The ubiquity of consistent inter-individual differences in behavior (“animal personalities”) [] suggests that they might play a fundamental role in driving the movements and functioning of animal groups [], including their collective decision-making, foraging performance, and predator avoidance. Despite increasing evidence that highlights their importance [], we still lack a unified mechanistic framework to explain and to predict how consistent inter-individual differences may drive collective behavior. Here we investigate how the structure, leadership, movement dynamics, and foraging performance of groups can emerge from inter-individual differences by high-resolution tracking of known behavioral types in free-swimming stickleback (Gasterosteus aculeatus) shoals. We show that individual’s propensity to stay near others, measured by a classic “sociability” assay, was negatively linked to swim speed across a range of contexts, and predicted spatial positioning and leadership within groups as well as differences in structure and movement dynamics between groups. In turn, this trait, together with individual’s exploratory tendency, measured by a classic “boldness” assay, explained individual and group foraging performance. These effects of consistent individual differences on group-level states emerged naturally from a generic model of self-organizing groups composed of individuals differing in speed and goal-orientedness. Our study provides experimental and theoretical evidence for a simple mechanism to explain the emergence of collective behavior from consistent individual differences, including variation in the structure, leadership, movement dynamics, and functional capabilities of groups, across social and ecological scales. In addition, we demonstrate individual performance is conditional on group composition, indicating how social selection may drive behavioral differentiation between individuals.

The role of social attraction and its link with boldness in the collective movements of three-spined sticklebacks.

Results and Discussion

1 Réale D.

Reader S.M.

Sol D.

McDougall P.T.

Dingemanse N.J. Integrating animal temperament within ecology and evolution. 2 Bell A.M.

Hankison S.J.

Laskowski K.L. The repeatability of behaviour: a meta-analysis. 17 Smith B.R.

Blumstein D.T. Fitness consequences of personality: a meta-analysis. 18 Sih A.

Cote J.

Evans M.

Fogarty S.

Pruitt J. Ecological implications of behavioural syndromes. 19 Réale D.

Dingemanse N.J.

Kazem A.J.N.

Wright J. Evolutionary and ecological approaches to the study of personality. 5 Ward A.J.W.

Thomas P.

Hart P.J.B.

Krause J. Correlates of boldness in three-spined sticklebacks (Gasterosteus aculeatus). 6 Kurvers R.H.J.M.

Eijkelenkamp B.

van Oers K.

van Lith B.

van Wieren S.E.

Ydenberg R.C.

Prins H.H.T. Personality differences explain leadership in barnacle geese. 7 Harcourt J.L.

Ang T.Z.

Sweetman G.

Johnstone R.A.

Manica A. Social feedback and the emergence of leaders and followers. 8 Pettit B.

Ákos Z.

Vicsek T.

Biro D. Speed determines leadership and leadership determines learning during pigeon flocking. 9 Pike T.W.

Samanta M.

Lindström J.

Royle N.J. Behavioural phenotype affects social interactions in an animal network. 10 Aplin L.M.

Farine D.R.

Morand-Ferron J.

Cole E.F.

Cockburn A.

Sheldon B.C. Individual personalities predict social behaviour in wild networks of great tits (Parus major). 11 Jolles J.W.

Fleetwood-Wilson A.

Nakayama S.

Stumpe M.C.

Johnstone R.A.

Manica A. The role of social attraction and its link with boldness in the collective movements of three-spined sticklebacks. 12 Farine D.R.

Strandburg-Peshkin A.

Couzin I.D.

Berger-Wolf T.Y.

Crofoot M.C. Individual variation in local interaction rules can explain emergent patterns of spatial organization in wild baboons. 13 Dyer J.R.G.

Croft D.P.

Morrell L.J.

Krause J. Shoal composition determines foraging success in the guppy. 14 Laskowski K.L.

Montiglio P.O.

Pruitt J.N. Individual and group performance suffers from social niche disruption. 15 Pruitt J.N.

Riechert S.E. How within-group behavioural variation and task efficiency enhance fitness in a social group. 16 Ioannou C.C.

Dall S.R.X. Individuals that are consistent in risk-taking benefit during collective foraging. 12 Farine D.R.

Strandburg-Peshkin A.

Couzin I.D.

Berger-Wolf T.Y.

Crofoot M.C. Individual variation in local interaction rules can explain emergent patterns of spatial organization in wild baboons. 20 Schaerf, T.M., Herbert-Read, J.E., Myerscough, M.R., Sumpter, D.J.T., and Ward, A.J.W. (2016). Identifying differences in the rules of interaction between individuals in moving animal groups. arXiv, arXiv:1601.08202, http://arxiv.org/abs/1601.08202. 21 Couzin I.D.

Krause J. Self-organization and collective behavior in vertebrates. 22 Sumpter D.J.T. Collective Animal Behavior. 23 Herbert-Read J.E. Understanding how animal groups achieve coordinated movement. In recent years, it has become apparent that across a wide range of animal taxa, individuals commonly differ consistently from one another in their behavior [] (“animal personalities”), often with large fitness consequences [] and wide-ranging ecological and evolutionary implications []. Such variation could provide a level of heterogeneity within animal groups that may drive collective behavior. Indeed, recent studies have started to provide support for that notion and have shown that consistent behavioral differences can influence leadership [], social network structure [], collective dynamics [], and group performance []. However, rarely are consistent behavioral differences integrated within the mechanistic framework of collective behavior research [], which has demonstrated that relatively simple interaction rules play an important role in the emergence of collective behavior []. It therefore remains unclear how consistent individual differences in behavior drive the structure, movement dynamics, and functioning of animal groups.

12 Farine D.R.

Strandburg-Peshkin A.

Couzin I.D.

Berger-Wolf T.Y.

Crofoot M.C. Individual variation in local interaction rules can explain emergent patterns of spatial organization in wild baboons. 24 Couzin I.D.

Krause J.

James R.

Ruxton G.D.

Franks N.R. Collective memory and spatial sorting in animal groups. 25 Tunstrøm K.

Katz Y.

Ioannou C.C.

Huepe C.

Lutz M.J.

Couzin I.D. Collective states, multistability and transitional behavior in schooling fish. 26 Couzin I.D.

Krause J.

Franks N.R.

Levin S.A. Effective leadership and decision-making in animal groups on the move. 27 Ioannou C.C.

Singh M.

Couzin I.D. Potential leaders trade off goal-oriented and socially oriented behavior in mobile animal groups. Here, we combine high-resolution tracking of individuals with known behavioral types in free-swimming stickleback (Gasterosteus aculeatus) shoals, with agent-based models of self-organizing groups, to provide a more mechanistic and predictive understanding of the behavior, structure, and performance of groups across ecological contexts. To capture the essential dynamics within and between groups, we employ a deliberately simple, spatially explicit model, which has previously been used successfully to explain the emergence of leadership, group structure, and consensus decision-making in a range of species [].

C = 0.48, 95% confidence intervals: 0.33–0.60). This exploratory tendency, which is traditionally referred to as “boldness” since it may increase potential predation risk [ 28 Persson L.

Eklöv P. Prey refuges affecting interactions between piscivorous perch and juvenile perch and roach. 29 Jolles J.W.

Manica A.

Boogert N.J. Food intake rates of inactive fish are positively linked to boldness in three-spined sticklebacks Gasterosteus aculeatus. C = 0.58, 0.46–0.68), classically used to define “sociability” [ 30 Krause J.

Ruxton G.D. Living in Groups. 31 Ward A.

Webster M. Sociality: The Behaviour of Group-Living Animals. 123 = −0.05, p = 0.658). Based on the detailed tracking data, we found that individual fish slowed down the closer they were to the confined shoal and that fish that consistently stayed closer to the shoal also swam at consistently lower speeds. This was even the case when controlling for boundary effects (r 123 = −0.79, p = 0.001) and when measured in the asocial boldness assay (see 25 Tunstrøm K.

Katz Y.

Ioannou C.C.

Huepe C.

Lutz M.J.

Couzin I.D. Collective states, multistability and transitional behavior in schooling fish. We first determined the behavioral tendencies of 125 fish by exposing them to two classic personality assays and tracking their movements (see Figure S1 ). We found consistent inter-individual variation in fish’s tendency to leave a refuge and explore an open environment (repeatability R= 0.48, 95% confidence intervals: 0.33–0.60). This exploratory tendency, which is traditionally referred to as “boldness” since it may increase potential predation risk [], was positively linked to individuals’ food consumption even in the safety of the holding compartment [], reflecting an intrinsic higher motivation for food. We also found consistent individual differences in fish’s proximity to a confined shoal of conspecifics (R= 0.58, 0.46–0.68), classically used to define “sociability” [], which was not correlated with their exploratory tendency (r= −0.05, p = 0.658). Based on the detailed tracking data, we found that individual fish slowed down the closer they were to the confined shoal and that fish that consistently stayed closer to the shoal also swam at consistently lower speeds. This was even the case when controlling for boundary effects (r= −0.79, p = 0.001) and when measured in the asocial boldness assay (see Figure S1 ). These results show that a fundamental link exists between social proximity and speed and concord with the general observation that slow-moving individuals tend to form more cohesive groups []. As consistent differences in social proximity can thus potentially be both a cause and a result of differences in speed, we prefer to refer to this trait as fish’s “social proximity tendency.”

30 Krause J.

Ruxton G.D. Living in Groups. 31 Ward A.

Webster M. Sociality: The Behaviour of Group-Living Animals. Figure 1 Group Shoaling Experiments Show full caption (A–C) Schematics of (A) the free-schooling context, (B) the open foraging context with patches of food, and (C) the semi-covered foraging context with patches of food and plant cover. Schematics show tracking segments of one randomly selected group, with colors corresponding to the individual fish. Triangles point in the direction of motion. (D) Graphic illustrating key spatial and movement characteristics with arrows depicting movement vectors. For the individual assays, see Figure S1 After quantifying the behavioral tendencies of the fish, we tagged all individuals for identification (see STAR Methods ) and allocated them randomly to groups of five (n = 25 groups; see Figure S1 ). In their natural habitat, animals may experience open, homogeneous spaces, encounter resources in spatial and temporal patches, and use habitat structures to hide from predators []. We therefore tested the groups repeatedly in three contexts that reflect these different, ecologically relevant scenarios, each set up in the same large, circular tanks ( Figures 1 A–1C). Using custom-written software, we automatically identified and tracked the position of each fish in the freely moving groups and computed fine-scale spatial, movement, and foraging data ( Figure 1 D; see STAR Methods ).

32 Katz Y.

Tunstrøm K.

Ioannou C.C.

Huepe C.

Couzin I.D. Inferring the structure and dynamics of interactions in schooling fish. 33 Herbert-Read J.E.

Perna A.

Mann R.P.

Schaerf T.M.

Sumpter D.J.T.

Ward A.J.W. Inferring the rules of interaction of shoaling fish. On average, sticklebacks moved in highly cohesive, ordered shoals and maintained clear zones of attraction and repulsion, mediated by relative changes in their speed and heading ( Figure S2 ), in high accordance with other fish species []. However, large and consistent differences existed between the 25 groups in terms of their structure and movement dynamics. To investigate how this variability could be explained by the behavioral tendencies of individuals within the groups, we employed a linear mixed modeling approach (see STAR Methods ).

23 Herbert-Read J.E. Understanding how animal groups achieve coordinated movement. 2 = 7.84, p = 0.012), and individuals with lower social proximity tendencies, which had higher speeds in the individual assays, swam significantly faster in this group context (χ2 = 8.70, p = 0.009). Fish also strongly conformed in their speed (c.f. [ 34 Herbert-Read J.E.

Krause S.

Morrell L.J.

Schaerf T.M.

Krause J.

Ward A.J.W. The role of individuality in collective group movement. 2 = 7.68, p = 0.012). We first exposed the groups to the conventional collective scenario [], free movement within an open, homogeneous environment ( Figure 1 A). The speed that fish adopted in the freely moving groups was positively linked to their speed in the individual personality assays (χ= 7.84, p = 0.012), and individuals with lower social proximity tendencies, which had higher speeds in the individual assays, swam significantly faster in this group context (χ= 8.70, p = 0.009). Fish also strongly conformed in their speed (c.f. []), a requirement to maintain group cohesion, and, on average, slowed down or sped up when grouped with others that had, respectively, a high or low mean social proximity tendency (χ= 7.68, p = 0.012).

2 = 26.79, p < 0.001; 2 = 29.98, p < 0.001; 2 = 9.14, p = 0.008). This result is in line with theory [ 24 Couzin I.D.

Krause J.

James R.

Ruxton G.D.

Franks N.R. Collective memory and spatial sorting in animal groups. 8 Pettit B.

Ákos Z.

Vicsek T.

Biro D. Speed determines leadership and leadership determines learning during pigeon flocking. 35 Nagy M.

Akos Z.

Biro D.

Vicsek T. Hierarchical group dynamics in pigeon flocks. 2 = 0.64, p = 0.495) or leadership (proportion of time in front: χ2 = 0.06, p = 0.804). Figure 2 Effect of Social Proximity Tendency on Spatial Positioning and Leadership Show full caption (A) Fish nearest neighbor distance in groups as a function of their social proximity tendency, shown in five equally sized categories (mean ± 2 SEM; n = 120 fish). (B) Proportion of time fish occupied the most central to the most peripheral position in the group, calculated for each frame and averaged per individual across all frames (mean ± 2 SEM). (C) Density plot of the proportion of time individuals spent in front of the group center for the full 30 min trial. (D) Visualization of a leadership network in terms of propagation of speeding changes of one randomly selected group. Numbers indicate the average temporal delay in seconds and arrows point in the direction of propagation; see Figure S3 For plots (B) and (C), individuals were evenly distributed into three categories, with the intermediate category not shown for clarity. All data were analyzed as a continuous variable. See also Figures S2 and S4 for model simulations. In terms of spatial positioning, fish had smaller nearest-neighbor distances the higher their social proximity tendency (χ= 26.79, p < 0.001; Figure 2 A). As a result of relative differences within groups, it was the fish with relatively low social proximity tendencies (which were also faster) who occupied positions toward the periphery (χ= 29.98, p < 0.001; Figure 2 B) and front ( Figure 2 C) of their group, an effect that strengthened over time (5 min: ΔAIC = 38.59 versus 30 min: χ= 9.14, p = 0.008). This result is in line with theory [] and recent work on pigeons [] that show that faster individuals tend to lead. By assessing the propagation of movement changes in the groups [], we further found that such faster-moving, leading fish with lower social proximity tendencies were also much more influential in deciding group motion ( Figure S3 ) and that, as a result, directional leader-follower networks emerged ( Figure 2 D). These findings suggest a potential self-organizing mechanism for the emergence of group structure and leadership from individual differences in speed, with individuals’ behavior being determined by their own tendencies as well as the tendencies of other group members. In the open, homogeneous environment, fish’s exploratory tendency had no effect on either spatial positioning (center distance rank: χ= 0.64, p = 0.495) or leadership (proportion of time in front: χ= 0.06, p = 0.804).

s = −0.52, p = 0.014). In contrast, shoals with a high mean social proximity tendency moved relatively slowly and with little alignment but were much more cohesive (F 1,22 = 9.31, p = 0.012; 32 Katz Y.

Tunstrøm K.

Ioannou C.C.

Huepe C.

Couzin I.D. Inferring the structure and dynamics of interactions in schooling fish. 1,22 = 1.51, p = 0.305) or schooling dynamics (r s = 0.23, p = 0.337) of the groups. Figure 3 Group Structure and Movement Dynamics in Relation to Group Mean Social Proximity Tendency Show full caption th s, with groups evenly allocated to two categories based on their mean social proximity tendency. Units are in mean body length (BL; 40.6 mm), and contours represent iso-levels in percentage of the highest bin for all groups combined; see (A–C) Heatmaps showing the distribution and link between the three key components of collective motion for groups with a low mean social proximity tendency (n = 13) relative to groups with a high mean social proximity tendency (n = 12). Groups with a relatively high social proximity tendency were more likely to be found in the bluer regions of the plots, whereas groups with relatively low social proximity tendency were more likely to be found in the redder regions of the plots. Group speed depicts the mean median swimming speed of the individuals in a group and is qualitatively similar to the speed of the group centroid. Plots are based on frame-by-frame data at time steps of 1/24s, with groups evenly allocated to two categories based on their mean social proximity tendency. Units are in mean body length (BL; 40.6 mm), and contours represent iso-levels in percentage of the highest bin for all groups combined; see Figure S2 (D) Proportion of time groups were schooling, characterized based on the raw distributions of group speed, cohesion, and polarization (see STAR Methods ). Solid gray line and dashed gray lines indicate a linear fit to the data with 95% confidence intervals. From the behavioral tendencies of the individual fish, large differences in structure and movement dynamics also emerged between the groups. When together as a group, those shoals of individuals with, on average, low social proximity tendencies (and thus high individual speeds) moved relatively quickly, with high alignment and spacing between individuals, and predominantly schooled ( Figure 3 ; r= −0.52, p = 0.014). In contrast, shoals with a high mean social proximity tendency moved relatively slowly and with little alignment but were much more cohesive (F= 9.31, p = 0.012; Figure 3 ). Further, when measuring the strength of social interactions in the groups, we found the strongest social forces (i.e., stronger responsiveness) were exhibited in the fastest-moving groups ( Figure S2 G; c.f. []). This suggest that groups that would conventionally be labeled as highly sociable based on the classic assay actually have the weakest social forces, linked to their low speeds, highlighting the need for a mechanistic assessment and careful terminology when considering individual and group behavior. As for individual spatial positioning and leadership, the exploratory tendencies of the fish also had no effect on the cohesion (F= 1.51, p = 0.305) or schooling dynamics (r= 0.23, p = 0.337) of the groups.

24 Couzin I.D.

Krause J.

James R.

Ruxton G.D.

Franks N.R. Collective memory and spatial sorting in animal groups. 27 Ioannou C.C.

Singh M.

Couzin I.D. Potential leaders trade off goal-oriented and socially oriented behavior in mobile animal groups. To relate our experimental results to theory and to seek a parsimonious explanation for the observed patterns, we conducted simulations of a generic model of self-organized groups. We integrated consistent individual differences in the classic parameters of speed and goal-orientedness (ω), defined as the likelihood that an individual biases its motion toward a desired goal rather than respond to social information []. We found that this simple agent-based model qualitatively recreated the patterns observed experimentally, both in terms of fish’s social proximity tendency driving the spatial positioning and leadership of individuals and the structure and movement dynamics of groups and in terms of the lack of such effects for fish’s exploratory tendency ( Figure S4 ).

8 Pettit B.

Ákos Z.

Vicsek T.

Biro D. Speed determines leadership and leadership determines learning during pigeon flocking. 25 Tunstrøm K.

Katz Y.

Ioannou C.C.

Huepe C.

Lutz M.J.

Couzin I.D. Collective states, multistability and transitional behavior in schooling fish. 32 Katz Y.

Tunstrøm K.

Ioannou C.C.

Huepe C.

Couzin I.D. Inferring the structure and dynamics of interactions in schooling fish. Building on previous work [], our study combines empirical data from individual and group assays with model simulations to provide evidence that heterogeneity in speed is a causal mechanism that drives group states, including the structure, leadership, cohesion, and alignment of groups. Due to differences in swim speed, faster group members passively arrive at positions near the edge and front of groups, which in turn increases their propensity to lead. At the same time, higher individual speeds increase the speed of the group, which thereby passively results in higher order (alignment) and spacing between individuals. Differences in individual speed can be intrinsic or an emergent property, both of other intrinsic (e.g., size) and labile (e.g., nutritional state) characteristics, as well as external factors (e.g., predation risk). These results thus provide a relatively simple candidate mechanism by which collective behavior can emerge passively from individual differences without the need for global knowledge. Our finding that social proximity was strongly, negatively linked with speed across social and asocial contexts warrants further work to investigate the extent that consistency in social proximity, classically termed “sociability,” is driven by an intrinsic social tendency rather than the preferred movement speed of individuals.

2 = 5.77, p = 0.030). After the discovery of the food, it was exploratory fish that were fastest to actually consume the food, both in the open and in the semi-covered foraging environment (survival model [SM]: z = 3.63, p = 0.001; 2 = 8.15, p = 0.011), but also to spent more time out of cover alone (χ2 = 10.28, p = 0.005; 28 Persson L.

Eklöv P. Prey refuges affecting interactions between piscivorous perch and juvenile perch and roach. 30 Krause J.

Ruxton G.D. Living in Groups. Figure 4 Effects of Individual Social Proximity and Exploratory Tendencies on Group Foraging Dynamics Show full caption (A) Total number of foraging areas discovered during the open foraging context trials (out of 295 discoveries). (B) Inverted survival plot with confidence intervals of fish's likelihood to feed in the open and semi-covered foraging context. (C) Boxplots depicting total time spent out of plant cover alone in the semi-covered foraging context when food was still available. (D) Density plot of the mean number of food items eaten per trial across both foraging contexts. For plots (A)–(D), individual tendencies were evenly distributed into low, medium, and high categories (n = 42, n = 42, and n = 41 fish, respectively), with the intermediate category not shown for clarity. (E) Group foraging speed in the open (top) and semi-covered foraging cover context (bottom) in terms of the latency to consume each food item (15 provided per trial). The plot shows latencies averaged across trials for each group, and groups split into four categories based on their mean exploration and social proximity tendencies (low-low, low-high, high-low, and high-high: n = 5, 8, 8, and 4, respectively). (F) Surface plot of the mean number of food items eaten (log transformed) in the open foraging context (points indicate individual fish), based on a generalized linear mixed model (GLMM) fit to the data, cropped to 90% to show the effect excluding fish with the most extreme tendencies (n = 12 fish). Relative social proximity tendency is shown inverted such that faster fish are on the right and slower fish on the left, directly comparable with the model simulations of speed (see Figure S4 ). To further investigate the functional consequences of the behavioral tendencies of individuals within groups, we exposed the shoals to an open and to a semi-covered environment with patches of food ( Figures 1 B and 1C; see STAR Methods ) and analyzed group foraging dynamics and performance. Fish with a low social proximity tendency (which tended to move relatively fast) were most likely to first discover the foraging areas in the open foraging context ( Figure 4 A), in line with their tendency to be in front (see Figure 2 C), whereas in the semi-covered foraging environment it was highly exploratory fish that made most discoveries (traits × context: χ= 5.77, p = 0.030). After the discovery of the food, it was exploratory fish that were fastest to actually consume the food, both in the open and in the semi-covered foraging environment (survival model [SM]: z = 3.63, p = 0.001; Figure 4 B). Due to the availability of cover, individuals spent considerable time hiding and groups often split, with exploratory fish being the most likely to initiate foraging trips and thereby lead their group-mates out of cover (χ= 8.15, p = 0.011), but also to spent more time out of cover alone (χ= 10.28, p = 0.005; Figure 4 C), a behavior that may lead to higher potential predation risk [].

2 = 10.32, p = 0.005; 41,39 = 2.06, p = 0.044; 36 Johnstone R.A.

Manica A. Evolution of personality differences in leadership. Ultimately, it was the combined effects of fish’s social proximity and exploratory tendencies that explained the foraging performance of both groups and individuals. Overall, groups composed of exploratory fish that had a low social proximity tendency (and thus moved relatively fast) found and depleted the food patches most quickly (SM: z = −2.20, p = 0.046), with the relative effect of fish’s exploratory tendency intensified by the availability of cover (z = 3.15, p = 0.006; Figure 4 E). The interaction of both traits also predicted the foraging performance of the individual fish, with again the relative tendencies (rather than the absolute tendencies) being important (ΔAIC = +13.94): exploratory fish with low social proximity tendencies had the highest food intake, with the food intake of more exploratory fish being enhanced in the semi-covered environment (traits × context: χ= 10.32, p = 0.005; Figure 4 F). Overall, fish with low social proximity tendencies experienced greater variance in food intake (F= 2.06, p = 0.044; Figures 4 D and 4F), in line with the prediction that leadership positions come with higher variance in fitness [].

5 Ward A.J.W.

Thomas P.

Hart P.J.B.

Krause J. Correlates of boldness in three-spined sticklebacks (Gasterosteus aculeatus). 16 Ioannou C.C.

Dall S.R.X. Individuals that are consistent in risk-taking benefit during collective foraging. 29 Jolles J.W.

Manica A.

Boogert N.J. Food intake rates of inactive fish are positively linked to boldness in three-spined sticklebacks Gasterosteus aculeatus. Again, the general effects of the behavioral tendencies of the fish, here on the foraging performance of both individuals and groups, emerged naturally in simulations of our agent-based model: groups with high mean speed and goal-orientedness depleted food patches most quickly, and individuals with a high speed and a goal-oriented tendency had the highest food intake ( Figure S4 ). These findings show that the exploratory or “boldness” tendency of individuals is intrinsically linked to their goal-directedness and motivation for food [] and thereby drives foraging performance directly, whereas the social proximity tendency of individuals had an indirect effect on foraging performance by the effects of speed.