Figure 1
Bistability and switching in the experiments and simulations. (AB) Snaphots of a polarized group (A) and a mill (B) from a simulation. Black dots represent the particle positions and the red rods indicate the current heading of the particles. Note that in a polarized group (A) the polarization measure O p will be high and the rotation measure O r low, whereas a mill will have O r high and O p low. (C) Time evolution of the order parameters in simulations. (D) Time evolution of the order parameters in the experiments. In both experiments and simulations there are switches between polarized motion (O p large and O r small) and milling (O p small and O r large) and the proportion of milling seems to increase with group size. (E) Density plots of the order parameters in simulations. (F) Density plots of the order parameters in simulations. In both the experiments and simulations the group of 30 fish/particles spend almost all of its time in a polarized state (O p large and O r small), the group of 300 fish/particles spend almost all of its time in a rotating state (O p small and O r large), and the intermediate groups (70 and 150) show clear evidence of bistability with a significant amount of time spent in a polarized state and in a milling state. Panels (D) and (F) are from [9] (Tunstrøm et al. CC-BY). The P, S, and M markings in (F) illustrate the regions considered to correspond to polarized, swarm, and mill configurations, respectively, and the inset in the 30 fish panel shows the result when fish are moving in an arena 1/10 the size of the original. See [9] for details.
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Moving animal groups such as schools of fish and flocks of birds frequently switch between different group structures. Standard models of collective motion have been used successfully to explain how stable groups form via local interactions between individuals, but they are typically unable to produce groups that exhibit spontaneous switching. We a...
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... bistability and switching behavior generated by the model share several features with the golden shiner data (See Fig. 1). Figures 1AB shows the two types of groups that emerge in the simulations, polarized groups (A) and milling groups (B), and for all group sizes we observe switches between these two group types. Figures 1CD shows the time evolution of the order parameters over 15 minutes in the simulations (Fig. 1C) and in the experiments (Fig. 1D) ...
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... bistability and switching behavior generated by the model share several features with the golden shiner data (See Fig. 1). Figures 1AB shows the two types of groups that emerge in the simulations, polarized groups (A) and milling groups (B), and for all group sizes we observe switches between these two group types. Figures 1CD shows the time evolution of the order parameters over 15 minutes in the simulations (Fig. 1C) and in the experiments (Fig. 1D) with 30, 70, 150 and 300 particles/fish. ...
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... 1AB shows the two types of groups that emerge in the simulations, polarized groups (A) and milling groups (B), and for all group sizes we observe switches between these two group types. Figures 1CD shows the time evolution of the order parameters over 15 minutes in the simulations (Fig. 1C) and in the experiments (Fig. 1D) with 30, 70, 150 and 300 particles/fish. We observe several switches back and forth between milling and polarized motion in both the experiments and the simulations. ...
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... several features with the golden shiner data (See Fig. 1). Figures 1AB shows the two types of groups that emerge in the simulations, polarized groups (A) and milling groups (B), and for all group sizes we observe switches between these two group types. Figures 1CD shows the time evolution of the order parameters over 15 minutes in the simulations (Fig. 1C) and in the experiments (Fig. 1D) with 30, 70, 150 and 300 particles/fish. We observe several switches back and forth between milling and polarized motion in both the experiments and the simulations. See Supplementary Movies 1-4 for examples of this switching behavior in simulations, and Video S1-S4 in [9] for switches in the golden ...
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... shiner data (See Fig. 1). Figures 1AB shows the two types of groups that emerge in the simulations, polarized groups (A) and milling groups (B), and for all group sizes we observe switches between these two group types. Figures 1CD shows the time evolution of the order parameters over 15 minutes in the simulations (Fig. 1C) and in the experiments (Fig. 1D) with 30, 70, 150 and 300 particles/fish. We observe several switches back and forth between milling and polarized motion in both the experiments and the simulations. See Supplementary Movies 1-4 for examples of this switching behavior in simulations, and Video S1-S4 in [9] for switches in the golden shiner experiments. Figures 1EF ...
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... several switches back and forth between milling and polarized motion in both the experiments and the simulations. See Supplementary Movies 1-4 for examples of this switching behavior in simulations, and Video S1-S4 in [9] for switches in the golden shiner experiments. Figures 1EF shows density plots of the (O p , O r ) values in the experiments (Fig. 1F) and in the corresponding simulations (Fig. 1E). We note that the amount of polarized motion relative to milling decreases with group size in both experiments and simulations. Groups exhibiting bistability and switching is generated in both the roosting site model and the migration model (Fig. 2). In the migration model simulations ...
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... and polarized motion in both the experiments and the simulations. See Supplementary Movies 1-4 for examples of this switching behavior in simulations, and Video S1-S4 in [9] for switches in the golden shiner experiments. Figures 1EF shows density plots of the (O p , O r ) values in the experiments (Fig. 1F) and in the corresponding simulations (Fig. 1E). We note that the amount of polarized motion relative to milling decreases with group size in both experiments and simulations. Groups exhibiting bistability and switching is generated in both the roosting site model and the migration model (Fig. 2). In the migration model simulations (Fig. 2AC) we note that while switches do occur ...
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... density plot (Fig. 2C) confirms that there is indeed proper bistability in this case. Similarly, the 150 particle group confirms that there is frequent switching (Fig. 2B) and that proper bistability emerges (Fig. 2D) in the in the roost site model. Interestingly, both of these boundary-free models show the same trend as the bounded region model (Fig. 1AC) and the data (Fig. 1BD) in that polarization relative to milling tend to decrease with group size. Suggesting that this is a generic feature of the model and possibly in golden shiner schools and other natural ...
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... confirms that there is indeed proper bistability in this case. Similarly, the 150 particle group confirms that there is frequent switching (Fig. 2B) and that proper bistability emerges (Fig. 2D) in the in the roost site model. Interestingly, both of these boundary-free models show the same trend as the bounded region model (Fig. 1AC) and the data (Fig. 1BD) in that polarization relative to milling tend to decrease with group size. Suggesting that this is a generic feature of the model and possibly in golden shiner schools and other natural ...
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The collective motion observed in living active matter, such as fish schools and bird flocks, is characterized by its dynamic and complex nature, involving various moving states and transitions. By tailoring physical interactions or incorporating information exchange capabilities, inanimate active particles can exhibit similar behavior. However, th...
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... We derive conditions under which a collective biological control (CBC) will emerge in terms of the model parameters, in particular, the proportion of the pest population that feeds on the toxicity-inducing plant. We study this model both in its non-spatial mathematical form, and when implemented into a spatially explicit model of flocking in bird-like animals [50] that we adapted to include foraging of lanternfly-like agents. Flocking models have been used to explain collective motion in a range of animals across taxa from cells, via fish and birds, to humans [41,51] over the past few decades, but has not yet been used to model social learning in foraging situations of this type. ...
... See figure 1b. The bird flocking is modelled by a version of the roost site model in [50], and we add social learning and predation of lanternfly upon encounter into this flocking model. At the start of each simulation, all birds are undecided as to whether to try and eat lanternfly, but will try one if encountered with probability π, and once it has tried one it will become either a lanternfly eater if it had a good experience (i.e. the lanternfly it ate was not toxic) or a lanternfly non-eater if it had a bad experience (i.e. the lanternfly it ate was toxic). ...
... For the underlying flocking model itself [50], we use the same interactions and parameter values as for their roosting site model. See eqn (3) and §2.2 in [50]. ...
The spotted lanternfly is an emerging global invasive insect pest. Due to a lack of natural enemies where it is invasive, human intervention is required. Extensive management has been applied but the spread continues. Recently, the idea of bird-based biological controls has re-emerged and shown effective in studies. However, it is questionable, if birds are able to effectively control unfamiliar and occasionally toxic invasive pests in short timeframes. Unless, perhaps, the birds are effective social learners and toxicity of the invaders is rare. Here, we introduce a mathematical model for social learning in a great tit-like bird to investigate conditions for the emergence of a collective biological control of a pest that is occasionally toxic, like the lanternfly. We find that the social observation rate relative to the proportion of toxic lanternfly dictate when collective biological controls will emerge. We also implement the social learning model into a model of collective motion in bird-like animals, and find that it produces results consistent with the mathematical model. Our work suggests that social birds may be useful in managing the spotted lanternfly, and that removing the toxicity-inducing preferred host of the lanternfly should be a priority to facilitate this.
... Although the impact of behavioural differences between individuals on the collective behaviour has been investigated (e.g. [1,22,44,46]), the attention given in the literature to discordant behaviours of a single individual or small groups, which emerge from a model in which all individuals have identical characteristics, has been rather limited so far [17,42,47,48]. This paper analyses the case of a fish that, while the school of fish mills within a torus in a certain direction, begins a mill within the torus occupied by the other individuals, but in the opposite direction to them. ...
... Open Sci. 10: 231618 mechanisms governing transitions of schools of fish from one collective motion pattern to another [17,42,47,48]. In particular, analyses of experimental observations of groups of golden shiners in a shallow tank [42] revealed that some individuals initiate a temporary counter-rotation when the rotating school encounters a tank wall and, because of this, it undergoes a transition from the milling state to the polar state. ...
... In particular, analyses of experimental observations of groups of golden shiners in a shallow tank [42] revealed that some individuals initiate a temporary counter-rotation when the rotating school encounters a tank wall and, because of this, it undergoes a transition from the milling state to the polar state. Moving from experimental observations to simulations, the electronic supplementary material videos in [47] show some counter-rotations of very short duration in schools of fish repeatedly transitioning from the milling state to the polar state and vice versa. However, the attention of these papers does not focus on counter-rotations as such, but focuses more generally on the mechanisms (including the discordant behaviours of a few individuals) involved in transitions between different collective motion patterns. ...
Computational models of collective motion successfully reproduce the most common behaviours of a school of fish, using only a few elementary interactions between individuals. However, their ability to also reproduce individual behaviours that are discordant from those of the group has not yet been adequately investigated. In this paper, a self-propelled particle model using three interaction zones is considered in relation to the counter-rotation of an individual: a phenomenon observable in real schools of fish milling in a torus, when an individual moves in the same torus but in the opposite direction for a certain period of time. This study shows that the interactions of repulsion, orientation and attraction between individuals moving at constant speed in a three-dimensional space, with asynchronous updating, can generate temporary counter-rotations. The analysis of such events sheds light on the mechanisms that start the counter-rotation and those that end it. Although the contribution of the repulsion interaction is often significant to start and terminate the counter-rotation, it does not prove to be decisive. Indeed, it is observed that even when interactions between individuals are limited to attraction alone, temporary counter-rotations of individuals occur, provided the fish density along the circumference is not uniform. Some of these conclusions, deduced from the simulations performed, are visually consistent with what is observed in some underwater video recordings of milling schools of fish.
... Recently, a number of studies have shown that several properties of moving animal groups previously thought to require the alignment interaction can be generated without it [35][36][37][38][39][40][41][42][43]. For example, attraction alone and combinations of attraction and repulsion have been shown sufficient to generate all three standard group types that alignment-based models can generate, including polarized (or aligned) groups [36,41,44] previously thought to require alignment interactions. ...
... For example, attraction alone and combinations of attraction and repulsion have been shown sufficient to generate all three standard group types that alignment-based models can generate, including polarized (or aligned) groups [36,41,44] previously thought to require alignment interactions. Alignment-free models have also been shown capable of generating more disruptive phenomena, e.g., groups that spontaneously transition from one group type to another [42,43], as exemplified by schools of golden shiner fish [45]. Such dynamics had not previously been reported as producible using spp models and had even been conjectured impossible to generate using models of this type due to their inherent averaging of interactions [34]. ...
... Given the capacity of these recent alignment-free models to generate disruptive phenomena, investigating whether they can provide an attraction-and-repulsion-based explanation for collective predator evasion behavior in moving animal groups should be explored. This investigation is particularly important because several animals are thought to rely on attraction and repulsion alone to organize their groups [33,34,42,43]. This approach could also yield experimentally testable predictions for predator evasion in animals known to use alignment-free interactions. ...
Moving animal groups consist of many distinct individuals but can operate and function as one unit when performing different tasks. Effectively evading unexpected predator attacks is one primary task for many moving groups. The current explanation for predator evasion responses in moving animal groups require the individuals in the groups to interact via (velocity) alignment. However, experiments have shown that some animals do not use alignment. This suggests that another explanation for the predator evasion capacity in at least these species is needed. Here we establish that effective collective predator evasion does not require alignment, it can be induced via attraction and repulsion alone. We also show that speed differences between individuals that have directly observed the predator and those that have not influence evasion success and the speed of the collective evasion process, but are not required to induce the phenomenon. Our work here adds collective predator evasion to a number of phenomena previously thought to require alignment interactions that have recently been shown to emerge from attraction and repulsion alone. Based on our findings we suggest experiments and make predictions that may lead to a deeper understanding of not only collective predator evasion but also collective motion in general.
... The main observation was that for all group sizes the system exhibited bistability, in the sense that the schools formed both mills and polarized groups without any apparent changes in conditions, and that the schools regularly switched between these two states, with switch rate decreasing with group size (See videos S1-S4 in [12]). Recently, it was shown that a standard model based on attraction, repulsion, and asymmetric interactions via blind zones designed to model this specific experiment is capable of generating continuous switching between two distinct states, specifically between milling and polarized groups, that is consistent with the experimental observations [31]. (See videos referred to in [31]). ...
... Recently, it was shown that a standard model based on attraction, repulsion, and asymmetric interactions via blind zones designed to model this specific experiment is capable of generating continuous switching between two distinct states, specifically between milling and polarized groups, that is consistent with the experimental observations [31]. (See videos referred to in [31]). However, the mechanism behind the model's ability to generate these switches using only standard components (attraction, repulsion, and blind zones) found in a large number of other models is not known and the range of its capacity to do so has not been quantified. ...
... Given that asymmetric interactions are known to induce drastic changes in models when varied and lead to initial condition-dependent bistability, this component of the model in [31] is a natural starting point for seeking an explanation for the capacity in this model to generate groups that switch between group types within individual simulations. If it turns out that asymmetric interactions implemented via blind zones can be shown to drive robust bistability and switching in this model, this would suggest that there may be other published spp models that also have this capacity, but it has yet to be detected in them. ...
Moving animal groups often spontaneously change their group structure and dynamics, but standard models used to explain collective motion in animal groups are typically unable to generate changes of this type. Recently, a model based on attraction, repulsion and asymmetric interactions designed for specific fish experiments was shown capable of producing such changes. However, the origin of the model’s ability to generate them, and the range of this capacity, remains unknown. Here we modify and extend this model to address these questions. We establish that its ability to generate groups exhibiting changes depends on the size of the blind zone parameter β. Specifically, we show that for small β swarms and mills are generated, for larger β polarized groups forms, and for a region of intermediate β values there is a bistability region where continuous switching between milling and polarized groups occurs. We also show that the location of the bistability region depends on group size and the relative strength of velocity alignment when this interaction is added to the model. These findings may contribute to advance the use of self-propelled particle models to explain a range of disruptive phenomena previously thought to be beyond the capabilities of such models.
... For details see Methods, Extended Data Fig. 2, Supplementary Videos 1 and 2 and Supplementary Note 2. These collective transitions are a fundamental and distinctive feature of intermittent collective motion. Specifically, the GP → CMP transition is a fast, complex collective decision-making Article https://doi.org/10.1038/s41567-022-01769-8 a recent model based only on attraction and repulsion that displays spontaneous switching 55 , which is arguably the closest model candidate. This is not surprising, because these models were proposed to describe different types of collective behaviour where the group remains always in a collective moving phase (that is, 'on the move') such as swarming, schooling or milling, eventually transitioning among them, but not collective transition to a non-moving phase-which implies the navigation mechanism is temporally switched off-such as in the GP, as occurs here. ...
... On the other hand, models that include attraction and blind angles-which lead to non-reciprocal interactions among identical individuals 56 without the need of assuming the mixture of different populations 57 -have been shown to account for line formation in a range of parameters in the presence 13,19 and, even more surprisingly, in the absence 46,49,53 of a velocity alignment mechanism. Furthermore, we observe that, in models with blind angle, attraction and repulsion, the presence of spontaneous transitions between milling and polarized motion patterns has been reported in ref. 55 and their coexistence in large systems in ref. 49 . We note that, in the parameter range where spontaneous switching and coexistence occur, the cohesion of all group members at all times cannot be ensured. ...
Flocking behaviour is often presented as an example of a self-organized process, where individuals continuously negotiate on the direction of travel and compromise by moving along a local average velocity until the group reaches a consensus. Such a collective behaviour does not take advantage of the benefits of hierarchical organizational strategies that confer the leader of the group full control over it with a reduced information flow overhead. Here we study the spontaneous behaviour of small sheep flocks and find that sheep exhibit a collective behaviour that consists of a series of collective motion episodes interrupted by grazing phases. Each motion episode has a temporal leader that guides the group in line formation. Combining experiments and a data-driven model, we provide evidence that group coordination in these episodes results from the propagation of positional information of the temporal leader to all group members through a strongly hierarchical, directed interaction network. Furthermore, we show that group members alternate the role of leader and follower by a random process, which is independent of the navigation mechanism that regulates collective motion episodes. Our analysis suggests that it is possible to conceive intermittent collective strategies that take advantage of both hierarchical and democratic organizational schemes.
Flocking and vortical are two typical motion modes in active matter. Although it is known that the two modes can spontaneously switch between each other in a finite-size system, the switching dynamics remain elusive. In this work, by computer simulation of a two-dimensional Vicsek-like system with 1000 particles, we find from the perspective of classical nucleation theory that the forward and backward switching dynamics are asymmetric: from flocking to vortical is a one-step nucleation process, while the opposite is a two-step nucleation process with the system staying in a metastable state before reaching the final flocking state.
The authors studied momentary motion leadership in small groups of black neon tetra (Hyphessobrycon herbertaxelrodi) and zebrafish (Danio rerio), its relationship with local interaction parameters, such as the acceleration and turning angle of the individuals, and the relative locations of the individuals within the group. The purpose was to know whether leadership tended to be monopolised by certain individuals or whether it was equitably shared between them and if there were differences in leadership sharing between these two species, which are known to have different degrees of cohesion and polarisation. The authors filmed groups of two, three, four and eight fishes of each species and tracked their individual motion by image analysis and trajectory extraction. In both species, motion leadership was not monopolized but egalitarian and very short lived, with leadership shifts distributed randomly over time. The duration of leadership episodes decreased as group size increased and was longer in black neon tetra than in zebrafish. Momentary leaders did not tend to be in the front positions, but closer to the centre of the group. Acceleration and turning angle were more extreme in zebrafish than in black neon tetra and in the momentary leaders than the followers in both species. In general, these differences between species and between leaders/followers were qualitatively similar with some differences in detail, indicating that the relationship between motion leadership and local interaction parameters is likely to conform to a general physical law.
