Source-linked AI summary
Disentangling and modeling interactions in fish with burst-and-coast swimming
Daniel S. Calovi, Alexandra Litchinko, Valentin Lecheval, Ugo Lopez, Alfonso Pérez Escudero, Hugues Chaté, Clément Sire, Guy Theraulaz
TL;DR
Individual fish interactions are difficult to disentangle and connect to group-level behavior, particularly when spontaneous behavioral variability is not incorporated into models. This study analyzes burst-and-coast decisions and uses symmetry constraints to characterize interactions; its model reproduces observed motion and spatial distributions, while the data constrain estimates of long-range attraction.
Problem
Earlier fish-interaction studies estimated effective turning and speeding responses but did not incorporate intrinsic behavioral stochasticity or validate findings by generating model trajectories.
Source: §I · p. 2Method
The authors analyze discrete fish kicks and use symmetry constraints to separate wall, attraction, and alignment interactions, then build a stochastic burst-and-coast model.
Source: §2 · p. 5, §III · p. 8Results
The model quantitatively reproduces observed motion and spatial distributions, and alignment dominates attraction below about 75 mm while attraction dominates at larger distances.
Source: §III · pp. 8–9Takeaways & Limitations
The method disentangles and characterizes pairwise animal interactions when large amounts of data are available, and may apply to collective motion at different biological scales.
Source: §III · p. 9Limited tank size and insufficient observations at large distances prevented measuring whether attraction decreases at longer ranges.
Source: §III · p. 8
Abstract
from arXiv · showhide
We combine extensive data analyses with a modeling approach to measure, disentangle, and reconstruct the actual functional form of interactions involved in the coordination of swimming in Rummy-nose tetra (Hemigrammus rhodostomus). This species of fish performs burst-and-coast swimming behavior that consists of sudden heading changes combined with brief accelerations followed by quasi-passive, straight decelerations. We quantify the spontaneous stochastic behavior of a fish and the interactions that govern wall avoidance and the attraction and alignment to a neighboring fish, the latter by exploiting general symmetry constraints for the interactions. In contrast with previous experimental works, we find that both attraction and alignment behaviors control the reaction of fish to a neighbor. We then exploit these results to build a model of spontaneous burst-and-coast swimming and interactions of fish, with all parameters being estimated or directly measured from experiments. This model quantitatively reproduces the key features of the motion and spatial distributions observed in experiments with a single fish and with two fish. This demonstrates the power of our method that exploits large amounts of data for disentangling and fully characterizing the interactions that govern collective behaviors in animals groups. Moreover, we introduce the notions of "dumb" and "intelligent" active matter and emphasize and clarify the strong differences between them.
I. INTRODUCTION
Social interactions help coordinate group behavior, but identifying how individual interactions combine and shape group-level dynamics remains a challenge. This study uses burst-and-coast swimming to measure fish responses and build a model that reproduces observed motion and spatial distributions.
I. INTRODUCTION
- Social interactions matter to ethology and behavioral ecology and have conceptual significance because social and physical forces play different roles in active-matter dynamics.Such interactions can help group members coordinate and collectively solve problems, with consequences for fitness.Source: §I · p. 1
- Fine-scale tracking and behavior analyses have improved the precision of available data on social interactions across many animal groups.The paper situates this work within efforts to use individual-level interactions to model collective behavior.Source: §I · p. 2
- Existing fish-interaction studies estimated effective turning and speeding responses but did not incorporate intrinsic behavioral stochasticity or validate findings by generating trajectories from a model.Connecting detailed individual-level interactions to emergent group dynamics is also difficult because interactions with the physical and social environment are entangled.Source: §I · p. 2
- The study extends an incremental approach to Hemigrammus rhodostomus, using discrete burst-and-coast decisions to characterize spontaneous motion and interactions.The supplied passage describes the swimming behavior as a series of discrete decisions in time and space.Source: §I · p. 2
- The authors measure responses to walls and neighboring fish, then use symmetry constraints to disentangle repulsion, attraction, and alignment interactions.Their model quantitatively reproduces motion and spatial distributions observed in single-fish and two-fish experiments.Source: §I · p. 2
A. Characterization of individual swimming behavior
The fish’s burst-and-coast motion makes its trajectory analyzable as straight segments between discrete kicks. The figure compares single- and two-fish swimming and defines variables used to describe wall and neighbor interactions.
A. Characterization of individual swimming behavior
- Most heading changes occur at the onset of acceleration, which the authors label a kick; trajectories can then be represented as straight segments between kicks.The swimming consists of sudden speed increases followed by mostly passive gliding.Source: A. Characterization of individual… · p. 2
- The mean interval between kicks is close to 0.5 s in both conditions, while the mean distance between kicks is slightly lower for two fish.Active-period velocity is of order 140 mm/s.Source: A. Characterization of individual… · p. 2
- Figure 1 shows solo and paired trajectories, speed time series, wall-relative variables, neighbor-relative variables, and kick-interval distributions.Panels G and H compare duration and distance between kicks for one- and two-fish experiments.Source: Figure 1 · p. 3
B. Quantifying the effect of the interaction of a single fish with the wall
Fish spend much of their time close to the tank wall, with trajectories and heading changes consistent with wall avoidance. The burst-and-coast motion and narrow turn-angle distribution help explain why they do not readily escape the curved boundary.
B. Quantifying the effect of the interaction of a single fish with the wall
- The wall-distance distribution shows that fish spend most of their time very close to the wall.Their relative angle to the wall is centered below 90°, indicating that they remain nearly parallel to it while often moving toward it.Source: B. Quantifying the effect of the… · p. 3
- Burst-and-coast segments averaging about 70 mm, shorter near the wall, together with narrow angle changes, prevent fish from efficiently escaping the curved boundary.This combination helps account for their concentration near the wall.Source: B. Quantifying the effect of the… · p. 3
- The signed post-kick angle change is centered near 15° away from the wall, indicating wall avoidance.For fish more than 60 mm from the wall, where its influence is negligible, the angle-change distribution becomes symmetric and approximately Gaussian, with width around 20°.Source: B. Quantifying the effect of the… · p. 3
C. Modeling and direct measurement of fish interaction with the wall
The authors build the model incrementally, starting with spontaneous swimming before adding wall and fish interactions. More than 300,000 single-fish kicks and 200,000 two-fish kicks support interaction estimates and tests against distributions.
C. Modeling and direct measurement of fish interaction with the wall
- The modeling sequence starts with spontaneous burst-and-coast motion for one fish, adds wall interaction, and then considers interactions between two fish.The stages are intended to separate effects of the physical and social environment.Source: C. Modeling and direct measurement of… · p. 3
- The dataset contains more than 300,000 recorded kicks for one fish and 200,000 for two fish.The authors use this volume of data to characterize interactions and test the model.Source: C. Modeling and direct measurement of… · p. 3
- Model tests compare full fish-wall and fish-fish distance and angle distributions, rather than only their means.These observables are selected as quantities sensitive to changes in the model or its parameters.Source: C. Modeling and direct measurement of… · p. 3
1. Swimming dynamics without any interaction
The fish’s motion is modeled as discrete kicks followed by straight gliding with decaying speed. Spontaneous heading changes are treated as random increments, while measured single-fish dynamics inform the model.
1. Swimming dynamics without any interaction
- Each kick selects a new heading and motion parameters, then the fish glides in a straight line as its speed decays.The model uses kick length and duration, with the third quantity determined from the other two and the measured decay time.Source: §1 · pp. 3–4
- Near the tank center, spontaneous heading changes are approximately Gaussian, with fluctuation intensity about 0.35 rad (≈20°).The near-center distribution is used to represent random heading decisions when wall influence is negligible.Source: §1 · p. 4, Figure 2 · p. 4
- τ0 ≈0.80 s describes the approximately exponential decay of speed after a kick.The decay timescale is measured from the average speed profile.Source: Figure 3 · p. 4, §1 · p. 4
- The continuous-time reconstruction uses the empirically observed exponential speed decay to generate real-time trajectories consistent with the discrete kick dynamics.At the end of a kick, the position update recovers the discrete model’s next position.Source: §1 · p. 4
2. Fish interaction with the wall
The wall interaction depends on both distance and orientation: it acts over roughly 60 mm and weakens when the fish is parallel to the wall. The fitted response functions are smooth without regularization, and simulations reproduce key wall-related distributions.
2. Fish interaction with the wall
- Wall-induced turning depends on wall distance and relative orientation, with no statistically relevant left-right asymmetry.The model uses an odd angular response and an even phenomenological term to account for anisotropic perception.Source: §2 · pp. 4–5
- Near the wall, spontaneous angular fluctuations are reduced, recovering free spontaneous motion when wall influence becomes negligible.The distance weighting tends to zero far beyond the wall-interaction range and is normalized to one at the wall.Source: §2 · p. 5
- The wall interaction extends about 60 mm and is weaker when the fish swims parallel to the wall; its strength decreases as tank radius increases.The measured functional forms show no significant dependence on tank radius, although interaction strength decreases in larger tanks.Source: §2 · p. 5, Figure 4 · p. 5
- The fitted scatter plots form smooth curves despite the absence of regularization, which the authors regard as implicit validation of the fitting procedure.The plotted experimental responses and analytic forms are shown across three tank radii.Source: §2 · p. 5, Figure 4 · p. 5
- Simulations show satisfactory agreement with experiments for wall distance, relative wall angle, and angle change across all three tank radii.The model fish also qualitatively mimics real-fish motion.Source: §2 · pp. 5–6
D. Quantifying the effect of interactions between two fish
Experiments with two fish show attraction and alignment alongside differences in their positions relative to the wall. Their relative orientation and wall-related motion distributions provide measures for calibrating and testing the model.
D. Quantifying the effect of interactions between two fish
- The two-fish measurements comprise around 200,000 recorded kicks in a tank of radius 250 mm.Source: D. Quantifying the effect of… · p. 6
- The distance distribution shows strong attraction between the two fish, while their relative orientations are concentrated near 0°, indicating a tendency to align.The follower’s viewing-angle distribution is also peaked near 0° and resembles the relative-orientation distribution.Source: D. Quantifying the effect of… · p. 6, Figure 5 · p. 6
- The geometrical leader is closer to the wall than the follower, but both fish stay farther from it than an isolated fish.The leader is defined by the larger viewing angle; the fish can exchange this role.Source: D. Quantifying the effect of… · p. 6, Figure 5 · p. 6
- For both fish, wall-angle and signed turning distributions are wider than for an isolated fish, consistent with weaker wall constraint during paired swimming.The leader’s wall-angle distribution is sharper than the follower’s because it is closer to, and more parallel with, the wall.Source: D. Quantifying the effect of… · p. 6, Figure 5 · p. 6
E. Modeling and direct measurement of interactions between two fish
The paper models pairwise attraction and alignment as distinct, symmetry-constrained contributions to heading changes. Experimental measurements show distance- and orientation-dependent interactions, and simulations agree quantitatively with two-fish experiments.
E. Modeling and direct measurement of interactions between two fish
- The model adds random, wall, attraction, and alignment contributions to each heading change, with the pairwise terms depending on distance, viewing angle, and relative orientation.Mirror symmetry constrains the angular functions: attraction uses an odd viewing-angle function and an even orientation function, while alignment uses an odd orientation function and an even viewing-angle function.Source: E. Modeling and direct measurement of… · p. 6
- Experimental data show distinct attraction and alignment responses: attraction includes short-range repulsion, while alignment is strongest when the neighbor is ahead.Attraction has a characteristic distance of about 200 mm and an apparent repulsive regime below about 30 mm; alignment nearly vanishes when the neighbor is behind.Source: E. Modeling and direct measurement of… · p. 7
- Attraction and alignment both depend on inter-fish distance, but values beyond 280 mm could not be properly measured because observations there were sparse.The typical inter-fish distance was about 75 mm; the attraction fit uses a characteristic scale near 200 mm, and the alignment fit has a similar scale.Source: E. Modeling and direct measurement of… · p. 7
- The angular response to attraction is reduced when fish are aligned, while alignment is stronger for a neighbor ahead and nearly vanishes for one behind.The measured attraction orientation factor has a minimum at relative angle ∆φ = 0; alignment is strongest for |ψ| < 90° and nearly absent at ψ = ±180°.Source: E. Modeling and direct measurement of… · p. 7
- The interaction model achieves qualitative and quantitative agreement with experiments on two-fish swimming.The simulations are compared with experimental probability distributions in Fig. 5.Source: E. Modeling and direct measurement of… · pp. 7–8
- The product forms are symmetry-preserving generalizations of simple physical attraction and alignment analogies, chosen to limit overfitting while capturing the main measured effects.The authors note that adding terms could risk overfitting and make weaker terms difficult to interpret.Source: E. Modeling and direct measurement of… · pp. 7–8
III. DISCUSSION AND CONCLUSION
The study identifies four behavioral modes in fish interactions and shows that their effects depend on distance and orientation. A calibrated model reproduces key motion and distribution patterns for individual fish and pairs.
III. DISCUSSION AND CONCLUSION
- The four measured modes include wall avoidance below 2 BL and short-range fish-to-fish repulsion below 30 mm, or about 1 BL.These interactions were quantified using discrete heading decisions, or kicks, as a proxy for behavioral responses.Source: §III · p. 8
- Attraction reaches a maximum near 200 mm, while alignment saturates near 100 mm; alignment dominates below about 75 mm and attraction at greater distances.The authors could not measure the long-distance decline in attraction because the tanks were limited in size and large-distance data were insufficient.Source: §III · p. 8
- Behavior is anisotropic: wall repulsion peaks near a 45° approach, and alignment is strongest for neighbors ahead, fading toward the rear.Alignment nearly vanishes when the neighbor is behind the focal fish.Source: §III · p. 8
- Symmetry constraints let the authors separate attraction from alignment, finding explicit alignment in Rummy-nose tetra rather than alignment arising only from attraction and repulsion.Earlier studies of Golden shiners and Mosquito fish had not found clear evidence for explicit body-orientation matching.Source: §III · p. 8
- The calibrated model reproduces swimming and spatial and angular distributions for solo fish and pairs, including near-wall trajectories and alternating temporary leader–follower roles.The temporary leader is mostly governed by wall interactions, while the follower is mostly influenced by the leader.Source: §III · pp. 8–9
- The authors propose applying the data-driven method to other biological collective-motion systems and using the validated model to test multi-neighbor hypotheses.They also suggest studying collective phases in unbounded groups as attraction and alignment strength or range varies.Source: §III · p. 9
Appendix: Intelligent and dumb active matter
The appendix introduces a physical-particle description in a thermal bath subject to external forces. It relates the particle’s stationary distribution to the Boltzmann distribution when those forces are conservative.
Appendix: Intelligent and dumb active matter
- The appendix frames a particle moving in a thermal bath as subject to external physical forces from other particles or fields.The medium is described as inducing friction and stochastic forcing.Source: Appendix: Intelligent and dumb active… · p. 9
- The particle’s temperature and time-correlated Gaussian stochastic noise characterize the thermal forcing in this description.The noise correlation is specified as delta-correlated in time.Source: Appendix: Intelligent and dumb active… · p. 9
- For conservative physical forces, the stationary velocity and position distribution is the Boltzmann distribution, with energy given by kinetic energy plus potential.The normalization constant is denoted by Z.Source: Appendix: Intelligent and dumb active… · p. 9
1. Dumb active matter
The appendix distinguishes particles whose physical forces affect only actual velocity from animals whose social interactions can also change intrinsic velocity. It models spontaneous animal motion as stochastic noise.
1. Dumb active matter
- In the dumb-particle description, the intrinsic velocity is modeled as an Ornstein–Uhlenbeck process driven by Gaussian noise, with a correlation time not necessarily tied to the velocity relaxation time.The stationary distribution is generally unknown, though analytical results are available in some limits.Source: §1 · p. 9
- A “dumb” active particle is defined by physical forces changing its actual velocity without directly changing its intrinsic or desired velocity.The appendix assumes intrinsic velocity follows a simple Ornstein–Uhlenbeck stochastic process.Source: §1 · pp. 9–10
2. Intelligent active matter
- An “intelligent” active particle is defined by social interactions that directly affect intrinsic velocity; for animals, the noise models spontaneous motion.Social forces are generally nonconservative and can depend on relative direction and viewing angle; the fish–wall response also depends on viewing angle.Source: §2 · p. 10