AstudyofhominindispersaloutofAfricausingcomputersimulationsP.Nikitasa,*,E.NikitabaLaboratoryofPhysicalChemistry,DepartmentofChemistry,AristotleUniversityofThessaloniki,54124Thessaloniki,GreecebStageiriti15B,AnoToumba,54352Thessaloniki,GreeceReceived6January2005;accepted5July2005AbstractA
study of hominin dispersal out of Africa using computer simulations
is presented. Attention is focused on the jointprobability of the
colonizationof Western Europe later than 1 Ma and that of Eastern
Asia prior to 1.6 or 1.8 Ma, ascurrentarchaeological
estimatessuggest. Wefoundthatthedeterminantfactortohominindispersal
isthemodeofhominin movement. If the movement of all populations is
uniform and their number great enough, greater than 300 inour
models, then such movement favors the colonization of Eastern Asia
and Western Europe at more or less the sametime. Ontheother hand,
thecolonizationacquires prominent probabilistic features if the
number of populationsmigrating is small enough, smaller than 10 in
our models, or when all hominin populations may move but there are
onlyafewwithmuchhighermobility.Inthiscase,thejointprobabilityfortheearliestdispersalsofhomininsinWesternEurope
after 1 Ma and Eastern Asia prior to 1.6 Ma ranges from 0.02 to
0.05. The single probability of colonization ofWestern Europe after
1 Ma is very high, about 0.5 for the majority of the colonization
routes, whereas thecorresponding probability of the colonization of
Eastern Asia prior to 1.6 Ma is ten times lower, about 0.05. The
leastprobable event is the earliest colonization of Java prior to
1.6 Ma, to which our simulation attributes a probability of ca0.01.
Deserts, mountains, and mountain ranges may delay the arrival at a
certain location; nevertheless, their eect
onthejointprobabilityisverysmall.2005ElsevierLtd.Allrightsreserved.Keywords:Hominindispersal;Colonization;Computersimulation*Correspondingauthor.Tel.:
C302310997773;fax:
C302310997709.E-mailaddresses:[email protected](P.Nikitas),[email protected](E.Nikita).0047-2484/$-seefrontmatter
2005ElsevierLtd.Allrightsreserved.doi:10.1016/j.jhevol.2005.07.001JournalofHumanEvolution49(2005)602e617IntroductionOur
knowledge of hominin dispersals out
ofAfricahasbeenconsiderablyadvancedduringthelast decades. However,
there are still crucialaspects that call for further investigation.
Forexample,itisnotcleariftheearliestcolonizationhasbeenconductedatthedatesproposedbytheexistingarchaeological
data, whichinmanycasesarecontroversial.
Alsouncleararethecombinedeects of various environmental factors on
thecolonization of Eurasia and the routes thisexpansion followed.
Finally, we can only speculateabout the eect onthe
colonizationfromalter-ations in hominin behavior as a result of
theirevolutionoradaptationtovariousenvironmentalanddietaryconditions.Aninterestingapproach,subsidiarytoconven-tionalarchaeological
methodsofexamininghom-inindispersal,istheuseofcomputersimulations,adevelopingeldthathasproducedanumberofnoteworthy
studies so far. A simulation ofhominin dispersal may be transacted
either bysolving Fishers classic equation (Fisher,
1937),adiusiontype equation, or
byapplyinglatticemodels.Therstapproachhasbeendevelopedbythe work of
Williamson (1996), Shigecada andKawasaki(1997),aswell
asYoungandBettinger(1995). Anapplicationof this methodhas
beencarried out by Steele et al. (1998)
concerningPaleoindiandispersals, that ishominindispersalsin North
America from13,000 to 10,000 yearsago.
Thismethodpresumestheknowledgeoftheenvironmentalcarryingcapacityandthediusioncoecientestimatedbyethnographicandarchae-ological
data. Diusion coecients of early HomohavebeenestimatedbyAnto
netal.(2000,2002).Thesecondapproach, that of thelatticemodels,is
based on the theory of cellular automata(Hogeweg, 1988) andthe most
interestingappli-cationtomodel hominindispersal out of Africahas
been realized by Mithen and Reed
(2002).Theseauthorshaveexaminedthecombinedeectof a variety of
parameters suchas colonizationrates, paleoenvironmental conditions,
topographicbarriers, land-bridges, and hominin environ-mental
anddietary preferences onthe coloniza-tion of Eurasia. Their study
concludes thatthe dierent hominin types occupying WesternAsia have
led to a more variable fossil recordthanthat of
Europeandarmsthecolonizationof Europe prior to 1.5 Ma (mega
annum),contrary to the archaeological evidence whichsuggests that
this happened only after 1 Ma(Carbonell et al., 1995, 1999).
Althoughthere issome discussion of early lithic sites in Spain(Mart
nez-Navarroetal., 1997; Omsetal., 2000)providing evidence for human
occupation inSouthernEurope aroundandprior to1 Ma, ingeneral, the
models predictions about the colo-nization dates of both Western
Europe andEastern Asia do not converge with the
corre-spondingarchaeological data.MithenandReeds studyfocuses
ondistribu-tions of arrival dates at certaintarget sites
andcomparesthesewithcurrent archaeological data.However,
thedistributionsarerathernarrowandleavenoprobabilityforratherextremeeventslikethegreatdierencebetweentheearliestcoloniza-tions
of EasternAsiaandWesternEurope.
Thenarrownessofthesedistributionsmightbeduetothe smallnumberof
iterations usedin their model(30), and/or to the way that Mithen
and Reedmodeledhomininmovement.In the present study, our primary
goal is toattempt to estimate the various probabilities ofevents
associated with the earliest dispersal ofhominins throughout
Eurasia. At this point weshouldclarifythat the hominindispersal out
ofAfricaisatypicalprobabilisticexperiment.Hom-inins are moving from
one place to another on thebasis of certain probabilities
determined fromenvironmental factors. But their dispersal isa
probabilistic experiment that has occurredjust once and
itshallnever berepeated.Thisrulesout any possibility of knowing
whether thecolonization has proceeded through the mostprobable
route or if it has followedone of theleast likely routes. When a
randomexperimenttakes place once, any result can be
realizedprovidedthat itbelongstotheset ofall possibleresults of
this experiment. Therefore, undoubtedly,neither this nor anyother
simulationmodel cangive nal answers as to what exactly has
happenedin the past. The only thing we can do by means ofsimulation
models is to estimate the probability of603 P.Nikitas,E.Nikita /
JournalofHumanEvolution49(2005)602e617the earliest distributionof
hominins throughoutEurasiaassuggestedbyarchaeologicaldata.We have
adopted the lattice model in anattempttoestimatetheoverall
probabilityoftheearliest hominin colonizations throughout
Eurasiaand to estimate the single probabilities of
theearliestoccupationofspecicsitesofarchaeolog-icalinterest.Inordertoachievethis,weincreasedthe
number of iterations to 500, reduced theenvironmental factors that
aect hominindispersal tothose we consideredsignicant, andwe mainly
examined the eect of the mode ofmovement on dispersal since the
model shows thatthis is the dominant factor aecting
hominindistributiontoEurasia.Inthisway,wearetryingto nd the
optimumscenario for the earliestcolonization of Eurasia and compare
it withcolonizationevents
assuggestedbypaleoanthro-pologicalandarchaeologicalrecords(ArribasandPalmqvist,1999).These
records have shownthat EasternAsiawas inhabited between 1.6 and 1.8
Ma. Morespecically,LonggupoCaveinChinawasconsid-ered the
earliestpresence of hominins in continen-tal EasternAsia,
datedto1.8 Ma(Huanget
al.,1995),whereasthecolonizationofJavaIndonesiahasbeendatedto1.7
Ma(Se mahetal., 2000). Ifthe Longgupomandible fragment is not
consid-ered hominin (Schwartz and Tattersall, 1996;Wolpo, 1999; Wu,
1999), thentheoldestrecordof hominin occupation in continental
Eastern Asiais Majuangou in the Nihewan basin dated to1.66 Ma (Zhu
et al., 2004). As far as thecolonization of Indonesia is concerned,
despitethe controversial views expressedconcerningthedate of this
event (Dennell, 2003; Anto n andSwisher, 2004), the colonization
probably occurredat about 1.8 Ma at Perningand shortlyafterward,1.7
Ma, at Sangiran (Swisher et al., 1994). A recentre-evaluation of
the data conrmed the above viewand indicated that the earliest
hominin occupationin Sangiran is likely to be older than 1.6
Ma(Anto nandSwisher,2004).In contrast to Far-East Asia, Western
Europe isestimatedtohavebeenoccupiedforthersttimearound 0.8 Ma,
since the discoveries at Atapuerca,Spain are dated to that time
(Carbonell et al., 1995,1999) and0.3millionyears later, at 0.5 Ma,
weobserve the earliest occupation of England atBoxgrove (Roberts
and Partt, 1999). Nevertheless,theworkcarriedout byMart
nez-Navarroet al.(1997) and Oms et al. (2000) on early lithic sites
inSpainprovidesevidenceforhumanoccupationinSouthern Europe around
and prior to 1 Ma.Basedontheabovedata,
wedenetheoverallprobabilityfromthejointprobabilityofWesternEurope
having been colonized after 1 Ma andEastern Asia prior to 1.6 or
1.8 Ma. In the presentstudy, we estimate this
probabilityandexaminethe impact that various environmental factors,
likedeserts, mountain-ranges, land-bridges, and routeshave on it as
well as test whether it can bemaximizedbydierentiations
onthemobilityofthe hominins themselves. Because the estimationof
the joint probability is closely relatedtotheestimation of single
probabilities of the earliestcolonization of specic sites or areas,
such a modelcan evaluate the several environmental factors
thatintervene inthe procedure of hominindispersaltogether with
their combined eects and
thevarioushypothesesoeredtoexplainthearchae-ologicalcolonizationdates.ModelingthehominindispersalBasicfeaturesIn
the lattice models the dispersal area is dividedinto cells by means
of a regular lattice. Themovement of a population from one cell to
anotherisdeterminedbythe probabilitiesof occupancy ofeach cell,
dened in advance. In this paper we haveadopted a square lattice. In
order to examine if thenumber of cells aects theresults,
wehaveusedtwo dierent grids of 16,308 Z108 !151 (grid A)and7,272
Z72 !101(gridB) cells, respectively,each one covering Africa, Asia,
and Europe(Fig. 1). Note that MithenandReedhave useda total of
7,406 triangular cells in their simulations.Eachcell is
characterizedbyacertainproba-bility,Pc,ofbeingoccupiedbyahomininpopula-tion.
Three types of cells have beenconsidered.The rst type includes
cells that correspond to sea,wide lakes, mountains higher than4,000
m, andthe zone above the 60th parallel. For these cells the604
P.Nikitas,E.Nikita /
JournalofHumanEvolution49(2005)602e617probability of occupancy by a
hominin
populationiszero(PcZ0),meaningthattheaboveobstaclesremaininaccessibleunderanycircumstances.Thesecond
type of cell corresponds to mountains
withaltitudesrangingfrom2,000to4,000 m, thesub-arctic zone between
the 55th and 60th parallel, andthe deserts. In this case Pc varies
from 0 to 1 and isdenoted further by Pc,m, Pc,n, and Pc,dwhen
itreferstomountains,sub-arcticzones,anddeserts,respectively.
Figure1depictsthedistributionandthe areacoveredbythe deserts,
mountains, andlakesassumedinthepresentstudy.
Thedistribu-tionandthesizeof theseenvironmental featuresmay be
questioned for the time period underexamination. However, as shown
in the resultssection, they do not play any important role in
thedistributionofhomininsinEurasiaatleastforPcrangingfrom0.1to1.TherestofthecellsbelongtothethirdtypewherenoenvironmentalbarriersexistandtheprobabilityPcisequaltoone.Basedonthepaleontological
record, webeganthemodelat2
Mawithasmallnumberofcells(1to100)occupiedinEastAfrica.Inthisapproach,the
total population is equal to the number of cellsoccupied by
hominins. Then at each time step(iteration) the hominin population
of a certain cellhasfouroptions: (1) remaininthesamecell,
(2)movetoaneighbor cell, (3) colonizeaneighborcell, or (4) become
extinct. Note that duringcolonizationinoption3,
thepopulationoccupiesthe original cell and a neighboring cell,
whereas inoption2thewholepopulationmovestoanothercell.
TheprobabilitiesofthelastthreeeventsaredenotedbyPmov, Pcol,
andPext, respectively. Itisevident that the probability of a
populationremainingwithout anychangeinitsoriginal cellisequalto1
Pmov Pcol Pext.On the basis of the above probabilities,
theinitialpopulationsmayincreaseanddisperse.Thesimulationrecords
the time steps neededfor atleast one population to enter for the
rst time intoEasternAsia, WesternEurope,
andWesternAsia(asproxiedbythesiteofDmanisiintheRepublicof Georgia).
Thesetarget locationsareshowninFig. 1. In addition, we have
considered three moretarget locations: Boxgrove in England, Java
inFig. 1.Map of hominin dispersal out of Africa indicating the
target locations of Eastern Asia, Western Europe, and Dmanisi area
aswell as thepassagesof Suez(S), Gibraltar(G), Afar (Af),
Hormuz(Ho), andDardanelles(D). Desertsareshowninlight
gray,mountainswithaltitudefrom2,000to4,000
mingray,andmountainshigherthan4,000 minblack.605 P.Nikitas,E.Nikita
/ JournalofHumanEvolution49(2005)602e617Indonesia, andtheentranceof
theMalayPenin-sula.Thelatterwasincludedinordertoestablishhowmanyofthehomininpopulationsarrivingatthe
entrance of this peninsula were likely
toproceedontoJava.ModelsofdispersionInthisstudy, threemodelsof
dispersionhavebeenexamined.InModelA, thetotal
populationsizeremainsstable, inModel Bthepopulationisvariable
dependingonthe probabilities PcolandPext, and in Model Cthe rst two
models
arecombined.ModelAThestabilityofthetotalpopulationisattainedby
choosing PcolZPextZ0. Note that in thelattice approachadopted,
eachpopulationoccu-pies just one cell. Therefore, in model
Athenumber Nof cells withhomininpopulations isconstant andequal
totheinitial population. ThedefaultvaluesofNusedwere1, 10, 50,
and100.At each iteration and for every occupied
cellaneighboringcell or the same cell is
chosenbymeansofrandomnumbers.Inthecasewherethesame cell is chosen,
the population of this cell doesnot move. If a neighboring cell is
chosen withaprobabilityPc, thenthe inequalityPcOrndisexamined,
whererndisarandomnumbeructu-atingbetween0and1. If
thisinequalityisvalid,thepopulationmovestotheneighboringcell andthe
initial cell is emptied provided that theneighboringcell isempty.
Apopulationmayalsomove back to the original cell but at the
nextiteration. For simplicity, the probability of movingback does
not take into account the resource/environmental
limitationswhichimposedtherstmovement. That is, weassumethat
theselimita-tions have nowbeen withdrawn. Moreover, ateach
iteration we check whether any of thepopulations has reached the
target locations(Eastern Asia, Western Europe, Dmanisi, Box-grove,
Java, and the entrance of the MalayPeninsula) for the rst time. The
number ofiterations neededfor anyof theaboveevents tohappenfor
therst timeis stored. Whenall theabove six events have occurred,
the program ends.ModelBIn this model, the default values for
theprobabilities Pmov, Pext, andPcolwere 0.1, 0.02,and0.04,
respectively. Thedefault values of Pextand Pcol are close to those
adopted by Mithen andReed.Thedefault valueof Pmov wasselected
aftermany preliminary tests which showed that thisprobability, as
well as Pext and Pcol, aect only thetotal number of populations and
therefore the timeneededtocompleteonesimulation, whereastheyhave a
small or even a negligible eect on hominindistribution. During each
iteration, we examinewhether a population will move or colonize
orbecome extinct based on Pmov, Pext, and Pcol. In thecase of
movement, the procedure described inmodel Ais followed. The
colonization followsasimilarprocesstothatofthemovement,
butinthiscasetheinitialcellremainsoccupied.Finally,if extinction
occurs, the cell is emptied. At the endof each iteration we check
the number of cellsoccupiedby hominins as well as theirposition.
Asinmodel A, we count the number of iterationsnecessary for the
occupation of all the targetregionsforthersttime.ModelCThis model
is acombinationof the rst twomodels. That is, the total population
size is variablebut within the populations there exists a small
andconstantnumberofthemwithhighmobilitysincethey can move at each
iteration. In order to achievethat, the rst npopulations are
examinedas inmodel A, while the rest followthe processes ofmodel B.
In our study we have used n Z10, a
valueobtainedfromtheresultsofmodelA.Notethat in this study,we have
not consideredchanges in sea level and dierentiations in
homininpopulationsduetodierentadaptationtoclimatevariations
anddietary preferences for twomainreasons: a) to reduce the
computation time, and
b)becausetheresultsofthepresentstudyshowthatsuchdierentiations are
not expectedtosigni-cantly inuence the probability of the
colonizationofacertainarea.Thisissueisfurtherdiscussedintheresultssection.Forthestatistical
analysis of theresults, eachsimulation involved 500 runs with the
sameparametervalues.606 P.Nikitas,E.Nikita /
JournalofHumanEvolution49(2005)602e617ColonizationroutesSincethegeographyofAfricaandEurasiaforthe
time period of 2 Ma is not known in detail andmight have been
variable, we have examinedseveral possibilities concerning
land-bridges andcolonizationroutes. The exit fromAfricamighthave
been conducted through the Suez passage (S),or through the Afar
passage (Af) (i.e., the
crossingfromEastAfricatopresentdayYemenshowninFig. 1), or even
through the strait of Gibraltar
(G),althoughthelatterisratherunlikely(ArribasandPalmquist,1999;Straus,2001).Thearrival
inAsiaprobablyoccurredthroughmoderndayIraq, Iran, or throughthe
strait ofHormuz (Ho). The hominin penetration of Europemay have
taken place from the Dardanelles straits(D), through modern Russia,
or even
throughGibraltar.ForthelandbridgesofAfar,Hormuz,Dardanelles, and
Gibraltar we have used models inwhichthese passages are
assumedtohave beenopen or alternatively closed. Finally, we
havestudied the extreme scenario in which the exit
fromAfricatookplacethroughtheAfarandHormuzpassages assuming that
the Sahara and the Arabiandesert made impossible any other exit
from Africa.We call this the Arabian (Ar) route. Note that
thisisanextremescenariosincethereconstructionofthe northern
hemisphere climate and vegetation inthe Late Pliocene does not
support such anextension for the Sahara and Arabian deserts(Dowsett
et al.,1994;Dennell,2003).Usingtheaboveabbreviations,
asimulationinwhich, say, Suez, Afar, andDardanelles are theonly
openpassages is denotedby SAfD. ArSDindicates hominindispersal
throughthe ArabianroutewithDardanelles and Suez open, and nallySis
usedtoshowthat onlythe Suezpassage isopen. Note that the Suez
passage is openinallsimulations. All
thecolonizationroutesexaminedas well as all the input parameters of
thesimulationaccordingtomodels A, B, andCareshowninTable1.The
output of the simulation was the number ofiterations needed for the
populations to reach eachof the target locations for the rst time.
In addition,thesimulationrecords thetotal number of
pop-ulationswhenhomininsarriveforthersttimeatDmanisi andJava. This
number is constant andequal to the initial number of populations
for modelA, but varies for models B and C. The examinationof this
variationshows that after arather
rapidTable1InputparametersofmodelsA,B,andCParameter Description
Range DefaultvalueModelA ModelB ModelC ModelA ModelB ModelCN
Numberofinitialpopulations 1-100 1-100 1-100 1,10,50,100 20 20n
Numberofpopulationswithhighmobility(inmodelC)e 0 1-100 e 0
10Pc,mProbabilityofapopulationtoexistinmountainsfrom2,000to4,000
m0-1 0-1 0-1 0.5 0.5
0.5Pc,dProbabilityofapopulationtoexistinadesert0-1 0-1 0-1 0.1 0.1
0.1Pc,nProbabilityofapopulationtoexistinthesub-arcticzone0-1 0-1
0-1 0.2 0.2 0.2PcolProbabilityofcolonization 0 0-1 0-1 0 0.04
0.04PmovProbabilityofmovement 1 0-1 0-1 1 0.1
0.1PextProbabilityofextinction 0 0-1 0-1 0 0.02 0.02Route
Thefollowingroutesareconsidered:SD,SAfD,S,SAf,SAfHoD,SAfHo,ArSD,ArS,andSGDYesorno
Yesorno Yesorno YesforSD YesforSD YesforSDGrid A. 16,308cellsB.
7,272cellsAorB AorB AorB A A A607 P.Nikitas,E.Nikita /
JournalofHumanEvolution49(2005)602e617initial increase, the total
population of hominins isgradually stabilized around an average
value,which, dependingontheinputparameter, rangesfrom ca 200 to ca
1000 occupied
cells.CalculationofprobabilitiesInthelatticeapproachadoptedinthis
paper,time is not explicitly taken into account. However,it is
related to the number of steps (iterations)neededfor a certainevent
totake place. Morespecically, time and steps are interrelated
throughthefollowingexpression:YearsZaCb$steps 1where a and b are
constants that can be de-termined by knowing the dates of at least
twoevents. In the present study, we have taken asa starting point
Africa at 2 Ma following theconventional view. Thus, a Z2.
Forthedetermi-nationofb,threecaseshavebeenconsidered:1)Method A:
Dating based on the Dmanisicolonization. We assume, as
didMithenandReed, that the colonization of Dmanisi at1.7 Ma
corresponds to the rst arrival ofhomininsinthisarea.
Underthisassumption,wemakethehistogramof
500runsconcern-ingthearrival atDmanisi
andfromthepeakofthisgraphwecalculatethenumberofstepsrequired for
hominins to colonize this area.This value is substituted in Eq. (1)
tocalculate b, since we have adoptedYears Z1.7 and a Z2. After
having determinedconstant b, the above equation is used
forconvertingthenumberofstepsintoyearsfortherstarrival
atthetargetareasofEurasia.From this data we can
straightforwardlydetermine the number of cases where
thecolonization of Europe has occurred after1 Maandtheoccupancyof
Asiapriorto1.6or1.8 Ma.Bydividingthesenumbersby500,we nd the
corresponding probabilities,P(Eu !1) and P(As O1.6) or P(As
O1.8),that is the probabilityof the
colonizationofWesternEuropeafter1 MaandEasternAsiaprior to 1.6 or
1.8 Ma. The combinedprobabilityPof boththese events
occurringisnowcalculatedfromP1:6ZPEu!1$PAsO1:6 orP1:8ZPEu!1$PAsO1:8
2Eq. (2)isvalidundertheassumptionthatthetwoevents,P(Eu !1)andP(As
O1.6or1.8),areindependent.
Inthepresenttreatmentthisisareasonableassumptionduetotherandommovement
of the various populations, whichhas the result that movement of
populations toEastern Asia has no eect on the movement
ofpopulationstoWesternEurope.2) MethodB:
DatingbasedontheEasternAsiacolonization. Here we assume hominin
arrival inEastern Asia at 1.6 Ma. The procedure is similarto the
above. That is, fromthe histogramconcerning the colonization of
Asia we de-termine the average number of steps, whichintroduced
into Eq. (1) leads to the determina-tion of b.3) Method C: Dating
by maximization. If wechangebwithinacertainrange,
P1.6andP1.8calculatedfromEq. (2)becomeafunctionofb. Inthis
methodthevalueof
bselectedfordatingistheonethatmaximizestheprobabil-ityP1.6orP1.8.Fromthese
three methods, the rst presumesthat the colonization of Dmanisi
took place for therst time at 1.7 Ma. However, there is no
evidencethat this event didnot occur muchearlier. Thesame is true
for the second method, whichadditionallyrelies onarather
controversial datefor the earliest colonization of Eastern
Asia.Finally, the third method clearly estimates
themaximumvalueofP1.6orP1.8.The minimum value of P(Eu !1) andP(As
O1.6 or 1.8), which can be estimated
bythe500runsofoursimulations,is1/500 Z0.002.It is evident that due
to the probabilistic nature ofthe simulations, if the probability
of an eventoccurringis just 0.002, thenthe simulationmayshow that
this event does not happen or it happenswith probabilities 0.002,
0.004, or even higher.Thisistheaccuracyofoursimulation.
Similarly,theminimumvalueofP1.6andP1.8whichwecan608
P.Nikitas,E.Nikita /
JournalofHumanEvolution49(2005)602e617calculateis0.000004providedthatP(Eu
!1)andP(As O1.6or1.8)havebeendetermined.ResultsWerst examinedthe
probabilityof homininarrival in Eastern Asia earlier than in
WesternEurope,P(As !Eu),as seemsto bethe
casefromthecurrentlyavailablearchaeological data. Someof
theresultsareshowninFig. 2andhavebeencalculated directly fromthe
present simulationwithout applying a particular dating procedure.
InFig.2(A),P(As !Eu)iscalculatedfrommodelAandit is plottedas
afunctionof N, whereas inFig. 2(B) P(As !Eu) arising frommodel
Bisshowninterms of the average value of N, CND,because in this
model the total population isvariable. It is seenthat this
probabilitydependsalmost exclusivelyonthedispersal routeandforNR50
it tends to stabilize. As expected, theprobabilityof
AsiahavingbeencolonizedbeforeEurope is higher when the Afar and
Hormuzpassages are both open. In addition, we found thatthis
probability is almost independent of the numberof cells of the
square lattice adopted (see Fig.
2(B))aswellasoftheenvironmentalbarriers,providedthatthesebarriersarenotcompletelyimpassable.Thus,evenifthedesertsandmountainsshowninFig.
1are considered, P(As !Eu) is almost un-aected for Pc values
ranging from 0.1 to 1.WhileP(As !Eu) rangesfrom0.1to0.9, thejoint
probabilities P1.6andP1.8take lowvalues,which for the majority of
the routes are below 0.1,as depicted in Figs. 3 and 4. The values
of the jointprobabilities shown in these Figures have
beencalculated from the method of
maximization0.20.40.60.81.027654310 20 40 60 80 100(A)P(As
