Properties of neuronal facilitation that improve target tracking in natural pursuit simulations

Although flying insects have limited visual acuity (approx. 1°) and relatively small brains, many species pursue tiny targets against cluttered backgrounds with high success. Our previous computational model, inspired by electrophysiological recordings from insect ‘small target motion detector’ (STMD) neurons, did not account for several key properties described from the biological system. These include the recent observations of response ‘facilitation’ (a slow build-up of response to targets that move on long, continuous trajectories) and ‘selective attention’, a competitive mechanism that selects one target from alternatives. Here, we present an elaborated STMD-inspired model, implemented in a closed loop target-tracking system that uses an active saccadic gaze fixation strategy inspired by insect pursuit. We test this system against heavily cluttered natural scenes. Inclusion of facilitation not only substantially improves success for even short-duration pursuits, but it also enhances the ability to ‘attend’ to one target in the presence of distracters. Our model predicts optimal facilitation parameters that are static in space and dynamic in time, changing with respect to the amount of background clutter and the intended purpose of the pursuit. Our results provide insights into insect neurophysiology and show the potential of this algorithm for implementation in artificial visual systems and robotic applications.     

The principles of pedestrian route choice

Pedestrian route choice, the process by which individuals decide on their walking path between two locations, is a fundamental problem across disciplines. Because this behaviour is investigated from different conceptual and methodological angles, and because it strongly depends on the environmental context, it is challenging to establish a systematic framework for research. Here, by reviewing previous work, we identify four principles for pedestrian route choice that are relevant across disciplines. First, ‘information perception’ deals with how pedestrians can perceive information selectively and purposely, given the limited available information. Second, ‘information integration’ considers how pedestrians subjectively integrate environmental spatial information into mental representations. Third, ‘responding to information’ is concerned with how pedestrians tend to be attracted and repelled by specific attributes individually and how this can lead to positive or negative feedback loops across many individuals. Fourth ‘decision-making mechanisms'' describe how pedestrians trade off the evidence provided by different attributes. How pedestrians perceive, integrate, respond to, and act upon information is not fixed but varies with the context. We give examples for each principle and explain how these principles shape pedestrian choice behaviours. We hope this contribution provides a systematic overview of the field and helps to spark inspiration among specialists.     

A unifying framework for quantifying the nature of animal interactions

Collective phenomena, whereby agent–agent interactions determine spatial patterns, are ubiquitous in the animal kingdom. On the other hand, movement and space use are also greatly influenced by the interactions between animals and their environment. Despite both types of interaction fundamentally influencing animal behaviour, there has hitherto been no unifying framework for the models proposed in both areas. Here, we construct a general method for inferring population-level spatial patterns from underlying individual movement and interaction processes, a key ingredient in building a statistical mechanics for ecological systems. We show that resource selection functions, as well as several examples of collective motion models, arise as special cases of our framework, thus bringing together resource selection analysis and collective animal behaviour into a single theory. In particular, we focus on combining the various mechanistic models of territorial interactions in the literature with step selection functions, by incorporating interactions into the step selection framework and demonstrating how to derive territorial patterns from the resulting models. We demonstrate the efficacy of our model by application to a population of insectivore birds in the Amazon rainforest.     

Fish and robots swimming together: attraction towards the robot demands biomimetic locomotion

The integration of biomimetic robots in a fish school may enable a better understanding of collective behaviour, offering a new experimental method to test group feedback in response to behavioural modulations of its ‘engineered’ member. Here, we analyse a robotic fish and individual golden shiners (Notemigonus crysoleucas) swimming together in a water tunnel at different flow velocities. We determine the positional preference of fish with respect to the robot, and we study the flow structure using a digital particle image velocimetry system. We find that biomimetic locomotion is a determinant of fish preference as fish are more attracted towards the robot when its tail is beating rather than when it is statically immersed in the water as a ‘dummy’. At specific conditions, the fish hold station behind the robot, which may be due to the hydrodynamic advantage obtained by swimming in the robot''s wake. This work makes a compelling case for the need of biomimetic locomotion in promoting robot–animal interactions and it strengthens the hypothesis that biomimetic robots can be used to study and modulate collective animal behaviour.     

The entropic basis of collective behaviour

We identify a unique viewpoint on the collective behaviour of intelligent agents. We first develop a highly general abstract model for the possible future lives these agents may encounter as a result of their decisions. In the context of these possibilities, we show that the causal entropic principle, whereby agents follow behavioural rules that maximize their entropy over all paths through the future, predicts many of the observed features of social interactions among both human and animal groups. Our results indicate that agents are often able to maximize their future path entropy by remaining cohesive as a group and that this cohesion leads to collectively intelligent outcomes that depend strongly on the distribution of the number of possible future paths. We derive social interaction rules that are consistent with maximum entropy group behaviour for both discrete and continuous decision spaces. Our analysis further predicts that social interactions are likely to be fundamentally based on Weber''s law of response to proportional stimuli, supporting many studies that find a neurological basis for this stimulus–response mechanism and providing a novel basis for the common assumption of linearly additive ‘social forces’ in simulation studies of collective behaviour.     

Bridging the gulf between correlated random walks and Lévy walks: autocorrelation as a source of Lévy walk movement patterns

For many years, the dominant conceptual framework for describing non-oriented animal movement patterns has been the correlated random walk (CRW) model in which an individual''s trajectory through space is represented by a sequence of distinct, independent randomly oriented ‘moves’. It has long been recognized that the transformation of an animal''s continuous movement path into a broken line is necessarily arbitrary and that probability distributions of move lengths and turning angles are model artefacts. Continuous-time analogues of CRWs that overcome this inherent shortcoming have appeared in the literature and are gaining prominence. In these models, velocities evolve as a Markovian process and have exponential autocorrelation. Integration of the velocity process gives the position process. Here, through a simple scaling argument and through an exact analytical analysis, it is shown that autocorrelation inevitably leads to Lévy walk (LW) movement patterns on timescales less than the autocorrelation timescale. This is significant because over recent years there has been an accumulation of evidence from a variety of experimental and theoretical studies that many organisms have movement patterns that can be approximated by LWs, and there is now intense debate about the relative merits of CRWs and LWs as representations of non-orientated animal movement patterns.     

Disordered animal multilayer reflectors and the localization of light

Multilayer optical reflectors constructed from ‘stacks’ of alternating layers of high and low refractive index dielectric materials are present in many animals. For example, stacks of guanine crystals with cytoplasm gaps occur within the skin and scales of fish, and stacks of protein platelets with cytoplasm gaps occur within the iridophores of cephalopods. Common to all these animal multilayer reflectors are different degrees of random variation in the thicknesses of the individual layers in the stack, ranging from highly periodic structures to strongly disordered systems. However, previous discussions of the optical effects of such thickness disorder have been made without quantitative reference to the propagation of light within the reflector. Here, we demonstrate that Anderson localization provides a general theoretical framework to explain the common coherent interference and optical properties of these biological reflectors. Firstly, we illustrate how the localization length enables the spectral properties of the reflections from more weakly disordered ‘coloured’ and more strongly disordered ‘silvery’ reflectors to be explained by the same physical process. Secondly, we show how the polarization properties of reflection can be controlled within guanine–cytoplasm reflectors, with an interplay of birefringence and thickness disorder explaining the origin of broadband polarization-insensitive reflectivity.     

Phase transitions and assortativity in models of gene regulatory networks evolved under different selection processes

We study a simplified model of gene regulatory network evolution in which links (regulatory interactions) are added via various selection rules that are based on the structural and dynamical features of the network nodes (genes). Similar to well-studied models of ‘explosive’ percolation, in our approach, links are selectively added so as to delay the transition to large-scale damage propagation, i.e. to make the network robust to small perturbations of gene states. We find that when selection depends only on structure, evolved networks are resistant to widespread damage propagation, even without knowledge of individual gene propensities for becoming ‘damaged’. We also observe that networks evolved to avoid damage propagation tend towards disassortativity (i.e. directed links preferentially connect high degree ‘source’ genes to low degree ‘target’ genes and vice versa). We compare our simulations to reconstructed gene regulatory networks for several different species, with genes and links added over evolutionary time, and we find a similar bias towards disassortativity in the reconstructed networks.     

Beyond contact-based transmission networks: the role of spatial coincidence

Animal societies rely on interactions between group members to effectively communicate and coordinate their actions. To date, the transmission properties of interaction networks formed by direct physical contacts have been extensively studied for many animal societies and in all cases found to inhibit spreading. Such direct interactions do not, however, represent the only viable pathways. When spreading agents can persist in the environment, indirect transmission via ‘same-place, different-time’ spatial coincidences becomes possible. Previous studies have neglected these indirect pathways and their role in transmission. Here, we use rock ant colonies, a model social species whose flat nest geometry, coupled with individually tagged workers, allowed us to build temporally and spatially explicit interaction networks in which edges represent either direct physical contacts or indirect spatial coincidences. We show how the addition of indirect pathways allows the network to enhance or inhibit the spreading of different types of agent. This dual-functionality arises from an interplay between the interaction-strength distribution generated by the ants'' movement and environmental decay characteristics of the spreading agent. These findings offer a general mechanism for understanding how interaction patterns might be tuned in animal societies to control the simultaneous transmission of harmful and beneficial agents.     

Modelling collective navigation via non-local communication

Collective migration occurs throughout the animal kingdom, and demands both the interpretation of navigational cues and the perception of other individuals within the group. Navigational cues orient individuals towards a destination, while it has been demonstrated that communication between individuals enhances navigation through a reduction in orientation error. We develop a mathematical model of collective navigation that synthesizes navigational cues and perception of other individuals. Crucially, this approach incorporates uncertainty inherent to cue interpretation and perception in the decision making process, which can arise due to noisy environments. We demonstrate that collective navigation is more efficient than individual navigation, provided a threshold number of other individuals are perceptible. This benefit is even more pronounced in low navigation information environments. In navigation ‘blindspots’, where no information is available, navigation is enhanced through a relay that connects individuals in information-poor regions to individuals in information-rich regions. As an expository case study, we apply our framework to minke whale migration in the northeast Atlantic Ocean, and quantify the decrease in navigation ability due to anthropogenic noise pollution.     

The feasibility of coherent energy transfer in microtubules

It was once purported that biological systems were far too ‘warm and wet’ to support quantum phenomena mainly owing to thermal effects disrupting quantum coherence. However, recent experimental results and theoretical analyses have shown that thermal energy may assist, rather than disrupt, quantum coherent transport, especially in the ‘dry’ hydrophobic interiors of biomolecules. Specifically, evidence has been accumulating for the necessary involvement of quantum coherent energy transfer between uniquely arranged chromophores in light harvesting photosynthetic complexes. The ‘tubulin’ subunit proteins, which comprise microtubules, also possess a distinct architecture of chromophores, namely aromatic amino acids, including tryptophan. The geometry and dipolar properties of these aromatics are similar to those found in photosynthetic units indicating that tubulin may support coherent energy transfer. Tubulin aggregated into microtubule geometric lattices may support such energy transfer, which could be important for biological signalling and communication essential to living processes. Here, we perform a computational investigation of energy transfer between chromophoric amino acids in tubulin via dipole excitations coupled to the surrounding thermal environment. We present the spatial structure and energetic properties of the tryptophan residues in the microtubule constituent protein tubulin. Plausibility arguments for the conditions favouring a quantum mechanism of signal propagation along a microtubule are provided. Overall, we find that coherent energy transfer in tubulin and microtubules is biologically feasible.     

Analysis of unstable modes distinguishes mathematical models of flagellar motion

The mechanisms underlying the coordinated beating of cilia and flagella remain incompletely understood despite the fundamental importance of these organelles. The axoneme (the cytoskeletal structure of cilia and flagella) consists of microtubule doublets connected by passive and active elements. The motor protein dynein is known to drive active bending, but dynein activity must be regulated to generate oscillatory, propulsive waveforms. Mathematical models of flagellar motion generate quantitative predictions that can be analysed to test hypotheses concerning dynein regulation. One approach has been to seek periodic solutions to the linearized equations of motion. However, models may simultaneously exhibit both periodic and unstable modes. Here, we investigate the emergence and coexistence of unstable and periodic modes in three mathematical models of flagellar motion, each based on a different dynein regulation hypothesis: (i) sliding control; (ii) curvature control and (iii) control by interdoublet separation (the ‘geometric clutch’ (GC)). The unstable modes predicted by each model are used to critically evaluate the underlying hypothesis. In particular, models of flagella with ‘sliding-controlled’ dynein activity admit unstable modes with non-propulsive, retrograde (tip-to-base) propagation, sometimes at the same parameter values that lead to periodic, propulsive modes. In the presence of these retrograde unstable modes, stable or periodic modes have little influence. In contrast, unstable modes of the GC model exhibit switching at the base and propulsive base-to-tip propagation.     

A minimal model of predator–swarm interactions

We propose a minimal model of predator–swarm interactions which captures many of the essential dynamics observed in nature. Different outcomes are observed depending on the predator strength. For a ‘weak’ predator, the swarm is able to escape the predator completely. As the strength is increased, the predator is able to catch up with the swarm as a whole, but the individual prey is able to escape by ‘confusing’ the predator: the prey forms a ring with the predator at the centre. For higher predator strength, complex chasing dynamics are observed which can become chaotic. For even higher strength, the predator is able to successfully capture the prey. Our model is simple enough to be amenable to a full mathematical analysis, which is used to predict the shape of the swarm as well as the resulting predator–prey dynamics as a function of model parameters. We show that, as the predator strength is increased, there is a transition (owing to a Hopf bifurcation) from confusion state to chasing dynamics, and we compute the threshold analytically. Our analysis indicates that the swarming behaviour is not helpful in avoiding the predator, suggesting that there are other reasons why the species may swarm. The complex shape of the swarm in our model during the chasing dynamics is similar to the shape of a flock of sheep avoiding a shepherd.     

Contact inhibition of locomotion probabilities drive solitary versus collective cell migration

Contact inhibition of locomotion (CIL) is the process whereby cells collide, cease migrating in the direction of the collision, and repolarize their migration machinery away from the collision. Quantitative analysis of CIL has remained elusive because cell-to-cell collisions are infrequent in traditional cell culture. Moreover, whereas CIL predicts mutual cell repulsion and ‘scattering’ of cells, the same cells in vivo are observed to undergo CIL at some developmental times and collective cell migration at others. It remains unclear whether CIL is simply absent during collective cell migration, or if the two processes coexist and are perhaps even related. Here, we used micropatterned stripes of extracellular matrix to restrict cell migration to linear paths such that cells polarized in one of two directions and collisions between cells occurred frequently and consistently, permitting quantitative and unbiased analysis of CIL. Observing repolarization events in different contexts, including head-to-head collision, head-to-tail collision, collision with an inert barrier, or no collision, and describing polarization as a two-state transition indicated that CIL occurs probabilistically, and most strongly upon head-to-head collisions. In addition to strong CIL, we also observed ‘trains’ of cells moving collectively with high persistence that appeared to emerge from single cells. To reconcile these seemingly conflicting observations of CIL and collective cell migration, we constructed an agent-based model to simulate our experiments. Our model quantitatively predicted the emergence of collective migration, and demonstrated the sensitivity of such emergence to the probability of CIL. Thus CIL and collective migration can coexist, and in fact a shift in CIL probabilities may underlie transitions between solitary cell migration and collective cell migration. Taken together, our data demonstrate the emergence of persistently polarized, collective cell movement arising from CIL between colliding cells.     

Quorum sensing and social networking in the microbial world

For many years, bacterial cells were considered primarily as selfish individuals, but, in recent years, it has become evident that, far from operating in isolation, they coordinate collective behaviour in response to environmental challenges using sophisticated intercellular communication networks. Cell-to-cell communication between bacteria is mediated by small diffusible signal molecules that trigger changes in gene expression in response to fluctuations in population density. This process, generally referred to as quorum sensing (QS), controls diverse phenotypes in numerous Gram-positive and Gram-negative bacteria. Recent advances have revealed that bacteria are not limited to communication within their own species but are capable of ‘listening in’ and ‘broadcasting to’ unrelated species to intercept messages and coerce cohabitants into behavioural modifications, either for the good of the population or for the benefit of one species over another. It is also evident that QS is not limited to the bacterial kingdom. The study of two-way intercellular signalling networks between bacteria and both uni- and multicellular eukaryotes as well as between eukaryotes is just beginning to unveil a rich diversity of communication pathways.     

The evolutionary dynamics of within-generation immune priming in invertebrate hosts

While invertebrates lack the machinery necessary for ‘acquired immunity’, there is increasing empirical evidence that exposure to low levels of disease may ‘prime’ an invertebrate''s immune response, increasing its defence to subsequent exposure. Despite this increasing empirical data, there has been little theoretical attention paid to immune priming. Here, we investigate the evolution of immune priming, focusing on the role of the unique feedbacks generated by a newly developed susceptible–primed–infected epidemiological model. Contrasting our results with previous models on the evolution of acquired immunity, we highlight that there are important implications to the evolution of immunity through priming owing to these different epidemiological feedbacks. In particular, we find that in contrast to acquired immunity, priming is strongly selected for at high as well as intermediate pathogen virulence. We also find that priming may be greatest at either intermediate or high host lifespans depending on the severity of disease. Furthermore, hosts faced with more severe pathogens are more likely to evolve diversity in priming. Finally, we show when the evolution of priming leads to the exclusion of the pathogens or hosts experiencing population cycles. Overall the model acts as a baseline for understanding the evolution of priming in host–pathogen systems.     

On the reliability of seasonal climate forecasts

Seasonal climate forecasts are being used increasingly across a range of application sectors. A recent UK governmental report asked: how good are seasonal forecasts on a scale of 1–5 (where 5 is very good), and how good can we expect them to be in 30 years time? Seasonal forecasts are made from ensembles of integrations of numerical models of climate. We argue that ‘goodness’ should be assessed first and foremost in terms of the probabilistic reliability of these ensemble-based forecasts; reliable inputs are essential for any forecast-based decision-making. We propose that a ‘5’ should be reserved for systems that are not only reliable overall, but where, in particular, small ensemble spread is a reliable indicator of low ensemble forecast error. We study the reliability of regional temperature and precipitation forecasts of the current operational seasonal forecast system of the European Centre for Medium-Range Weather Forecasts, universally regarded as one of the world-leading operational institutes producing seasonal climate forecasts. A wide range of ‘goodness’ rankings, depending on region and variable (with summer forecasts of rainfall over Northern Europe performing exceptionally poorly) is found. Finally, we discuss the prospects of reaching ‘5’ across all regions and variables in 30 years time.     

Fast,high-throughput measurement of collective behaviour in a bacterial population

Swimming bacteria explore their environment by performing a random walk, which is biased in response to, for example, chemical stimuli, resulting in a collective drift of bacterial populations towards ‘a better life’. This phenomenon, called chemotaxis, is one of the best known forms of collective behaviour in bacteria, crucial for bacterial survival and virulence. Both single-cell and macroscopic assays have investigated bacterial behaviours. However, theories that relate the two scales have previously been difficult to test directly. We present an image analysis method, inspired by light scattering, which measures the average collective motion of thousands of bacteria simultaneously. Using this method, a time-varying collective drift as small as 50 nm s⁻¹ can be measured. The method, validated using simulations, was applied to chemotactic Escherichia coli bacteria in linear gradients of the attractant α-methylaspartate. This enabled us to test a coarse-grained minimal model of chemotaxis. Our results clearly map the onset of receptor methylation, and the transition from linear to logarithmic sensing in the bacterial response to an external chemoeffector. Our method is broadly applicable to problems involving the measurement of collective drift with high time resolution, such as cell migration and fluid flows measurements, and enables fast screening of tactic behaviours.     

Effects of heterogeneity in infection-exposure history and immunity on the dynamics of a protozoan parasite

Infection systems where traits of the host, such as acquired immunity, interact with the infection process can show complex dynamic behaviour with counter-intuitive results. In this study, we consider the traits ‘immune status’ and ‘exposure history’, and our aim is to assess the influence of acquired individual heterogeneity in these traits. We have built an individual-based model of Eimeria acervulina infections, a protozoan parasite with an environmental stage that causes coccidiosis in chickens. With the model, we simulate outbreaks of the disease under varying initial contaminations. Heterogeneity in the traits arises stochastically through differences in the dose and frequency of parasites that individuals pick up from the environment. We find that the relationship between the initial contamination and the severity of an outbreak has a non-monotonous ‘wave-like’ pattern. This pattern can be explained by an increased heterogeneity in the host population caused by the infection process at the most severe outbreaks. We conclude that when dealing with these types of infection systems, models that are used to develop or evaluate control measures cannot neglect acquired heterogeneity in the host population traits that interact with the infection process.