Irregular walks and loops with handedness combines in smallscale movement of Onychiurus armatus (Collembola)

G RAN BENGTSSON*, ELNA NILSSON*, TOBIAS RYD N**, MARIA SJ GRENHRN*, AND MAGNUS WIKTORSSON**

*Department of Ecology, Lund University, S lvegatan 37, SE 223 62 Lund, Sweden

**Centre for Mathematical Sciences, Lund University, Box 118, SE 221 00 Lund, Sweden

Abstract

A combination of video recordings, descriptive statistics, and walking simulations was used toevaluate the small scale movement pattern of a soil dwelling species of Collembola,Onychiurus armatus. Individuals were found to link periods of irregular walk with those oflooping in a homogeneous environment as well as in one structured to heterogeneity byphysical obstacles. The number of loops varied between 0 and 44 per hour from oneindividual to another, and some individuals made loops by turning right and others by turningleft. If individuals that made at least between 70 and 80% of their loops in either directionwere classified as right and left loopers, the estimated genotype frequencies could not bedistinguished from those expected based on inheritance of the looping direction by theHardy Weinberg model. The distance walked at the edge of an obstacle increased with itsdiameter and it is suggested that the curvature of the obstacle is the cue used to cut off theturn alternation behaviour holding the individual at the obstacle. Food deprived O. armatushad a more winding movement, made more circular loops, and spent more time at theobstacles than those that were well fed. This behaviour as well as the looping is interpreted asa more systematic and effective searching strategy than a random walk.

Key words: spatial heterogeneity, video tracking, migration, dispersal, soil animal, HardyWeinberg, random walk

INTRODUCTION

Knowledge about the movement pattern of organisms is crucial in understanding andpredicting population dynamics in space and time. Recent interest in developingmetapopulation theory to estimate survival probabilities in fragmented habitats hasemphasised the importance of detailed descriptions of the movement of animals colonising amosaic of habitat patches in a landscape (Kareiva and Wennergren 1995, Gustafson andGardner 1996, Shippers et al. 1996). The release of nonindigenous species, e.g. as biocontrolagents, into new environments is another recent phenomenon that calls for an understandingof movement patterns (Dean 1998, Thomas and Willis 1998).

Depending on the species and the environment considered it is more or less difficult to studymovement of individuals in their natural environment without affecting their behaviour.When the small scale movement pattern of an organism is unknown, it has proven useful toassume that animals move randomly, and to model dispersal by diffusion approaches(Skellam 1951). Diffusion models have been extended by adding population growth dynamics(Holmes 1993, Murray 1993), attraction or repulsion of conspecifics (Gurney and Nisbet

1975, Shigesada et al. 1979, Shigesada 1980, Turchin 1989) and factors describing thetendency of animals to move to higher quality habitats (Shigesada et al. 1979, Shigesada1980).

Another common approach has been to carefully study the small scale movement pattern ofan animal (Jones 19771976, Turchin 1991, Schippers et al. 1996) or to assume a movementpattern of a model organism and then develop individual based simulation models (Gardneret al. 1989, Gustafson and Gardner 1996, White and Gilligan 1998). These models can be asdetailed as one wants but since each investigator uses different simulation algorithms, it maybe difficult to compare results even when the same species is studied (Turchin 1991). Effortsto describe the movement pattern as e.g. a correlated random walk fall in between those usingthe general diffusion model and those developing realistic simulation models (Kareiva andShigesada 1983). Correlated random walks have been successfully applied to describe andsimulate movement from empirical data (Kareiva 1983, Kareiva and Shigesada 1983, Wallinand Ekbom 1994).

Heterogeneity in space and time is a characteristic facing soil organisms. Abiotic factors, suchas soil structure (i.e. arrangement of the solid particles and of the pore space located betweenthem), water content, pH, aeration, temperature, and toxic compound concentration, andbiotic factors, such as food abundance, conspecifics, density of mates, other species andpredators may vary substantially regardless of the scale considered and affect the distributionof individuals (Giller 1996 and references therein). This is true for collembolans, which is anabundant group of invertebrates in many soils (H gvar 1982). Their distribution andpropensity to move depends on the soil structure (Didden 1987), soil moisture (Joosse andGroen 1970, Testerink 1983), temperature (Van der Woude and Verhoef 1986, Babenko1993), food odours (Hassall et al. 1986, Bengtsson et al. 1988, Bengtsson et al. 1991,Michelozzi et al. 1997), pheromones (Leinaas 1983, Verhoef 1984, Leonard and Bradbury1984, Purrington et al. 1991) and metal concentration (Bengtsson et al. 1994). Some attemptshave been made to use that information to predict dispersal of collembolans by discreteprobability distribution models and stochastic diffusion models (Bengtsson et al. 1994,Bengtsson et al. 2000). However, those models are not based on knowledge about individualmovements but rather assume different patterns of individual movements or differentprobabilities of dispersal in a population.

Our main goal here was to describe the small scale movement pattern of a soil dwellingCollembola, Onychiurus armatus. We made video recordings of their movement in ahomogeneous environment as well as in environments structured by impermeable physicalobstacles, representing e.g. pieces of rocks and detritus of different size and density. Anumber of descriptive statistics, such as speed of movement and turning angles, wereextracted from the recordings to test whether the movements were indistinguishable from arandom walk pattern. We assumed that the obstacles would brake a walk only in the sense ofadsorbing the walk and deflecting its direction, so that after resuming the walk, the animalwould return to its basic movement pattern. The time spent and the distance walked along anobstacle and the angular change in walking direction imposed by the obstacle was extractedfrom the recordings. Some of the individuals were food deprived in an effort to test whetherthat would enhance the locomotory activity, such as in e.g. carabidae beetles (Mols 1993). Weused the descriptive statistics to compare and test for differences of walking behaviour indifferent environments and under food deprivation.

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METHODS

Organisms usedSpecimens of the collembolan Onychiurus armatus (Tullb.) were extracted from a mor soil ofa deciduous forest near Lund (Sweden) and kept in darkness in Petri discs with a bottom ofmoistened plaster of Paris and activated charcoal for several generations before used. Theanimals were continuously fed with the fungus Verticillum bulbillosum (W. Gams and Malla).One group of animals was kept without food for one week before used in the experiments.Individuals chosen for the experiments were of the same length (1 1.5 mm corresponding toan age > 70 days according to Bengtsson et al. 1983), to normalise for size dependenttravelling distances (Johnson and Wellington, 1983).

Experimental setupObservations of the movement pattern were made on arenas of glass dishes (diameter 20 cm)half filled with clay (Skromberga clay Hb20; 45% quarts, 5% chlorite, 50% illite), dyed toblack by adding Fe3O4 (8:1). Spatial heterogeneity was created by adding obstacles ofdifferent sizes (5, 10 and 14 mm in diameter) and at different densities (10 and 20 mm apart).The obstacles were glass tubes placed vertically in the clay. One treatment was withoutobstacles where the movement pattern without spatial heterogeneity could be observed. Theclay surface was exchanged between each set of observations so that odour from a previousindividual should not affect the movement pattern of the next one.

Video trackingThe observations were made in a temperature controlled room (20 0.5 C). To avoiddisturbing the animals with daylight, the video recordings were made in red light from foursources (red darkroom lamp 230V Philips). The surface of the arena was moistened beforeeach set of observations by adding water. One individual at a time was placed on the arenafor 15 hours before the observations and kept within a smaller area of the surface by a glasscylinder (14 mm in diameter). The cylinder was then removed and the movement of theindividual was tracked for one hour. At least ten replicates were used for each treatment. Theimage of the arena was captured by a monochrome video camera (Cohu 4710), and digitisedby a framegrabber (VIGA+) connected to a personal computer. Image processing wasperformed by using EthoVision (Noldus Information Technology, Wageningen, TheNetherlands), which both provides object detection and data analysis. Detection of the animalswas based on a grey scaling. One image per second was processed and resulted in a timeseries of X,Y co ordinates indicating the position of the animal.

Data analysisData analysis was carried out in two different ways; first, using the built in functionality ofEthoVision , and second by transferring the data files with co ordinates to a workstation andprocessing them using Matlab (Mathworks). A sub routine was written in Matlab to identifyindividuals that were closer to an obstacle than 2 mm and calculate the average distance andtime spent along the obstacle.

To avoid image noise, body wobbles and pivoting to be recorded as movements, a thresholdfor the minimal distance moved was set to 2 mm when analysing the tracks by EthoVision .Hence, the parameters were only calculated when an animal had moved at least 2 mm. Thefollowing parameters were extracted:1. Relative turning angle (degrees/move), the signed angle between the movement vectors of

two consecutive sampling intervals

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2. Total distance moved (cm), the sum of distances moved (straight line) betweenconsecutive samples

3. Velocity (mm/s), distance moved per unit time.

RESULTS

Movement patternThe collembolans were observed to carry out two distinct types of walking behaviour, loopingand reversals (returning to the same track), followed by longer or shorter periods of morerandom movements (Fig. 1). For each individual, the number of loops and the orientation ofeach loop were extracted to Matlab. All loops (i) shorter than 1 cm, (ii) shorter than 8 s, (iii)longer than 150 s and (iv) with an area smaller than 2 square pixels were discarded. Thereason for (iii) was that we considered such very long loops to be the result of the animalrandomly crossing its own path rather than the result of a persistent movement strategy. Theintensity of looping varied between individuals (Table 1), and some individuals had apreference for repeatedly looping to the left or to the right (Table 2, Fig. 2).

To test whether the observed loops were consistent with random walk behaviour, we extractedthe empirical distribution of one time step (that is, 1 s) moves for each individual. We thenused these distributions to perform simulations of random walks, that is movement withindependent steps. Simulated loops satisfying any of the criteria (i) (iv) above were removed,and the remaining ones were compared to the observed ones by computing their lengths and

shape ratios, 2/4 CA= , where A and C are the area and the circumference, respectively, of

a loop. The shape ratio satisfies 10 and 1= for a circle (the circle being thegeometrical object having maximal A for a fixed C). For each type of arena, we comparedsimulated loops to observed ones by simulating, for each individual, as many loops as wereobserved and then pooling observed and simulated data, respectively, over all individuals in agiven arena. In general, the observed loops were much longer and with a shape ratiodistribution more dispersed than that of the simulated loops (Fig. 3). For each arena, wecompared the simulated and empirical length distributions using Mann Whitney’s U test(one sided), with p values below 0.001 in all cases, and the variances of the shape ratiodistributions using Levene’s test (Kotz and Johnson 1983), known for robustness againstdepartures from normality, with p values at most equal to 0.0011.

The observed pattern of some individuals looping preferably to the left or right was tested forconsistency with the Hardy Weinberg principle. First, individuals having done less than 10loops were excluded and, using a pragmatic approach, the remaining 61 classified as right orleft loopers if their observed fraction of right or left loops, respectively, was at least ;others were classified as indifferent. The choice of value is clearly somewhat arbitrary,which is also the reason why we considered several values in the interval 0.6 0.95. Here is acut off threshold determining the required fraction of loops in a certain orientation for anindividual to be assigned a preference in that orientation. For example, with =0.8, individualsmaking at least 80% of their loops to the right or left were classified as right or left loopers,respectively, while others were considered as indifferent. For each value of we calculated

the expected allele frequencies p and q, the 2

goodness of fit statistic and thecorresponding p value (Hartl and Clark 1997). In the range 0.6 0.95, the expected p and qfrequencies varied from 0.51 0.57 and from 0.43 0.49, respectively, the genotype

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frequencies p2, 2pq, and q2 varied in the intervals 0.26 0.32, 0.49 0.50, and 0.19

0.24,respectively, and the corresponding 2

statistics between 0.12 and 34.7 (Table 3).

The smallest 2

statistic, 0.124 (p value 0.72), was obtained for =0.72, yielding 0.53 as anestimate of the right looping allele frequency. Individuals that made at least between 70%and 80% of their loops in either direction (0.69 0.80) had expected genotype frequenciesthat could not be separated from those that were observed (p>0.05), and whatever departuresfrom the assumptions there may be, they were not sufficiently large to reject the HardyWeinberg principle as a basis for the inheritance of the looping direction. The dependence ofthe expected genotype frequencies on the lower limit used to exclude loops from thecalculations was challenged by removing individuals with less than 12, 8 or 6 loops as well,producing similar results as with 10 loops as a limit (estimated allele frequencies 0.56, 0.52and 0.51).

The presence of obstacles and their density had no significant effect on the velocity ofmovement (ANOVA, F=1.6 p=0.21) or on the number of loops (ANOVA, F=1.2, p=0.34).The distance walked along the edge of an obstacle increased linearly with the diameter of it(Kruskall Wallis, p< 0.001) (Fig. 4). The mean change in movement direction imposed bythe obstacle decreased with its diameter (Kruskall Wallis, p<0.001) (Fig. 5).

Movement pattern of "hungry" versus fed animalsThe average velocity, 0.86 0.05 mm/s (mean s.e., n = 72, Student’s t test, t=0.25, p=0.81)and the total distance moved, 1470 92 mm (mean s.e., n = 72, Student’s t test, t=0.10, p=0.92) was independent of the feeding conditions of the animals prior to the observations.Hungry Collembola had a lower percent turning angles around zero (test for difference inparameter p of two binomial distributions, p<0.001), indicating a more winding movementpattern than those fed (Fig. 6), although there was no significant difference in the distributionof the number of loops (Mann Whitney U test, p=0.24). Neither was there any significantdifference between the loop length distributions (Mann Whitney U test, p=0.97), but thehungry animals made more circular loops than the fed ones (Mann Whitney U test, onesided, p=0.011), that is, loops with larger and hence larger area. Hungry animals also tendedto follow obstacles for a larger distance than those fed did (Mann Whitney U test, p=0.004).

DISCUSSION

The looping pattern that we observed in the collembolans is known from other insects(Turchin 1998, Conradt et al. 2000), birds (Weimerskirch et al. 2000), and mammals(Cameron et al. 1988), and has been suggested to be an effective search strategy (Bell 1991).It may be a response to an unsuitable (lack of food, shelter, conspecifics, etc.) or unknownarea, such as the arena in the experiments, or the habitat in which Conradt et al. (2000)released butterflies that continued to fly in large loops around the release site. The authorsargued that looping, especially by returning to the same patch, is advantageous in a landscapewhere the distance between patches may be large. An individual that fails to find a betterpatch by this searching behaviour can return to the original patch and replenish the resourcesthere before leaving for another search.

Simulations of animal movement in environments with patches of resources clumped,randomly or regularly distributed demonstrate that the most efficient search strategy coincideswith an Archimedean spiral (an Archimedean spiral circles outward from a focus in a

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continuous curve), in which the distance between spiral loops equals the mean distancebetween patches (Zollner and Lima 1999). The Archimedean spiralling is limited inapplicability to resources that distribute themselves with the same mean distance between thepatches, e.g. food items, and resources distributed with other mean distances between them,e.g. mates, would require another search strategy. This equidistant distribution condition isrelaxed in the search strategy based on spiral movement in which the distance between thespiral loops is twice as large as the perceptual range of the animal. This search strategy issuperior to correlated random walk when the resources are randomly distributed or aggregated(Zollner and Lima 1999). The perceptual distance to e.g. food odours and mates in O.armatus is unknown but we know that both collembolans and their fungal food are patchilydistributed in the soil (Bengtsson 1997). O. armatus did not make perfect Archimedean spiralsin the experiments but rather overlapping loops of differing size and shape so the distancebetween loops is difficult to measure. A reason why spiral search is rarely observed comparedto the less efficient looping behaviour may be the difficulty for an animal to implement it(Dusenbery 1992). Whether O. armatus move in loops in the soil is unknown but thepersistence of the behaviour on the plaster of Paris surface broken up by physicalheterogeneity suggests that it is not unlikely. Similar looping behaviour has been observed inother soil living animals both outside their natural habitat (Anderson et al. 1997) and in thesoil (Cameron et al. 1988).

By standardisation of the experimental conditions and exclusion of memories of odour fromconspecifics, the movement assay was designed to minimise the influence of external factorson the walking behaviour. The preference for making loops by either right or left turns (Fig.2) could then be interpreted as an expression for an innate property, similar to the handednessof bumblebees moving around an inflorescence (Kells and Goulson 2001). In thebumblebees, most of the individuals made turns in both directions with varying frequency, butwhen all turns were pooled, there was a bias towards one turning direction. Hence,handedness was a continuous variable, and whether an individual bumblebee could beclassified as a right or left or indifferent turner may depend on the limit of turning frequencyused to define a preference for one or the other, as in O. armatus. As a comparison, truehandedness in nonhuman primates has a bimodal distribution (Hopkins 1995 and referencestherein), but the differences may be more quantitative than qualitative, reflecting anunderlying Mendelian inheritance. Characteristics of locomotory pattern, such as path length,are inherited and under simple genetic control in larvae of Drosophila melanogaster(Sokolowski 1985), in which one morph moves over a large area and the other over a morelimited area (Bell 1985). Likewise, the tendency of an individual of O. armatus to turn in onedirection may be inherited, unless it turns out to be temporary and becomes indifferent in asecond trial.

An obstacle like the glass cylinder standing in the way of O. armatus might evoke one ofthree reactions: the animal might depart from the obstacle as soon as it recognises theboundary, it might follow the boundary forever, or it might follow the boundary for a certaindistance and then depart. The animals followed the boundary and then departed from it, butboth the distance walked along the boundary and the time spent there increased with thediameter of the obstacles. The correlation between the stay at the edge of the obstacle and thecircumference of it may reflect a response to the curvature of it in combination with turnalternation behaviour. Turn alternation, the turn at the first choice point in the oppositedirection to that which the individual was originally forced, is widespread among animals(Barnwell 1965 and references therein, Hughes 1987) and thought to keep it in contact with asurface (Kupfermann 1966). The surface will tend to force the animal to turn away from it,and the turn alternation behaviour will take the animal in the opposite direction, that is,

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towards the wall. The turn alternation behaviour requires some form of short term memory(did I turn right last time?) and some cut off mechanism, which ensures that the animalabandons that surface and moves to explore another one. The curvature may be the cut offcue – a steep curvature cut offs the turn alternation sooner than a gradual one, meaning thatthe same proportion of the surface is explored regardless of the diameter of the obstacle. Onewould then expect the change in angular direction ((distance moved along theobstacle/diameter)*360) to be constant but it decreased with the diameter (Fig. 5). More than25% of the visits at an obstacle were shorter than one body length (Fig. 4), so the individualleft before or just after the whole body was placed along the boundary. This behaviourtranslates into a larger change in angular direction for an obstacle with a small diametercompared with a larger and will conceal the relationship between the diameter of the obstacleand the change in angular direction of individuals following the boundary.

Food deprivation is known to increase the walking speed in e.g. carabidae (Mols 1993) and inother species of Collembola (Verhoef 1984) but had no influence on the velocity of O.armatus. This difference may be related to the experimental conditions. Verhoef (1984) foundthat starvation decreased the production of aggregation pheromones in Collembola, whichincreased their locomotory activity. We used only one animal at a time and replaced thesurface of the arena between each trial to eliminate the influence of pheromones on themovement. However, food deprivation induced other changes in the movement pattern of O.armatus. They followed obstacles for a longer distance, they moved more windingly (lowerpercent of turning angles around zero, Fig. 6), and they made more circular loops (Fig.3). Byfollowing obstacles for a longer distance individuals may allow themselves to examine theobstacles more thoroughly. Similarly, food deprived individuals may remain at the wall of asoil pore a bit further than fed animals and hence increase the probability of ending up in anew patch. Another way of extending the area searched is to make more circular loops sincethe more circular a loop is the larger the area it covers.

The walking behaviour of O. armatus along physical obstacles, their non random looping andresponse to food deprivation will make net squared displacement calculations from acorrelated random walk model to an overestimation of the dispersal. The systematic searchstrategy represented by looping will increase the probability to find resources in a patchylandscape (Andersen 1996, Zollner and Lima 1999) and subsequently reduce the mortalityrisk often associated with dispersal. If individuals can combine the search behaviour bylooping in a structurally heterogeneous environment with perception of “obstacles” ofconspecifics, food, and predators, the movement pattern of O. armatus will call for moresophisticated and individual based descriptions than represented by diffusion models orcorrelated random walk.

ACKNOWLEDGMENTSThe work was supported by grants from the Swedish Natural Science Research Councilpromotion programme on mathematics and natural sciences and Carl Tryggers Stiftelse f rvetenskaplig forskning. The clay used in constructing the arenas was a gift from PartekH gan s Mining Company.

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Table 1. The number of loops made by an individual of O. armatus in an arena. The arenaswere labelled from 1 to 8, and the recording of loops were made from 10 13 individuals ofO. armatus in each arena.

Arena number

1 2 3 4 5 6 7 8

34 2 9 10 14 7 4 19

14 18 14 14 16 34 11 7

8 10 41 3 18 18 4 18

3 37 24 18 31 18 5 10

12 21 7 4 13 15 13 5

22 11 13 12 4 17 24 27

30 8 10 8 7 4 22 15

19 2 8 30 12 21 19 26

7 11 14 21 17 23 14 21

8 1 13 6 44 25 12 15

12 0 20 37

12

21

Table 2. Fraction of loops made to the right by the different individuals of O. armatusobserved in each arenas.

Arena number

1 2 3 4 5 6 7 8

1.00 0.00 1.00 0.30 0.36 0.29 0.25 0.84

0.71 0.72 1.00 1.00 0.69 0.91 0.27 0.14

0.50 0.40 0.95 0.00 0.61 0.56 0.00 1.00

1.00 0.05 0.79 0.39 0.26 0.06 0.40 0.40

0.58 0.52 0.43 0.50 1.00 0.27 0.69 0.40

0.45 0.27 0.23 0.42 0.50 0.18 0.83 0.96

0.13 0.62 0.50 0.38 0.57 0.75 0.18 0.80

0.42 0.50 0.25 0.30 0.67 0.48 0.32 0.81

0.71 0.55 0.79 0.00 0.12 0.35 0.07 0.86

0.12 1.00 0.69 0.33 0.09 0.92 0.58 0.93

0.58 0.40 0.59

0.42

0.57

12

Table 3. Classification threshold ( ), observed phenotype frequencies, expected genotypefrequencies, 2 values and corresponding probability values (p) for chance alone to accountfor deviations between observed and expected genotype frequencies. g Observed phenotype frequency Expected genotype frequency

Rightloopers

Indifferent Leftloopers

p2 2pq q2

2 p

0.60 0.39 0.23 0.38 0.26 0.50 0.24 17.84 0.00

0.65 0.38 0.33 0.30 0.29 0.50 0.21 7.04 0.01

0.70 0.31 0.43 0.26 0.28 0.50 0.23 1.29 0.26

0.75 0.28 0.56 0.16 0.31 0.49 0.20 1.03 0.31

0.80 0.25 0.61 0.15 0.30 0.50 0.20 3.09 0.08

0.85 0.18 0.70 0.11 0.28 0.50 0.22 10.55 0.00

0.90 0.16 0.75 0.08 0.29 0.50 0.21 16.39 0.00

0.95 0.11 0.87 0.02 0.30 0.50 0.20 34.74 0.00

13

Figures

Figure 1. Movement pattern of one individual of O. armatus monitored for 1000 s in absenceof obstacles.

Figure 2. Distribution of the relative turning angle (the signed angle between the movementvectors of two consecutive sampling intervals) made by two individuals of O.armatusOnychiurus armatus. One preferring to turn left (a) and one to turn right (b).

14

0

5

10

15

20

25

30

35

Perc

ent

180 0 180Relative turning angle ( /move)

a

0

5

10

15

20

25

30

35

Perc

ent

180 0 180Relative turning angle ( /move)

b

Figure 3. Empirical distributions of loop shape (a ) and loop length (b) for observed andsimulated random walk data. Loop shape = 4 *A/C2 where A is the area and C is thecircumference of a loop. If the loop shape equals one, the loop is a circle.

Figure 4. Distance walked at along an obstacle in relation to the diameter of the obstacle. Theplot shows the 10th, 25th, 50th (median), 75th and 90th percentiles of the variable.

15

0

,2

,4

,6

,8

1C

umul

ativ

e pe

rcen

t

0 ,2 ,4 ,6 ,8 1

Loopform

simulated

observed

a

0

,2

,4

,6

,8

1

Cum

ulat

ive

perc

ent

0 5 10 15Looplength

simulated

observed

b

0

2

4

6

8

10

12

14

16

Dis

tanc

e m

oved

alo

ng a

n ob

stac

le (

mm

)

5 10 14

Diameter of obstacle (mm)

Figure 5. Distribution of angular change in direction ((distance moved along theobstacle/diameter)*360) imposed by an obstacle. The diameter of an obstacle is 5 mm (a), 10mm (b) and 14 mm (c).

16

0

2

4

6

8

10

12

14

16

18

Per

cent

0 20 40 60 80 100 120 140 160 180

a

0

2

4

6

8

10

12

14

16

18

Per

cent

0 20 40 60 80 100 120 140 160 180

b

0

2

4

6

8

10

12

14

16

18

Per

cent

0 20 40 60 80 100 120 140 160 180

c

Angular change in direction (degrees)

Figure 6. Distribution of absolute turning angles of hungry (a) and fed (b) O. armatus. Theabsolute values of the turning angles are used.

Figure 5. Distance walked at obstacles by hungry and fed Onychiurus armatus.

17

0

5

10

15

20

25

30

Perc

ent

0 20 40 60 80 100

120

140

160

180Absolute angle ( /move)

a

0

5

10

15

20

25

30

Perc

ent

0 20 40 60 80 100

120

140

160

180Absolute angle ( /move)

b