20131092 published 15 January 201411 2014 J R Soc Interface Liliana C M Salvador Frederic Bartumeus Simon A Levin and William S Ryu Caenorhabditis elegansMechanistic analysis of the search behaviour of

Supplementary data

l httprsifroyalsocietypublishingorgcontentsuppl20140114rsif20131092DC1htm

Data Supplement

Referenceshttprsifroyalsocietypublishingorgcontent119220131092fullhtmlref-list-1

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rsifroyalsocietypublishingorg

ResearchCite this article Salvador LCM Bartumeus F

Levin SA Ryu WS 2014 Mechanistic analysis of

the search behaviour of Caenorhabditis elegans

J R Soc Interface 11 20131092

httpdxdoiorg101098rsif20131092

Received 23 November 2013

Accepted 16 December 2013

Subject Areasbiocomplexity biophysics

computational biology

Keywordssearch behaviour reorientation patterns

environmental uncertainty stochasticity

superdiffusion Caenorhabditis elegans

Author for correspondenceLiliana C M Salvador

e-mail lilianasalvadorglasgowacuk

daggerThese authors contributed equally to this

study

Electronic supplementary material is available

at httpdxdoiorg101098rsif20131092 or

via httprsifroyalsocietypublishingorg

amp 2014 The Author(s) Published by the Royal Society All rights reserved

Mechanistic analysis of the searchbehaviour of Caenorhabditis elegans

Liliana C M Salvador123dagger Frederic Bartumeus24dagger Simon A Levin1

and William S Ryu5

1Department of Ecology and Evolutionary Biology Princeton University Guyot Hall Princeton NJ 08542 USA2ICREA-Movement Ecology Laboratory Centre for Advanced Studies of Blanes (CEAB-CSIC) Cala St Francesc 14Blanes 17300 Spain3Departamento de Biologia Vegetal Faculdade de Ciencias da Universidade de Lisboa Campo GrandeLisboa 1749-016 Portugal4CREAF Cerdanyola del Valles Barcelona 08193 Spain5Department of Physics and the Donnelly Centre University of Toronto 60 St George St TorontoCanada M5S1A7

A central question in movement research is how animals use information and

movement to promote encounter success Current random search theory

identifies reorientation patterns as key to the compromise between optimizing

encounters for both nearby and faraway targets but how the balance between

intrinsic motor programmes and previous environmental experience deter-

mines the occurrence of these reorientation behaviours remains unknown

We used high-resolution tracking and imaging data to describe the complete

motor behaviour of Caenorhabditis elegans when placed in a novel environment

(one in which food is absent) Movement in C elegans is structured around

different reorientation behaviours and we measured how these contributed

to changing search strategies as worms became familiar with their new

environment This behavioural transition shows that different reorientation

behaviours are governed by two processes (i) an environmentally informed

lsquoextrinsicrsquo strategy that is influenced by recent experience and that controls

for area-restricted search behaviour and (ii) a time-independent lsquointrinsicrsquo

strategy that reduces spatial oversampling and improves random encounter

success Our results show how movement strategies arise from a balance

between intrinsic and extrinsic mechanisms that search behaviour in C elegansis initially determined by expectations developed from previous environ-

mental experiences and which reorientation behaviours are modified as

information is acquired from new environments

1 IntroductionNearly all organisms from single cells to large animals forage by controlling their

motor patterns [1ndash3] Foraging is a complex and multifaceted behaviour

It includes pre-detection components such as search and taxis and complex

post-detection events such as pursuing (chasing down) or handling (opening

subduing swallowing) prey [245] Foraging animals change their motor patterns

in response to surrounding environmental cues or as a result of previous experi-

ences and learning processes [2] An animalrsquos response to environmental cues

depends substantially on the spatial and temporal structure of environmental

information [1ndash3] Highly localized cues may trigger area-restricted searching

[67] or acute avoidance reactions [8] whereas environmental gradients are

exploited by both performing taxis where animals move towards a desirable

environment or avoid an unfavourable one or by different types of kinesis (eg

klinokinesis orthokinesis) where movement is modulated by a non-directional

response of the local cue intensity [29] Foraging movement should not only be

thought of as a set of stereotyped behavioural reactions to specific environmental

stimuli [10] External cues may be diffuse (non-directional) of variable quality

(low signal-to-noise ratio) intermittent (complex presencendashabsence dynamics)

or simply absent Under such conditions organisms may undertake specific

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search strategies to efficiently explore space [11] until some

useful environmental information can be followed and

exploited and such strategies can be thought of as a major com-

ponent of pre-detection foraging behaviour when information

is substantially limited

How should animals interact with the environment and use

information when cues are scarce On the one hand current

random search theory [1213] has shown that reorientation

behaviour can provide an adequate balance between inten-

sive (local) and extensive (non-local) search [1415] releasing

the tension between optimizing for local and distant targets

without previous information about the target spatial dis-

tribution On the other hand we know animals learn and

have expectations based on previous experiences about their

environment Unfortunately even though attempts have

been made [16ndash20] it is still extremely difficult to relate

field-recorded animal trajectories convincingly to recently

developed stochastic search theory [2122] Accurate control

of sensory inputs memory and internal states of the animal

in the wild is overwhelmingly difficult and that limits the

possibility of showing how animals use information to

modify their reorientation patterns or to what extent in the

absence of information intrinsic motor programmes optimize

the balance between intensive (local) and extensive (non-

local) search In movement ecology studies [23] the size

sampling quality and statistical analysis of animal movement

datasets are critical factors Ideally data should be collected

continuously at high frequency to capture fast dynamics

but also over a long timescale to generate statistically

significant samples The determination of behavioural states

[2324] needs to be quantified in a comprehensive and objective

way Environmental conditions also need to be handled

carefully to control the amount of information available to

the animal

An experiment that fits these requirements is the study of

Caenorhabditis elegans search behaviour in a well-controlled

homogeneous laboratory environment C elegans is a small

nematode (1 mm) with a compact well-described neuronal

system and can be studied at many scales genes neurons

and networks [25ndash28] It has a complex yet tractable search

strategy that is generated by a relatively simple locomotive

repertoire [29] On the surface of agar plates worms crawl

forward (crawl) and backwards (reversal) by propagating

undulatory waves along their body These worms can also

interrupt their crawling motions (ie reorientation beha-

viours) by bending their body deeply to form the shape of

the Greek letter omega (omega) by pausing ( pause) or by

executing a more complex composite behaviour ( pirouette)

which is a sequence of a reversal and an omega performed

closely in time [30]

We quantified the wormrsquos search behaviour with a high-

level of detail to characterize the underlying behavioural

mechanisms governing their search patterns We performed

a relocation experiment from a resourced environment to

one without resources in order to investigate how past experi-

ence modulates search with minimal intervention of external

cues and to determine whether innate stochastic search be-

haviour exists Before the experiment C elegans were well

fed and during the experiment they searched the surface of

an agar plate without food The tracking data were sampled

at high resolution and magnification capturing both the tra-

jectory and body posture of single worms freely behaving as

they move on the surface of agar plates [3132] We improved

previous image processing software [31] to be able to detect

worm behaviours with high accuracy and provide a complete

behavioural dataset of individual searching distinguishing

crawling and reorientation types that enable us to characterize

the worm search patterns

2 Material and methods21 Experimental set-up211 Tracking microscopyThe tracking microscope has been described previously [3132] and

is similar to other tracking systems [33ndash36] In summary the ima-

ging system was designed to translocate around a fixed-position

assay plate As the worm moves on the surface of the plate the

system follows the movements of the worm while capturing

images at 4 Hz and recording its centre-of-mass position

212 Worm preparationFifty-two individuals C elegans strain N2 were grown at 208C and

maintained under standard laboratory conditions [37] Fresh

nematode growth medium (NGM) assay plates (17 Bacto agar

025 Bacto-peptone 03 NaCl 1 mM CaCl2 1 mM MgSO4

25 mM potassium phosphate buffer 5 mg ml21 cholesterol) were

partially dried by leaving uncovered for 1 h A copper ring

(51 cm inner diameter) pressed into the agar surface prevented

worms from crawling to the side of the plate Young adults were

rinsed of Escherichia coli by transferring them from OP50 food

plates into NGM buffer (same inorganic ion concentration as

NGM assay plates) and letting them swim for 1 min Individual

worms were transferred from the NGM buffer to the centre

of the assay plate (9 cm Petri dish) The plates were covered and

tracking began after 1 min and lasted no longer than 60 min

22 Diffusive properties of searchTo quantify the worm diffusive properties of the 52 individuals we

computed the mean-squared displacement (MSD) kx2ethtTHORNl of all

worm trajectories (population level) and checked whether the diffu-

sion process was normal (ie MSD increasing linearly with time) or

anomalous (nonlinear relationship with time) The MSD of a set of Nindividual displacements xn from an origin location to a location at

time t is given by kx2ethtTHORNl frac14PN

nfrac141 x2n and kx2ethtTHORNl Ksts where Ks

is the generalized diffusion coefficient and s is the diffusion expo-

nent Diffusivity domains can be distinguished by analysis of the

anomalous diffusion exponent s subdiffusion for 0 s 1 super-

diffusion for s 1 normal Brownian diffusion for s frac14 1 and

ballistic motion for s frac14 2

23 Behavioural flaggingReorientation events of the population of 52 worms were detected

from the segmented binary images using standard imaging pro-

cessing computer vision techniques [37ndash40] and eigenworm

analysis [3141] Binary images were skeletonized to derive the

wormrsquos centreline Omegas were detected by calculating solidity

(less than 070) and errors in skeletonization which occur when

worms touch or cross during omegas If a reversal followed

within two frames (05 s) then the behaviour is flagged as a pirou-

ette The frequency distribution of the time between omegas

following reversals was bimodal therefore we used the maximum

time of the first peak (two frames) as a threshold for the pirouette

behaviour Velocity of the wormrsquos undulatory cycle was measured

using eigenworm analysis [3141] and used to flag reversals and

pauses The behavioural detection algorithm (see electronic sup-

plementary material figure S1) was applied to the image dataset

of 52 individuals 30 min each (total of 374 400 frames) and in

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total it detected 937 reversals 1064 omegas 1125 pirouettes and

387 pauses This method was validated by computing the percen-

tage of behaviours detected by the algorithm to the ones detected

by human observation We used a control dataset of behaviours

observed by eye for five experimental runs (a total of 36 000

frames) representing 10 of the entire dataset The algorithm

detected over 92 (on average) of the number of omegas and rever-

sals that were identified by eye (see the electronic supplementary

material table S1) The 8 misidentified behavioural responses

were due to noisy images in which the worm body could not be

extracted Omegas with low body compressibility (lsquowidersquo omega

bends) and pauses coinciding with a straight body posture were

misidentified by crawls and reversals respectively

SocInterface1120131092

24 Pre-filtering data before analysisIf the worm stopped moving before the completion of the run

then the data were excluded We could see a clear and separable

behavioural effect caused by mechanical stimulus on the reorien-

tation frequency time series for the first 760 frames (32 min)

which we explicitly removed in our final dataset In the end

the following analyses are based on tracks and images of 52 indi-

viduals Tracks were of 268 s each and with a total number

of 2889 reorientation behaviours 788 reversals 860 omegas

935 pirouettes and 306 pauses

25 Orientational memory lossTo study the role of reorientation behaviours on the loss of orien-

tational memory we quantified the effect of each reorientation

type on the overall direction of the trajectory For that we com-

puted (i) the turning angle distribution generated by each

reorientation type and (ii) the angular correlation of the trajec-

tory as a function of reorientation type for each one of the

52 individual worms of our study

Turning angle distribution generated by each reorientation typereorientations are located in between two crawls (periods of

forward motion) The turning angle u generated via a specific reor-

ientation was computed by calculating the difference between the

absolute angles of the vectors following the overall direction of

the crawl just before and just after the reorientation The vectors

are defined using the first and last time frames of each crawl

Angular correlation of the trajectory as a function of reorientation typethe angular correlation function

CaethtTHORN frac141

n

Xn

jfrac141

kcosfrac12aethtthorn tTHORN aethtTHORNlj

where a(t) is the local tangent angle at time t t is the time lag

(from 1 to 13 s) j is the worm id and n is the total number of

worms (52) was calculated from the centre-of-mass data (trajec-

tory) to study the wormrsquos directionality of motion over time We

combined the behavioural data with the trajectory data and

sampled segment types ST from the trajectory that are crawls sep-

arated by a specific type T of reorientation (eg crawlndashreversalndash

crawl) The angular correlation function was computed for both

the original segments ST and their correspondent null model

which is a bootstrapping (499 times) of random segments of the

same length as ST of the same trajectory (see the electronic sup-

plementary material figure S8) The correlation function Ca(t)

was computed for each ST using different lag sizes t and it was

averaged over all the segments over all the 52 individuals (black

line in figure 3) For the null model case standard error bars of

the mean of Ca(t) were computed for each lag size t (dashed line

in figure 3) The difference between the solid lines representing

sequences of crawls interrupted by reorientation types and the

dashed line representing the null model (random segments of

the original trajectory) show how strong the contribution of each

behaviour is towards changes in direction The further the lines

are from each other the larger the contribution of the reorientation

behaviour is evident

26 Probability distribution of omega time inter-eventsWe selected among three probabilistic models of the exponential

family (simple double and stretched exponentials) to identify the

best-fitting probability distribution of the time intervals between

omegas at both the individual and population levels of the 52 indi-

vidual worms In particular we used KolmogorovndashSmirnov (KS)

tests [42] and the likelihood functions of the probability density

functions (pdfs of the three models) over a bounded range and

for pre-binned data [17] We described the three pdfs their corre-

sponding transformation when considering pre-binned data and

their resulting likelihood function in the electronic supplementary

material text S1 For model selection we include only those indi-

viduals that had performed at least 30 omegas during the

tracking period for the individual level analysis

27 Relationship between reorientation and crawl typesTo test the statistical independence between reorientation and

crawl types in our worm population we performed a contingency

table analysis followed by a chi-squared approximation for

proportions [43] We determined both the relationship between

reorientations and crawls occurring immediately after and

between reorientations and crawls that preceded them For the

dependent relationship between reorientations and their previous

crawls we studied in more detail the connection between the

different types of behaviours In particular we performed a two-

tailed Z-score test statistic Z (a frac14 005) [43] to test the null

hypothesis H0 pethCijRjTHORN frac14 pethCiTHORN against the alternative hypothesis

HA pethCijRjTHORN= pethCiTHORN where i and j represent respectively the

different crawl and reorientation types presented in figure 5b

For the behaviours with dependent relationships we used the

departures from the expected frequency between reorientation

events and their previous crawls to determine whether they are

positively (above expected frequency) or negatively (below the

expected frequency) correlated

28 Average time to close a loop and characteristicinter-event times for omegas

The average time to close a loop was calculated as the average time

to close a circle t frac14 2prs where r frac14 1jkj and s is the speed These

averages are taken over all the trajectories that contain loops The

average speed of a loop is 03 mm s21 and the median of loopsrsquo

curvature k is 41 mmndash 1 so t frac14 54 s The characteristic inter-

event time for omegas q frac14 67 s was taken directly from the

stretched exponential likelihood fit at the population level

29 Models of search behaviourInspired by our data analyses we have developed a modelling

framework that allows us to compare the search efficiency in a

patchy landscape of simple correlated random walks with dif-

ferent degrees of sinuosity r (crawling behaviour) to strategies

that additionally incorporate both stationarynon-modulated

(omega) and non-stationarysignal-modulated (pirouette) reor-

ientation behaviours To do so we use four behavioural

combinations according to the models in the electronic sup-

plementary material table S2 model 1 crawling behaviour

(correlated random walk) model 2 crawling behaviour with

omegas model 3 crawling behaviour with pirouettes and

model 4 crawling behaviour with both omegas and pirouettes

The details of the modelling framework are provided in the elec-

tronic supplementary material Search efficiency was computed

as the number of encounters per travelled distance averaged

over 500 individuals

0 103

(a)

(c)

(b)

102

s1 = 137

s2 = 046

10

1

10ndash1

5 pause

pirou

omeg

rev

crawls

10

15

20

25

30indi

vidu

als

35

40

45

50

5 10 15time (min)

20 25

10 102

log(t)

log(

MSD

)

103

end start

behavioursreversalsomegas pauses

pirouettes

25 5 mm

Figure 1 Individual worm track and population ethogram (a) A 30 min tracking run showing the centre-of-mass movements of a single C elegans worm Insetshows raw worm image Behavioural events are labelled as crawls (black) reversals (blue) omegas (cyan) pirouettes (orange) and pauses (red) (b) Spreadingcapacity of the worm population measured as the MSD across time (52 worm trajectories starting from the same origin point) Two regimes were found super-diffusive with slope s1 frac14 137 1 (solid line) and subdiffusive with 0 s2 frac14 046 1 (dashed line) The worm population does not passively diffuse throughthe environment Their spreading is accelerated covering a range of spatio-temporal scales up to the limiting scale of the experimental system (51 cm) wherespreading then becomes subdiffusive (c) Population ethogram (n frac14 52) showing individual behavioural variability Behavioural events are colour coded as aboveexcept crawls that are in grey

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3 ResultsThe tracking system captures both the trajectory and the body

postures of single worms freely moving on the surface of agar

plates (Material and methods) Figure 1a shows representative

high-resolution tracking data and a detailed image of the

worm captured during the experiment The scaling behaviour

of the MSD across time shows that the worms do not passively

diffuse while searching but instead perform more complex

movements such that the population spreading while searching

is superdiffusive with an anomalous diffusion exponent s1 frac14

137 (greater than 1) up to the limiting scale of the experimen-

tal system that can be associated with the crossover towards a

subdiffusive regime s2 frac14 046 (less than 1 figure 1b) The

pairing of large-scale tracks (worm centre-of-mass trajectory)

and small-scale behavioural data (body postures) allows us to

flag crawls and reorientation behavioural events and produce

comprehensive trajectories (figure 1a) and ethograms (figure

1c) that show the transition between a number of crawling

and reorientation behaviours used by worms to explore the

environment Our analysis indicates a number of different

types of crawling motions and reorientation behaviours Crawl-

ing motions are not always straight but often form arcing or

looping trajectories [32] We flagged crawling behaviour

based on curvature and angular concordance [44] into four cat-

egories lines open arcs closed arcs and loops (see the

electronic supplementary material text S2 and figures S2 and

S3) We identified four types of reorientation behaviour

reversals omegas pauses and pirouettes (figure 1c Material

and methods)

The overall movement patterns did not show any direction-

al bias (Rayleigh tests of uniformity [45] applied to the first and

0

005

010

015

020

025

rela

tive

freq

uenc

y of

reo

rien

tatio

ns p

er 1

8deg in

terv

al

reversals (n = 788) omegas (n = 860)

0 50 100 150

005

010

015

020

025

turning angle q (deg) turning angle q (deg)

rela

tive

freq

uenc

y of

reo

rien

tatio

ns p

er 1

8deg in

terv

al

pirouettes (n = 935)

0 50 100 150

pauses (n = 306)

(b)(a)

(c) (d )

Figure 2 The frequency distribution of turning angles generated by each reorientation behaviour The frequency distribution of turning angles (188 interval bars)generated by (a) reversals (b) omegas (c) pirouettes and (d ) pauses was computed from the analysis of 52 worms during the approximately 27 min assay periodReversal and omega distributions are close to uniformity The pirouette frequency distribution is centred around large turning angles (90 ndash 1808) values whereaspause frequency distribution is centred around small turning angles (0 ndash 908)

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last positions of each trajectory p-value frac14 056 n frac14 52) con-

firming the absence of landscape gradients or cue-biased

large-scale movement ie search and not taxis was the main

driver of the overall movement pattern We quantified how

each type of reorientation contributed to the loss of orientation-

al memory by both calculating turning angle distributions and

performing angular correlation analyses of trajectories (figures

2 and 3) Pirouettes generated a distribution centred at 1808turns and accounted for the strongest effect on the loss of orien-

tational memory at the trajectory scale Contrary to what has

been reported for insects [46] pauses generated almost no turn-

ing at all Reversals and omegas generated almost uniformly

distributed turning angles showing a notable effect on orienta-

tional memory loss (figure 3) but not as strong as with

pirouetting Our results show that different types of reorienta-

tions generate different turning angle distributions and break

the directional persistence of the animal to different degrees

suggesting that distinct reorientation strategies may have

different roles within the search process

We further investigated the temporal dynamics of the

different types of reorientations and crawls (figure 4 electronic

supplementary material text S3) We found that the wormrsquos

searching behaviour is a combination of time-dependent and

time-independent components The frequency of certain

types of reorientations (pirouettes and reversals) and crawls

(lines and arcs) decreased through time (Spearmanrsquos cor-

relation range rs [ [21 2058] p-value 005 electronic

supplementary material tables S2 and S3) whereas the fre-

quency of omegas pausing and looping is time-independent

(rs[[-030 020] p-value frac14 031 051 and 099 respectively

electronic supplementary material tables S2 and S3)

For the observation window of our experiments (about

30 min) our results indicate that omegas which lead to uni-

formly distributed turning angle distributions (figure 2)

control for basal time-independent exploratory behaviour

In comparison pirouette and reversals are related to a behav-

ioural or physiological memory that decays through time

Assuming that time-dependent and time-independent reor-

ientations represent two separate behavioural modules we

characterized the inter-event time distribution for omegas to

explore the efficiency of the underlying stationary stochastic

process in promoting encounter success [16] The shape of

the distribution determines whether large but rare inter-

event times are less (simple exponential) or more probable

(double exponential stretched exponential) The latter feature

implies a wide range of crawl lengths and the presence of inten-

siveextensive search patterns We found that the omega

inter-event time distribution is best characterized by a stretched

exponential at the population level (figure 5a Material and

methods electronic supplementary material tables S4

and S5 KS test p-value frac14 059 G-test p-value frac14 092) whereas

the double exponential distribution is the best fit at the individ-

ual level (see the electronic supplementary material figure S4

tables S6 and S7 text S4) Despite the presence of characteristic

times for omegas both the combination of fast and slow omega

turning rates (double exponential [47]) or the presence of a

heavy-tailed time inter-event distribution (stretched exponen-

tial) can promote intensiveextensive search patterns and

ndash02

0

02

04

06

08(a)

(c)

(b)

(d )

Ca(

t)C

a(t)

crawls with reversalsnull model 1

crawls with omegasnull model 2

2 4 6 8 10 12ndash02

0

02

04

06

08

t(s) t(s)

crawls with pirouettesnull model 3

2 4 6 8 10 12

crawls with pausesnull model 4

Figure 3 The role of reorientations in the direction of motion Black lines correspond to the angular correlation decay of a consecutive sequence of crawls separatedby a specific reorientation behaviour Dashed lines (null models) show the angular correlation decay of segments sampled from the original trajectory (that can haveany reorientation type within them) of the same size as the sequence of crawls represented by the black line (a) Crawls with only reversals or (b) with only omegasproduce sequences with a similar angular correlation as the null model indicating that reversals and omegas have a lower impact on the average orientationalmemory loss of the trajectory compared with pirouetting (c) Crawls with only pirouettes show shorter correlation times (stronger decay) than the nullmodel indicating a strong impact on the orientational memory loss (d ) Crawls with only pausing show longer correlation times (smaller decay) than thenull model indicating a minimal effect of this reorientation type on the average orientational memory loss

mea

n nu

mbe

r re

orie

ntat

ions

pe

r 2

min

inte

rval

mea

n nu

mbe

r cr

awls

pe

r 2

min

inte

rval

30(a) (b)

pirouettesreversalsomegaspauses loops

closed arcsopen arcslines

20

15

10

05

0 5 10 15time (min)

20 25 0 5 10 15time (min)

20 25

25

30

20

15

10

05

25

Figure 4 Temporal patterns of C elegans search behaviour The mean number of behaviours of (a) reorientation events and (b) crawling events was computed per38 s time periods over an approximately 27 min assay search Pirouettes (open circle) and reversals (open square) decrease over time whereas omegas (filled circle)and pauses (filled square) are constant over time Lines (open circle) open arcs (open square) and closed arcs ( filled circle) crawling types decrease over timewhereas loops (filled square) are constant over time

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accelerated (superdiffusive) spreading over a range of scales

(figure 1a) In addition we found that the emerging character-

istic timescales of omega turn distributions could be associated

with an intrinsic locomotory constraint of C elegans on aver-

age crawls have some finite curvature [32] hence the longer

the crawl the larger the possibility of looping (ie spatial over-

sampling see electronic supplementary material figure S5)

We estimated (Material and methods) that the average time

for closing loops (54 s) is of the same order as the characteristic

inter-event time for omegas (67 s stretched exponential fit)

0

loop rev

arc

line pir

W

1 2 3 4log(t)

ndash3

ndash2

ndash1

0(a)

(b)

P(T

gtt)

datastretcheddoublesimple

Figure 5 Caenorhabditis elegans omega-based search template and interdepen-dencies between reorientation-crawl pairings (a) Probability distribution ofomega inter-events at the population level (52 worms) The fit between theempirical data and the stretched exponential distribution (solid line) is betterthan those obtained with the double exponential (dashed line) and thesimple exponential (dotted line) distributions (b) Loop ndash omega and arc ndashomega pairings are positively correlated (solid arrows) whereas loop ndash pirouettearc ndash reversal and linendash omega pairings are negatively correlated (dashedarrows) The non-existence of an arrow between a reorientation ndash crawl pairingindicates independency between them

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Hence an important function of omegas in the exploratory

behavioural template may be to avoid spatial oversampling

by preventing excessive looping

To understand better the inherent structure of C eleganssearch patterns we also investigated whether crawling and reor-

ientation behaviours were independent of each other (Material

and methods) We found that reorientations were all indepen-

dent of the following crawl type ( p-value frac14 006 n frac14 1717) but

dependent on the previous crawl type ( p-value frac14 328 1027

n frac14 1714 see the electronic supplementary material figure S6

tables S8 and S9) Omegas were positively correlated with

previous loops ( p-value frac14 0037 n frac14 41) and arcs ( p-value frac14

0004 n frac14 214) and negatively correlated with lines

( p-value frac14 12 1024 n frac14 204) Pirouettes and reversals rarely

finished loops or arcs respectively (figures 5b electronic sup-

plementary material table S10) The hypothesis that omegas

are commonly used to break curved crawls was not only sup-

ported by the latter results but we also found that there was a

significant negative correlation between the number of omegas

in a trajectory and the average length of loops (Spearmanrsquos

rank correlation r frac14 2053 p-value 001)

Our simulations (Material and methods and the electronic

supplementary material) showed that stationary reorienta-

tion templates (omegas) interrupting sinuous movements

at times drawn from stretched exponentials can indeed

improve the search efficiency (figure 6) If signal-modulated

then area-restricted search behaviour is added to the station-

ary reorientation template (pirouettes) then the search

efficiency further improves As expected the search efficiency

improves much more based on reactive (non-stationary) turn-

ing behaviour linked to environmental cues or past memory

than based on non-reactivestationary stochastic reorienta-

tion templates Nonetheless the best search strategy comes

out when combining both types of reorientation behaviours

4 DiscussionCaenorhabditis elegans moves with a limited locomotory reper-

toire but we have shown that in homogeneous information-

limited environments it produces complex and flexible search

behaviours by combining locomotion primitives These basic

movement behaviours are not independently controlled There

are at least first-order correlations between behavioural states

where reorientation events are dependent on the previous crawl-

ing events The movement of many organisms has been

described by a run-and-tumble model [9164648] however

the wormrsquos search movement cannot be represented by such a

strategy [32] for a number of reasons (i) crawl types differ in

their straightness (ii) there are correlations between reorientation

and crawling events (iii) some of the behavioural transitions

are time-dependent and (iv) the stationary components of

behaviour generate complex movement patterns

Omegas are responsible for a stationary multi-scale search

component that holds over 30 min and covers a wide range of

spatial scales These features have been recognized as efficient

random search behaviour that adequately trades-off for

nearby and distant targets in heterogeneous landscapes

[121316] where scale-free reorientation patterns comprise the

limiting optimal case [1516] Multi-scale search templates are

also observed in other organisms [4649ndash51] but there has

been little understanding on what sets these scales Despite

the huge variability of omega turn inter-event times here we

found that C elegans exhibits a characteristic timescale for

omegas connected to intrinsic locomotory constraints such as

not being able to move straight for a long time Worms tend to

end looping trajectories with omegas reducing the risk of self-

crossing paths Examples of other motor behaviours responding

to similar constraints are spiral motions of microorganisms [49]

which are thought to allow the organism to average out locomo-

tory biases and to swim in straighter paths and characteristic

turning frequencies in flagellated bacteria which are constrained

by sampling limits for diffusive sensing [52]

In addition to a stationary and multi-scale search

movement template C elegans also exhibits a non-stationary

080 085 090r

095 100

sear

ch e

ffic

ienc

y (times

10ndash2

)

0

10

10

20

20

30

30

40

40

50(a)

(c)

(b)

50

165

160

155

150

145

140

135

crawling

reorientationclocks

onoff

omegasmulti-scale

search

onoff

model 1model 2model 3model 4

pirouettesarea-restricted

search

Figure 6 Caenorhabditis elegans search modelling framework (a) Conceptual diagram showing the presence of signal-modulated (non-stationary) and non-modulated (stationary) reorientation behaviour and the four potential behavioural combinations implemented Round shapes C elegans behaviours Grey polygonsbehavioural switches (b) Visualization of the path generated by model 4 (crawling behaviour plus omegas frac14 On and pirouettes frac14 On) with sinuosity r frac14 09 ina heterogeneous target landscape Black dotted line trajectory Grey circles targets Blue circles omegas Red circles pirouettes Red-dotted line subsets of thetrajectory influenced by area-restricted-search behaviour (c) Average search efficiency (number of targets found per distance travelled) for different values of direc-tional correlation (r) and the different random walk models Model 1 crawling behaviour (correlated random walk with sinuosity r) Model 2 crawling withomegas Model 3 crawling with pirouettes Model 4 crawling with both omegas and pirouettes

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adjustable reorientation pattern (pirouettes and reversal turns)

that changes in time in relation to expectations of food location

It is well known that the worm intensifies the search to a

restricted area (high pirouette rates) when food or rewarding

environmental cues are present [2753] Here we show that

well-fed C elegans influenced by past environmental

memory or a present measure of internal state [53] also per-

forms area-restricted search (based on both pirouettes and

reversals) where food encounter expectations are high and gradu-

ally decreases pirouette and reversal rates when it fails to find

food expanding its search range

Previous experiments have revealed that as the memory

of a past resource-rich environment is gradually lost and

cues for new resources are missing animals switch their strat-

egies from intensive to extensive search modes [4654] The

relevance of our results is to show that at least for C elegans

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the story is not that simple Our results reveal that these

worms constantly maintain in the background a statio-

nary and complex movement template that combines both

intensive and extensive searches and controls for excessive

oversampling An important question remains as to why

such a random search template is needed for the survival

of animals that can learn and use environmental information

for their own profit Learning and memory generate expec-

tations on the environment which undoubtedly animals

use for search and survival However the environment is

noisy and the animalrsquos expectations (their model of the

world) are not always accurate For example in our exper-

iment C elegans performs an intense area-restricted search

in an empty area for about 20 min based on an erroneous

association of past environmental information The worms

expect to find food nearby based on a pre-condition that

does not hold anymore Yet animals have a way to hedge

their bets on their world model by generating an efficient

background search template This background search tem-

plate is an important behavioural module often disregarded

(see [1051]) but may be present in animals to deal with

environmental uncertainty We suggest that such a template

should accommodate motor constraints and incorporate

generalized views on target locations for example the expec-

tation of targets being nearby and faraway from onersquos

position More generally our results suggest that motor

behaviour that is not reinforced by environmental stimuli

(eg taxis) can be constructed on the basis of empirically

grounded expectation reflecting both information learned by

recent individual experiences (flexible and adjustable com-

ponents) or fixed in motor programmes across evolutionary

times (intrinsic less flexible templates)

Based on the above arguments one could make the follow-

ing predictions (i) incorporating complex reorientation patterns

(eg stretched exponential omega turns) should increase

the search efficiency when compared with pure correlated

random walking (pure crawling behaviour) (ii) the impact of

such (omega) reorientation templates on search efficiency

should be larger as we generate more straight-lined crawls

(iii) signal- or memory-modulated reorientations (pirouettes)

should have a much stronger positive effect on search efficiency

than stationary reorientation templates (omegas) (iv) the incor-

poration of both stationary and non-stationary (responding to

memory or to environmental cues) reorientation components

into a search strategy should lead to the best search efficiency

outcome All of these predictions are fulfilled in our simulations

run in patchy landscapes where reorientation mechanisms

become important [1415] Our simulation results depend on

specific parametrizations and should be taken as a qualitative

demonstration of these concepts

Our results show the great potential of studying the motor

mechanisms of C elegans in controlled laboratory environ-

ments to unravel both internal and external drivers of animal

movement behaviour Many of the current (but also classic)

questions about search optimal foraging theory and more

generally movement ecology [23] can be addressed by means

of model organisms Future research on C elegans can uncover

neuronal [26] and genetic [25] mechanisms underlying the

intrinsic stochastic behaviour of organisms as well as quantify

higher correlations between behavioural templates and the

wormrsquos adaptiveness for survival Our results extend beyond

C elegans (see the electronic supplementary material figure S7)

and suggest that in a search process animals perform reorienta-

tion patterns that not only respond to external cues andor

gradients but also are driven by their past memory and stochas-

tic search templates which highlight fundamental principles of

organismsrsquo probabilistic models of the world and how to explore

efficiently in the absence of environmental information

Acknowledgements LCMS was part of the PhD programme in Compu-tational Biology at Gulbenkian Institute of Science Portugal and isgrateful for the financial support from Portuguese Foundation forScience and Technology (FCT) Portugal SFRHBD329602006FB acknowledges the Ramon y Cajal Programme Ministry ofScience and Innovation Spain ref RyC-2009-04133 FB andLCMS work was also supported by Plan Nacional I thorn D thorn i Min-istry of Science and Innovation Spain ref BFU2010-22337 WSRand FB acknowledge the HFSP grant ref RGY00842011 SusanaBernal Katie Hampson and Daniel T Haydon provided valuablefeedback

Data accessibility The C elegans image data are stored in the followingrepository httpwwwryulabca5000fbsharingP1Ncl80x

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44 Fortin M-J Dale MRT 2005 Spatial analysis a guide forecologists Cambridge UK Cambridge University Press

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48 Turchin P 1998 Quantitative analysis of movementmeasuring and modeling population redistribution inanimals and plants Sunderland MA SinauerAssociates

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51 Brembs B 2011 Towards a scientific concept of freewill as a biological trait spontaneous actions anddecision-making in invertebrates Proc R Soc B278 930 ndash 939 (doi101098rspb20102325)

52 Berg HC Purcell EM 1977 Physics ofchemoreception Biophys J 29 193 ndash 219 (doi101016S0006-3495(77)85544-6)

53 Hills T Brockie PJ Maricq AV 2004 Dopamine andglutamate control area-restricted search behavior inCaenorhabditis elegans J Neurosci 24 1217 ndash 1225(doi101523JNEUROSCI1569-032004)

54 Kraemer PJ Golding JM 1997 Adaptive forgettingin animals Psychon Bull Rev 4 480 ndash 491 (doi103758BF03214337)