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������ � ��� �� ��� ��������������� �������� ���� ������� ������ ������ � ��� �� �� ���� ������ ��� ������ ���� �� ����� ��� ������������ ��� ���� ���������� ��� �������� ���� ���� � ���������� ��� �������� ��� ������
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̶ 339 ̶���� ������ �� ��� � ������������� ������� ��� ������������ �� ������ ������������ ������ ��� ������� ��� ��� ������� ��� �������
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����������� ��� � ��������� ����������������

̶ 340 ̶

̶ 341 ̶̶ 342 ̶̶ 343 ̶̶ 344 ̶̶ 345 ̶̶ 346 ̶̶ 347 ̶̶ 348 ̶̶ 349 ̶̶ 350 ̶̶ 351 ̶̶ 352 ̶̶ 353 ̶̶ 354 ̶̶ 355 ̶̶ 356 ̶̶ 357 ̶̶ 358 ̶̶ 359 ̶̶ 360 ̶̶ 361 ̶̶ 362 ̶̶ 363 ̶

Ethology 095\ 094*005 "1999#
Þ 1999 Blackwell Wissenschafts!Verlag\ Berlin
ISSN 9068Ð0502

RESEARCH PAPERS
Instituto Piernaico de Ecolo`ia "CSIC#\ Zara`oza\ and Primate Research Institute\
Kyoto

Fractal Long!Range Correlations in Behavioural Sequences of Wild
Chimpanzees] a Non!Invasive Analytical Tool for the Evaluation of
HealthC[ L[ Alados + M[ A[ Hu}man
Alados\ C[ L[ + Hu}man\ M[ A[ 1999] Fractal long!range correlations in behavioural sequences ofwild chimpanzees] a non!invasive analytical tool for the evaluation of health[ Ethology 095\ 094*005[

Abstract
Quantitative evaluation of health impairments in wild chimpanzees was
explored using fractal long!range correlations of behavioural sequences[ The healthstatus of 02 chimpanzees in the Mahale Mountains National Park\ Tanzania wasevaluated non!invasively using standard behavioural observation and para!
sitological analysis of stool samples[ Based on these data\ individuals were classi_ed
as being either healthy or sick[ Behavioural sequences were analysed and shown to
exhibit long!range power law correlations[ The behavioural sequences of indi!
viduals in healthy and sick states were quantitatively evaluated using detrended~uctuation analysis of social and non!social behaviours within behaviouralsequences[ These values were compared and signi_cant di}erences in long!range
correlations were found between health states[ Sex di}erences were also noted\with female social behaviour displaying a larger fractal dimension than malesocial behaviour[ The fractal dimension of females declined signi_cantly in sickindividuals[ This analysis of behaviour provides a new and e}ective non!invasive
method to record and evaluate the general state of health and related stress ofanimals in the wild[ Possible applications of this method in captive situations
include the monitoring and evaluating of stress levels over time[
Corresponding author] C[ L[ Alados\ Instituto Piernaico de Ecologia "CSIC#\
Avda[ Montanana\ 066\ Apto 191\ 49979 Zaragoza\ Spain[ E!mail] aladosÝ
ipe[csic[esIntroduction
Fractal analysis of behavioural sequences has proved to be an e}ective tool
for the non!invasive assessment of the general health of wild animals "Alados et
U[ S[ Copyright Clearance Center Code Statement] 9068!0502:99:0951Ð9094,04[99:9̶ 364 ̶̶ 365 ̶

095

096

C[ L[ Alados + M[ A[ Hu}man

Fractal Long!Range Correlation Analysis of Chimpanzee Behavioural[ 0885#[ Fractal structures are considered to have {scale symmetry|\ that is\ theylook the same on many di}erent scales of magni_cation[ Fractal objects in natureare considered to be either random or statistically self!similar[ They are di}er!
entiated from non!random fractals\ which look exactly the same at in_nite lengthscales "Mandelbrot 0871^ Bunde + Havlin 0883#[ A fractal process occurs when
the distribution of an event on a temporal scale presents a fractal structure[ These
processes have statistical self!similarity on all scales[ The fractal structure of timeseries has traditionally been investigated by 0:f noise "Voss 0877^ Schroeder 0880#[
The signi_cance of analysing time series such as behavioural sequences lies inwhether the observed variations are due to random phenomena or in fact arise
from deterministic interactions of several variables whose number and type are
generally unknown[ The duration of behavioural sequences displays complex pat!
terns that reveal apparent non!random periodicities in the case of interscan inter!
vals "Quenette + Desportes 0881#[ Cole "0884# and Escos et al[ "0884# observedthat behavioural sequences have a self!similar structure that may provide a power!
ful tool for understanding the temporal structure of behaviour[
Behavioural sequences\ though they often appear erratic\ reveal 0:f like spectra"Alados et al[ 0885#\ but long!term correlation properties of behavioural sequences
have not been directly investigated except in fathead minnows "Pimephales pro!
melas# "Alados + Weber 0888#[ Long!range correlations have been observed inheart!beat intervals\ DNA nucleotide sequences "Stanley et al[ 0881# and in thestride interval of the human gait "Hausdor} et al[ 0884#[ This indicates that thesetime series are neither random "white noise# nor the result of only short!termcorrelations\ but rather the result of highly organized complex processes that may
generate long!term autocorrelation[
In recent years an increasing number of studies are demonstrating the import!
ance of fractal analyses to discriminate morphological structures and time series
that may be used in diagnosis\ and that may be quantitatively characterized by thefractal dimension "Bassingthwaighte et al[ 0883#[ For example\ the fractal dimen!
sion of an electroencephalogram declines with the advancement of Alzheimers
disease "Woyshiville + Calabresa 0883#[ Heart rate variability spectral analysis has
been used to detect cardiovascular complexity alterations\ indicating that reduced
complexity might be incompatible with cardiovascular homeostasis "Butler et al[
0882#[ Stride interval ~uctuations also present a fractal scaling property that
depends on body condition[ Elderly subjects and subjects with Huntington|s disease
present more random ~uctuations than young\ healthy individuals "Hausdor} etal[ 0886#[
As part of a long!term study in progress investigating behavioural adaptations
for the control of parasite infection and other forms of self!medication in African
great apes "Hu}man 0886#\ longitudinal parasitological and behavioural data havebeen collected from known individuals of the fully habituated Mahale M group of
wild chimpanzees "Pan troglodytes schweinfurthii# in western Tanzania "e[g[ Hu}!
man et al[ 0882\ 0885\ 0886#[ Short!term changes in health status vary from thedramatic "Hu}man + Seifu 0878^ Hu}man et al[ 0882# to the often more subtle"Hu}man et al[ 0885#[ Available measures of health status\ such as parasite load\when considered alone\ can be problematic as the e}ects may vary from individual
to individual[ The same parasite load may have a greater impact on some indi!
viduals than on others\ depending upon the overall stamina and _tness of theindividual "e[g[ Hu}man et al[ 0886#[ An independent and supplementary measureof physical condition which allowed statistical comparison would enable better
assessment of health status and changes thereof over time[ In this paper we inves!
tigate whether fractal analysis of long!range correlations of behavioural sequences
can be used to assess the health condition of wild chimpanzees[

̶ 366 ̶

̶ 367 ̶Methods
Chimpanzees of the Mahale M group were observed by focal animal sampling\
recording\ as precisely as possible\ the onset and ending of all behavioural sequencesand events "Martin + Bateson 0882#[ The behavioural data used in the following
analyses were collected by M[A[H[ from 02 individuals "six females and sevenmales# between Nov[ 1 and Dec[ 17\ 0880[ Table 0 shows the major categories into
which observed behaviours were classi_ed[
For this study\ we selected behavioural sequences from the focal data in which
the animals spent more time in active social behaviours[ To do this\ we removed
observations where the focal animal was resting at the beginning or the end of thesequence to avoid sequence interruption\ given that it is the correlation between
times of the sequence that we are interested in[ For calculations\ each change inactivity from active social behaviour "S\ SP and SGG# to the other behaviours "SS\

Table 0] Behaviours used in coding behavioural sequences
Active social behavioursSPsocial play\ i[e[ wrestling\ play chase\ etc[
SGG
grooming others\ mutual groomingS
miscellaneous behaviour directed at others\ i[e[ courtship\ agonistic displays\
copulation\ chase\ supplant\ self!grooming and approach
Other activitiesSS
sitting in a social gathering without mutual interaction^ pause between activities
SRsitting and resting in a social gathering or alone^ rest intervals between otheractivities^ stationary activities\ sitting up\ looking around\ inanimate substrate
manipulation\ etc[
SGR
unidirectional receipt of groomingLlying down in day bed on ground or in tree to sleepF
feeding!foraging^ includes time spent moving from one patch to another\ but
not stopping between feeding bouts for more than 4 minTtravelling\ moving between places^ activities\ taking few rests\ rarely pausing tosit and restM
moving^ intermittent rests\ moving slowly and pausing to rest for periods
frequently as long as time spent walking^ not intermixed with other activities̶ 368 ̶

healthyhealthyhealthysick
sickMA "AM#

4[31
4[41
4[41
0[19
6[42
DE "AM#

80[00[05
80[00[93 080[01[93 1
80[00[91 080[01[96 1healthyhealthy
sick
4[34
3[36
4[28
80[00[2980[00[9880[00[96sick
3[4780[01[05 1̶ 369 ̶NS "AM#
MU "AM#
TB "ADM#

sick
sick
3[89
6[67
80[01[0280[00[17 0
BA "AM#
AJ "AM#sick
5[19
80[00[94sick
7[0980[00[01 1

out of nest later than others^ malaise^ frequently sleeps^ low O[s[ infection
appetite^ o parasite infection detected^ interacts socially with others
malaise^ frequently sleeps in day bed^ deep cough\ constipation\ low S[f[ infection
appetite^ normal stools^ no parasites detectedmalaise^ frequent sleeps on ground^ severe diarrhoea\ ~atulence\ med[ O[s[ infection
malaise^ frequently sleeps in day bed^ lags behind group^ med[ O[s[ infection
frequent defecation^ diarrhoea\ runny nose\ bronchial congestion\ no parasite infection
detected^ in night bed earlyout of bed later than others^ malaise^ frequently sleeps\ rests^ appears to have lower backpains^ no parasite infection detectedmalaise^ frequently sleeps^ appears weak\ lags behind party^ deep cough\ constipation\
low O[s[ infection
runny diarrhoeal stools^ low E[c infection^ interacts socially with others
malaise^ thin^ often attempts to defecate in crouched posture^ later diarrhoea^ expels
worms\ high O[s[ infection^ interacts socially with others but moves o} to rest alone later
often attempts to defecate^ later diarrhoea^ expels worms\ med[ O[s[ infection^ moves o}from others and rests alone^ lower back pain\ ~atulencesocially active^ courtship^ aggressive displayssocially active^ no parasite infection detectedsocially active^ courtship observed but builds ground cushions or day nest and often
sleeps^ low O[s[ infection
no parasite infection detected^ socially active^ good appetite
socially active^ courtship^ good appetite^ agonisitic display^ low E[c[ infectionsocially active^ good appetite
socially active^ courtship^ runny nose\ ~atulence\ diarrhoea
frequently sleeps in day beds^ often sits alone^ some social interaction^ low T[t[ infection
sickhealthysickhealthy
sick
sick
sick
6[32
1[67
2[65
3[17
2[35
3[14
5[13
80[00[0480[00[07 0
80[01[17 1
80[00[08 080[01[12 180[01[9180[00[00 0

Observational and parasitological evaluation of health status
Focal "h# Status
Date

WA "AF#[WL "AF#
TY "AF#N

FT "AF#Sðyb"t#−y1⁄4b"t#Ł1

Name

F1"b# 

Table 1] Records of health status used in qualitative evaluation of individuals used in fractal analysis "Hu}man et al[ 0885\ 0886#

SR\ SGR\ L\ F\ T and M# and vice versa was used\ including short!term events
such as when an animal changed grooming partners[ Descriptions of the behaviours
used in this evaluation are given in Table 0[ Active social behaviour was de_ned as
those behaviours displayed when the subject was involved in social interactions as
the actor\ and the receiver was its companion[ The total amount of time for which
the animal was observed in each behavioural sequence was divided into 4!s intervals
in order to make the sequence easily computable without loosing accuracy\ granted
that the duration of an activity was never shorter than 4 s[ The total duration ofdata recording per focal individual is presented in Table 1\ while per individual
sequence duration in 4!s units is presented in Table 2[
The general state of health of an individual during focal observations was
non!invasively evaluated using multiple qualitative and quantitative measures ofhealth adopted from standard preliminary veterinary diagnosis in the _eld[ Themeasures used were visual classi_cation of stool type "diarrhoeal or normal#\presence:absence of adult parasites in the stool\ microscopic analysis of intestinal
parasite infection and qualitative behavioural signs clearly indicative of healthstatus such as appetite\ stamina and such obvious involuntary behaviours "cough!
ing\ sneezing\ ~atulence\ wheezing\ etc[# indicative of illness and:or a physiologicalimbalance[ Based upon these observations\ individuals were then classi_ed as being
either sick or healthy on the day on which data were used for the following analyses[
Individuals displaying at least three of these independent measures of ill healthwere classi_ed as sick[ No attempts were made to grade health on a point scale[
The diagnostic symptoms observed and health status assigned to each case are
given in Table 1[
Detrended ~uctuation analysis "DFA# was performed to measure the cor!
relation between data sequence points for a one!dimensional random walk[ Themethod is described by Peng et al[ "0881#\ and its posterior modi_cation in Peng etal[ "0883#[ The procedure applied to behavioural data is detailed in Alados +Weber "0888#[ It has the advantage that it removes local trends and\ in consequence\is not a}ected by non!stationarities[ A time series is stationary if there is no
systematic change in mean "no trend#\ and if strict periodic variations have been
removed[ In many series these conditions are violated[
Applying the method of Peng et al[ "0881#\ we examined a binary sequence
ðz"i#Ł of active or social behaviour denoted by 0\ and non!active or non!social
behaviour denoted by Ð0 at 4!s time intervals "i# taken from continuous obser!
vations[ We can generate a behaviour sequence random walk\ y"t#\ obtained byiN
adding the previous sequence such that y"t#  Si0z"i#[ This provides a graphicalrepresentation that permits calculation of the degree of correlation in the behaviour
time series[ The entire sequence of data of length N is divided into non!overlapping
subsequences\ or {boxes|\ of length b[ In each box we _t a least square line to thedata[ Let y1⁄4b"t# be the regression estimate of yb"t# for each box size b[ The ~uctuationof yb"t# about y1⁄4b"t# was calculated for each data point\ and then averaged ~uctuation
for that box size b was determined as

098

Fractal Long!Range Correlation Analysis of Chimpanzee Behaviour

OAF] old adult female "over 30 years old#^ AF] adult female "04Ð39 years old#^ AM] adult male "05Ð39 years old#^ ADM] adolescent male"7Ð04 years old#^ O[s[] Oesophagostomum staphanostomum\ E[c[] E[ coli^ T[t[ ] Trichuris trichiura[

C[ L[ Alados + M[ A[ Hu}man

BO "OAF#
GW "AF#097

009

Fractal Long!Range Correlation Analysis of Chimpanzee Behaviour

C[ L[ Alados + M[ A[ Hu}man

000

Table 2] Alpha exponent and curve _tting estimator "R1# of the equation F"b# 3 ba for
portion of behavioural sequences used in analysis
Name

Date

Sequence"s#StatusAlpha

R1BO "OAF#
GW "AF#80[00[0480[00[07 0
80[01[17 1
80[00[08 080[01[12 180[01[9180[00[00 080[00[01 1
80[00[9480[01[0280[00[17 080[01[05 1
80[00[2980[00[9880[00[96 080[00[05 1
80[00[93 080[01[93 1
80[00[91 080[01[96 1

2477
1601
1994
2973
1385
2951
3389
2201
2641
1839
4593
2299
2814
2105
2419
1239
2861
2860
1402
4934

sick
healthysickhealthy
sick
sick
sick
sick
sick
sick
sick
sick
healthyhealthysickhealthyhealthyhealthy
sick
sick

0[019
0[039
0[179
9[809
0[159
0[239
0[191
0[026
0[170
0[180
0[110
0[135
0[184
0[301
0[137
0[170
0[159
0[179
0[184
0[325

9[852
9[863
9[883
9[840
9[871
9[878
9[866
9[836
9[883
9[883
9[876
9[875
9[883
9[883
9[878
9[883
9[874
9[880
9[881
9[881

FT "AF#WL "AF#
TY "AF#
WA "AF#BA "AM#
AJ "AM#
NS "AM#
MU "AM#
TB "ADM#
DE "AM#
MA "AM#

OAF] old adult female "over 30 years old#^ AF] adult female "04Ð39 years old#^ AM] adultmale "05Ð39 years old#^ ADM] adolescent male "7Ð04 years old#[

If this procedure is repeated for various box sizes\ b\ the residual variances should_t the relation
F"b# 3 bawhere a  0:1 indicates no correlations in the sequence "white noise#\ and a  0:1
indicates long!range power law correlations "the social interaction bout length
depends on the history of the actors| social patterns#[ If a exceeds 0:1\ the sequenceis persistent^ if a ³ 0:1 the sequence is anti!persistent "a long bout is more likely to
be followed by a short one and vice versa#[ We considered boxes of size nearest
integer to 11\ 11[4\ 12\[ [ [18[ The box sizes were equally spaced on a log scale to
avoid biasing the linear regression in favour of the larger box sizes[

Fig[ 0] Behavioural sequence walks for an adult female "GW# when classi_ed as sick and healthy[ X!
axes represent the time in 4!s units[ a[ Y!axes represent the binary behavioural sequence ðz"i#Ł "0 for
active social behaviour and Ð0 for activity!lag#[ b[ Y!axes represent the generated random walk\ y"t#\obtained by adding the previous sequence such that y"t#  SiNi0 z"i#[ c[ Fluctuation analysis^ X!axes
represent the natural logarithm of box size "b#^ Y!axes represent the natural logarithm of the average~uctuation ðF"b#Ł^ the a exponent is the slope of the regression equation

Fig[ 0 presents scatter plots of the behaviour sequence for an adult female"GW# when classi_ed as sick and again as healthy on another day[ We generated
a random walk\ y"t#\ obtained by successive addition on the binary sequence\

providing a graphical representation that permits calculation of the degree ofcorrelation in the behaviour time series[ Calculation results of each chimpanzee
analysed are presented in Table 2[ The average a value for the 02 chimpanzees
analysed is a  0[136 2 9[91\ n  19 behavioural sequences[ Our results reveal thatthe social behaviour sequence exhibits long!range power law correlations\ that isthe present behaviour depends on long!term activity[ DFA analyses of randomized
data sets of six di}erent sequences give an average a value of 9[4 2 9[995\ close to
the 9[4!value of random ~uctuation of in_nite length sequences\ signi_cantly

̶ 370 ̶

̶ 371 ̶Results

001

002

C[ L[ Alados + M[ A[ Hu}man

Fractal Long!Range Correlation Analysis of Chimpanzee Behaviour

di}erent "t  8[56\ df  3\ p ³ 9[990# from the social behaviour sequence of chim!
panzees[ That is\ randomly shu/ed data are not autocorrelated^ the direction ofeach step is independent of previous steps[ However\ in the autocorrelated behav!
iour sequences of chimpanzee social activity\ the direction of the step depends on
the history of the walker[ Additionally\ high accuracy of curve _tting is observed
for the DFA analysis "R1  9[873 2 9[992\ n  19#[
In order to gain insight into the underlying conditions for this long!term depen!
dence\ we investigated the e}ects of health status and sex on social behaviour
sequence correlations[ Because time length sequences are not the same in all
observations\ one!way analysis of covariance was performed with time length
included as a covariant[ The results showed no signi_cant e}ect of sequence
duration on the alpha exponent "F0\03  9[13\ ns#[ In consequence the covariate
was eliminated in posterior analyses[ Female social interval ~uctuations increased
slowly with time scale "a  0[017 2 9[923\ n  8#\ in comparison with males"a  0[186 2 9[916\ n  09#[ In general a is equivalent to the Hurst exponent H"Hausdor} et al[ 0886#\ and it is inversely related to the fractal dimension by the
relation H  1 Ð D\ for one!dimensional series[ In consequence\ we can say thatfemale social behaviour presents a larger fractal dimension\ that is\ it is more
complex than male social behaviour[ This e}ect is signi_cant only when healthy
individuals are analysed "Table 3#[ Additionally\ healthy chimpanzees present lower
a _gures "0[054 2 9[925\ n  6# than do sick individuals "0[15 2 9[914\ n  01#\
but because an interaction between sex and body condition exists "F0\04  5[35\p ³ 9[94#\ two separated one!way ANOVAs were performed "Table 3#[ The results
showed a change in the slope of the power law relation between the root meansquare ~uctuation ðF"b#Ł about the average displacement and box size "b# forindividuals belonging to di}erent categories[ Healthy females have signi_cantly
lower a values than do sick females[ That is\ the fractal dimension\ inversely related
to the a exponent\ declined in sick individuals[of whether behaviour sequence ~uctuations are due to long!range correlations\where present behaviour depends on past history of activity "a × 9[4#\ or whether
they are simply random ~uctuations or the consequences of short!range cor!
relations "a  9[4#[ We observed that social behaviour sequences are long!termcorrelated\ that is the present behaviour depends on long!term activity\ and thus\
the fractal properties of the behavioural sequence are characterized by a powerlaw scaling of the correlation\ as observed in numerous phenomena having a fractal
origin[ For example\ 0:f temporal ~uctuations are found in the heart rate ofhealthy individuals "Kobayashi + Musha 0871^ West 0889^ Meesmann et al[ 0882#\
respiratory intervals in animals "Kawahara et al[ 0878# and neuronal discharges
during sleep "Yamamoto et al[ 0875#[ The mechanisms responsible for the long!
term correlations in the behavioural sequences are still unknown\ and their function
remains to be determined[ Several authors have suggested long!term ~uctuations
as mechanisms to maintain stable homeostasis in living systems "Butler et al[
0882^ Uritsky + Muzalevskaya 0882#[ These ~uctuations may be in~uenced by theenvironment to the point that it has been reported that low electromagnetic 0:f~uctuations have a stabilizing e}ect on many biological processes and can act as a
powerful therapeutic agent "Uritsky + Muzalevskaya 0882#[
In general\ we observed that\ among chimpanzees classi_ed as being healthy
on behavioural and parasitological measures\ males presented more predictablebehavioural sequences than females[ Also\ healthy females presented higher fractal
dimensions than sick females[ This change is similar to that observed in power
spectrum analyses of female Spanish ibex "Capra pyrenaica# "Alados et al[ 0885#[
The di}erent scaling of behaviour sequences of healthy and sick individuals must be
related to the underlying dynamics of physiological components[ In consequence\
fractal!like ~uctuations in the behaviour sequence may be a feature of the behaviour
system that reveals the health condition of individuals[ Thus the change in thefractal dimension of behavioural sequences may be an indicator of in~uences ofthe state of health on temporal patterns[
Changes in the fractal structure of behavioural sequences have also beenreported in toxicological studies\ revealing a reduction in the fractal dimension of
locomotor activity in rats under the e}ects of toxic substances "Motohashi et al[
0882#\ or the complexity of reproductive _sh behaviour under Pb exposure "Alados+ Weber 0888#[ According to Buldyrev et al[ "0883#\ long!range correlation in
biological systems is adaptive because it serves as an organizing principle for highly
complex\ non!linear processes\ and because it prevents restriction of the functional
response of an organism to a highly periodic behaviour[ When physiological sys!
tems "Goldberger 0886# and behavioural responses "Alados et al[ 0885# lose theirfractal complexity\ they reduce the e.cient transport of substances and information
over a complex interacting system[ As a result\ they are less adaptable and less able
to cope with the exigencies of an unpredictable changing environment "Goldberger
0886#[ Comparisons of interbeat intervals of healthy subjects and patients withsevere cardiac disease showed that healthy heartbeat time series present more
complex ~uctuations than diseased heart ~uctuations[ However\ not all the studies
have reported a fractal dimension increase with health status[ Hausdor} et al[

Discussion
The calculation of a using DFA provides a new quantitative method tomeasure the degree of correlation in behavioural sequences\ and to analyticallydistinguish healthy from sick individuals[ In this study we addressed the question

Table 3] Fractal complexity of social behaviour time series[ x¹ 2 SE "n#\ a values and F
values of the one!way analysis of variance

Males
Females

HealthySick

0[295 2 9[922 "4#0[914 2 9[958 "1#
F0\4  02[53\ p ³ 9[940[178 2 9[922 "4#0[121 2 9[926 "6#F0\09  0[28\ ns

̶ 372 ̶F
F 0\ 7  9[01\ ns
F 0\ 6  6[91\ p ³ 9[94

̶ 373 ̶

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004

C[ L[ Alados + M[ A[ Hu}man

Fractal Long!Range Correlation Analysis of Chimpanzee Behaviour"0886# observed that complexity of stride intervals in humans increases with age
and Huntington|s disease[ These contradictory results must be related to the advan!
tages of performing one or another behaviour[ A steady path probably confers agreater advantage to prevent overbalancing[ On the other hand\ scanning unpre!
dictability is considered to be an adaptive strategy "Pulliam 0862^ Lendrem et al[
0875# because the probability of detecting a predator depends\ in part\ on thepattern distribution of scanning sequences[ Similarly\ the structural patterns ofsocial activity intervals may have important implications for anti!predator behav!
iour given that\ when chimpanzees are occupied interacting with each other\ theylose predator awareness[
The fact that male chimpanzees\ unlike females\ do not change the complexityof their social activity when they are sick may be interpreted as re~ecting thedi}erent underlying mechanisms leading to social behaviour in each sex[ Similarly\
a study "Alados + Webber 0888# on _sh behaviour under Pb exposure revealed
that the complexity of the reproductive behaviour of males _shes after sexual
maturity did not change signi_cantly\ while the fractal complexity declined under9[4 p[p[m[ Pb exposure before sexual maturity[
Further investigations are needed to elucidate long!range correlation of behav!
ioural sequences[ Some questions remain to be answered[ Which behaviouralsequences are more tolerant of internal and environmental perturbations< Howstable is the degree of correlation in the behavioural time series under identicalconditions< What is the range of variation in the scaling exponent of thosesequences< Because the accuracy of analysis is limited by the length of the available
behavioural sequences\ it is important to investigate the e}ect of _nite length on
the exponents calculated and to estimate the optimal length sequence needed for ahigh!accuracy estimation of health status[ Some will argue that health status is apoint on a continuum[ It is not the purpose of this paper to grade states of illness
but to evaluate observable di}erences in health status using detrended fractal
analysis as an independent analytical tool[
From this study we conclude that behavioural sequences are heterogeneousover time in a non!random pattern\ showing long!range correlation[ We also
conclude that DFA analysis is a dynamic\ non!invasive technique to quantify
changes in body conditions and may be a useful method for evaluating the behav!
ioural e}ects of environmental variables[ From a wildlife conservation standpoint\
this may prove to be an indispensable method for monitoring and assessing thelong!term impact of such factors as eco!tourism or habitat degradation on endang!
ered species like the chimpanzee[ In captive situations\ DFA analysis may prove
useful in monitoring or evaluating the e}ects of environmental enrichment pro!
grammes on the stress levels of animals[ From a wildlife conservation standpoint\
this may prove to be an indispensable method for monitoring and assessing thelong!term impact of such factors on chimpanzee in their natural habitat[

Serengeti Wildlife Research Institute\ Mahale Mountains Wildlife Research Centre and the Universityof Dar es Salaam[ Juan Escos provided computer facilities and developed software for fractal analyses[
Field research presented here conducted in 0889Ð80 was generously supported by grants from the
Monbusho International Scienti_c Research Program to T[ Nishida "No[ 52932906#[ During the write!
up and analysis\ M[ A[ Hu}man was generously supported by a Center of Excellence Research
Fellowship at the Primate Research Institute\ Kyoto University[

Literature Cited

We thank the people and Government of Tanzania for their long!term cooperation and commit!
ment\ in particular the Tanzanian National Scienti_c Research Council\ Tanzanian National Parks\

Alados\ C[ L[ + Weber\ D[ 0888] Lead e}ects on the predictability of reproductive behavior in fatheadminnows "Pimephales promelas#] a mathematical model[ Env[ Toxicol[ Chem[ 07\ <*<[
Alados\ C[ L[\ Escos\ J[ + Emlen\ J[ M[ 0885] Fractal structure of sequential behaviour patterns] anindicator of stress[ Anim[ Behav[ 40\ 326*332[
Bassingthwaighte\ J[ B[\ Liebovitch\ L[ S[ + West\ B[ J[ 0883] Fractal Physiology[ Oxford Univ[ Press\
Oxford[Buldyrev\ S[ V[\ Goldberger\ A[ L[\ Havlin\ S[\ Peng\ C[ K[ + Stanley\ H[ E[ 0883] Fractals in biology
and medicine] from DNA to the heartbeat[ In] Fractals in Science "Bunde\ A[ + Havlin\ S[\ eds#[
Springer!Verlag\ Berlin[ pp[ 38*76[
Bunde\ A[ + Havlin\ S[ "eds# 0883] Fractals in Science[ Springer!Verlag\ Berlin[
Butler\ G[ C[\ Yamamoto\ Y[\ Chen King\ H[\ Northey\ D[ R[ + Hughson\ R[ L[ 0882] Heart ratevariability and fractal dimension during orthostatic challenges[ J[ Appl[ Physiol[ 64\ 1591*1501[
Cole\ B[ J[ 0884] Fractal time in animal behaviour] the movement activity of Drosophila[ Anim[ Behav[
49\ 0206*0213[
Escos\ J[\ Alados\ C[ L[ + Emlen\ J[ M[ 0884] Fractal structures and fractal functions as disease
indicators[ Oikos 63\ 209*203[
Goldberger\ A[ L[ 0886] Fractal variability versus pathologic periodicity] complexity loss and stereotypy
in disease[ Perspect[ Biol[ Med[ 39\ 432Ð450[
Hausdor}\ J[ M[\ Peng\ C[ K[\ Ladin\ Z[\ Wei\ J[ Y[ + Goldberger\ A[ L[ 0884] Is walking a random
walk< Evidence for long!range correlations in stride interval of human gait[ J[ Appl[ Physiol[ 67\238*247[
Hausdor}\ J[ M[\ Mitchell\ S[ L[\ Firtion\ R[\ Peng\ C[ K[\ Cudkowicz\ M[ E[\ Wei\ J[ Y[ + Goldberger\
A[ L[ 0886] Altered fractal dynamics of gait] reduced stride!interval correlations with aging andHuntingtons disease[ J[ Appl[ Physiol[ 71\ 151*158[
Hu}man\ M[ A[ 0886] Current evidence for self!medication in primates] a multidisciplinary perspective[
Yrbk[ Physic[ Anthropol[ 39\ 060*199[
Hu}man\ M[ A[ + Seifu\ M[ 0878] Observations on the illness and consumption of a medicinal plant
Vernonia amygdalina by a wild chimpanzee in the Mahale Mountains[ Tanzania Primates 29\ 40*52[Hu}man\ M[ A[\ Gotoh\ S[\ Izutsu\ D[\ Koshimizu\ K[ + Kalunde\ M[ S[ 0882] Further observations
on the use of the medicinal plant\ Vernonia amygdalina "Del# by a wild chimpanzee\ its possiblee}ect on parasite load\ and its phytochemistry[ African Study Monogr[ 03\ 116*139[
Hu}man\ M[ A[\ Page\ J[ E[\ Sukhdeo\ M[ V[ K[\ Gotoh\ S[\ Kalunde\ M[ S[\ Chandrasiri\ T[ + Towers\
G[ H[ N[ 0885] Leaf!swallowing by chimpanzees\ a behavioral adaptation for the control ofstrongyle nematode infections[ Int[ J[ Primatol[ 61\ 364*492[Hu}man\ M[ A[\ Gotoh\ S[\ Turner\ L[ A[\ Hamai\ M[ + Yoshida\ K[ 0886] Seasonal trends in intestinal
nematode infection and medicinal plant use among chimpanzees in the Mahale Mountains National
Park[ Tanzania Primates 27\ 000*014[
Kawahara\ K[\ Yamauchi\ Y[\ Nakazono\ Y[ + Miyamoto\ Y[ 0878] Spectral analysis on low frequency~uctuation in respiratory rhythm in the decerebrate cat[ Biol[ Cybern[ 50\ 154*169[
Kobayashi\ M[ + Musha\ T[ 0871] 0:f!~uctuations of heartbeat period[ IEEE Trans[ Biomed[ Eng[
BME 18\ 345*346[
Lendrem\ D[ W[\ Stretch\ D[\ Metcalfe\ N[ + Jonest\ P[ 0875] Scanning for predators in the purple
sandpiper^ a time!dependent or time!independent process< Anim[ Behav[ 23\ 0466*0467[
Mandelbrot\ B[ B[ 0871] The Fractal Geometry of Nature[ Freeman\ San Francisco[Martin\ P[ + Bateson\ P[ 0882] Measuring Behaviour[ Cambridge Univ[ Press\ Cambridge[
Meesmann\ M[\ Boese\ J[\ Chialvo\ D[ R[\ Kowallik\ P[\ Bauer\ W[ R[\ Peters\ W[\ Greis\ F[ + Kni}ki\

̶ 374 ̶

̶ 375 ̶Acknowledgements

005

C[ L[ Alados + M[ A[ Hu}man

K[ D[ 0882] Demonstration of 0:f ~uctuations and white noise in the human heart rate by thevariance!time!curve] implications for self!similarity[ Fractals 0\ 201*219[
Motohashi\ Y[\ Miyazaki\ Y[ + Takano\ T[ 0882] Assessment of behavioral e}ects of tetrachloroethylene
using a set of time!series analyses[ Neurotoxicol[ Teratol[ 04\ 2*09[
Peng\ C[ K[\ Buldyrev\ S[ V[\ Goldberger\ A[ L[\ Havlin\ S[\ Sciortino\ F[\ Simons\ M[ + Stanley\ H[ E[0881] Long!range correlations in nucleotide sequences[ Nature 245\ 057*069[
Peng\ C[ K[\ Buldyrev\ S[ V[\ Havlin\ S[\ Simons\ M[\ Stanley\ H[ E[ + Goldberger\ A[ L[ 0883] Mosaic
organization of DNA nucleotides[ Phys[ Rev[ 38\ 0574*0578[
Pulliam\ H[ R[ 0862] On the advantages of ~ocking[ J[ Theor[ Biol[ 27\ 308*311[
Quenette\ P[ Y[ + Desportes\ J[ P[ 0881] Temporal and sequential structures of vigilance behavior ofwild boars "Sus scrofa#[ J[ Mammal[ 62\ 424*439[
Schroeder\ M[ 0880] Fractals\ Chaos\ Power Laws[ W[ H[ Freeman\ New York[
Stanley\ H[ E[\ Buldyrev\ S[ V[\ Goldberger\ A[ L[\ Hausdor}\ J[ M[\ Havlin\ S[\ Mietus\ J[\ Peng\ C[
K[\ Sciortino\ F[ + Simons\ M[ 0881] Fractal landscapes in biological systems] long!range cor!
relations in DNA and interbeat heart intervals[ Physica[ A 080\ 0*01[
Uritsky\ V[ M[ + Muzalevskaya\ N[ I[ 0882] Fractal stochastic electromagnetic stabilizing processes ofvital activity[ Fractals 0\ 210*214[
Voss\ R[ F[ 0877] Fractals in nature] from characterization to simulation[ In] The Science of Fractal
Images "Peitgen\ H[ O[ + Saupe\ D[\ eds#[ Springer Verlag\ New York[ pp[ 10*69[
West\ B[ J[ 0889] Fractal Physiology and Chaos in Medicine[ World Scienti_c\ Singapore[
Woyshiville\ M[ J[ + Calabresa\ J[ R[ 0883] Quanti_cation of occipital EEG changes in Alzheimer|sdisease utilizing a new metric] the fractal dimension[ Biol[ Psychiatry 24\ 270*276[
Yamamoto\ M[\ Nakahama\ H[\ Shima\ K[\ Aya\ K[\ Kodama\ T[\ Mushiake\ H[ + Inase\ M[ 0875]
Neuronal activities during paradoxical sleep[ Adv[ Neurolog[ Sci[ 29\ 0909*0911[
Received] March 04\ 0888
Initial acceptance] May 19\ 0888
Final acceptance June 07\ 0888 "W[ Wickler#

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