fits the large scale behaviour of the system, but does not capture the observed locality of interactions. Traditional self-propelled particle models fail to capture the fine scale dynamics of the system. The most sophisticated model, the non-Markovian model, provides a good match to the data at both the fine scale and in terms of reproducing global dynamics, while maintaining a biologically plausible perceptual range. We conclude that prawns' movements are influenced by not just the current direction of nearby conspecifics, but also those encountered in the recent past. Given the simplicity of prawns as a study system our research suggests that self-propelled particle models of collective motion should, if they are to be realistic at multiple biological scales, include memory of previous interactions and other non-Markovian effects.

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  • 40.
    Mann, Richard P.
    et al.
    Univ Leeds, Sch Math, Dept Stat, Leeds, W Yorkshire, England;Alan Turing Inst, London, England.
    Spaiser, Viktoria
    Univ Leeds, Sch Polit & Int Studies, Leeds 3, W Yorkshire, England.
    Bergström, Lina
    Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Institute for Housing and Urban Research. Delft Univ Technol, Fac Architecture & Built Environm, OTB Res Built Environm, Delft, Netherlands.
    Sumpter, David J. T.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Choice modelling with Gaussian processes in the social sciences: A case study of neighbourhood choice in Stockholm2018In: PLOS ONE, E-ISSN 1932-6203, Vol. 13, no 11, article id e0206687Article in journal (Refereed)
    Abstract [en]

    We present a non parametric extension of the conditional logit model, using Gaussian process priors. The conditional logit model is used in quantitative social science for inferring interaction effects between personal features and choice characteristics from observations of individual multinomial decisions, such as where to live, which car to buy or which school to choose. The classic, parametric model presupposes a latent utility function that is a linear combination of choice characteristics and their interactions with personal features. This imposes strong and unrealistic constraints on the form of individuals' preferences. Extensions using non-linear basis functions derived from the original features can ameliorate this problem but at the cost of high model complexity and increased reliance on the user in model specification. In this paper we develop a non-parametric conditional logit model based on Gaussian process logit models. We demonstrate its application on housing choice data from over 50,000 moving households from the Stockholm area over a two year period to reveal complex homophilic patterns in income, ethnicity and parental status.

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  • 41.
    Nannyonga, Betty
    et al.
    Makerere Univ, Coll Nat Sci, Sch Phys Sci, Dept Math, Kampala, Uganda..
    Sumpter, David J. T.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Modelling optimal allocation of resources in the context of an incurable disease2017In: PLOS ONE, E-ISSN 1932-6203, Vol. 12, no 3, article id e0172401Article in journal (Refereed)
    Abstract [en]

    Nodding syndrome has affected and led to the deaths of children between the ages of 5 and 15 in Northern Uganda since 2009. There is no reliable explanation of the disease, and currently the only treatment is through a nutritional programme of vitamins, combined with medication to prevent symptoms. In the absence of a proper medical treatment, we develop a dynamic compartmental model to plan the management of the syndrome and to curb its effects. We use incidence data from 2012 and 2013 from Pader, Lamwo and Kitgum regions of Uganda to parameterize the model. The model is then used to look at how to best plan the nutritional programme in terms of first getting children on to the programme through outreach, and then making sure they remain on the programme, through follow-up. For the current outbreak of nodding disease, we estimate that about half of available resources should be put into outreach. We show how to optimize the balance between outreach and follow-up in this particular example, and provide a general methodology for allocating resources in similar situations. Given the uncertainty of parameter estimates in such situations, we perform a robustness analysis to identify the best investment strategy. Our analysis offers a way of using available data to determine the best investment strategy of controlling nodding syndrome.

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  • 42. Nannyonga, Betty
    et al.
    Sumpter, David J. T.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Mugisha, Joseph Y. T.
    Luboobi, Livingstone S.
    The Dynamics, Causes and Possible Prevention of Hepatitis E Outbreaks2012In: PLOS ONE, E-ISSN 1932-6203, Vol. 7, no 7, p. e41135-Article in journal (Refereed)
    Abstract [en]

    Rapidly spreading infectious diseases are a serious risk to public health. The dynamics and the factors causing outbreaks of these diseases can be better understood using mathematical models, which are fit to data. Here we investigate the dynamics of a Hepatitis E outbreak in the Kitgum region of northern Uganda during 2007 to 2009. First, we use the data to determine that R-0 is approximately 2.25 for the outbreak. Secondly, we use a model to estimate that the critical level of latrine and bore hole coverages needed to eradicate the epidemic is at least 16% and 17% respectively. Lastly, we further investigate the relationship between the co-infection factor for malaria and Hepatitis E on the value of R0 for Hepatitis E. Taken together, these results provide us with a better understanding of the dynamics and possible causes of Hepatitis E outbreaks.

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  • 43.
    Nicolis, Stamatios C.
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Fernandez, J.
    Perez-Penichet, C.
    Noda, C.
    Tejera, F.
    Ramos, O.
    Sumpter, David J. T.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Altshuler, E.
    Foraging at the Edge of Chaos: Internal Clock versus External Forcing2013In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 110, no 26, p. 268104-Article in journal (Refereed)
    Abstract [en]

    Activity rhythms in animal groups arise both from external changes in the environment, as well as from internal group dynamics. These cycles are reminiscent of physical and chemical systems with quasiperiodic and even chaotic behavior resulting from "autocatalytic'' mechanisms. We use nonlinear differential equations to model how the coupling between the self-excitatory interactions of individuals and external forcing can produce four different types of activity rhythms: quasiperiodic, chaotic, phase locked, and displaying over or under shooting. At the transition between quasiperiodic and chaotic regimes, activity cycles are asymmetrical, with rapid activity increases and slower decreases and a phase shift between external forcing and activity. We find similar activity patterns in ant colonies in response to varying temperature during the day. Thus foraging ants operate in a region of quasiperiodicity close to a cascade of transitions leading to chaos. The model suggests that a wide range of temporal structures and irregularities seen in the activity of animal and human groups might be accounted for by the coupling between collectively generated internal clocks and external forcings.

  • 44.
    Nicolis, Stamatios C.
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Sumpter, David J. T.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    A dynamical approach to stock market fluctuations2011In: International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, ISSN 0218-1274, Vol. 21, no 12, p. 3557-3564Article in journal (Refereed)
    Abstract [en]

    The recent turbulence on the world's stock markets has reinvigorated the attack on classical economic models of stock market fluctuations. The key problem is determining a dynamic model, which is consistent with observed fluctuations and which reflects investor behavior. Here, we use a novel equation-free approach developed in nonlinear dynamics literature to identify the salient statistical features of fluctuations of the Dow Jones Industrial Average over the past 80 years. We then develop a minimal dynamical model in the form of a stochastic differential equation involving both additive and multiplicative system-noise couplings, which captures these features and whose parameterization on a time scale of days can be used to capture market distributions up to a time scale of months. The terms in the model can be directly linked to "herding" behavior on the part of traders. However, we show that parameters in this model have changed over a number of decades producing different market regimes. This result partially explains how, during some periods of history, "classic" economic models may work well and at other periods "econo-physics" models prove better.

  • 45.
    Perna, Andrea
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Granovskiy, Boris
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Garnier, Simon
    Nicolis, Stamatios C.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Labédan, Marjorie
    Theraulaz, Guy
    Fourcassié, Vincent
    Sumpter, David J. T.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Individual Rules for Trail Pattern Formation in Argentine Ants (Linepithema humile)2012In: PloS Computational Biology, ISSN 1553-734X, E-ISSN 1553-7358, Vol. 8, no 7, p. e1002592-Article in journal (Refereed)
    Abstract [en]

    Many ant species produce large dendritic networks of trails around their nest. These networks result from self-organized feedback mechanisms: ants leave small amounts of a chemical -a pheromone- as they move across space. In turn, they are attracted by this same pheromone so that eventually a trail is formed. In our study, we introduce a new image analysis technique to estimate the concentrations of pheromone directly on the trails. In this way, we can characterise the ingredients of the feedback loop that ultimately leads to the formation of trails. We show that the response to pheromone concentrations is linear: an ant will turn to the left with frequency proportional to the difference between the pheromone concentrations on its left and right sides. Such a linear individual response was rejected by previous literature, as it would be incompatible with the results of a large number of experiments: trails can only be reinforced if the ants have a disproportionally higher probability to select the trail with higher pheromone concentration. However, we show that the required non-linearity does not reside in the perceptual response of the ants, but in the noise associated with their movement.

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  • 46. Pettit, Benjamin
    et al.
    Perna, Andrea
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Biro, Dora
    Sumpter, David J. T.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Interaction rules underlying group decisions in homing pigeons2013In: Journal of the Royal Society Interface, ISSN 1742-5689, E-ISSN 1742-5662, Vol. 10, no 89, p. 20130529-Article in journal (Refereed)
    Abstract [en]

    Travelling in groups gives animals opportunities to share route information by following cues from each other's movement. The outcome of group navigation will depend on how individuals respond to each other within a flock, school, swarm or herd. Despite the abundance of modelling studies, only recently have researchers developed techniques to determine the interaction rules among real animals. Here, we use high-resolution GPS (global positioning system) tracking to study these interactions in pairs of pigeons flying home from a familiar site. Momentary changes in velocity indicate alignment with the neighbour's direction, as well as attraction or avoidance depending on distance. Responses were stronger when the neighbour was in front. From the flocking behaviour, we develop a model to predict features of group navigation. Specifically, we show that the interactions between pigeons stabilize a side-by-side configuration, promoting bidirectional information transfer and reducing the risk of separation. However, if one bird gets in front it will lead directional choices. Our model further predicts, and observations confirm, that a faster bird (as measured from solo flights) will fly slightly in front and thus dominate the choice of homing route. Our results explain how group decisions emerge from individual differences in homing flight behaviour.

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  • 47.
    Ranganathan, Shyam
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Bali Swain, Ranjula
    Sumpter, David J. T.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    The Demographic Transition and Economic Growth: Implications for Development Policy2015In: Palgrave Communications, E-ISSN 2055-1045, Vol. 1, article id 15033Article in journal (Refereed)
    Abstract [en]

    An important transition in the economic history of countries occurs when they move from a regime of low prosperity, high child mortality and high fertility to a state of high prosperity, low child mortality and low fertility. Researchers have proposed various theories to explain this demographic transition and its relation to economic growth. In this article, we test the validity of some of these theories by fitting a non-linear dynamic model for the available cross-country data. Our approach fills the gap between the micro-level models that discuss causative mechanisms but do not consider if alternative models may fit the data well, and models from growth econometrics that show the impact of different factors on economic growth but do not include non-linearities and complex interactions. In our model, mortality and fertility decline and economic growth are endogenized by considering a simultaneous system of equations in the change variables. The model shows that the transition is best described in terms of a development cycle involving child mortality, fertility and GDP per capita. Fertility rate decreases when child mortality is low, and is weakly dependent on GDP. As fertility rates fall, GDP increases, and as GDP increases, child mortality falls. We further test the hypothesis that female education drives down fertility rates rather than child mortality, but find only weak evidence for it. The Bayesian methodology we use ensures robust models and we identify non-linear interactions between indicators to capture real-world non-linearities. Hence, our models can be used in policymaking to predict short-term evolutions in the indicator variables. We also discuss how our approach can be used to evaluate policy initiatives such as the Millennium Development Goals or the Sustainable Development Goals and set more accurate, country-specific development targets.

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  • 48.
    Ranganathan, Shyam
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Bali Swain, Ranjula
    Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Economics.
    Sumpter, David J.T
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    A Dynamical Systems Approach to Modeling Human Development2014Report (Other academic)
    Abstract [en]

    A key aim of economics is to set goals and investigate the relationship between various socio-economic indicators. By tting time series data using a Bayesian dynamical systems approach we identify non-linear interactions between GDP, child mortality, fertility rate and female education. We show that reduction in child mortality is best predicted by the level of GDP in a country over the preceding 5 years. Fertility rate decreases when current or predicted child mortality is low, and is weakly dependent on female education and economic growth. As fertility drops, GDP increases producing a cycle that drives the demographic transition.

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  • 49.
    Ranganathan, Shyam
    et al.
    Virginia Polytech Inst & State Univ, Dept Stat, Blacksburg, VA 24061 USA.
    Nicolis, Stamatios
    Univ Libre Bruxelles, Fac Sci, Serv Chim Phys & Biol Theor, Campus Plaine,CP 231, Brussels, Belgium.
    Bali Swain, Ranjula
    Stockholm Sch Econ, Mistra Ctr Sustainable Markets, Stockholm, Sweden.; Sodertorn Univ, Stockholm, Sweden.
    Sumpter, David
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Setting development goals using stochastic, dynamical system models2017In: Plos One, Vol. 12, no 2, article id e0171560Article in journal (Refereed)
    Abstract [en]

    The Millennium Development Goals (MDG) programme was an ambitious attempt to encourage a globalised solution to important but often-overlooked development problems. The programme led to wide-ranging development but it has also been criticised for unrealistic and arbitrary targets. In this paper, we show how country-specific development targets can be set using stochastic, dynamical system models built from historical data. In particular, we show that the MDG target of two-thirds reduction of child mortality from 1990 levels was infeasible for most countries, especially in sub-Saharan Africa. At the same time, the MDG targets were not ambitious enough for fast-developing countries such as Brazil and China. We suggest that model-based setting of country-specific targets is essential for the success of global development programmes such as the Sustainable Development Goals (SDG). This approach should provide clear, quantifiable targets for policymakers.

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  • 50.
    Ranganathan, Shyam
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Spaiser, Viktoria
    Mann, Richard P.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Sumpter, David J. T.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Bayesian Dynamical Systems Modelling in the Social Sciences2014In: PLOS ONE, E-ISSN 1932-6203, Vol. 9, no 1, p. e86468-Article in journal (Refereed)
    Abstract [en]

    Data arising from social systems is often highly complex, involving non-linear relationships between the macro-level variables that characterize these systems. We present a method for analyzing this type of longitudinal or panel data using differential equations. We identify the best non-linear functions that capture interactions between variables, employing Bayes factor to decide how many interaction terms should be included in the model. This method punishes overly complicated models and identifies models with the most explanatory power. We illustrate our approach on the classic example of relating democracy and economic growth, identifying non-linear relationships between these two variables. We show how multiple variables and variable lags can be accounted for and provide a toolbox in R to implement our approach.

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