Larval zebrafish minimize energy consumption during hunting via adaptive movement selection

Significance

Animals must balance the need to move with the energetic costs of doing so, a trade-off which is particularly important during prey hunting. We studied how energy constraints may shape hunting behavior in larval zebrafish, a model organism with well-characterized neural circuits. Using fluid dynamics to calculate energy costs, we found that zebrafish match the frequency of different movement patterns while hunting to the energy each pattern consumes. A simulated agent trained with reinforcement learning revealed that this matching strategy minimizes energy. This strategy was actively maintained with changing energy constraints, due to both normal development and environmental perturbation. These findings suggest a general principle by which animals could optimize motor behavior to accommodate changing energy landscapes.

Abstract

Animals must balance behavioral goals with the energetic costs of movement. How such trade-offs are implemented algorithmically during natural behavior, and how they adapt to changing energetic constraints, remains poorly understood. Here we show that larval zebrafish adjust their motor strategies during prey hunting to minimize energy expenditure. Using high-speed video tracking and 3D computational fluid dynamics simulations, we quantified the energy costs (in Joules) of different movement types across three developmental stages. While the structure of discrete movement types (“bouts”) remained stable with age, their selection probabilities changed depending on their energetic cost, such that more expensive bouts were always used less frequently. This relationship was conserved across development despite shifts in the relative costs of different bouts. A reinforcement learning model trained to catch prey while minimizing energy use reproduced this relationship, demonstrating that it is an energetically optimal strategy. Furthermore, when fish were reared in a high-viscosity environment that altered energetic costs, they readapted their movement probabilities to preserve the same energy-based control rule, demonstrating active optimization rather than a predetermined developmental program. These findings reveal how goal-directed animals can dynamically regulate movement selection to minimize energetic costs, even under changing environmental and biomechanical conditions. Our results provide a quantitative link between biomechanics, development, behavior, and computational control theory in a freely moving animal.

Animals must continuously balance behavioral goals with the energetic costs of achieving them. This trade-off is especially critical during hunting and foraging, where movement is essential but metabolically expensive. Understanding how such trade-offs are implemented algorithmically in the brain, and how they adapt to changes in the body and environment, remains a central question in neuroscience and ethology (1–4). In particular, how animals dynamically adjust action selection to minimize energetic cost during natural behavior has rarely been quantified directly, and its developmental robustness and environmental flexibility remain largely unexplored.

Larval zebrafish offer a powerful model system for investigating these issues. By 5 d postfertilization (dpf), they engage in visually guided prey capture using a discrete set of stereotyped movement bouts (5, 6). These bouts are generated by a relatively well-understood neural circuit architecture (7, 8), and the biomechanics of larval swimming are governed by relatively simple fluid dynamics (9, 10). Previous studies have proposed that zebrafish behavior may be energy-aware or reward-maximizing, but these inferences have been largely indirect (11, 12). Critically, no prior work has directly quantified the energetic costs in Joules of individual movement bouts, nor examined how the nervous system adapts action selection in response to changing energetic constraints during growth or environmental perturbation.

Here, we combined high-speed behavioral imaging, computational fluid dynamics (CFD), and reinforcement learning to test whether larval zebrafish use an energy-aware control strategy during prey hunting. We show that, while the repertoire of movement types remains stable over development, the relative frequency with which each type is selected changes systematically to match its energetic cost. This energy–probability relationship is preserved across developmental changes in relative energy costs and is actively reoptimized when fish are reared in a high-viscosity environment. A reinforcement learning agent trained to minimize energy while catching prey independently learns the same strategy. These results suggest that larval zebrafish implement a flexible, energy-minimizing control policy for goal-directed behavior. This provides direct evidence that freely behaving animals can integrate energetic considerations into motor planning, and that this optimization emerges robustly across development and in novel environments. By linking biomechanics, behavior, and computational models of control, our results reveal a generalizable principle of action selection under energy constraints.

Results

Bout Types Are Stable over Development but Their Selection Probabilities Change.

Zebrafish larvae move in discrete bouts lasting 100 to 200 ms, separated by up to about 1 s of inactivity (Movies S1 and S2). To capture developmental changes in these bouts we made 2D video recordings of individual larval zebrafish hunting Paramecia at 5, 9, and 14 dpf ($N=19$, 20, and 11 fish respectively) for 15 min at 500 fps (Fig. 1A). The midline of each fish was automatically tracked using a custom image-processing pipeline (Fig. 1B; see Materials and Methods), yielding a total of 34,660 swim bouts (92-1367 bouts per fish). Behavior was then classified as either hunting or exploratory based primarily on whether the eyes were converged (13) (Materials and Methods, see Movie S1 for an example hunting event and Movie S2 for an example of exploration). Averaged over all ages fish spent 8% of their time in the assay hunting and 92% exploring. There was a developmental increase in the proportion of hunting events that were successful (hit rate): 32% for 5 dpf, 35% for 9 dpf, and 44% for 14 dpf.

Fig. 1.

Larval zebrafish bout type shapes are similar over development, however bout type selection probabilities change. (A) A single larvae was placed in a 20 mm diameter dish with $\sim$35 Paramecia and recorded for hunting behavior for 15 min. (B) In each movie frame the eye midpoint (blue) and 101 points along the tail (red) were tracked. (C) The shapes of the first 5 PCs (eigenfish). (D) An example PC trajectory of a 9 dpf Slow 1 bout. (E) 2-dimensional Isomap projection of exemplars; hierarchical clustering was performed on the 20-dimensional Isomap embedding. (F) Mean and variance of tail-tip angles for each bout type were very similar between 5, 9, and 14 dpf (J-turn shown here). Thick lines indicate averages across age groups, shading shows 1 SD. Insets: example tail traces (lines drawn every 2 ms); There were no statistical differences in the areas covered by age groups in the 2-dimensional Isomap embedding space (shuffle test, see Materials and Methods). Shaded regions are the outer layers of contour plots for each age group, crosses represent center of mass for each age group. (G) There were significant changes in bout-type probabilities for Slow 2s, Routine turns, Slow 1s, and Approach bouts between 5 and 14 dpf. (H) Bout-type probabilities changed over development for both hunting and exploratory behavior (two-sample discrete Kolmogorov–Smirnov test; asterisks indicate $P<0.0001$).

Our bout analysis followed the pipeline of Mearns et al. (6). First we performed Principal Components Analysis (PCA) on local tail curvatures to extract low-dimensional movement features. Pooling all ages, five principal components (PCs) explained $>$99% of tail curvature variance (SI Appendix, Fig. S1A), which can be visualized as “eigenfish” (Fig. 1C). Performing PCA on each age separately produced no obvious differences in eigenfish or variance explained (SI Appendix, Fig. S1 B and C), and we therefore continued with all ages pooled together. To identify different bout types, Dynamic Time Warping (DTW) (14) was used to compute the similarity between each bout’s trajectory through PCA space (example in Fig. 1D). Affinity Propagation clustering (15) was then used to find representative “exemplar” bouts for the resultant pairwise similarity matrix. We then performed a 20-dimensional Isomap embedding on the exemplar DTW similarity matrix, and used hierarchical clustering on the embedding space to extract 7 clusters. By comparing bout-type shapes with those previously reported (6, 16), we labeled these clusters as High Angle Turns (HATs, sometimes called C-starts, C-bends, or O-bends), J-turns, Routine turns, Slow 1s, Slow 2s, Approach, and Capture Strikes (Fig. 1E). Although bout space is likely somewhat continuous (6), and other approaches can produce different numbers of clusters (e.g. ref. 16), we show later that our key conclusions do not depend on the exact number of bout types extracted. SI Appendix, Fig. S2 shows an example sequence of bouts and the detailed mechanics of each of the 7 bout types.

We then asked whether bout movements changed over development by comparing several standard kinematic variables. Tail-beat frequency decreased over development (SI Appendix, Fig. S1D), while both tail-beat amplitude (SI Appendix, Fig. S1E) and tail curvature increased (SI Appendix, Fig. S1F). While Slow 1 and Approach bouts changed in both tail-beat frequency and amplitude (SI Appendix, Fig. S1 G and H), these changes were small relative to the differences between bout types (SI Appendix, Fig. S1 I and J). Visualizing mean tail-tip angles across time for each bout type, we found no qualitative differences in structure or variance over development (Fig. 1F and SI Appendix, Fig. S3 A–G). Additionally there were no differences in the occupied areas of the Isomap embedding over development (Fig. 1F and SI Appendix, Fig. S3 A–F, Insets). Thus the basic structure of bout types was stable from 5 to 14 dpf.

An alternative way in which the behavioral space could change is by alterations in bout-type probabilities. Consistent with this, there were significant changes in selection probabilities between 5 and 14 dpf for Slow 1, Slow 2, Routine Turns and Approach bouts, with Slow 2 bouts showing the largest increase and Slow 1 and Approach bouts showing the largest decreases (Fig. 1G). The distributions of bout-type probabilities were different at each age group both when considering hunting and exploring together (SI Appendix, Fig. S3H) and separately (Fig. 1H). These changes led to increasing entropy for the distributions of bout-type probabilities, indicating more complexity over development (SI Appendix, Fig. S3I). We also examined whether the structure of bout-type transition probabilities changed over development, but found this relatively stable with age compared to the large changes in bout probabilities (SI Appendix, Fig. S3 J–O). In summary, over this period of development bout structure remained stable but bout probabilities changed.

A CFD Simulation of Naturally Swimming Fish Reproduces Velocities and Turn Angles.

Could changing bout-type probabilities over development be related to the changing relationship between the fish and the fluid? To address this, we quantified the hydrodynamic interaction between larval zebrafish and fluid using the Immersed Boundary Adaptive Mesh Refinement infrastructure (IBAMR) package (17), which efficiently and accurately models freely moving fluid–structure interactions. In particular, we adapted the 3D larval zebrafish method used in Bale et al. (9).

Larval zebrafish undergo substantial morphological changes between 5 and 14 dpf, including the receding of the fin fold and consumption of the yolk sac (18). To incorporate these changes into our simulations we volumetrically imaged phalloidin-stained larvae to generate 3D models of a typical fish for each age (Fig. 2A and SI Appendix, Fig. S4 A and B; see Materials and Methods). We also measured and incorporated a developmental increase in fish mass (SI Appendix, Fig. S4C). To prepare the experimental tracking data for simulation in IBAMR, we removed all translation in forward/lateral directions and rotation according to the heading angle. During simulations we mapped the relative description of movement for each bout onto the 3D model, similar to Bale et al. (9) (Materials and Methods), producing a prediction of the translational and rotational movement for each bout.

Fig. 2.

CFD method closely approximates consequences of natural tail movements and bout energies change over development. (A) 5 dpf 3D model used for CFD simulations (color represents height). (B) There was a good match between simulated and experimental eye-midpoint velocities for all bouts types (J-turn example). (C and D) There was a high correlation between mean experimental and simulation velocities, and between experimental and simulation turn angles, across the entire dataset. Blue shaded regions show a contour plot of the experimental values for all bouts plotted against corresponding simulation values, red lines represent a perfect match, R-squared values are from the fit to y $=$ x. (E) Fluid velocity fields for an example HAT show the tail tip creating vortices in the fluid. T $=$ 0 corresponds to the start of the simulation. Fields are a 2-dimensional z-slice of the 3-dimensional simulation arena. (F) Reynolds number increased over development. (G) This increase was dependent on bout type. Asterisk denote significant differences between 5 and 14 dpf. (H) Energy cost per bout increases over development. Dashed line gives P-value from ANOVA, solid lines give P-values from pairwise comparisons. (I) Energy increases depend on bout type. Asterisks denote significant difference between 5 and 14 dpf. (J) There was no change in Event Cost over development.

We then examined simulation accuracy by comparing CFD-predicted eye-midpoint velocity with experimental eye-midpoint velocity (examples shown in Fig. 2B and SI Appendix, Fig. S4D). First we computed relative error (RE; see Materials and Methods) for velocity and excluded bouts where RE $>$ 0.5 ($n=900$; SI Appendix, Fig. S4 E and F). The remaining bouts showed a high correlation between experiment and simulation for mean velocity and turn angle (Fig. 2 C and D). Simulation accuracy was very similar across age groups (SI Appendix, Fig. S4G) and bout types (SI Appendix, Fig. S4H). The combined median RE was 0.10. Predicted displacements in the vertical axis were very small, consistent with the experimental recording being in 2D, and were therefore excluded from further analysis (SI Appendix, Fig. S4I). Simulation accuracy was insensitive to reducing the number of experimental tracking points (SI Appendix, Fig. S4J). Examples of the fluid velocity and pressure fields generated by a typical HAT are shown in (Fig. 2E and SI Appendix, Fig. S4K), and typical examples of the remaining 6 bout types in SI Appendix, Fig. S5. Movies of the CFD velocity field for examples of each of the 7 bout types are provided in Movies S3–S9. In summary the IBAMR CFD package accurately reproduced the movement of free-swimming larval zebrafish, and can be used to explore the relationship between larval zebrafish and their fluid environment.

Behavioral Space Energetics Change Over Development.

As expected the Reynolds number increased over development (Fig. 2F). However the size of this increase depended on the bout type (Fig. 2G and SI Appendix, Fig. S6A), suggesting that development could affect the energy requirements of some bout types more than others. We therefore focused on how the energy costs of bouts change over development.

From each simulation we extracted the hydrodynamic power, which represents the net instantaneous power exerted by the fish into the fluid (SI Appendix, Fig. S6 B–D). By summing the axis components and integrating over time we obtained the total energy cost per bout. The average energy per bout across all bout types and fish was 0.065 $\pm$ 0.065 ergs. How does this compare with the total energy budget of the fish? Due to their small size, for larval zebrafish measurements of the energy use of different physiological processes are challenging. However by averaging over multiple larvae it has been estimated that 10 dpf larvae consume oxygen at the rate of $\sim$40 umol/g/h (19). For oxidation of glucose this corresponds to an energy usage of $\sim$20 J/g/h. For a fish weighing 0.3 mg (SI Appendix, Fig. S4) this converts to $\sim$0.006 J/h, or equivalently $\sim$16 erg/s. During hunting, the average interbout interval was 0.3 s. Considering that fish turn metabolic energy into mechanical energy with an efficiency of 10 to 20% (20, 21), this means that during hunting locomotion consumes as much as 10% of the fish’s total energy usage (see also ref. 22). This is a significant fraction, suggesting that constraining energy use during hunting could be an important priority.

Bouts achieving higher displacement required more energy (SI Appendix, Fig. S6E). The energies also increased over development (Fig. 2H), but the size of this increase depended on bout type (Fig. 2I and SI Appendix, Fig. S6F). Although there was high variability between fish, the energy ordering of bout types for each fish was generally consistent (SI Appendix, Fig. S6 G–I). Together these results suggest that bout-type energies change differentially over development.

We found a developmental increase in energy cost for exploratory (SI Appendix, Fig. S6J) but not hunting (SI Appendix, Fig. S6K) behavior. For hunting there was a nonsignificant increase in Capture cost (mean energy cost for capture events, SI Appendix, Fig. S6L), but no changes in Event cost (mean energy cost for hunting events, Fig. 2J), Total cost (sum of energies for all hunting events divided by number of Paramecia captured, SI Appendix, Fig. S6M), or Abort cost (mean energy cost for abort events, SI Appendix, Fig. S6N). This was despite an increase in fish mass and in the energy required for a J-turn to produce a particular angular change (SI Appendix, Fig. S6O). Thus, while there was a robust increase in energy usage over development for exploration, the cost of hunting events was relatively stable. This suggests the possibility of a bout selection strategy that adapts bout usage during hunting in the face of increasing bout costs.

Bout Probabilities Reflect Bout Energies.

Are changes in bout probabilities over development related to bout energies? Remarkably, during hunting, there was at all ages a monotonic relationship between bout-type probability and bout-type energy cost, such that more expensive bouts were used less often (Fig. 3A–C). Besides being present when probabilities and energies were averaged over all fish, this relationship was also present for the majority of fish considered individually (SI Appendix, Fig. S7). The slope of the relationship between probabilities and energies became steeper over development (Fig. 3A–C and SI Appendix, Fig. S8 A–B). In contrast for exploratory behavior, while there was a monotonic relationship at 5 dpf, this was not present at later developmental stages (SI Appendix, Fig. S8 C–E).

Fig. 3.

Larval fish maintain a monotonic relationship between selection probability and energy cost during hunting. (A–C) There was a monotonic relationship between bout-type probabilities and bout-type energy costs during hunting behavior for 5, 9, and 14 dpf. Dots show bout type averages across all fish; error bars show the 95% CI. The slope of the relationship between probabilities and energies also became steeper over development. P-value is for the Mann–Kendall test for a monotonic trend. r-value is the Spearman correlation coefficient for assessing monotonic relationships. (D) A monotonic relationship for hunting was maintained across development via changes in bout-type probability: swapping probabilities and energy costs leads to nonmonotonic relationships (matrix entries are Bonferroni-corrected p-values for Mann-Kendall test of monotonicity, $n=6$).

We performed two different tests to determine whether these relationships could simply be an artifact of our bout-clustering procedure. First, to test whether the number of clusters was important, we altered the clustering to yield each of $n=4$ to 10 bout types. For hunting the monotonic relationship was still significant for every n, indicating that this relationship was robust to bout-type number (SI Appendix, Fig. S8F). For exploration the monotonic relationship at 5 dpf was only present for 7 bout types; for all other ages and bout-type numbers the nonmonotonicity was robust to bout-type number (SI Appendix, Fig. S8G). Second, we avoided clustering entirely and simply binned individual bouts by their energy, effectively treating bouts as a continuum. For all ages a monotonic relationship between bin energy and bin probability was present for hunting (SI Appendix, Fig. S8H) but not for exploration (SI Appendix, Fig. S8I).

Over development both energy costs and bout probabilities changed. To determine whether these changes in probabilities facilitated conservation of the monotonic relationship during hunting, we swapped bout-type costs and probabilities between age groups. The monotonic relationship was no longer present when 5 dpf energies were mixed with 9 dpf or 14 dpf probabilities, or vice versa (Fig. 3D and SI Appendix, Fig. S8 J–L). Together this suggests that bout-type utilization depends adaptively on energy costs. Consistent with this hypothesis, there was a negative correlation between percentage increase in energy cost and percentage increase in bout-type probability (SI Appendix, Fig. S8M). Energy multiplied by probability was generally relatively flat over age for each bout type (SI Appendix, Fig. S8N). Together these results suggest that larval zebrafish hunting adapts to changing energy constraints over development.

A Reinforcement Learning Model Reproduces the Monotonic Relationship.

The data described above reveals a remarkably conserved relationship between bout probabilities and energy costs during hunting. Can this be explained by attempting to minimize energy consumption while catching prey? To address this, we built a reinforcement learning model (Fig. 4A) where an artificial fish agent receives a large positive reward when it catches a Paramecium, but incurs negative rewards equal to the experimentally determined energy costs of each bout it makes. To determine an appropriate reward size we estimated the energy content of one Paramecium as follows. The dry weight is $\mathcal{O}$(10) ng (23), while the dry energy content is $\mathcal{O}$(10) J/mg (24). This yields $\mathcal{O}$(1000) ergs/Paramecium, as compared to $\mathcal{O}$(0.1) ergs/bout. However we also investigated the dependence of the results on the size of this reward.

Fig. 4.

A reinforcement learning model reproduces the monotonic relationship between bouts and energy during hunting. (A) Schematic of the reinforcement learning agent. The agent observed the relative prey location and its current heading angle (state). A neural network was then used to approximate the strategy for selecting the optimal bout type (action). (B) Example hunting event after training. Prey, black dot (Top Right); fish mouth, red dot. (C) Hit rate increased during training. Shaded region indicates 68% CI of the mean from 100 independent agents initialized with different random seeds. A training step is one action (bout). (D) The correlation between energy cost and selection probability became increasingly negative during training. (E) The slope of a linear regression fit decreased during training, indicating that bout types with higher energy were used less after training. (F) The relation between probability and energy for an example agent after 5,000 training steps for this case; error bars show the 95% CI. (G) When energy costs for movements were absent there was no significant correlation between selection probability and energy cost. (H) Selection probability and energy cost after 5,000 training steps. (I and J) Selection probability and energy cost in control experiments where bout energies for Slow 1 were altered, results after 5,000 training steps. Energy values for Slow 1 were multiplied by 2 (I) and 5 (J).

The observation space was continuous, namely the agent’s angle and distance from the prey. The action space was discrete, consisting of the bout types empirically observed during hunting. Once a particular bout type was chosen, a random draw of translation and turn angle was made from the distribution of the empirical data corresponding to that bout type, conditioned on the current observation space, along with the energy cost corresponding to the bout chosen. Bout energies were smoothly interpolated during training between 5, 9, and 14 dpf (SI Appendix, Fig. S9A). The goal was then to find the action sequences that maximize the agent’s total reward. This was achieved via a neural network as the value function, similar to refs. 25 and 26, enabling the model to learn a mapping from states to value distributions associated with each action.

We focus on the early stages of training, which we take to be analogous to the relatively early stages of the development of prey capture that we measured experimentally (for results for longer model training see SI Appendix, Fig. S9 B–E). In particular, we consider results after 5,000 hunting events, the same order of magnitude as a larval zebrafish may have experienced within a few days of beginning to hunt. Over this period the agent gradually learned to catch prey (Fig. 4 B and C). Simultaneously a negative correlation developed between bout energies and probabilities that became increasingly strong (Fig. 4D), matching the experimental data. With training the steepness of this relationship increased (Fig. 4E), similar to the increase in steepness observed experimentally over development (Fig. 3D). By step 5,000 there was a significant monotonic relationship between bout energies and probabilities, similar to the experimental data (Fig. 4F). The correlation and slope of this relationship was quite insensitive to the size of the reward in the range of 1 to 1,000 erg (SI Appendix, Fig. S9 F and G). The distribution of the lengths of successful hunting events was similar to that observed experimentally (SI Appendix, Fig. S9 H and I).

The slope after 5,000 hunting events was $-$1.8, which is in the range observed experimentally ($-$1.4 at 5 dpf to $-$2.3 at 14 dpf). We suggest there are two principal reasons that the slope becomes more negative with age. First, in the model bout probabilities are initially random (slope $\sim$0), and so to achieve the final negative slope, it trivially must become more negative over time. Second, in linear regression the slope is inversely proportional to the standard deviation of the x-axis variables. The variance of the energy values at 14 dpf is less than those at 5 dpf (SI Appendix, Fig. S8B), which naturally increases the magnitude of the slope.

One possibility is that the differences in bout probabilities are related simply to their usefulness for capturing prey, independent of energy costs. To address this, we first considered a model with the same bouts but no costs for movements, so that the only contribution to the reward was from capturing the prey. The correlation was now lost (Fig. 4 G and H), showing that bout costs are important for the negative correlation between probabilities and energies. Second, we investigated the Q-values of trained agents. While Q-values are inherently state-dependent, we can obtain a rough estimate of the “importance” of each bout type by averaging its Q-values over all states. When energy costs were included in the training, agents showed monotonicity between bout energy and average Q-values (SI Appendix, Fig. S9J). However agents trained to catch prey without energy costs showed no systematic relationship between average Q-values and energies (SI Appendix, Fig. S9K). Together these results support the hypothesis that the monotonic relationship is a policy that emerges in response to energetic constraints.

The model also allowed us to test the generality of the monotonicity principle, by asking whether arbitrary reassignments of bout energies would be reflected in changes in selection probabilities. To test this, we first multiplied the energy of Slow 1 bouts by a factor of 2. After training these bouts had lower probabilities than before, preserving the monotonic relationship (Fig. 4I). The hit rate was similar to before (37%). We then multiplied Slow 1 energies by a factor of 5 so that overall they were one of the most costly bout types. Again the training resulted in much lower probabilities for Slow 1 bouts and the preservation of a monotonic relationship (Fig. 4J, hit rate 39%). Altering energies for other bout types produced similar results (SI Appendix, Fig. S9 L–Q). This demonstrates that the energy of a bout is a critical factor for the agent in determining selection probability. Together these results support the hypothesis that the negative correlation between bout energies and probabilities results from a principle of energy minimization during hunting.

An alternative hypothesis is that the fish has a fixed energy budget of B ergs for each hunting event, and desires to stay within this limit (somewhat analogous to a Lagrange multiplier). To test if this could be the case we modified the model to include the constraint that the hunting event is aborted if B is exceeded. For low values of B, equivalent to just a few bouts, the resulting energy–probability relationship after training was not monotonic and did not match our experimental results (SI Appendix, Fig. S9R). Once B exceeded the amount of energy typically used in a hunting event the results were the same as the model without the additional constraint, as expected (SI Appendix, Fig. S9S). Thus overall our results are better explained by energy minimization rather than a fixed energy budget.

Environmental Perturbation Temporarily Disrupts Energy Optimization.

We have demonstrated that zebrafish maintain an energy-minimizing bout-selection rule as their Reynolds number changes over development. However these results do not exclude the possibility that these changes result from a predetermined developmental program rather than a process of active adaptation. To directly test whether larval zebrafish actively adapt to novel conditions, we reared larvae from 1 dpf in water where the viscosity had been increased by a factor of 3.3 (Materials and Methods) by adding a small amount of dextran (“viscous water”). We then compared hunting at 8 dpf in viscous water (“v2v”) with hunting at 8 dpf in normal water (“v2w”) (Fig. 5A). We compared these results with the 9 dpf data collected for Fig. 1, where the fish were both reared and tested in water (“w2w”).

Fig. 5.

Altered viscosity changes hunting metrics and destroys the monotonic relationship between selection probability and energy cost. (A) Fish were initially reared in viscous water from birth, transferred to either water (v2w) or viscous water (v2v) at 8 dpf, and then recorded hunting Paramecia. (B and C) The v2v fish had lower speeds and turning angles, while the v2w fish had higher speeds and turning angles compared to w2w fish. (D) The v2w fish had lower hit ratio compared to w2w and v2v fish. (E) There were differences in the distributions of bout-type probabilities between w2w, v2v, and v2w fish, for both hunting and exploring behavior (two-sample discrete Kolmogorov–Smirnov test; asterisks indicate $P<0.0001$). (F) Both the v2v and v2w fish used more energy per movement than w2w fish. (G and H) There was a monotonic relationship between bout-type energy and probability for both v2v fish but not v2w fish (monotonicity tested via Mann–Kendall). Error bars show the 95% CI. (I) Experimental design to determine the timeline for viscosity adaptation. (J and K) 9w2w fish swim speeds and turning angles were smaller than 8v2w and 9v2w fish. (L) Hit rate was higher for 9w2w compared to 8v2w/9v2w fish. (M) There were differences in the distributions of bout-type probabilities between 9v2w and 9w2w fish for both hunting and exploring behavior. (N–P) During hunting there was no monotonic relationship between energy and selection probability in 8v2w (N) and 9v2w (O) cases but a monotonic relationship was observed for 9v2w fish (P).

Consistent with viscous environments being more challenging for movement, v2v fish had smaller swim speeds and turn angles than w2w fish (Fig. 5 B and C). However v2w fish displayed larger speeds and angles than w2w fish, indicating miscalibration with the unexpectedly permissive water environment. v2v fish were just as successful at catching prey as w2w fish, indicating successful adaptation, however v2w fish were much worse, again indicating miscalibration (Fig. 5D and SI Appendix, Fig. S10A).

Bout types and structures were very similar between conditions (SI Appendix, Fig. S11). However there were significant changes in bout probabilities (Fig. 5E and SI Appendix, Fig. S10 B and C) (since HATs were very infrequent in some of these experiments, making calculations of their probabilities unreliable, we excluded them from this analysis). We then asked whether these changes were related to energetic considerations. Consistent with viscous water being more challenging for movement, v2v fish had higher energy usage (calculated from the CFD simulations using appropriately increased viscosity) than w2w fish (Fig. 5F). v2w fish also had higher energy usage than w2w fish (Fig. 5F), indicating miscalibration. Remarkably, for v2v fish the relationship between energies and probabilities was again monotonic (Fig. 5G), suggesting active adaptation to altered energy demands. In contrast the monotonicity was lost in v2w fish (Fig. 5H).

To test whether this lack of monotonicity was due to insufficient time to adapt to the new environment, we asked whether fish reared in a viscous environment could adapt to the altered energy demands of a water environment given 24 h of experience (Fig. 5I). After rearing fish from 1 dpf in viscous water we recorded hunting in water at 8 dpf (“8v2w”) as a baseline. Half of the fish then remained in water for 24 h while the other half were returned to viscous water for 24 h. Both groups were then recorded hunting in water (“9w2w” and “9v2w” respectively). Swim speeds, turn angles, and hit rates were the same for 8v2w and 9v2w fish, but 9w2w fish were similar to the original water-raised fish (Fig. 5J–L, cf w2w in Fig. 5B–D). Bout probabilities were similar for 8v2w and 9v2w but altered for 9w2w (Fig. 5M). Consistent with the v2w fish in the previous experiment, neither 8v2w or 9v2w showed a monotonic relationship between energies and probabilities (Fig. 5 N and O). Remarkably however after 24 h in water, 9w2w had recovered monotonicity. Together these perturbations reveal processes of optimal adaptation to changing energy demands as the environment changes.

Discussion

Animals often exhibit behavioral flexibility that appears well-matched to environmental demands, yet the principles guiding this flexibility remain incompletely understood. Our study reveals a quantitative and generalizable control principle by which larval zebrafish select actions during hunting: they systematically match the frequency of movement types to the energetic cost each incurs. This energy–probability relationship is preserved across substantial developmental changes in morphology and biomechanics and is reestablished after environmental perturbation. A reinforcement learning agent trained to maximize reward while minimizing empirically derived energetic cost independently converged on the same strategy, demonstrating that this behavioral pattern can emerge from first principles of optimal control (25, 27).

To divide the behavioral space of larval zebrafish into discrete bouts we followed the clustering pipeline of Mearns et al. (6) and, consistent with ref. 6, identified 7 bout types. While early work identified similar bout types based on manual labeling (e.g., refs. 28 and 29), starting with ref. 30 more recent work has employed automated methods. Marques et al. (16) applied density-based clustering on a broader behavioral range to identify 13 bout types, while Johnson et al. (12) applied density-based clustering on a different dataset to identify 5 bout types, which for some analyses they further subdivided into 18 bout types. However, as noted by Mearns et al. (6), the behavioral space of bouts is likely to be largely continuous, thus there is likely no uniquely correct number of bout types. In our analyses, we applied the clustering pipeline consistently across all ages and conditions. Critically, we showed that our overall conclusions regarding the monotonic relationship between bout probabilities and bout energies are robust to both the number of clusters chosen (SI Appendix, Fig. S8 F and G), and the alternative approach of binning energies across a continuous space rather than clustering into bout types (SI Appendix, Fig. S8 H and I). Thus our main conclusion does not depend on asserting 7 bout types, nor the assertion of discrete bout types.

Swimming gaits have been well characterized in fish substantially larger than zebrafish larvae (31), and the relative performance of these different gaits have been analyzed (32). However larval zebrafish bouts operate in a different regime. Each bout lasts only $\approx$100 to 150 ms and consists of at most about 5 tail beat oscillation cycles, the amplitude of which decays with time. There is thus insufficient data within each bout to define stable gait parameters, and so characterizations based on a specific gait style and its associated energy requirements would not be reliable. In addition gait calculations (e.g., ref. 33) generally assume stereotyped, noiseless forward movements and do not take into account individual bout variability, which in zebrafish larvae occurs even within the same bout type for one fish. This variability is both systematic, for instance J-turns are adjusted depending on the angle of the prey (5), and stochastic (see error bars in Fig. 1F and SI Appendix, Fig. S2 A–F). By simulating each bout individually using CFD we have captured bouts energies much more accurately than relying on matching to average templates determined from fish swimming at much higher Reynolds numbers.

Previous work has also shown that energetic considerations help shape behavior. Optimal foraging theory (3, 4) helps explain how animals decide to leave one food patch in search of another, but does not directly address hunting behavior. Both animals (34) and humans (35) optimize gait to minimize energy consumption (as measured by rate of oxygen consumption), and typical migratory swimming speeds in fish minimize the aerobic cost of transport (36). Similarly, trade-offs in reaching movements in humans can be explained by minimizing cost functions that include metabolic energy (37). However, our work goes beyond these earlier studies by precisely calculating the mechanical energy in Joules of the complete set of movements that a model organism performs, and revealing a control strategy for minimizing energy while hunting prey. While mechanical energy is a proxy for the metabolic energy consumed by the fish, the reinforcement learning model based on mechanical energy matched the observed behavior of the fish, and the optimality of the probability matching strategy depends primarily on the ordering of bout energies rather than their absolute values.

The monotonicity principle was robust during hunting behavior but absent or degraded during exploratory movements. This likely reflects differences in behavioral objectives. Whereas hunting has a clear and immediate goal—capturing prey with minimal cost—exploration may prioritize broader space coverage or sensory acquisition. In our data, during exploration, bouts with higher displacement (and thus higher energy) remained common, suggesting that maximizing spatial spread may override energy minimization in this context (38, 39).

Our findings also raise important questions about underlying neural mechanisms. How does the nervous system represent and update estimates of movement cost? Are these estimates learned through sensory feedback, computed from efference copy, or encoded by neuromodulatory signals such as dopamine or serotonin that reflect internal energy budgets or opportunity costs (40, 41)? Previous work has implicated dopaminergic systems in effort-based decisions and cost–benefit integration (42–44), but how such mechanisms operate in the context of real-time motor control remains unknown. The zebrafish model, with its optical accessibility and genetic tractability, provides an ideal system for addressing these questions.

From a theoretical perspective, our results parallel key principles in motor control theory, including minimum effort or cost-to-go frameworks (2, 45), but extend them to ecologically grounded behavior in developing animals. Notably, the empirical matching of energy and action probability may reflect an implementation of reward shaping or cost-sensitive policy learning. The convergence of biological and artificial agents on the same strategy also strengthens the utility of normative models for understanding behavior.

Finally, the broader implications of these findings span fields. For neuroscience, they suggest that energetic constraints are not peripheral but central to action selection, and that cost estimation may be a fundamental computation across species and contexts. For robotics and AI, they highlight the utility of cost-sensitive control policies that adapt to environmental change. And for developmental biology, they show how even early-stage animals can implement flexible strategies that integrate biomechanical realities with task demands.

In summary, we uncover a simple but powerful principle, energy-based action selection, that shapes hunting behavior in larval zebrafish. This principle is developmentally robust, environmentally adaptive, and computationally tractable. It provides a compelling example of how biological systems can optimize behavior under physical constraints and offers a foundation for future studies of the neural and computational substrates of energy-aware decision-making.

Materials and Methods

Full details are provided in SI Appendix. In brief, larval zebrafish bouts were derived from a pipeline adapted from ref. 6. CFD simulations were adapted from ref. 17. The RL model was similar to refs. 25 and 26 and was implemented in Gymnasium (46).

Supplementary Material

Appendix 01 (PDF)

Movie S1.

Example movie of a hunting event.

Movie S2.

Example movie of exploring behavior.

Movie S3.

Velocity field for approach bout. The velocity field during an example approach bout (slowed down 10x).

Movie S4.

Velocity field for capture swim bout.

Movie S5.

Velocity field for HAT.

Movie S6.

Velocity field for J-turn.

Movie S7.

Velocity field for routine-turn.

Movie S8.

Velocity field for slow 1 bout.

Movie S9.

Velocity field for slow 2 bout.

Data, Materials, and Software Availability

Data and code for bout and energy analyses and plotting, code for the RL model and plotting, and the CFD simulation repository have been deposited in Zenodo (47).