Caste-specific origins of Lévy-like movement in social termites reveal social modulation of scaling laws

Caste-specific origins of Lévy-like movement in social termites reveal social modulation of scaling laws | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Caste-specific origins of Lévy-like movement in social termites reveal social modulation of scaling laws Zhuang-Dong Bai, Jia-Xu Han, Nan Ye, Chao Wang, David Sillam-Dussès, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8145915/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 03 Apr, 2026 Read the published version in Movement Ecology → Version 1 posted 9 You are reading this latest preprint version Abstract Lévy walks, the scale-free movement patterns emerging across taxa, are thought to reflect optimal search strategies shaped by intrinsic physiology or environmental constraints. Yet how social organization modulates the emergence of Lévy-like movements remains unclear. Here we combine high-resolution tracking and agent-based modelling to compare the movement of queens and workers of the termite Reticulitermes labralis under varying group densities. Both castes displayed step-length distributions consistent with truncated power laws, but their scaling exponents diverged: workers maintained Lévy-like movement across densities, whereas queens tended to shift toward Brownian-like movement in high-density groups. Behavioral kinematics paralleled these patterns: workers moved faster, turned less frequently, and explored larger spatial areas, while queens showed slower, more confined trajectories; turning frequency was positively associated with the scaling exponent, linking local reorientation to heavy-tailed step lengths. Simulations revealed that caste-specific turning dynamics and encounter-driven modulation could reproduce the empirical divergence, mechanistically linking the effects of caste-specific traits and social contacts on the formation of differences in Lévy-like movement patterns. Functional tests further showed that swapping scaling exponents between castes reduced encounter efficiency and movement performance-especially for workers, indicating adaptive tuning of Lévy parameters to social role. These finding reveal that Lévy-like movements in social insects arise from the interplay between intrinsic behavioral roles and extrinsic crowding, providing a framework for how division of labour and spatial interactions shape the evolution of movement behaviour. Lévy walk termite social modulation movement scaling division of labor Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Introduction Across taxa, from bacteria and mollusks to birds and humans, organisms often move in scale-free patterns known as Lévy walks, characterized by heavy-tailed step-length distributions that enhance search efficiency in patchy or unpredictable environments [ 1 – 3 ]. The “Lévy-foraging hypothesis” posits that such movements maximize encounter rates while minimizing redundant exploration [ 4 – 7 ]. Despite their apparent ubiquity, the mechanisms generating Lévy-like behavior remain controversial. Some studies attribute these patterns to intrinsic processes, such as neuromotor rhythms or internal decision rules that spontaneously produce scale-free displacements [ 8 – 12 ]. Others emphasize for extrinsic drivers, where environmental heterogeneity, predation risk, or social interactions impose external constraints that shape movement [ 13 – 15 ]. Yet, how social organization, a defining feature of many animal societies modulates the emergence and adaptive significance of Lévy-like movements remains largely unexplored. Social insects provide a powerful system for addressing this question because individual movement is both a behavioral expression of division of labour and a dynamic response to the surrounding social context. Within colonies of ants and termites, queens specialize in reproduction, whereas workers perform tasks such as foraging, nest maintenance, and brood care [ 16 – 18 ]. These functional differences are tightly linked to caste-specific movement behaviours, which determine how information, resources, and individuals flow within the colony [ 19 ]. Workers benefit from exploratory trajectories that maximize spatial coverage and contact rates, whereas queens may adopt more conservative, energy-saving movements that maintain social connectivity while minimizing exposure [ 20 ]. Termites, in particular, exhibit strong social structuring and frequent physical encounters, making them ideal for testing whether collective organization can actively shape the scaling properties of individual movement [ 21 ]. Previous studies have shown that termite workers display Lévy-like movements influenced by group density and local interactions [ 22 , 23 ], yet whether and how these effects differ between castes remains unknown. Moreover, most analyses have focused on solitary or small groups [ 24 – 26 ], leaving the impact of social density, a central aspect of colony organization largely untested in larger societies. If social encounters regulate individual turning and displacement, the scaling exponent of Lévy walks should vary systematically with crowding. Conversely, if caste-specific traits dominate, intrinsic behavioral rules may override environmental effects. Here, we integrate high-resolution behavioral tracking with agent-based modelling in the termite Reticulitermes labralis to examine how social organization modulates the emergence of Lévy-like movement. By comparing queens and workers across a gradient of group densities, we test whether Lévy patterns arise primarily from intrinsic caste differences or from extrinsic social interactions. This integrative framework bridges behavioral ecology and collective dynamics, revealing how the interplay between social roles and crowding generates the complex scaling laws that govern movement in social systems. Material and Methods Termite collection and maintenance Five colonies of Reticulitermes labralis were collected from decayed wood in the northern Qinling Mountains, Xi’an, Shaanxi Province, China (108°46′E, 34°00′N). Colonies were transferred to ventilated plastic boxes (80 × 50 × 40 cm) and maintained at 25°C for one week under controlled humidity to allow acclimation. Approximately 1,000 individuals from each colony were placed in 9-cm Petri dishes (five replicates per colony) with damp filter paper as food and moisture sources. Caste identity was confirmed based on standard morphological traits, including body pigmentation and abdominal shape. After one month, supplementary reproductives (replacement queens and kings) differentiated within each group, identified by characteristic head pigmentation and slight abdominal enlargement in queens [ 27 – 29 ]. From each colony, one queen or worker was randomly selected for individual tracking. Additional groups of 100 (94 workers, 4 soldiers, one queen, and one king), 200 (190 workers, 8 soldiers, one queen, and one king), and 1,000 individuals (≈ 958 workers, 40 soldiers, one queen, and one king) were established under identical conditions (25°C, 70% relative humidity, 14 h light/10 h dark). All groups were acclimated for 24 h before behavioral recording. Movement recordings To enable individual identification, the abdomen of each focal queen or worker was marked with a small spot of non-toxic white glue mixed with dye following Marins et al. [ 30 ]. Groups were then transferred sequentially to a recording arena and allowed to acclimate for one hour before filming. Movements were recorded continuously for one hour using a Sony AX100E camera at 30 frames s⁻¹ under uniform illumination. Video files were downsampled to 5 frames s⁻¹ for analysis in EthoVision XT (Noldus, Beijing), and X–Y coordinates of the focal individual were extracted for subsequent processing in MATLAB ( Figure S1 ). Each experimental session yielded approximately 15,000 positional data points per individual across four group sizes (1, 100, 200, and 1,000 individuals), totaling 20 complete recordings. In high-density groups, three to four recordings contained short interruptions caused by individuals climbing the dish walls, but trajectories remained continuous after their return and were thus retained without affecting the analyses. Analyzing movement The kinematic features of the color-marked queen and worker were quantified using six complementary parameters that together describe the structure and dynamics of their trajectories. (i) Step-length distribution, defined as the frequency of short and long one-dimensional (1D) steps following the framework of Humphries et al. [31]; (ii) Mean speed, representing the average displacement rate during active movement; (iii) Total movement time, the cumulative duration of locomotor activity; (iv) Turning frequency, calculated as the number of direction changes per second of active movement; (v) Straightness index, the ratio of net displacement to total path length (values approaching 1 indicate more linear movement, whereas those near 0 reflect more tortuous paths); and (vi) Proportion of movement within the inner region, defined as the fraction of time spent within the central 80% of the arena (radius ≤ 36 mm). These metrics jointly capture both the spatial and temporal organization of individual movement, describing how queens and workers combine short and long steps, modulate speed and turning, and distribute their activity across spatial zones. Extremely small 1D step lengths were corrected following the procedure of Castiblanco et al. to ensure consistency in step-length estimation [23]. Step-length distribution analysis Step lengths were defined as the linear distance between consecutive termite positions sampled at fixed 1-s intervals (corresponding to 5 frames). No arbitrary turning-angle thresholds were applied. Instead, step segmentation followed the one-dimensional (1D) projection method of Humphries et al. [ 31 ], which identifies turns objectively at points where the direction of travel reverses along a single axis. This approach minimizes subjective bias from predefined critical angles and has become standard in analyzing animal movement trajectories [ 8 , 15 , 22 , 32 ]. For each individual, independent step-length distributions were constructed and fitted to candidate statistical models using maximum likelihood estimation (MLE). The models included the power-law, truncated power-law, exponential, and truncated exponential distributions. Model selection followed a decision-tree framework based on Akaike weights (AICw) and goodness-of-fit criteria [ 31 ]. The truncated power-law distribution, characterizes superdiffusive, scale-free motion with exponent µ , where lower µ indicates longer steps and stronger intermittency. In contrast, the exponential distribution, represents memoryless Brownian motion. Biologically, the exponential model reflects uncorrelated, diffusive movement, whereas the truncated power-law describes Lévy-like behavior that combines frequent short steps with occasional long displacements. We focused on comparing these two ecologically meaningful models, truncated power-law versus exponential, because they capture the essential difference between superdiffusive and diffusive movement. The truncated form of the power-law accounts for the biological constraint that animals cannot take infinitely long steps, while avoiding the risk of artificially suppressing rare long steps inherent in truncated exponentials. Although more complex models (e.g., multiphasic or lognormal) may achieve marginally better statistical fits, our analysis specifically aimed to test for the presence of Lévy-like scaling and to compare its expression between termite castes. All parameter estimation and model selection procedures were conducted using the software provided by Humphries et al. Agent-based model To examine whether caste-specific turning rules during social encounters could generate distinct Lévy-like patterns, we developed an agent-based model simulating termite movement within a circular arena (9 cm in diameter; Movie S1 ). The arena contained 100 mobile agents represented as solid spheres moving in continuous space with randomly assigned initial directions. Based on empirical measurements of body size, the first sphere (representing the queen) had a diameter of 4 mm, while the remaining 99 spheres (representing workers) had diameters of 2 mm. Each sphere moved at a fixed probability per time step (0.3 for the queen and 0.6 for the workers), corresponding to the proportion of active movement time observed experimentally over 51 min. The simulation proceeded for 2,000 time steps, with periodic updates governed by the following rules. Agents were confined within the arena boundaries and reflected upon reaching the edge. Turning intervals followed a power-law distribution, derived from empirical data ( Fig. S2 ), with exponents β = 2.7 for the queen and β = 2.0 for the workers. Turning angles were drawn from a normal distribution to introduce directional variability ( Fig. S3 ). Directional updates occurred upon encounters with other agents, representing social modulation of movement. When two agents came into contact, the focal agent changed direction only if the elapsed time since its previous turn exceeded its current power-law-sampled interval; otherwise, the trajectory remained unchanged. At the end of each simulation, trajectories and encounter counts were recorded for all agents, and representative paths of the queen (first sphere) and a worker (second sphere) were visualized for comparison. Calculation of encounters, movement distance, and spatial exploration To quantify social interaction, movement performance, and spatial exploration, we analyzed the recordings of color-marked queens and workers in 100-individual groups. Encounters were defined as antennal contacts between the focal (marked) individual and any nestmate, with each contact recorded as a single event. The total number of encounters was counted separately for queens and workers across five replicate colonies. Movement distance was computed as the cumulative path length derived from the two-dimensional positional coordinates of each marked individual. To assess spatial exploration, the arena was divided into a grid of equal-sized cells, and the coverage rate was calculated as the proportion of cells traversed by the focal termite relative to the total number of cells within the 9-cm Petri dish. This metric represents the proportion of space explored during the observation period and allows comparison of exploratory efficiency between castes. Simulative analysis of Lévy patterns in queens and workers To assess whether the distinct Lévy-like patterns observed in queens and workers confer different functional advantages, we performed a simulation experiment comparing movement efficiency under caste-specific scaling exponents. The model consisted of 100 moving agents represented as spheres. In the first scenario, the focal sphere (representing the queen) followed a truncated Lévy walk characterized by the empirically estimated scaling exponent of queens, while the remaining 99 spheres (representing workers) followed the workers’ scaling exponent. In a second scenario, the exponents were reversed: the focal sphere adopted the workers’ exponent, whereas all others followed the queens’ exponent. For each scenario, three metrics were quantified: (i) the number of encounters between spheres, (ii) the total movement distance of all spheres, and (iii) the mean distance required for the focal sphere and three randomly selected workers to encounter others. The simulation proceeded iteratively, updating the position and state of each sphere at every time step. Motion was governed by stochastic intervals drawn from a power-law distribution, determining whether the sphere remained stationary or initiated a new displacement. After each movement, direction changes were sampled from a normal distribution, and step velocity was proportional to the sampled step length. Encounters were recorded whenever the distance between two spheres was less than 3 mm, a threshold corresponding to the combined body size and estimated antennal reach of R. labralis . Each simulation ran for a fixed duration, and trajectories were analyzed to quantify both the encounter efficiency and total distance traveled under each Lévy parameter regime. Statistical analyses All colonies were tested under each of the four group-size conditions, introducing potential non-independence due to shared genetic and environmental backgrounds. To account for this, behavioral and kinematic parameters (mean speed, movement time, turning frequency, straightness index, exploration rate, and the proportion of movement within the inner region) were analyzed using linear mixed-effects models (LMMs) or beta regression models for bounded data (0–1 range). Caste (queen vs. worker), group size, and their interaction were treated as fixed effects, and colony identity was included as a random intercept to control for repeated measures across groups. The significance of fixed factors was assessed using Wald χ² tests or ANOVA, and post hoc pairwise contrasts were performed with Tukey’s HSD tests based on estimated marginal means, with p -values adjusted for multiple comparisons. For comparisons derived from simulation outputs, such as encounter frequency, total movement distance, and distance per encounter, differences between castes or parameter settings were evaluated using two-tailed independent-sample t-tests. Variance equality was verified using Levene’s or Bartlett’s tests. Model adequacy was evaluated through residual inspection, variance homogeneity, and random-effect diagnostics to ensure compliance with model assumptions. All statistical analyses and data visualization were conducted in R (v. 4.3.2; R Core Team, 2023), using the lme4 , lmerTest , glmmTMB , car , emmeans , and performance packages. Results Movement trajectory High-resolution video tracking revealed clear caste-specific differences in movement trajectories across group sizes (Fig. 1 ). Queens predominantly occupied the central region of the arena, whereas workers frequently traced the periphery. Beta-regression analyses indicated significant main effects of caste and group size on the proportion of movement occurring within the inner region (Wald χ² tests: caste, χ²₁ = 58.07, p < 0.001; group size, χ²₃ = 29.20, p < 0.001), with no significant interaction between the two factors (χ²₃ = 5.16, p = 0.16). Post-hoc Tukey comparisons confirmed that queens consistently spent a greater proportion of time in the inner region than workers under all group-size conditions (1-individual: z = 2.79, p = 0.0052; 100-individual: z = 3.80, p = 0.0001; 200-individual: z = − 5.31, p < 0.0001; 1000-individual: z = 4.49, p < 0.0001; Fig. S4 ). These results demonstrate that spatial positioning within the group is strongly shaped by caste identity: workers exhibit boundary-following, exploratory movement, whereas queens maintain more centralized and spatially confined trajectories. Step-length distributions Across all group sizes, step-length distributions of both castes were better described by a truncated power law than by an exponential model (Fig. 2 ). Maximum-likelihood fits, together with goodness-of-fit and AIC comparisons, consistently supported the truncated power-law model ( Table S1 ), indicating that both queens and workers exhibit Lévy-like movement patterns rather than Brownian diffusion. Linear mixed-effects modeling revealed significant effects of caste (F₁,₃₂ = 38.07, p < 0.001), group size (F₃,₃₂ = 27.64, p < 0.001), and their interaction (F₃,₃₂ = 3.84, p = 0.019) on the scaling exponent ( µ ) of the truncated power-law fits. Post-hoc Tukey comparisons showed that µ did not differ between queens and workers in solitary conditions (t₂₈ = 0.40, p = 0.70), but queens exhibited significantly higher µ values than workers in larger groups (t₂₈ = 4.70, p = 0.0001 for 100-individual; t₂₈ = 2.88, p = 0.0075 for 200-individual; t₂₈ = 4.36, p = 0.0002 for 1000-individual; Fig. 3 ). These results demonstrate that social context modulates the scaling properties of movement, with a stronger effect on queens than on workers. Movement attributes Caste and group size jointly influenced multiple aspects of termite locomotion, including speed, movement duration, turning frequency, and trajectory straightness (Fig. 4 ). For average speed, both caste and group size had significant effects, with a significant interaction (F₁,₂₆ = 17.57, p < 0.001; F₃,₂₆ = 4.50, p = 0.011; interaction: F₃,₂₆ = 3.97, p = 0.019). Queens moved significantly slower than workers in the 1- and 100-individual groups (t₂₆ = −3.37, p = 0.002; t₂₆ = −4.32, p = 0.0002), whereas the difference disappeared at higher densities (200- and 1000-individual groups). Movement duration followed a similar pattern, being significantly affected by caste, group size, and their interaction (F₁,₂₈ = 13.14, p = 0.001; F₃,₂₈ = 15.69, p < 0.001; interaction: F₃,₂₈ = 4.70, p = 0.009). Queens exhibited shorter movement times than workers in the 100-individual groups (t₂₈ = −5.02, p < 0.0001), but no caste difference in other densities. Turning frequency also differed significantly by caste, group size, and their interaction (F₁,₃₀ = 30.12, p < 0.001; F₃,₃₀ = 18.52, p < 0.001; interaction: F₃,₃₀ = 4.41, p = 0.011). Queens turned more frequently than workers in the 100- and 1000-individual groups (t₂₆ = 4.11, p = 0.0003; t₂₆ = 4.84, p = 0.0001), with a marginal trend at 200 individuals (t₂₆ = 1.99, p = 0.057). The straightness index (SI) was significantly influenced by group size and its interaction with caste (F₃,₃₂ = 28.66, p < 0.001; interaction: F₃,₃₂ = 7.40, p < 0.001), but not by caste alone (F₁,₃₂ = 0.93, p = 0.34). Queens exhibited slightly straighter trajectories than workers in small groups (1-individual: t₂₈ = 1.89, p = 0.07; 100-individual: t₂₈ = 3.58, p = 0.0013), but less straight paths in the largest groups (1000-individual: t₂₈ = −2.27, p = 0.031). These results demonstrate that group size modulates caste-specific locomotor behaviours: queens move more slowly and along straighter paths in small and moderate groups, but their motion becomes less directed and more interrupted under high crowding, whereas workers maintain higher activity and turning rates that enhance space coverage in dense social environments. Mechanistic and functional origins of caste-specific Lévy dynamics To understand how social organization modulates the emergence of Lévy-like movements, we first examined whether directional dynamics could account for the caste-specific scaling exponents observed above. Turning frequency was tightly correlated with the scaling exponent of the step-length distribution (adjusted R² = 0.81, p < 0.0001; Fig. 5 , Table S2 ), indicating that individuals with higher turning rates produced steeper, more Brownian-like distributions. To test this relationship mechanistically, we constructed an agent-based model in which queens and workers followed caste-specific turning rules derived from empirical observations, and directional updates occurred upon encounters with other agents (Fig. 6 ). The simulations successfully reproduced the observed divergence in scaling exponents, with queens exhibiting significantly higher µ values than workers (t (8) = 3.43, p = 0.0096; Fig. S5 ). Together, these findings demonstrate that differences in Lévy walk characteristics can arise from caste-specific turning dynamics coupled with encounter-driven modulation. Building on these insights, we evaluated the functional advantages of the distinct Lévy walks performed by each caste. Workers experienced significantly more encounters than queens (t (4) = 4.24, p = 0.013) and traveled longer total distances (t (4) = 3.71, p = 0.021), whereas the mean distance per encounter did not differ significantly (t (4) = 1.91, p = 0.13). Across all group sizes, workers explored a larger proportion of available space than queens (1-individual: t (28) = 2.87, p = 0.0077; 100-individual: t (28) = 7.21, p < 0.0001; 200-individual: t (28) = 3.73, p = 0.0009; 1000-individual: t (28) = 2.66, p = 0.013; Fig. 7 ). To assess whether these performance differences arose from caste-specific scaling parameters, we simulated scenarios in which queens and workers exchanged their empirical scaling exponents. When queens adopted the worker’s exponent, encounter rate and encounter distance remained unchanged (t (10) = − 0.15, p = 0.896; t (10) = 2.83, p = 0.105), though total distance tended to increase (t (10) = 3.63, p = 0.053). In contrast, when workers adopted the queen’s exponent, their encounter rate, total distance, and encounter distance all declined sharply (t (10) = − 2.14, p = 0.049; t (10) = − 5.22, p < 0.001; t (10) = − 7.28, p < 0.001; Fig. S6 ). These simulations indicate that the worker’s scaling exponent is functionally tuned to maximize encounter efficiency and spatial exploration, whereas the queen’s performance is comparatively insensitive to parameter changes. Collectively, these results reveal that caste-specific Lévy patterns in termites arise from simple local rules governing turning and encounters, yet yield distinct adaptive outcomes. Workers, intrinsically motivated to explore and sustain information flow, maintain Lévy dynamics that enhance spatial coverage and contact efficiency. Queens, by contrast, exhibit movement that is more constrained and socially responsive, minimizing energy expenditure while preserving connectivity within the colony. Thus, the emergence of Lévy-like movement in social insects reflects how hierarchical organization and social feedbacks reshape the statistical laws of individual motion. Discussion Our results reveal a fundamental principle of collective behavior: social organization can reshape the statistical laws of individual movement. By comparing termite queens and workers across densities, we show that the emergence of Lévy-like movement, long regarded as a universal scale-free search strategy, is not a fixed individual property but a socially modulated outcome. Workers consistently maintained Lévy-like patterns, whereas queens exhibited a tendency to shift toward Brownian-like motion at high densities. This divergence demonstrates that the same movement rule can bifurcate into distinct regimes when embedded in a structured social context. In other words, how social organization modulates the emergence of Lévy-like movements provides a mechanistic window into how collective structure feeds back to constrain or amplify individual variability [ 25 , 33 ]. This socially induced divergence arises from the interaction between intrinsic caste-specific drives and extrinsic encounter dynamics. Workers, intrinsically motivated to explore and sustain information flow, exhibit persistent trajectories that maximize encounter efficiency and spatial coverage, properties consistent with self-organized Lévy dynamics [ 22 , 34 ]. Queens, in contrast, operate under a different optimization regime: their mobility is shaped less by exploration and more by maintaining proximity to workers for care and protection [ 35 ]. As density rises, repeated encounters increase turning frequency and fragment long displacements, pushing their trajectories toward Brownian regimes [ 36 ]. These findings align with evidence from other eusocial systems, where reproductive individuals exhibit restricted motion to stabilize the colony’s social network [ 19 , 37 ]. Thus, what appears as a change in a statistical exponent (µ ) in fact reflects a shift in the dominant feedback loop, from internal drive to social coupling. At a conceptual level, these results extend the scope of Lévy walk theory beyond individual optimal foraging. Classical models treat Lévy exponents as static parameters tuned by environmental randomness [ 38 , 39 ], but our findings show that in social systems, these parameters are themselves emergent variables molded by the structure of interaction networks. Social organization therefore acts as a higher-order constraint that dynamically tunes movement scaling, analogous to how metabolic scaling laws are modulated by network topology or energy flux within organisms [ 40 , 41 ]. By embedding individuals within feedback-rich social architectures, colonies can generate complex, non-Gaussian mobility distributions without requiring cognitive optimization, which represents an emergent statistical signature of collective life. Functionally, the distinct Lévy parameters of queens and workers reveal adaptive tuning between exploration and efficiency. Simulations confirmed that swapping exponents disrupted colony-level performance: queens became energetically wasteful, while workers lost spatial efficiency. This role-dependent asymmetry suggests that the colony’s behavioral diversity is not noise but design, each caste occupies a different region of the movement landscape optimized for its social function [ 42 ]. Such division of movement behaviours mirrors the division of labor itself: exploratory Lévy dynamics sustain the flow of information and resources, while constrained Brownian motion stabilizes the reproductive core [ 43 – 45 ]. This dual mechanism exemplifies how evolution can translate social feedback into scaling adaptation, producing both stability and flexibility within a single collective framework. In sum, how social organization modulates the emergence of Lévy-like movements offers a quantitative route to connect behavioral scaling, feedback regulation, and social evolution. Termite colonies illustrate a general principle that may extend to other collective systems, from bacterial swarms to human societies, where individual movement statistics encode the structure of interaction networks. Understanding these feedbacks transforms Lévy walks from a foraging paradigm into a universal model of how local rules and social architecture generate emergent complexity. Declarations Ethics declarations Ethics, consent to Participate, and consent to publish declarations Not applicable. Competing Interests The authors declare no competing interests. Funding This work was supported by the National Natural Science Foundation of China (32171482) and the NSFC-Yunnan United fund (U2102221). Author Contribution RW, JH and ZB designed the research; ZB and NY performed the experiments; ZB and NY collected the data; JH and CW performed the data analysis; ZB, JH and NY drafted the manuscript; DSD and RW contributed on writing the manuscript. CW and RW acquired funding for the project. All authors have approved the final vresion of the manuscript for publication. Acknowledgement We thank Dr. Yanping Liu for valuable conceptual discussions during the early stages of study design, which greatly strengthened the development of this work. We are also grateful to Yibin Liu, Chongyang Shi, Meng Hou and Xiancun Ma for their assistance with sample collection and experimental procedures. Their dedication and support were essential to the successful progress of this project. Data Availability All data generated or analyzed during this study are included in the supplementary material. References Reynolds, A.M. 2018 Current status and future directions of Lévy walk research. 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Supplementary Files Supplementarymaterials10.30.docx dataandcodes.zip MovieS1.avi Cite Share Download PDF Status: Published Journal Publication published 03 Apr, 2026 Read the published version in Movement Ecology → Version 1 posted Editorial decision: Revision requested 20 Dec, 2025 Reviews received at journal 19 Dec, 2025 Reviewers agreed at journal 08 Dec, 2025 Reviews received at journal 07 Dec, 2025 Reviewers agreed at journal 03 Dec, 2025 Reviewers invited by journal 02 Dec, 2025 Editor assigned by journal 20 Nov, 2025 Submission checks completed at journal 20 Nov, 2025 First submitted to journal 18 Nov, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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1","display":"","copyAsset":false,"role":"figure","size":1378327,"visible":true,"origin":"","legend":"\u003cp\u003eRepresentative movement trajectories of termite queens and workers across social densities. Trajectories of queens (red) and workers (green) were recorded in circular arenas containing 1, 100, 200, or 1,000 individuals. Each line represents the path of a single marked individual. In solitary conditions (top row), workers exhibited persistent edge-following paths resembling ballistic motion, whereas queens showed more variable trajectories. As group density increased (bottom row), movements of both castes became more constrained and interwoven, with queens showing stronger central confinement and workers maintaining wider exploratory coverage.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-8145915/v1/e616f8527959aba4bd937b10.png"},{"id":97524466,"identity":"24d2bceb-34d1-4de9-b8f9-431e7470771f","added_by":"auto","created_at":"2025-12-05 12:05:08","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":665664,"visible":true,"origin":"","legend":"\u003cp\u003eStep-length distributions of termite queens and workers across social densities.\u003cbr\u003e\nCumulative frequency distributions of step lengths for workers (top row) and queens (bottom row) under different group sizes (1, 100, 200, and 1,000 individuals). Open circles represent observed data, red lines indicate truncated power-law fits, and green lines denote exponential fits. Across all conditions, the truncated power-law provided a superior fit to the data, capturing the heavy-tailed structure of step lengths (see Table S2 for model selection results). Scaling exponents (\u003cem\u003eμ\u003c/em\u003e) increased with group size, particularly in queens, indicating a shift of Lévy-like movement as social density increased.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-8145915/v1/e72fd95f54b8cd51c0ccc69d.png"},{"id":97524463,"identity":"2572cafe-8b78-41c6-a35c-daa93b633278","added_by":"auto","created_at":"2025-12-05 12:05:08","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":114100,"visible":true,"origin":"","legend":"\u003cp\u003eScaling exponents (\u003cem\u003eμ\u003c/em\u003e) of step-length distributions for queens and workers across social densities. Boxplots show \u003cem\u003eμ\u003c/em\u003e values estimated from truncated power-law fits for queens (blue) and workers (red) in groups of 1, 100, 200, and 1,000 individuals. Both castes exhibited an overall increase in \u003cem\u003eμ\u003c/em\u003ewith group size, but the effect was more pronounced in queens. At low density (1-individual), \u003cem\u003eμ\u003c/em\u003e values did not differ between castes, whereas in larger groups queens showed significantly higher \u003cem\u003eμ\u003c/em\u003e than workers. These results indicate that social density modulates the scaling properties of termite movement, with queens exhibiting stronger deviation from Lévy-like dynamics under crowding. Asterisks denote post hoc Tukey test results (*\u003cem\u003ep\u003c/em\u003e\u0026lt; 0.05; **\u003cem\u003ep\u003c/em\u003e \u0026lt; 0.01; **\u003cem\u003ep\u003c/em\u003e \u0026lt; 0.001; ns, not significant).\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-8145915/v1/3c854d518c167cfffa401afd.png"},{"id":97670719,"identity":"da1db4a2-f5d3-4660-8c92-47e8d846dd5a","added_by":"auto","created_at":"2025-12-08 09:31:12","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":395349,"visible":true,"origin":"","legend":"\u003cp\u003eEffects of caste and group size on termite locomotor dynamics. (A) Average speed, (B) movement duration, (C) turning frequency, and (D) straightness index (SI) of queens (blue) and workers (red) across four group sizes (1, 100, 200, and 1,000 individuals). Boxplots display medians (horizontal lines), interquartile ranges (boxes), and data ranges excluding outliers (whiskers). Queens moved significantly slower than workers in small groups (A), exhibited shorter movement durations in intermediate groups (B), and turned more frequently in large groups (C). Their trajectories were straighter in small groups but became less directed under crowding (D). Together, these results indicate that caste-specific locomotor patterns are strongly modulated by group size, with queens showing density-dependent behavioral adjustments and workers maintaining high mobility and spatial coverage. Asterisks denote post hoc Tukey test results (*\u003cem\u003ep\u003c/em\u003e \u0026lt; 0.05; **\u003cem\u003ep\u003c/em\u003e\u0026lt; 0.01; ***\u003cem\u003ep\u003c/em\u003e \u0026lt; 0.001; ns, not significant).\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-8145915/v1/e8c93e17fbc5f0c777749db2.png"},{"id":97524472,"identity":"1fc4f3f7-6553-4bd8-8cdb-16a27e4be8b1","added_by":"auto","created_at":"2025-12-05 12:05:08","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":453700,"visible":true,"origin":"","legend":"\u003cp\u003eLinear regression analysis of the relationship between turning frequency and the scaling exponent (\u003cem\u003eμ\u003c/em\u003e) of the step-length distribution. Scatter plot showing the relationship between turning frequency (x-axis) and \u003cem\u003eμ\u003c/em\u003e (y-axis). The red line represents the fitted linear regression model, and the shaded region indicates the 95% confidence interval. The analysis revealed a strong positive linear relationship between turning frequency and \u003cem\u003eμ \u003c/em\u003e(adjusted R² = 0.819, F₁,₃₆ = 162.4, \u003cem\u003ep\u003c/em\u003e \u0026lt; 0.0001).\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-8145915/v1/5ca358300f8513221d90701c.png"},{"id":97671555,"identity":"5e4dd2f3-63dd-4b42-8cd6-9a5a9e3026de","added_by":"auto","created_at":"2025-12-08 09:32:44","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":609361,"visible":true,"origin":"","legend":"\u003cp\u003eAgent-based simulation of caste-specific Lévy walk formation in termites.\u003cbr\u003e\n(A) Schematic of the individual-based simulation showing one queen (red dot) and 99 workers (blue dots) moving within a 90-mm-diameter circular arena. Each agent moved along straight trajectories and updated its direction upon encounters according to caste-specific turning intervals. (B) Simulated trajectories of the queen and workers after 2,000 time steps, illustrating that the queen exhibited more confined movement whereas workers maintained longer, exploratory paths. (C, D) Cumulative frequency distributions of simulated step lengths for queens and workers, respectively. The red and green curves represent truncated power-law and exponential fits. The truncated power law provided a superior fit, reproducing the empirical divergence in scaling exponents.\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-8145915/v1/528505e7ff909bc28d38f6c8.png"},{"id":97524470,"identity":"45441053-79d0-41c7-86fb-d2174d12a047","added_by":"auto","created_at":"2025-12-05 12:05:08","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":598530,"visible":true,"origin":"","legend":"\u003cp\u003eFunctional consequences of caste-specific Lévy walks in termites. (A–C) Boxplots comparing encounter efficiency between queens and workers in 100-individual groups, including the number of encounters (A), total distance traveled (B), and mean distance per encounter (C). Workers exhibited significantly higher encounter frequencies and longer movement distances than queens, while the mean distance per encounter did not differ between castes. (D) Representative spatial exploration map showing the trajectories of queens (green) and workers (blue) within the circular arena. Workers explored a substantially broader spatial range than queens. (E) Comparison of exploration rate (%) between queens and workers across group sizes (1, 100, 200, and 1,000 individuals). Workers consistently explored a larger proportion of the arena than queens, and caste differences became more pronounced at moderate densities. Boxplots display medians (horizontal lines), interquartile ranges (boxes), and outliers (points).\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-8145915/v1/75df5424299fefc915d459a4.png"},{"id":106344361,"identity":"0fd4035b-4020-4e48-b1c8-90db1902c387","added_by":"auto","created_at":"2026-04-07 16:13:48","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":4802491,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8145915/v1/c810efb4-2dfa-41e2-acbc-480e8aa9d2e0.pdf"},{"id":97672116,"identity":"3b135275-a853-4778-b9d4-8cef5407402f","added_by":"auto","created_at":"2025-12-08 09:34:16","extension":"docx","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":1553090,"visible":true,"origin":"","legend":"","description":"","filename":"Supplementarymaterials10.30.docx","url":"https://assets-eu.researchsquare.com/files/rs-8145915/v1/5cfaaa99bdaaa8a82fb5fa9e.docx"},{"id":97524471,"identity":"2bd8c07a-739a-4b18-be1f-2f5e17687907","added_by":"auto","created_at":"2025-12-05 12:05:08","extension":"zip","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":4764954,"visible":true,"origin":"","legend":"","description":"","filename":"dataandcodes.zip","url":"https://assets-eu.researchsquare.com/files/rs-8145915/v1/2fd935b9f6ed62f9c64cae97.zip"},{"id":97524499,"identity":"9d2ca769-ff16-41af-a6ea-3e39ebb4838a","added_by":"auto","created_at":"2025-12-05 12:05:11","extension":"avi","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":64128170,"visible":true,"origin":"","legend":"","description":"","filename":"MovieS1.avi","url":"https://assets-eu.researchsquare.com/files/rs-8145915/v1/5abc3d270728643492550482.avi"}],"financialInterests":"No competing interests reported.","formattedTitle":"Caste-specific origins of Lévy-like movement in social termites reveal social modulation of scaling laws","fulltext":[{"header":"Introduction","content":"\u003cp\u003eAcross taxa, from bacteria and mollusks to birds and humans, organisms often move in scale-free patterns known as L\u0026eacute;vy walks, characterized by heavy-tailed step-length distributions that enhance search efficiency in patchy or unpredictable environments [\u003cspan additionalcitationids=\"CR2\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. The \u0026ldquo;L\u0026eacute;vy-foraging hypothesis\u0026rdquo; posits that such movements maximize encounter rates while minimizing redundant exploration [\u003cspan additionalcitationids=\"CR5 CR6\" citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]. Despite their apparent ubiquity, the mechanisms generating L\u0026eacute;vy-like behavior remain controversial. Some studies attribute these patterns to intrinsic processes, such as neuromotor rhythms or internal decision rules that spontaneously produce scale-free displacements [\u003cspan additionalcitationids=\"CR9 CR10 CR11\" citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. Others emphasize for extrinsic drivers, where environmental heterogeneity, predation risk, or social interactions impose external constraints that shape movement [\u003cspan additionalcitationids=\"CR14\" citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. Yet, how social organization, a defining feature of many animal societies modulates the emergence and adaptive significance of L\u0026eacute;vy-like movements remains largely unexplored.\u003c/p\u003e\u003cp\u003eSocial insects provide a powerful system for addressing this question because individual movement is both a behavioral expression of division of labour and a dynamic response to the surrounding social context. Within colonies of ants and termites, queens specialize in reproduction, whereas workers perform tasks such as foraging, nest maintenance, and brood care [\u003cspan additionalcitationids=\"CR17\" citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]. These functional differences are tightly linked to caste-specific movement behaviours, which determine how information, resources, and individuals flow within the colony [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. Workers benefit from exploratory trajectories that maximize spatial coverage and contact rates, whereas queens may adopt more conservative, energy-saving movements that maintain social connectivity while minimizing exposure [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]. Termites, in particular, exhibit strong social structuring and frequent physical encounters, making them ideal for testing whether collective organization can actively shape the scaling properties of individual movement [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e].\u003c/p\u003e\u003cp\u003ePrevious studies have shown that termite workers display L\u0026eacute;vy-like movements influenced by group density and local interactions [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e, \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e], yet whether and how these effects differ between castes remains unknown. Moreover, most analyses have focused on solitary or small groups [\u003cspan additionalcitationids=\"CR25\" citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e], leaving the impact of social density, a central aspect of colony organization largely untested in larger societies. If social encounters regulate individual turning and displacement, the scaling exponent of L\u0026eacute;vy walks should vary systematically with crowding. Conversely, if caste-specific traits dominate, intrinsic behavioral rules may override environmental effects.\u003c/p\u003e\u003cp\u003eHere, we integrate high-resolution behavioral tracking with agent-based modelling in the termite \u003cem\u003eReticulitermes labralis\u003c/em\u003e to examine how social organization modulates the emergence of L\u0026eacute;vy-like movement. By comparing queens and workers across a gradient of group densities, we test whether L\u0026eacute;vy patterns arise primarily from intrinsic caste differences or from extrinsic social interactions. This integrative framework bridges behavioral ecology and collective dynamics, revealing how the interplay between social roles and crowding generates the complex scaling laws that govern movement in social systems.\u003c/p\u003e"},{"header":"Material and Methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\n \u003ch2\u003eTermite collection and maintenance\u003c/h2\u003e\n \u003cp\u003eFive colonies of \u003cem\u003eReticulitermes labralis\u003c/em\u003e were collected from decayed wood in the northern Qinling Mountains, Xi\u0026rsquo;an, Shaanxi Province, China (108\u0026deg;46\u0026prime;E, 34\u0026deg;00\u0026prime;N). Colonies were transferred to ventilated plastic boxes (80 \u0026times; 50 \u0026times; 40 cm) and maintained at 25\u0026deg;C for one week under controlled humidity to allow acclimation. Approximately 1,000 individuals from each colony were placed in 9-cm Petri dishes (five replicates per colony) with damp filter paper as food and moisture sources. Caste identity was confirmed based on standard morphological traits, including body pigmentation and abdominal shape. After one month, supplementary reproductives (replacement queens and kings) differentiated within each group, identified by characteristic head pigmentation and slight abdominal enlargement in queens [\u003cspan class=\"CitationRef\"\u003e27\u003c/span\u003e\u0026ndash;\u003cspan class=\"CitationRef\"\u003e29\u003c/span\u003e].\u003c/p\u003e\n \u003cp\u003eFrom each colony, one queen or worker was randomly selected for individual tracking. Additional groups of 100 (94 workers, 4 soldiers, one queen, and one king), 200 (190 workers, 8 soldiers, one queen, and one king), and 1,000 individuals (\u0026asymp;\u0026thinsp;958 workers, 40 soldiers, one queen, and one king) were established under identical conditions (25\u0026deg;C, 70% relative humidity, 14 h light/10 h dark). All groups were acclimated for 24 h before behavioral recording.\u003c/p\u003e\n\u003c/div\u003e\n\u003ch3\u003eMovement recordings\u003c/h3\u003e\n\u003cp\u003eTo enable individual identification, the abdomen of each focal queen or worker was marked with a small spot of non-toxic white glue mixed with dye following Marins et al. [\u003cspan class=\"CitationRef\"\u003e30\u003c/span\u003e]. Groups were then transferred sequentially to a recording arena and allowed to acclimate for one hour before filming. Movements were recorded continuously for one hour using a Sony AX100E camera at 30 frames s⁻\u0026sup1; under uniform illumination. Video files were downsampled to 5 frames s⁻\u0026sup1; for analysis in EthoVision XT (Noldus, Beijing), and X\u0026ndash;Y coordinates of the focal individual were extracted for subsequent processing in MATLAB (\u003cstrong\u003eFigure \u003cspan class=\"InternalRef\"\u003eS1\u003c/span\u003e\u003c/strong\u003e).\u003c/p\u003e\n\u003cp\u003eEach experimental session yielded approximately 15,000 positional data points per individual across four group sizes (1, 100, 200, and 1,000 individuals), totaling 20 complete recordings. In high-density groups, three to four recordings contained short interruptions caused by individuals climbing the dish walls, but trajectories remained continuous after their return and were thus retained without affecting the analyses.\u003c/p\u003e\n\u003ch3\u003eAnalyzing movement\u003c/h3\u003e\n\u003cp\u003eThe kinematic features of the color-marked queen and worker were quantified using six complementary parameters that together describe the structure and dynamics of their trajectories.\u003cbr\u003e\u0026nbsp;(i) Step-length distribution, defined as the frequency of short and long one-dimensional (1D) steps following the framework of Humphries et al. [31];\u003cbr\u003e\u0026nbsp;(ii) Mean speed, representing the average displacement rate during active movement;\u003cbr\u003e\u0026nbsp;(iii) Total movement time, the cumulative duration of locomotor activity;\u003cbr\u003e\u0026nbsp;(iv) Turning frequency, calculated as the number of direction changes per second of active movement;\u003cbr\u003e\u0026nbsp;(v) Straightness index, the ratio of net displacement to total path length (values approaching 1 indicate more linear movement, whereas those near 0 reflect more tortuous paths); and\u003cbr\u003e\u0026nbsp;(vi) Proportion of movement within the inner region, defined as the fraction of time spent within the central 80% of the arena (radius \u0026le; 36 mm).\u003c/p\u003e\n\u003cp\u003eThese metrics jointly capture both the spatial and temporal organization of individual movement, describing how queens and workers combine short and long steps, modulate speed and turning, and distribute their activity across spatial zones. Extremely small 1D step lengths were corrected following the procedure of Castiblanco et al. to ensure consistency in step-length estimation [23].\u003c/p\u003e\n\u003ch3\u003eStep-length distribution analysis\u003c/h3\u003e\n\u003cp\u003eStep lengths were defined as the linear distance between consecutive termite positions sampled at fixed 1-s intervals (corresponding to 5 frames). No arbitrary turning-angle thresholds were applied. Instead, step segmentation followed the one-dimensional (1D) projection method of Humphries et al. [\u003cspan class=\"CitationRef\"\u003e31\u003c/span\u003e], which identifies turns objectively at points where the direction of travel reverses along a single axis. This approach minimizes subjective bias from predefined critical angles and has become standard in analyzing animal movement trajectories [\u003cspan class=\"CitationRef\"\u003e8\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e15\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e22\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e32\u003c/span\u003e].\u003c/p\u003e\n\u003cp\u003eFor each individual, independent step-length distributions were constructed and fitted to candidate statistical models using maximum likelihood estimation (MLE). The models included the power-law, truncated power-law, exponential, and truncated exponential distributions. Model selection followed a decision-tree framework based on Akaike weights (AICw) and goodness-of-fit criteria [\u003cspan class=\"CitationRef\"\u003e31\u003c/span\u003e].\u003c/p\u003e\n\u003cp\u003eThe truncated power-law distribution,\u003c/p\u003e\n\u003cp\u003e\u003cimg src=\"https://myfiles.space/user_files/58895_8739fc6c57c1c19a/58895_custom_files/img1764935616.png\" width=\"327\" height=\"138\"\u003e\u003c/p\u003e\n\u003cp\u003echaracterizes superdiffusive, scale-free motion with exponent \u003cem\u003e\u0026micro;\u003c/em\u003e, where lower \u003cem\u003e\u0026micro;\u003c/em\u003e indicates longer steps and stronger intermittency. In contrast, the exponential distribution,\u003c/p\u003e\n\u003cp\u003e\u003cimg src=\"https://myfiles.space/user_files/58895_8739fc6c57c1c19a/58895_custom_files/img1764935628.png\" width=\"247\" height=\"106\"\u003e\u003c/p\u003e\n\u003cp\u003erepresents memoryless Brownian motion. Biologically, the exponential model reflects uncorrelated, diffusive movement, whereas the truncated power-law describes L\u0026eacute;vy-like behavior that combines frequent short steps with occasional long displacements.\u003c/p\u003e\n\u003cp\u003eWe focused on comparing these two ecologically meaningful models, truncated power-law versus exponential, because they capture the essential difference between superdiffusive and diffusive movement. The truncated form of the power-law accounts for the biological constraint that animals cannot take infinitely long steps, while avoiding the risk of artificially suppressing rare long steps inherent in truncated exponentials. Although more complex models (e.g., multiphasic or lognormal) may achieve marginally better statistical fits, our analysis specifically aimed to test for the presence of L\u0026eacute;vy-like scaling and to compare its expression between termite castes. All parameter estimation and model selection procedures were conducted using the software provided by Humphries et al.\u003c/p\u003e\n\u003ch3\u003eAgent-based model\u003c/h3\u003e\n\u003cp\u003eTo examine whether caste-specific turning rules during social encounters could generate distinct L\u0026eacute;vy-like patterns, we developed an agent-based model simulating termite movement within a circular arena (9 cm in diameter; \u003cstrong\u003eMovie S1\u003c/strong\u003e). The arena contained 100 mobile agents represented as solid spheres moving in continuous space with randomly assigned initial directions. Based on empirical measurements of body size, the first sphere (representing the queen) had a diameter of 4 mm, while the remaining 99 spheres (representing workers) had diameters of 2 mm. Each sphere moved at a fixed probability per time step (0.3 for the queen and 0.6 for the workers), corresponding to the proportion of active movement time observed experimentally over 51 min.\u003c/p\u003e\n\u003cp\u003eThe simulation proceeded for 2,000 time steps, with periodic updates governed by the following rules. Agents were confined within the arena boundaries and reflected upon reaching the edge. Turning intervals followed a power-law distribution, derived from empirical data (\u003cstrong\u003eFig. \u003cspan class=\"InternalRef\"\u003eS2\u003c/span\u003e\u003c/strong\u003e), with exponents \u003cem\u003e\u0026beta;\u003c/em\u003e\u0026thinsp;=\u0026thinsp;2.7 for the queen and \u003cem\u003e\u0026beta;\u003c/em\u003e\u0026thinsp;=\u0026thinsp;2.0 for the workers. Turning angles were drawn from a normal distribution to introduce directional variability (\u003cstrong\u003eFig. \u003cspan class=\"InternalRef\"\u003eS3\u003c/span\u003e\u003c/strong\u003e). Directional updates occurred upon encounters with other agents, representing social modulation of movement. When two agents came into contact, the focal agent changed direction only if the elapsed time since its previous turn exceeded its current power-law-sampled interval; otherwise, the trajectory remained unchanged. At the end of each simulation, trajectories and encounter counts were recorded for all agents, and representative paths of the queen (first sphere) and a worker (second sphere) were visualized for comparison.\u003c/p\u003e\n\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e\n \u003ch2\u003eCalculation of encounters, movement distance, and spatial exploration\u003c/h2\u003e\n \u003cp\u003eTo quantify social interaction, movement performance, and spatial exploration, we analyzed the recordings of color-marked queens and workers in 100-individual groups. Encounters were defined as antennal contacts between the focal (marked) individual and any nestmate, with each contact recorded as a single event. The total number of encounters was counted separately for queens and workers across five replicate colonies.\u003c/p\u003e\n \u003cp\u003eMovement distance was computed as the cumulative path length derived from the two-dimensional positional coordinates of each marked individual. To assess spatial exploration, the arena was divided into a grid of equal-sized cells, and the coverage rate was calculated as the proportion of cells traversed by the focal termite relative to the total number of cells within the 9-cm Petri dish. This metric represents the proportion of space explored during the observation period and allows comparison of exploratory efficiency between castes.\u003c/p\u003e\n\u003c/div\u003e\n\u003ch3\u003eSimulative analysis of L\u0026eacute;vy patterns in queens and workers\u003c/h3\u003e\n\u003cp\u003eTo assess whether the distinct L\u0026eacute;vy-like patterns observed in queens and workers confer different functional advantages, we performed a simulation experiment comparing movement efficiency under caste-specific scaling exponents. The model consisted of 100 moving agents represented as spheres. In the first scenario, the focal sphere (representing the queen) followed a truncated L\u0026eacute;vy walk characterized by the empirically estimated scaling exponent of queens, while the remaining 99 spheres (representing workers) followed the workers\u0026rsquo; scaling exponent. In a second scenario, the exponents were reversed: the focal sphere adopted the workers\u0026rsquo; exponent, whereas all others followed the queens\u0026rsquo; exponent.\u003c/p\u003e\n\u003cp\u003eFor each scenario, three metrics were quantified: (i) the number of encounters between spheres, (ii) the total movement distance of all spheres, and (iii) the mean distance required for the focal sphere and three randomly selected workers to encounter others. The simulation proceeded iteratively, updating the position and state of each sphere at every time step. Motion was governed by stochastic intervals drawn from a power-law distribution, determining whether the sphere remained stationary or initiated a new displacement. After each movement, direction changes were sampled from a normal distribution, and step velocity was proportional to the sampled step length.\u003c/p\u003e\n\u003cp\u003eEncounters were recorded whenever the distance between two spheres was less than 3 mm, a threshold corresponding to the combined body size and estimated antennal reach of \u003cem\u003eR. labralis\u003c/em\u003e. Each simulation ran for a fixed duration, and trajectories were analyzed to quantify both the encounter efficiency and total distance traveled under each L\u0026eacute;vy parameter regime.\u003c/p\u003e\n\u003ch3\u003eStatistical analyses\u003c/h3\u003e\n\u003cp\u003eAll colonies were tested under each of the four group-size conditions, introducing potential non-independence due to shared genetic and environmental backgrounds. To account for this, behavioral and kinematic parameters (mean speed, movement time, turning frequency, straightness index, exploration rate, and the proportion of movement within the inner region) were analyzed using linear mixed-effects models (LMMs) or beta regression models for bounded data (0\u0026ndash;1 range). Caste (queen vs. worker), group size, and their interaction were treated as fixed effects, and colony identity was included as a random intercept to control for repeated measures across groups.\u003c/p\u003e\n\u003cp\u003eThe significance of fixed factors was assessed using Wald \u0026chi;\u0026sup2; tests or ANOVA, and post hoc pairwise contrasts were performed with Tukey\u0026rsquo;s HSD tests based on estimated marginal means, with \u003cem\u003ep\u003c/em\u003e-values adjusted for multiple comparisons. For comparisons derived from simulation outputs, such as encounter frequency, total movement distance, and distance per encounter, differences between castes or parameter settings were evaluated using two-tailed independent-sample t-tests. Variance equality was verified using Levene\u0026rsquo;s or Bartlett\u0026rsquo;s tests.\u003c/p\u003e\n\u003cp\u003eModel adequacy was evaluated through residual inspection, variance homogeneity, and random-effect diagnostics to ensure compliance with model assumptions. All statistical analyses and data visualization were conducted in R (v. 4.3.2; R Core Team, 2023), using the \u003cem\u003elme4\u003c/em\u003e, \u003cem\u003elmerTest\u003c/em\u003e, \u003cem\u003eglmmTMB\u003c/em\u003e, \u003cem\u003ecar\u003c/em\u003e, \u003cem\u003eemmeans\u003c/em\u003e, and \u003cem\u003eperformance\u003c/em\u003e packages.\u003c/p\u003e"},{"header":"Results","content":"\u003cdiv id=\"Sec12\" class=\"Section2\"\u003e\u003ch2\u003eMovement trajectory\u003c/h2\u003e\u003cp\u003eHigh-resolution video tracking revealed clear caste-specific differences in movement trajectories across group sizes (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). Queens predominantly occupied the central region of the arena, whereas workers frequently traced the periphery. Beta-regression analyses indicated significant main effects of caste and group size on the proportion of movement occurring within the inner region (Wald χ\u0026sup2; tests: caste, χ\u0026sup2;₁ = 58.07, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.001; group size, χ\u0026sup2;₃ = 29.20, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.001), with no significant interaction between the two factors (χ\u0026sup2;₃ = 5.16, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.16). Post-hoc Tukey comparisons confirmed that queens consistently spent a greater proportion of time in the inner region than workers under all group-size conditions (1-individual: z\u0026thinsp;=\u0026thinsp;2.79, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.0052; 100-individual: z\u0026thinsp;=\u0026thinsp;3.80, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.0001; 200-individual: z\u0026thinsp;=\u0026thinsp;\u0026minus;\u0026thinsp;5.31, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.0001; 1000-individual: z\u0026thinsp;=\u0026thinsp;4.49, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.0001; \u003cb\u003eFig. S4\u003c/b\u003e). These results demonstrate that spatial positioning within the group is strongly shaped by caste identity: workers exhibit boundary-following, exploratory movement, whereas queens maintain more centralized and spatially confined trajectories.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec13\" class=\"Section2\"\u003e\u003ch2\u003eStep-length distributions\u003c/h2\u003e\u003cp\u003eAcross all group sizes, step-length distributions of both castes were better described by a truncated power law than by an exponential model (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). Maximum-likelihood fits, together with goodness-of-fit and AIC comparisons, consistently supported the truncated power-law model (\u003cb\u003eTable \u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003e\u003c/b\u003e), indicating that both queens and workers exhibit L\u0026eacute;vy-like movement patterns rather than Brownian diffusion. Linear mixed-effects modeling revealed significant effects of caste (F₁,₃₂ = 38.07, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.001), group size (F₃,₃₂ = 27.64, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.001), and their interaction (F₃,₃₂ = 3.84, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.019) on the scaling exponent (\u003cem\u003e\u0026micro;\u003c/em\u003e) of the truncated power-law fits. Post-hoc Tukey comparisons showed that \u003cem\u003e\u0026micro;\u003c/em\u003e did not differ between queens and workers in solitary conditions (t₂₈ = 0.40, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.70), but queens exhibited significantly higher \u003cem\u003e\u0026micro;\u003c/em\u003e values than workers in larger groups (t₂₈ = 4.70, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.0001 for 100-individual; t₂₈ = 2.88, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.0075 for 200-individual; t₂₈ = 4.36, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.0002 for 1000-individual; Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e). These results demonstrate that social context modulates the scaling properties of movement, with a stronger effect on queens than on workers.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec14\" class=\"Section2\"\u003e\u003ch2\u003eMovement attributes\u003c/h2\u003e\u003cp\u003eCaste and group size jointly influenced multiple aspects of termite locomotion, including speed, movement duration, turning frequency, and trajectory straightness (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e). For average speed, both caste and group size had significant effects, with a significant interaction (F₁,₂₆ = 17.57, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.001; F₃,₂₆ = 4.50, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.011; interaction: F₃,₂₆ = 3.97, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.019). Queens moved significantly slower than workers in the 1- and 100-individual groups (t₂₆ = \u0026minus;3.37, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.002; t₂₆ = \u0026minus;4.32, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.0002), whereas the difference disappeared at higher densities (200- and 1000-individual groups). Movement duration followed a similar pattern, being significantly affected by caste, group size, and their interaction (F₁,₂₈ = 13.14, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.001; F₃,₂₈ = 15.69, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.001; interaction: F₃,₂₈ = 4.70, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.009). Queens exhibited shorter movement times than workers in the 100-individual groups (t₂₈ = \u0026minus;5.02, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.0001), but no caste difference in other densities.\u003c/p\u003e\u003cp\u003eTurning frequency also differed significantly by caste, group size, and their interaction (F₁,₃₀ = 30.12, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.001; F₃,₃₀ = 18.52, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.001; interaction: F₃,₃₀ = 4.41, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.011). Queens turned more frequently than workers in the 100- and 1000-individual groups (t₂₆ = 4.11, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.0003; t₂₆ = 4.84, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.0001), with a marginal trend at 200 individuals (t₂₆ = 1.99, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.057). The straightness index (SI) was significantly influenced by group size and its interaction with caste (F₃,₃₂ = 28.66, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.001; interaction: F₃,₃₂ = 7.40, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.001), but not by caste alone (F₁,₃₂ = 0.93, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.34). Queens exhibited slightly straighter trajectories than workers in small groups (1-individual: t₂₈ = 1.89, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.07; 100-individual: t₂₈ = 3.58, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.0013), but less straight paths in the largest groups (1000-individual: t₂₈ = \u0026minus;2.27, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.031). These results demonstrate that group size modulates caste-specific locomotor behaviours: queens move more slowly and along straighter paths in small and moderate groups, but their motion becomes less directed and more interrupted under high crowding, whereas workers maintain higher activity and turning rates that enhance space coverage in dense social environments.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec15\" class=\"Section2\"\u003e\u003ch2\u003eMechanistic and functional origins of caste-specific L\u0026eacute;vy dynamics\u003c/h2\u003e\u003cp\u003eTo understand how social organization modulates the emergence of L\u0026eacute;vy-like movements, we first examined whether directional dynamics could account for the caste-specific scaling exponents observed above. Turning frequency was tightly correlated with the scaling exponent of the step-length distribution (adjusted R\u0026sup2; = 0.81, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.0001; Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e, \u003cb\u003eTable \u003cspan refid=\"MOESM2\" class=\"InternalRef\"\u003eS2\u003c/span\u003e\u003c/b\u003e), indicating that individuals with higher turning rates produced steeper, more Brownian-like distributions. To test this relationship mechanistically, we constructed an agent-based model in which queens and workers followed caste-specific turning rules derived from empirical observations, and directional updates occurred upon encounters with other agents (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e). The simulations successfully reproduced the observed divergence in scaling exponents, with queens exhibiting significantly higher \u003cem\u003e\u0026micro;\u003c/em\u003e values than workers (t\u003csub\u003e(8)\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;3.43, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.0096; \u003cb\u003eFig. S5\u003c/b\u003e). Together, these findings demonstrate that differences in L\u0026eacute;vy walk characteristics can arise from caste-specific turning dynamics coupled with encounter-driven modulation.\u003c/p\u003e\u003cp\u003eBuilding on these insights, we evaluated the functional advantages of the distinct L\u0026eacute;vy walks performed by each caste. Workers experienced significantly more encounters than queens (t\u003csub\u003e(4)\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;4.24, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.013) and traveled longer total distances (t\u003csub\u003e(4)\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;3.71, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.021), whereas the mean distance per encounter did not differ significantly (t\u003csub\u003e(4)\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;1.91, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.13). Across all group sizes, workers explored a larger proportion of available space than queens (1-individual: t\u003csub\u003e(28)\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;2.87, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.0077; 100-individual: t\u003csub\u003e(28)\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;7.21, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.0001; 200-individual: t\u003csub\u003e(28)\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;3.73, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.0009; 1000-individual: t\u003csub\u003e(28)\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;2.66, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.013; Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eTo assess whether these performance differences arose from caste-specific scaling parameters, we simulated scenarios in which queens and workers exchanged their empirical scaling exponents. When queens adopted the worker\u0026rsquo;s exponent, encounter rate and encounter distance remained unchanged (t\u003csub\u003e(10)\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;\u0026minus;\u0026thinsp;0.15, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.896; t\u003csub\u003e(10)\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;2.83, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.105), though total distance tended to increase (t\u003csub\u003e(10)\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;3.63, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.053). In contrast, when workers adopted the queen\u0026rsquo;s exponent, their encounter rate, total distance, and encounter distance all declined sharply (t\u003csub\u003e(10)\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;\u0026minus;\u0026thinsp;2.14, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.049; t\u003csub\u003e(10)\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;\u0026minus;\u0026thinsp;5.22, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.001; t\u003csub\u003e(10)\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;\u0026minus;\u0026thinsp;7.28, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.001; \u003cb\u003eFig. S6\u003c/b\u003e). These simulations indicate that the worker\u0026rsquo;s scaling exponent is functionally tuned to maximize encounter efficiency and spatial exploration, whereas the queen\u0026rsquo;s performance is comparatively insensitive to parameter changes.\u003c/p\u003e\u003cp\u003eCollectively, these results reveal that caste-specific L\u0026eacute;vy patterns in termites arise from simple local rules governing turning and encounters, yet yield distinct adaptive outcomes. Workers, intrinsically motivated to explore and sustain information flow, maintain L\u0026eacute;vy dynamics that enhance spatial coverage and contact efficiency. Queens, by contrast, exhibit movement that is more constrained and socially responsive, minimizing energy expenditure while preserving connectivity within the colony. Thus, the emergence of L\u0026eacute;vy-like movement in social insects reflects how hierarchical organization and social feedbacks reshape the statistical laws of individual motion.\u003c/p\u003e\u003c/div\u003e"},{"header":"Discussion","content":"\u003cp\u003eOur results reveal a fundamental principle of collective behavior: social organization can reshape the statistical laws of individual movement. By comparing termite queens and workers across densities, we show that the emergence of L\u0026eacute;vy-like movement, long regarded as a universal scale-free search strategy, is not a fixed individual property but a socially modulated outcome. Workers consistently maintained L\u0026eacute;vy-like patterns, whereas queens exhibited a tendency to shift toward Brownian-like motion at high densities. This divergence demonstrates that the same movement rule can bifurcate into distinct regimes when embedded in a structured social context. In other words, how social organization modulates the emergence of L\u0026eacute;vy-like movements provides a mechanistic window into how collective structure feeds back to constrain or amplify individual variability [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e, \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eThis socially induced divergence arises from the interaction between intrinsic caste-specific drives and extrinsic encounter dynamics. Workers, intrinsically motivated to explore and sustain information flow, exhibit persistent trajectories that maximize encounter efficiency and spatial coverage, properties consistent with self-organized L\u0026eacute;vy dynamics [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e, \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e]. Queens, in contrast, operate under a different optimization regime: their mobility is shaped less by exploration and more by maintaining proximity to workers for care and protection [\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e]. As density rises, repeated encounters increase turning frequency and fragment long displacements, pushing their trajectories toward Brownian regimes [\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e]. These findings align with evidence from other eusocial systems, where reproductive individuals exhibit restricted motion to stabilize the colony\u0026rsquo;s social network [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e, \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e]. Thus, what appears as a change in a statistical exponent \u003cem\u003e(\u0026micro;\u003c/em\u003e) in fact reflects a shift in the dominant feedback loop, from internal drive to social coupling.\u003c/p\u003e\u003cp\u003eAt a conceptual level, these results extend the scope of L\u0026eacute;vy walk theory beyond individual optimal foraging. Classical models treat L\u0026eacute;vy exponents as static parameters tuned by environmental randomness [\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e, \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e], but our findings show that in social systems, these parameters are themselves emergent variables molded by the structure of interaction networks. Social organization therefore acts as a higher-order constraint that dynamically tunes movement scaling, analogous to how metabolic scaling laws are modulated by network topology or energy flux within organisms [\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e, \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e]. By embedding individuals within feedback-rich social architectures, colonies can generate complex, non-Gaussian mobility distributions without requiring cognitive optimization, which represents an emergent statistical signature of collective life.\u003c/p\u003e\u003cp\u003eFunctionally, the distinct L\u0026eacute;vy parameters of queens and workers reveal adaptive tuning between exploration and efficiency. Simulations confirmed that swapping exponents disrupted colony-level performance: queens became energetically wasteful, while workers lost spatial efficiency. This role-dependent asymmetry suggests that the colony\u0026rsquo;s behavioral diversity is not noise but design, each caste occupies a different region of the movement landscape optimized for its social function [\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e]. Such division of movement behaviours mirrors the division of labor itself: exploratory L\u0026eacute;vy dynamics sustain the flow of information and resources, while constrained Brownian motion stabilizes the reproductive core [\u003cspan additionalcitationids=\"CR44\" citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e]. This dual mechanism exemplifies how evolution can translate social feedback into scaling adaptation, producing both stability and flexibility within a single collective framework.\u003c/p\u003e\u003cp\u003eIn sum, how social organization modulates the emergence of L\u0026eacute;vy-like movements offers a quantitative route to connect behavioral scaling, feedback regulation, and social evolution. Termite colonies illustrate a general principle that may extend to other collective systems, from bacterial swarms to human societies, where individual movement statistics encode the structure of interaction networks. Understanding these feedbacks transforms L\u0026eacute;vy walks from a foraging paradigm into a universal model of how local rules and social architecture generate emergent complexity.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003e\u003cstrong\u003eEthics declarations\u003c/strong\u003e\u003c/h2\u003e\n\u003cp\u003eEthics, consent to Participate, and consent to publish declarations\u003c/p\u003e\n\u003cp\u003eNot applicable.\u003c/p\u003e\n\u003ch2\u003eCompeting Interests\u003c/h2\u003e\n\u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e\n\u003ch2\u003eFunding\u003c/h2\u003e\n\u003cp\u003eThis work was supported by the National Natural Science Foundation of China (32171482) and the NSFC-Yunnan United fund (U2102221).\u003c/p\u003e\n\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\n\u003cp\u003eRW, JH and ZB designed the research; ZB and NY performed the experiments; ZB and NY collected the data; JH and CW performed the data analysis; ZB, JH and NY drafted the manuscript; DSD and RW contributed on writing the manuscript. CW and RW acquired funding for the project. All authors have approved the final vresion of the manuscript for publication.\u003c/p\u003e\n\u003ch2\u003eAcknowledgement\u003c/h2\u003e\n\u003cp\u003eWe thank Dr. Yanping Liu for valuable conceptual discussions during the early stages of study design, which greatly strengthened the development of this work. We are also grateful to Yibin Liu, Chongyang Shi, Meng Hou and Xiancun Ma for their assistance with sample collection and experimental procedures. Their dedication and support were essential to the successful progress of this project.\u003c/p\u003e\n\u003ch2\u003eData Availability\u003c/h2\u003e\n\u003cp\u003eAll data generated or analyzed during this study are included in the supplementary material.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eReynolds, A.M. 2018 Current status and future directions of L\u0026eacute;vy walk research. \u003cem\u003eBiology open\u003c/em\u003e \u003cstrong\u003e7\u003c/strong\u003e, bio030106.\u003c/li\u003e\n\u003cli\u003eZaburdaev, V., Denisov, S. \u0026amp; Klafter, J. 2015 L\u0026eacute;vy walks. \u003cem\u003eReviews of Modern Physics\u003c/em\u003e \u003cstrong\u003e87\u003c/strong\u003e, 483-530.\u003c/li\u003e\n\u003cli\u003eKlages, R. 2023 Search for Food of Birds, Fish, and Insects. 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Rhodes, C.J. 2009 The L\u0026eacute;vy flight paradigm: random search patterns and mechanisms. \u003cem\u003eEcology\u003c/em\u003e \u003cstrong\u003e90\u003c/strong\u003e, 877-887.\u003c/li\u003e\n\u003cli\u003eBartumeus Ferr\u0026eacute;, F. 2005 \u003cem\u003eL\u0026eacute;vy processes in animal movement and dispersal\u003c/em\u003e, Universitat de Barcelona.\u003c/li\u003e\n\u003cli\u003eReynolds, A.M. 2009 Scale-free animal movement patterns: L\u0026eacute;vy walks outperform fractional Brownian motions and fractional L\u0026eacute;vy motions in random search scenarios. \u003cem\u003eJournal of Physics A: Mathematical and Theoretical\u003c/em\u003e \u003cstrong\u003e42\u003c/strong\u003e, 434006.\u003c/li\u003e\n\u003cli\u003eJames, A., Plank, M. \u0026amp; Brown, R. 2008 Optimizing the encounter rate in biological interactions: ballistic versus L\u0026eacute;vy versus Brownian strategies. \u003cem\u003ePhysical Review E\u0026mdash;Statistical, Nonlinear, and Soft Matter Physics\u003c/em\u003e \u003cstrong\u003e78\u003c/strong\u003e, 051128.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"movement-ecology","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"move","sideBox":"Learn more about [Movement Ecology](http://movementecologyjournal.biomedcentral.com/)","snPcode":"40462","submissionUrl":"https://submission.nature.com/new-submission/40462/3","title":"Movement Ecology","twitterHandle":"@BioMedCentral","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"BMC/SO AJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Lévy walk, termite, social modulation, movement scaling, division of labor","lastPublishedDoi":"10.21203/rs.3.rs-8145915/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8145915/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eL\u0026eacute;vy walks, the scale-free movement patterns emerging across taxa, are thought to reflect optimal search strategies shaped by intrinsic physiology or environmental constraints. Yet how social organization modulates the emergence of L\u0026eacute;vy-like movements remains unclear. Here we combine high-resolution tracking and agent-based modelling to compare the movement of queens and workers of the termite \u003cem\u003eReticulitermes labralis\u003c/em\u003e under varying group densities. Both castes displayed step-length distributions consistent with truncated power laws, but their scaling exponents diverged: workers maintained L\u0026eacute;vy-like movement across densities, whereas queens tended to shift toward Brownian-like movement in high-density groups. Behavioral kinematics paralleled these patterns: workers moved faster, turned less frequently, and explored larger spatial areas, while queens showed slower, more confined trajectories; turning frequency was positively associated with the scaling exponent, linking local reorientation to heavy-tailed step lengths. Simulations revealed that caste-specific turning dynamics and encounter-driven modulation could reproduce the empirical divergence, mechanistically linking the effects of caste-specific traits and social contacts on the formation of differences in L\u0026eacute;vy-like movement patterns. Functional tests further showed that swapping scaling exponents between castes reduced encounter efficiency and movement performance-especially for workers, indicating adaptive tuning of L\u0026eacute;vy parameters to social role. These finding reveal that L\u0026eacute;vy-like movements in social insects arise from the interplay between intrinsic behavioral roles and extrinsic crowding, providing a framework for how division of labour and spatial interactions shape the evolution of movement behaviour.\u003c/p\u003e","manuscriptTitle":"Caste-specific origins of Lévy-like movement in social termites reveal social modulation of scaling laws","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-12-05 12:05:03","doi":"10.21203/rs.3.rs-8145915/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-12-20T17:23:34+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-12-19T07:52:50+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"91879255247966520447583173869214589316","date":"2025-12-08T10:42:22+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-12-07T15:37:29+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"31676527395064158110242774989022623604","date":"2025-12-03T17:17:23+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-12-02T09:49:33+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-11-20T08:45:24+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-11-20T08:43:03+00:00","index":"","fulltext":""},{"type":"submitted","content":"Movement Ecology","date":"2025-11-18T13:08:05+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"movement-ecology","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"move","sideBox":"Learn more about [Movement Ecology](http://movementecologyjournal.biomedcentral.com/)","snPcode":"40462","submissionUrl":"https://submission.nature.com/new-submission/40462/3","title":"Movement Ecology","twitterHandle":"@BioMedCentral","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"BMC/SO AJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"67b77fad-6a15-436e-a3b8-d01215632600","owner":[],"postedDate":"December 5th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2026-04-07T16:09:53+00:00","versionOfRecord":{"articleIdentity":"rs-8145915","link":"https://doi.org/10.1186/s40462-026-00646-w","journal":{"identity":"movement-ecology","isVorOnly":false,"title":"Movement Ecology"},"publishedOn":"2026-04-03 16:00:03","publishedOnDateReadable":"April 3rd, 2026"},"versionCreatedAt":"2025-12-05 12:05:03","video":"","vorDoi":"10.1186/s40462-026-00646-w","vorDoiUrl":"https://doi.org/10.1186/s40462-026-00646-w","workflowStages":[]},"version":"v1","identity":"rs-8145915","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8145915","identity":"rs-8145915","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}