Body size affects the strength of social interactions and spatial organization of a schooling fish (Pseudomugil signifer)

Using neuronal models to capture burst-and-glide motion and leadership in fish

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.

Drone Observation for the Quantitative Study of Complex Multilevel Societies

Unmanned aerial vehicles (drones) have recently been used in various behavioral ecology studies. However, their application has been limited to single groups, and most studies have not implemented individual identification. A multilevel society refers to a social structure in which small stable "core units" gather and make a larger, multiple-unit group. Here, we introduce recent applications of drone technology and individual identification to complex social structures involving multiple groups, such as multilevel societies. Drones made it possible to obtain the identification, accurate positioning, or movement of more than a hundred individuals in a multilevel social group. In addition, in multilevel social groups, drones facilitate the observation of heterogeneous spatial positioning patterns and mechanisms of behavioral propagation, which are different from those in a single-level group. Such findings may contribute to the quantitative definition and assessment of multilevel societies and enhance our understanding of mechanisms of multiple group aggregation. The application of drones to various species may resolve various questions related to multilevel societies.

The lost art of mathematical modelling

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 an 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.

Social competence improves the performance of biomimetic robots leading live fish

Collective motion is commonly modeled with static interaction rules between agents. Substantial empirical evidence indicates, however, that animals may adapt their interaction rules depending on a variety of factors and social contexts. Here, we hypothesized that leadership performance is linked to the leader's responsiveness to the follower's actions and we predicted that a leader is followed longer if it adapts to the follower's avoidance movements. We tested this prediction with live guppies that interacted with a biomimetic robotic fish programmed to act as a 'socially competent' leader. Fish that were avoiding the robot were approached more carefully in future approaches. In two separate experiments we then asked how the leadership performance of the socially competent robot leader differed to that of a robot leader that either approached all fish in the same, non-responsive, way or one that did change its approach behavior randomly, irrespective of the fish's actions. We found that (1) behavioral variability itself appears attractive and that socially competent robots are better leaders which (2) require fewer approach attempts to (3) elicit longer average following behavior than non-competent agents. This work provides evidence that social responsiveness to avoidance reactions plays a role in the social dynamics of guppies. We showcase how social responsiveness can be modeled and tested directly embedded in a living animal model using adaptive, interactive robots.

Dynamics of collective motion across time and species

Most studies of collective animal behaviour rely on short-term observations, and comparisons of collective behaviour across different species and contexts are rare. We therefore have a limited understanding of intra- and interspecific variation in collective behaviour over time, which is crucial if we are to understand the ecological and evolutionary processes that shape collective behaviour. Here, we study the collective motion of four species: shoals of stickleback fish (Gasterosteus aculeatus), flocks of homing pigeons (Columba livia), a herd of goats (Capra aegagrus hircus) and a troop of chacma baboons (Papio ursinus). First, we describe how local patterns (inter-neighbour distances and positions), and group patterns (group shape, speed and polarization) during collective motion differ across each system. Based on these, we place data from each species within a 'swarm space', affording comparisons and generating predictions about the collective motion across species and contexts. We encourage researchers to add their own data to update the 'swarm space' for future comparative work. Second, we investigate intraspecific variation in collective motion over time and provide guidance for researchers on when observations made over different time scales can result in confident inferences regarding species collective motion. This article is part of a discussion meeting issue 'Collective behaviour through time'.

The limits of convergence in the collective behavior of competing marine taxa

Collective behaviors in biological systems such as coordinated movements have important ecological and evolutionary consequences. While many studies examine within-species variation in collective behavior, explicit comparisons between functionally similar species from different taxonomic groups are rare. Therefore, a fundamental question remains: how do collective behaviors compare between taxa with morphological and physiological convergence, and how might this relate to functional ecology and niche partitioning? We examined the collective motion of two ecologically similar species from unrelated clades that have competed for pelagic predatory niches for over 500 million years-California market squid, Doryteuthis opalescens (Mollusca) and Pacific sardine, Sardinops sagax (Chordata). We (1) found similarities in how groups of individuals from each species collectively aligned, measured by angular deviation, the difference between individual orientation and average group heading. We also (2) show that conspecific attraction, which we approximated using nearest neighbor distance, was greater in sardine than squid. Finally, we (3) found that individuals of each species explicitly matched the orientation of groupmates, but that these matching responses were less rapid in squid than sardine. Based on these results, we hypothesize that information sharing is a comparably important function of social grouping for both taxa. On the other hand, some capabilities, including hydrodynamically conferred energy savings and defense against predators, could stem from taxon-specific biology.

Systematic Analysis of Emergent Collective Motion Produced by a 3D Hybrid Zonal Model

Emergent patterns of collective motion are thought to arise from local rules of interaction that govern how individuals adjust their velocity in response to the relative locations and velocities of near neighbours. Many models of collective motion apply rules of interaction over a metric scale, based on the distances to neighbouring group members. However, empirical work suggests that some species apply interactions over a topological scale, based on distance determined neighbour rank. Here, we modify an important metric model of collective motion (Couzin et al. in J Theor Biol 218(1):1-11, 2002), so that interactions relating to orienting movements with neighbours and attraction towards more distant neighbours operate over topological scales. We examine the emergent group movement patterns generated by the model as the numbers of neighbours that contribute to orientation- and attraction-based velocity adjustments vary. Like the metric form of the model, simulated groups can fragment (when interactions are influenced by less than 10-15% of the group), swarm and move in parallel, but milling does not occur. The model also generates other cohesive group movements including cases where groups exhibit directed motion without strong overall alignment of individuals. Multiple emergent states are possible for the same set of underlying model parameters in some cases, suggesting sensitivity to initial conditions, and there is evidence that emergent states of the system depend on the history of the system. Groups that do not fragment tend to stay relatively compact in terms of neighbour distances. Even if a group does fragment, individuals remain relatively close to near neighbours, avoiding complete isolation.

A quantitative decision theory of animal conflict

Interactions between individuals are thought to shape evolution and speciation through natural selection, but little is known about how an individual (or player) strategically interacts with others to maximize its payoff. We develop a simple decision-theoretic model that generates four hypotheses about the choice of an optimal behavioral strategy by a player in response to the strategies of other players. The golden threshold hypothesis suggests that 62% is the critical threshold determining the transition of a larger player's strategy in reaction to its smaller dove-like partner. Below this critical point, the larger one exploits the smaller one, whereas above it, the larger one chooses to cooperate with the smaller one. The competition-to-cooperation shift hypothesis states that a larger player never cooperates with a smaller hawk-like player unless the former is reversely surpassed in size by the latter by 75%. The Fibonacci retracement mark hypothesis proposes that, faced with a larger dove-like player, a smaller player chooses to either cooperate or cheat, depending on whether its size relative to the larger player is less or more than 38%. The surrender-resistance hypothesis suggests that, in reaction to a larger hawk-like player, a smaller player can either gain some benefit from resistance or is sacrificed by choosing to surrender. We test these hypotheses by re-analyzing body mass data of full-sib fishes that were co-cultured in a common water pool. Pairwise analysis of these co-existing fishes broadly suggests the prediction of our hypotheses. Taken together, our model unveils detectable yet previously unknown quantitative mechanisms that mediate the strategic choice of animal behavior in populations or communities. Given the ubiquitous nature of biological interactions occurring at different levels of organizations and the paucity of quantitative approaches to understand them, results by our decision-theoretic model represent an initial step towards the deeper understanding of how biological entities interact with each other to drive their evolution.

Species interactions alter the selection of thermal environment in a coral reef fish

Increasing ocean temperatures and the resulting poleward range shifts of species has highlighted the importance of a species preferred temperature and thermal range in shaping ecological communities. Understanding the temperatures preferred and avoided by individual species, and how these are influenced by species interactions is critical in predicting the future trajectories of populations, assemblages, and ecosystems. Using an automated shuttlebox system, we established the preferred temperature and upper and lower threshold temperatures (i.e., avoided temperatures) of a common coral reef fish, the black-axil chromis, Chromis atripectoralis. We then investigated how the presence of conspecifics, heterospecifics (Neopomacentrus bankieri), or a predator (Cephalopholis spiloparaea) influenced the selection of these temperatures. Control C. atripectoralis preferred 27.5 ± 1.0 °C, with individuals avoiding temperatures below 23.5 ± 0.9 °C and above 29.7 ± 0.7 °C. When associating with either conspecifics or heterospecifics, C. atripectoralis selected significantly lower temperatures (conspecifics: preferred = 21.2 ± 1.4 °C, lower threshold = 18.1 ± 0.8 °C; heterospecifics: preferred = 21.1 ± 1.1 °C, lower threshold = 19.2 ± 0.9 °C), but not higher temperatures (conspecifics: preferred = 28.9 ± 1.2 °C, upper threshold = 30.8 ± 0.9 °C; heterospecifics: preferred = 29.7 ± 1.1 °C, upper threshold = 31.4 ± 0.8 °C). The presence of the predator, however, had a significant effect on both lower and upper thresholds. Individual C. atripectoralis exposed themselves to temperatures ~ 5.5 °C cooler or warmer (lower threshold: 18.6 ± 0.5 °C, upper threshold: 35.2 ± 0.5 °C) than control fish before moving into the chamber containing the predator. These findings demonstrate how behavioural responses due to species interactions influence the thermal ecology of a tropical reef fish; however, there appears to be limited scope for individuals to tolerate higher temperatures unless faced with the risk of predation.

Scale-Free Dynamics in Animal Groups and Brain Networks

Collective phenomena fascinate by the emergence of order in systems composed of a myriad of small entities. They are ubiquitous in nature and can be found over a vast range of scales in physical and biological systems. Their key feature is the seemingly effortless emergence of adaptive collective behavior that cannot be trivially explained by the properties of the system's individual components. This perspective focuses on recent insights into the similarities of correlations for two apparently disparate phenomena: flocking in animal groups and neuronal ensemble activity in the brain. We first will summarize findings on the spontaneous organization in bird flocks and macro-scale human brain activity utilizing correlation functions and insights from critical dynamics. We then will discuss recent experimental findings that apply these approaches to the collective response of neurons to visual and motor processing, i.e., to local perturbations of neuronal networks at the meso- and microscale. We show how scale-free correlation functions capture the collective organization of neuronal avalanches in evoked neuronal populations in nonhuman primates and between neurons during visual processing in rodents. These experimental findings suggest that the coherent collective neural activity observed at scales much larger than the length of the direct neuronal interactions is demonstrative of a phase transition and we discuss the experimental support for either discontinuous or continuous phase transitions. We conclude that at or near a phase-transition neuronal information can propagate in the brain with similar efficiency as proposed to occur in the collective adaptive response observed in some animal groups.

A behavioral model for mapping the genetic architecture of gut-microbiota networks

The gut microbiota may play an important role in affecting human health. To explore the genetic mechanisms underlying microbiota-host relationships, many genome-wide association studies have begun to identify host genes that shape the microbial composition of the gut. It is becoming increasingly clear that the gut microbiota impacts host processes not only through the action of individual microbes but also their interaction networks. However, a systematic characterization of microbial interactions that occur in densely packed aggregates of the gut bacteria has proven to be extremely difficult. We develop a computational rule of thumb for addressing this issue by integrating ecological behavioral theory and genetic mapping theory. We introduce behavioral ecology theory to derive mathematical descriptors of how each microbe interacts with every other microbe through a web of cooperation and competition. We estimate the emergent properties of gut-microbiota networks reconstructed from these descriptors and map host-driven mutualism, antagonism, aggression, and altruism QTLs. We further integrate path analysis and mapping theory to detect and visualize how host genetic variants affect human diseases by perturbing the internal workings of the gut microbiota. As the proof of concept, we apply our model to analyze a published dataset of the gut microbiota, showing its usefulness and potential to gain new insight into how microbes are organized in human guts. The new model provides an analytical tool for revealing the "endophenotype" role of microbial networks in linking genotype to end-point phenotypes.

Maternal predation risk increases offspring’s exploration but does not affect schooling behavior

The environment that parents experience can influence their reproductive output and their offspring’s fitness via parental effects. Perceived predation risk can affect both parent and offspring phenotype, but it remains unclear to what extent offspring behavioral traits are affected when the mother is exposed to predation risk. This is particularly unclear in live-bearing species where maternal effects could occur during embryogenesis. Here, using a half-sib design to control for paternal effects, we experimentally exposed females of a live-bearing fish, the guppy (Poecilia reticulata), to visual predator cues and conspecific alarm cues during their gestation. Females exposed to predation risk cues increased their antipredator behaviors throughout the entire treatment. Offspring of mothers exposed to the predation stimuli exhibited more pronounced exploratory behavior, but did not show any significant differences in their schooling behavior, compared to controls. Thus, while maternally perceived risk affected offspring’s exploration during early stages of life, offspring’s schooling behavior could be influenced more by direct environmental experience rather than via maternal cues. Our results suggest a rather limited role in predator-induced maternal effects on the behavior of juvenile guppies.

Guppies Prefer to Follow Large (Robot) Leaders Irrespective of Own Size

Body size is often assumed to determine how successfully an individual can lead others with larger individuals being better leaders than smaller ones. But even if larger individuals are more readily followed, body size often correlates with specific behavioral patterns and it is thus unclear whether larger individuals are more often followed than smaller ones because of their size or because they behave in a certain way. To control for behavioral differences among differentially-sized leaders, we used biomimetic robotic fish (Robofish) of different sizes. Live guppies (Poecilia reticulata) are known to interact with Robofish in a similar way as with live conspecifics. Consequently, Robofish may serve as a conspecific-like leader that provides standardized behaviors irrespective of its size. We asked whether larger Robofish leaders are preferentially followed and whether the preferences of followers depend on own body size or risk-taking behavior ("boldness"). We found that live female guppies followed larger Robofish leaders in closer proximity than smaller ones and this pattern was independent of the followers' own body size as well as risk-taking behavior. Our study shows a "bigger is better" pattern in leadership that is independent of behavioral differences among differentially-sized leaders, followers' own size and risk-taking behavior.

A Drive to Driven Model of Mapping Intraspecific Interaction Networks

Community ecology theory suggests that an individual's phenotype is determined by the phenotypes of its coexisting members to the extent at which this process can shape community evolution. Here, we develop a mapping theory to identify interaction quantitative trait loci (QTL) governing inter-individual dependence. We mathematically formulate the decision-making strategy of interacting individuals. We integrate these mathematical descriptors into a statistical procedure, enabling the joint characterization of how QTL drive the strengths of ecological interactions and how the genetic architecture of QTL is driven by ecological networks. In three fish full-sib mapping experiments, we identify a set of genome-wide QTL that control a range of societal behaviors, including mutualism, altruism, aggression, and antagonism, and find that these intraspecific interactions increase the genetic variation of body mass by about 50%. We showcase how the interaction QTL can be used as editors to reconstruct and engineer new social networks for ecological communities.

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We develop a new theory for complex-trait mapping by integrating behavioral ecology

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This theory can characterize how QTL drive cooperation or competition in populations

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It can also illustrate how the activation of QTL is driven by ecological interactions

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The new theory leverages interdisciplinary studies of genetics, ecology, and evolution

Social conformity and propagation of information in collective U-turns of fish schools

Moving animal groups such as schools of fishes or flocks of birds often undergo sudden collective changes of their travelling direction as a consequence of stochastic fluctuations in heading of the individuals. However, the mechanisms by which these behavioural fluctuations arise at the individual level and propagate within a group are still unclear. In this study, we combine an experimental and theoretical approach to investigate spontaneous collective U-turns in groups of rummy-nose tetra (Hemigrammus rhodostomus) swimming in a ring-shaped tank. U-turns imply that fish switch their heading between the clockwise and anticlockwise direction. We reconstruct trajectories of individuals moving alone and in groups of different sizes. We show that the group decreases its swimming speed before a collective U-turn. This is in agreement with previous theoretical predictions showing that speed decrease facilitates an amplification of fluctuations in heading in the group, which can trigger U-turns. These collective U-turns are mostly initiated by individuals at the front of the group. Once an individual has initiated a U-turn, the new direction propagates through the group from front to back without amplification or dampening, resembling the dynamics of falling dominoes. The mean time between collective U-turns sharply increases as the size of the group increases. We develop an Ising spin model integrating anisotropic and asymmetrical interactions between fish and their tendency to follow the majority of their neighbours nonlinearly (social conformity). The model quantitatively reproduces key features of the dynamics and the frequency of collective U-turns observed in experiments.

Using activity and sociability to characterize collective motion

A wide range of measurements can be made on the collective motion of groups, and the movement of individuals within them. These include, but are not limited to: group size, polarization, speed, turning speed, speed or directional correlations, and distances to near neighbours. From an ecological and evolutionary perspective, we would like to know which of these measurements capture biologically meaningful aspects of an animal's behaviour and contribute to its survival chances. Previous simulation studies have emphasized two main factors shaping individuals' behaviour in groups; attraction and alignment. Alignment responses appear to be important in transferring information between group members and providing synergistic benefits to group members. Likewise, attraction to conspecifics is thought to provide benefits through, for example, selfish herding. Here, we use a factor analysis on a wide range of simple measurements to identify two main axes of collective motion in guppies (Poecilia reticulata): (i) sociability, which corresponds to attraction (and to a lesser degree alignment) to neighbours, and (ii) activity, which combines alignment with directed movement. We show that for guppies, predation in a natural environment produces higher degrees of sociability and (in females) lower degrees of activity, while female guppies sorted for higher degrees of collective alignment have higher degrees of both sociability and activity. We suggest that the activity and sociability axes provide a useful framework for measuring the behaviour of animals in groups, allowing the comparison of individual and collective behaviours within and between species.This article is part of the theme issue 'Collective movement ecology'.

The Three Dimensional Spatial Structure of Antarctic Krill Schools in the Laboratory

Animal positions within moving groups may reflect multiple motivations including saving energy and sensing neighbors. These motivations have been proposed for schools of Antarctic krill, but little is known about their three-dimensional structure. Stereophotogrammetric images of Antarctic krill schooling in the laboratory are used to determine statistical distributions of swimming speed, nearest neighbor distance, and three-dimensional nearest neighbor positions. The krill schools swim at speeds of two body lengths per second at nearest neighbor distances of one body length and reach similarly high levels of organization as fish schools. The nearest neighbor position distribution is highly anisotropic and shows that Antarctic krill prefer to swim in the propulsion jet of their anterior neighbor. This position promotes communication and coordination among schoolmates via hydrodynamic signals within the pulsed jet created by the metachronal stroking of the neighboring krill’s pleopods. The hydrodynamic communication channel therefore plays a large role in structuring the school. Further, Antarctic krill avoid having a nearest neighbor directly overhead, possibly to avoid blockage of overhead light needed for orientation. Other factors, including the elongated body shape of Antarctic krill and potential energy savings, also may help determine the three dimensional spatial structure of tightly packed krill schools.

Using a robotic fish to investigate individual differences in social responsiveness in the guppy

Responding towards the actions of others is one of the most important behavioural traits whenever animals of the same species interact. Mutual influences among interacting individuals may modulate the social responsiveness seen and thus make it often difficult to study the level and individual variation in responsiveness. Here, open-loop biomimetic robots that provide standardized, non-interactive social cues can be a useful tool. These robots are not affected by the live animal's actions but are assumed to still represent valuable and biologically relevant social cues. As this assumption is crucial for the use of biomimetic robots in behavioural studies, we hypothesized (i) that meaningful social interactions can be assumed if live animals maintain individual differences in responsiveness when interacting with both a biomimetic robot and a live partner. Furthermore, to study the level of individual variation in social responsiveness, we hypothesized (ii) that individual differences should be maintained over the course of multiple tests with the robot. We investigated the response of live guppies (Poecilia reticulata) when allowed to interact either with a biomimetic open-loop-controlled fish robot-'Robofish'-or with a live companion. Furthermore, we investigated the responses of live guppies when tested three times with Robofish. We found that responses of live guppies towards Robofish were weaker compared with those of a live companion, most likely as a result of the non-interactive open-loop behaviour of Robofish. Guppies, however, were consistent in their individual responses between a live companion and Robofish, and similar individual differences in response towards Robofish were maintained over repeated testing even though habituation to the test environment was detectable. Biomimetic robots like Robofish are therefore a useful tool for the study of social responsiveness in guppies and possibly other small fish species.

Body size affects the strength of social interactions and spatial organization of a schooling fish (Pseudomugil signifer)

While a rich variety of self-propelled particle models propose to explain the collective motion of fish and other animals, rigorous statistical comparison between models and data remains a challenge. Plausible models should be flexible enough to capture changes in the collective behaviour of animal groups at their different developmental stages and group sizes. Here, we analyse the statistical properties of schooling fish (Pseudomugil signifer) through a combination of experiments and simulations. We make novel use of a Boltzmann inversion method, usually applied in molecular dynamics, to identify the effective potential of the mean force of fish interactions. Specifically, we show that larger fish have a larger repulsion zone, but stronger attraction, resulting in greater alignment in their collective motion. We model the collective dynamics of schools using a self-propelled particle model, modified to include varying particle speed and a local repulsion rule. We demonstrate that the statistical properties of the fish schools are reproduced by our model, thereby capturing a number of features of the behaviour and development of schooling fish.