On the Common Ancestors of All Living Humans - TedLab - MIT

30 Pages·2006·0.46 MB·English

On the Common Ancestors of All Living Humans
DouglasL.T.Rohde
MassachusettsInstituteofTechnology
November11,2003
Abstract years ago (Dorit, Akashi, & Gilbert, 1995), a rangethat
wasmorerecentlynarrowedto35,000(cid:150)89,000yearsago
Questions concerning the common ancestors of all (Keetal.,2001).
present-dayhumanshavereceivedconsiderableattention
Nevertheless, an individual’s strictly maternal and
oflateinboththescienti(cid:2)candlaycommunities. Princi-
strictlypaternallinesarejusttwoofavastnumberofpos-
pally, this attention has focusedon ‘MitochondrialEve,’
siblepathsbackthroughhisorherancestors. Whatifwe
de(cid:2)nedtobethewomanwholiesatthecon(cid:3)uenceofour
adopt a more common-sense notion of ancestry that in-
maternalancestrylines,andwhoisbelievedtohavelived
cludesancestorsreachablealonganypathofsuccession,
100,000(cid:150)200,000 years ago. More recent attention has
usingbothmothersandfathers? It seems likelythat our
beengiventoourcommonpaternalancestor,‘YChromo-
mostrecentcommonancestor(MRCA)underthisbroader
some Adam,’ who may have lived 35,000(cid:150)89,000years
de(cid:2)nitionwillbemuchmorerecentthaneitherMitochon-
ago. However,ifweconsidernotjustourall-femaleand
drial Eve or Y Chromosome Adam. Unfortunately, the
all-male lines, but our ancestors along all parental lines,
age of our MRCA cannot as easily be estimated on the
it turns out that everyoneon earth may share a common
basis of genetic information because the relevant genes
ancestorwhoisremarkablyrecent.
arenotpassedfromparentto childwith onlyoccasional
This studyintroducesa large-scale, detailedcomputer
mutations but are, rather, the product of recombination.
model of recent human history which suggests that the
Asa resultofrecombination,agivengenemaynotpass
commonancestorofeveryonealivetodayverylikelylived
from parent to child. In fact, an individual’s DNA may
between 2,000 and 5,000 years ago. Furthermore, the
retain none of the genes speci(cid:2)c to a particular ancestor
model indicates that nearly everyone living a few thou-
wholivedmanygenerationsinthepast. Theseadditional
sand years prior to that time is either the ancestor of no
complications make accurately dating the MRCA or re-
oneorofalllivinghumans.
constructingotherdetailsofpopulationhistoryontheba-
sisofourgenesextremelydif(cid:2)cult,ifnotimpossible(Hey
1 Introduction &Machado,2003).
However, alternative methods may be able to answer
Advances in genetics have sparked interest in our com- thisquestion. Someresearchershaveproducedestimates
monancestors,theindividualsfromwhichallpresent-day of the age of our MRCA by means of the theoretical
humans descend. Initial interest focused on the topic of analysis of mathematical models. Building on work by
‘Mitochondrial Eve,’ who is de(cid:2)ned to be the most re- Ka¤mmerle(1991)andMo¤hle(1994),Chang(1999)ana-
centfemaleancestorfromwhomall individualsdescend lyzedamodelthatassumesa (cid:2)xed-sizepopulation,with
alongstrictlymaternallines(Cann,Stoneking,&Wilson, discrete and non-overlapping generations, and random
1987; Vigilant, Stoneking,Harpending,Hawkes, & Wil- mating. Thatis,eachchildistheproductoftwoparents,
son, 1991). An approximatedate forMitochondrialEve randomlyselectedfromallmembersofthepreviousgen-
of100,000to200,000yearsagohasbeenestimatedbased eration. Changshowedthat,inthismodel,themixingof
onthesuccessivemutationsinmitochondrialDNA,which genesoccursquiterapidly. Infact,thenumberofgener-
are passed downfrommotherto child. A similar analy- ationsbacktotheMRCAisexpectedtobeaboutlog of
2
siscanbeperformedonthestrictlypaternallinesofsuc- thepopulationsize.Withapopulationof6billionpeople,
cession,usingtheYchromosome,whichispasseddown this model predicts that the MRCA is likely to occur in
fromfathertoson, todeterminetheapproximatedateof justover32generations,or800(cid:150)975years. Thissuggests
‘Y Chromosome Adam.’ This date was originally esti- thatourall-pathsMRCAmaybeexceptionallyrecent.
mated very loosely to fall between 27,000 and 270,000
But Chang was well aware of the limitations of the
(cid:3)Workinprogress.Donotcite. simple model he analyzed. (cid:147)What are the signi(cid:2)cance
ROHDE COMMONANCESTORSOF ALLLIVING HUMANS
of these results? An applicationto the worldpopulation Chang’s,aresomevariantofaWright-Fishermodel,with
of humans would be an obvious misuse...An important discretegenerationsandparentsselectedatrandomfrom
sourceof inapplicabilityof the modelto this situation is the preceding generation (Nordborg, 2001). Because
theobviousnon-randomnatureofmatinginthehistoryof computer simulations are tested empirically rather than
mankind.(cid:148) (pg. 1005) There are many factors that limit throughtheoreticalanalysis, they are notsubjectto such
therandomnessofhumanmating.Firstofall,clearly,are constraints.
sex differences, but Chang did address this, noting that However, there are practical limits to the complexity
addingdistinctsexestothemodelwouldnotcauseasub- ofacomputersimulation. Oneisthematterofcomputa-
stantial change in the estimate. Another factor is mar- tionalef(cid:2)ciency.Amodelcannotbesocomplexthatrun-
riage. Onceacouplehasonechild,theyarelikelytore- ningitrequiresanunreasonableamountoftimeorspace.
maintogetherastheyproducemorechildren. Moreover, A more signi(cid:2)cant limitation, from a scienti(cid:2)c perspec-
broadersociologicalandgeographicfactorsmayhavestill tive,mustbeplacedonthenumberoffreeparametersin
moreprofoundeffects. Inshort,althoughwearebecom- the model. Ideally, for the results of a model to be reli-
ing increasingly panmictic, humans groups have tended able, any free parameters should be constrained by his-
towards a high rate of endogamy, (cid:2)nding mates almost toricaldata,suchasstatisticsonactualbirthormigration
exclusively within the local population and social class, rates. However,muchoftherelevantdataforthecurrent
onlyoccasionallytranscendingbarriersofgeography,lan- modelsconcerneventsoccurringthousandsofyearsago
guage,race,andculture. and cannot be obtained with any accuracy. In this case,
It seems likely that these restrictions on the random- the parameters must be varied within the range of plau-
nessofhumanmatingmaydramaticallydecreasetherate siblevaluestoobtainboundsonthemodel’spredictions.
ofancestralmixinginthemodel.Asaresult,thetruedate Amodelwithtoomanyfreeparameters, especiallyones
oftheMRCAcouldbethousandsortensofthousandsof unconstrainedbyempiricaldata,willhavereducedpower
years ago, rather than just hundreds. Thus, an obvious and will be dif(cid:2)cult to study. Therefore, a good model
nextstepistotestthispossibilitybyexpandingthemodel must be complexenoughto includerelevantfactors, but
toincludesomeoralloftheseconstraints.Unfortunately, notoverlyburdenedbyirrelevantones.
conducting a theoretical analysis of a more complicated
Thisstudyexploresaprogressionofthreemodels.The
mathematicalmodelwouldbeverydif(cid:2)cult. Analterna-
(cid:2)rstextendsChang’sresultstoaworldconsistingof(cid:2)ve
tiveapproachistoimplementacomputersimulation.The
more or less panmictic islands, or continents, with only
principaladvantageofacomputersimulationisthatitcan
occasionalmigrantsbetweenanypairofcontinents. The
bearbitrarilycomplex. However,evengiventhespeedof
secondmodel,discussedinSection3arrangestheislands
today’scomputer,ef(cid:2)cientlysimulatingtheancestralhis-
in a graph that roughly re(cid:3)ects the topology of the ma-
toryofapopulationwhosesizeisevenclosetothescale
jor worldcontinents. The(cid:2)nal model,discussed in Sec-
of humanity is non-trivial. Furthermore, because a non-
tion4, is amoredetailedsimulationoftheactualworld,
randommodelwillnecessarilyinvolvenumerousparam-
with migration routes and dates based on historical data
eters that cannot be adequately constrained by available
orprehistoricestimates.
data,thesimulationmusttypicallyberunmanytimes to
exploretheconsequencesofvariousparametersettings.
Thisstudyinvolvestheimplementationandanalysisof
severallarge-scalecomputermodelsofrecenthumanhis-
2 Model A: Fully-connected
tory.Themodelssimulateindividualhumanlives,includ-
ing life span, birth rate, choice of mates, and migration, continents
andthedatatheyproduceisanalyzedtoobtainmoreac-
curate estimates of the date of our most recent common
The(cid:2)rstmodel,A,isquiteabstractbutincorporatessev-
ancestor. Given what seem to be reasonable parameter
eral levelsof detail beyondthose foundin most Wright-
choices,the(cid:2)nal,mostdetailedmodelpresentedherepre-
Fisher models. Themodeltypicallystarts between5000
dictsthatourmostrecentcommonancestorprobablylived
and20000BCandrunstothepresentday,whichistaken
between2000and5000yearsagoandthatnearlyevery-
to be the year 2000 AD. As the model runs, it simu-
onealivepriortoafewthousandyearsbeforethatarethe
lates important details in the lives of individual people,
ancestorsofeithernooneorofeveryonealivetoday.
knownassims, includingtheirlifespans,possiblemigra-
tions, choice of mate, and production of offspring. As
the model runs, it recordsthis informationin a series of
1.1 Modelinghuman genealogy
largecomputer(cid:2)les.Asecondprogram,discussedinSec-
Mathematicalmodelsofhumangenealogymustbequite tion2.2,tracesancestrallinesthroughthisdatato(cid:2)ndthe
simple if their analysis is to be possible. Most, like commonancestors.
2
ROHDE COMMONANCESTORSOF ALLLIVING HUMANS
2.1 Detailsofthe model contiguous, with no substantial geographical barrier to
migration, so they will be considereda single continent,
2.1.1 Lifespan
along with Africa, North America, and South America.
Thepresentmodelsdonotassumediscrete,uniformgen- Indonesia, Australia, and Oceania are, taken together,
erations. Each sim is born in a certain year and has a somewhatmoredif(cid:2)culttomodel,asthereisclearlysub-
particular life span. The maximum age of any sim was stantialinternalstructure.Forthepurposesofthe(cid:2)rsttwo
setto100,asitseemshighlyunlikelythatanyonewould models, they will be considered a single continent, but
live, let alone father children, beyondthat age. The age willbedealtwithmoreappropriatelyinthethirdmodel.
ofsexualmaturitywastakentobe16yearsforbothmen The models’continentsare dividedinto countries, ar-
andwomen.Anyonewhowouldhavediedbeforethatage ranged in a grid. These re(cid:3)ect major tribal, ethnic, or
couldnothaveproducedoffspringandisthusnotafactor languagegroups, with both geographicand cultural bar-
forthepurposesofthisstudy.Therefore,onlythelivesof rierstointermarriage. Countriesare,inturn,dividedinto
thosedestinedtoatleastreachadulthoodweresimulated. towns. These do not necessarily represent towns per se,
Asaresult,thepopulationsizesdiscussedthroughoutthis buttherelevantsocialunitfromwithinwhichmostpeo-
paperareeffectivelysomewhatlargerthanstatedbecause ple(cid:2)ndmates. Thus,atownmayactuallyre(cid:3)ectaclan,
theydonotincludeanychildren. a rural county, or even a particular social class within a
Otherwise,theprobabilitythatanindividualdiesatage largergroup.Thetownswithineachcountryareassumed
s,conditionalonnothavingdiedbeforeages,isassumed to bein relativelyfrequentcontact with one anotherand
to follow a discrete Gompertz-Makehamform (Pletcher, arenotinanyparticulargeographicarrangement.
1999): Notallhumanscon(cid:2)nethemselvestoasinglelocation
throughouttheirlivesandacriticalfactorinthemodelis
p(s)=(cid:11)+(1(cid:0)(cid:11))e(s(cid:0)100)=(cid:12)
therateatwhichpeoplemigratetodifferentplacesinthe
world. Although it seems likely that many people, and
Inthisequation,(cid:12)isthedeathrate.Ahigherdeathrate
perhapsthe vast majority historically, live out theirlives
resultsinshorterlifespansonaverage,althoughtheresult
closetowheretheywereborn,variousformsofmigration
isnotlinear. The(cid:11)parameteristheaccidentrate,which
leadtothegradualspreadofancestrallineagesoverlong
can beadjustedto re(cid:3)ect the probabilitythat an individ-
distances. When men and women fromdifferentgroups
ualofanyagediesofunnaturalcauses. Withanaccident
marry,oneofthem,oftenthewifebutsometimesthehus-
rate of 0.01 and a death rate of 10.5, this formula quite
band, moves to the other’s community. Merchants, sol-
closely models the life span data for the U.S. between
diers,andbureaucrats,whoaretypicallymale,sometimes
1900 and 1930 (U.S. National Of(cid:2)ce of Vital Statistics,
travelwidely,potentiallyfatheringchildrenfarfromtheir
1956). To accountfor historically shorterlife spans due
placeofbirth. And,occasionally,largegroupsofpeople
to poor nutrition, medicine, and so forth, the death rate,
haveconqueredorcolonizednewareas.
(cid:12),wasraisedto12.5forthepurposesofthemodel. This
In terms of realism, it would certainly be desirable to
producesanaveragelifespanof51.8forthosewhoreach
distinguishbetweentheseandotherspeci(cid:2)ctypesofmi-
maturity.
grationinthemodel. However,doingsowouldintroduce
Thepercentageofmalesbornintothepopulationwas
manynew parameters, for whichwe are unlikelyto (cid:2)nd
set at 50%. Itis truethatthe actualpercentageofmales
suf(cid:2)cientdata.Therefore,themodelusesasimpli(cid:2)edmi-
andfemalesreachingadulthoodmaydiffersomewhatdue
grationsystem,inwhicheachpersoncanmoveonlyonce
toinfanticidecoupledwiththefact thata slightlyhigher
inhisorherlife. Eachsim is borninthetownin which
percentageofnewbornsaremalethanfemale(Davis,Got-
his or her parents, or at least mother, lives, but then has
tlieb, & Stampnitzky,1998). But this probablydoes not
a chance to migrate to a different continent, country, or
havemuchbearingontheresultsofthemodel.Andwhile
townpriortoadulthood.Henceforth,thatpersoncanpro-
it is true that womentendto live longer,the life spanof
ducechildrenonlywithotherinhabitantsofhisorhernew
women past child-bearingage is also not relevant to the
town,provideditcontainspotentialmates.
outcomeofthemodel. Therefore,forsimplicity,thelife
spansofmalesandfemalesweregeneratedusingthesame As is the case in human mating patterns (Fix, 1979),
distribution. the rate of exogamy decreases substantially with larger
group size in the models. Adams and Kasakoff (1976)
foundthat,acrossavarietyofhumansocieties,therewas
2.1.2 Migration
a recognizable threshold in group size at around a 20%
Themodelsareorganizedintothreestructurallevels:con- exogamyrate,althoughthesizesofthesegroupsdiffered
tinents, countries, and towns. The continents represent asafunctionofpopulationdensity. This(cid:147)natural(cid:148)group
physically separated land masses that are likely to have size is taken here to be that of the town. The Change-
very low rates of inter-migration. Europe and Asia are TownProbparametercontrolsthepercentageofsimswho
3
ROHDE COMMONANCESTORSOF ALLLIVING HUMANS
parentalage. Inmost ofthesimulations,the majorityof
thesimsusingaportarebornlocally,initssourcecountry,
whileaproportionofportusers,governedbytheNonLo-
calPortProbparameter,aredrawnfromrandomcountries
withinthecontinent,includingthesourcecountry. These
long-distancemigrantsmight,forexample,bemerchants.
ANonLocalPortProbof0meansthatallmigrantsareborn
locally. Avalueof100%confersnospecialadvantageto
thesourcecountry.
Migrants using a port arrive in a random town within
thedestinationcountry.However,theythenhavetheusual
small chance of migrating to a new country within that
continent. A sim can use at most one port in his or her
lifetime.
Model A, depicted in Figure 1, consists of (cid:2)ve conti-
nentsarrangedinafully-connectedgraph. The(cid:2)vecon-
tinentsareeachcomposedof60countries,with80towns
per country,for a total of 24,000towns. Each continent
is connected to every other one, with ports lying at the
corners. Thisisnotmeanttobeanaccuratedepictionof
the world by any means, but is an extensionof the pan-
Figure1: ModelA: Afullyconnectedstructuredmodel. mictic modeltoasimpleformofstructuredmodelsimi-
Eachcontinentconsistsof60countrieswith80townsper lartothosethathavebeenstudiedpreviously(Nordborg,
country. 2001). Our primary goal in studyingsuch a model is to
gain a better understanding of its sensitivity to the vari-
ousparametersandtoprovideabaselineagainstwhichto
leave the townof their birthfor anothertown within the comparemodelswithmorerealisticgeography.
samecountry. Inthecurrentmodels it rangesfrom20%
downto1%.
2.1.3 Mating
Thereisamuchlowerchancethatasimwillleavehis
orherhomecountryforanothercountryonthesamecon- Alongwithmigration,therateofancestralmixingisalso
tinent. The probability that this occurs is governed in dependenton how mates are chosen and on the age dis-
the model by the ChangeCountryProbparameter, which tribution of the parents when children are born. In this
ranges from 0.1% to 0.001%(1 in 100,000). The coun- respect,themodelwasimplementedfromtheperspective
tries within a continent are arrangedin a gridand local- ofthemother. Theprogram(cid:2)rst determinestheyearsin
ityalsoplaysaroleininter-countrymigration. InModel whichthemotherwillgivebirth,andthenafatherischo-
A,showninFigure1,allcontinentscontain60countries senforeach child. The assumptionis madethatwomen
in a 6 by 10 rectangle. In the (cid:2)rst two models, inter- givebirthbetweentheagesof16and40,inclusive,with
countrymigrationinvolvesatwo-tieredsystem. Thema- anequalprobabilityofproducingachildineachofthese
jorityof the sims leavinga countrytravelto a neighbor- years. Of course,somewomenmay producemanychil-
ingcountry(includingdiagonalneighbors). Theremain- drenandotherswillproducenone,andsomemaydiebe-
der travel to a randomlychosen countrywithin the con- foretheageof40. Aftertakingthislatterfactorintoac-
tinent, includingtheneighboringcountries. Thefraction count,wecancontrolpopulationgrowthbyadjustingthe
ofsimswhochooserandomlyisgovernedbytheNonLo- average number of children (who reach adulthood) per
calCountryProb parameter. A value of 0 means that all woman. A value of 2.0 childrenper woman results in a
inter-countrytravel is to neighboringcountries. A value stablepopulationsize.
of100%meansthattraveltoallcountriesinthecontinent Once it has been determined that a woman will give
isequallylikely. birth in a certain year, the father is chosen. If possible,
Intercontinental migration takes place through ports. the fatheris always selected fromthe town in which the
Portsleadfromasourcecountryinonecontinenttoades- motherlives.Itsometimeshappens,especiallyearlyinthe
tinationcountryinanother.Therateofmigrationthrough simulationwhenpopulationsareloworwhenanewarea
aportcanberegulatedandmonitored. Itisexpressedin is(cid:2)rst colonized,thattherearenosuitable fathersliving
terms of migrants per generation, where a generation is inthesametownas awomanwho is tohave a child. In
taken to be 30 years, as that is the approximateaverage thiscase,fathersaresoughtintheothertownswithinthe
4
ROHDE COMMONANCESTORSOF ALLLIVING HUMANS
35%
Table1:Worldpopulationestimates,inmillions.
Women
Men (Models A and B)
30% Men (Model C)
Year Population
Women25% 1250000000BBCC 32
Men or 20% 10000BC 4
Percentage of 1105%% 521000000000BBBCCC 25505
5%
0%
0 2 4 6 8 10 12 14 allofthoselinesdieout,whichrarelyoccursbeyondthe
Number of Children
(cid:2)rst few generations. In the model empirically, we (cid:2)nd
that33.31%offemalesand45.42%ofmalesactuallybe-
Figure 2: Distributions of the number of children per
come extinct. These values are just slightly lower than
woman or man. Only childrenwho reach adulthoodare
we would predict based on the distributionsin Figure 2.
counted. Model C producesa slightlydifferentdistribu-
Thus, females have the reproductive advantage in terms
tionforthemen.
of the likelihood their genes will survive for all future
generations. In many cultures, sons are much preferred
samecountry. over daughters. However, unless one’s sons are power-
Thefatherofawoman’s(cid:2)rstchildischosenatrandom fulenoughtoprocuremultiplewives,it is actuallymore
fromthemenwhoareatleastasoldasthewoman. The advantageous,forthepurposeofcreatinganenduringlin-
prohibition against younger husbands was primarily for eage,toproducedaughters.
computationalreasons,butitseemstobeafairlyreason-
able, if not entirelyvalid, assumption. Thereis an addi-
2.1.4 PopulationGrowth
tionalbiassuchthatmenaretwiceaslikelytobechosen
iftheyarenotalreadymarried,inthesensethattheyhave Because life span was not manipulated, the growth rate
alreadyproducedachildwithanotherwoman. Afterthe of the population was controlled by adjusting the aver-
(cid:2)rst child, there is an 80% chance that the father of the age number of children per woman. As Chang’s results
previouschildwillalsofatherthenextone,thussimulat- suggest, the size of the populationmay be an important
ing marriage. There is a fundamental asymmetry in the determinerofthedateoftheMRCA.Given(cid:2)xedsizes,a
sexes,inthatawomancanonlybe(cid:147)married(cid:148)tooneman, largerpopulationwill tend to have a less recent MRCA.
althoughamancouldbemarriedtomorethanonewife,or But a larger population will also tend to have a greater
atleastfatheringchildrenbymorethanonewoman. But number of migrants, thus potentially leading to a more
there is a bias towards monogamousrelationships. Also recentMRCA.Theneteffectofpopulationsizeis,there-
notethatwomencannotbearchildrenpasttheageof40, fore,dif(cid:2)culttopredict,butwillbetestedempirically.
whilemencanfatherchildrenthroughouttheiradultlives. Ideally, the model should be capable of simulating a
Figure2showsthedistributionofchildrenperwoman full-sizeworldpopulation. However,duetotheavailable
andmaninthemodels.Thedistributionforwomenises- disk space for recording the necessary data, the models
sentially binomial, with 19% producingno children and werelimitedtoamaximumpopulationof60millionsims
only 2.8% producingmore than 5 children. The middle atanyonetime. Anaturalpopulationgrowthwas simu-
barshowsthedistributionformeninthe(cid:2)rsttwomodels. lated up to a point and then the population was capped.
It has greater variance than that for the women. Nearly Table1showstheworldwidepopulationsusedinthe(cid:2)rst
36% ofmen produceno adultchildren, while 8.6%pro- two models. These data are based on the estimates of
duce more than 5 children. Thus, there is a higher per- McEvedyandJones (1978), with the most ancient num-
centageof men thanwomen that produceno childrenor bers extrapolated. Population size was regulated by ad-
many children, but relatively fewer men who produce a justingthebirthratetoachievegeometricgrowthbetween
moderatenumberofchildren. thegiventargets. InmostofthemodelAandB simula-
Forlackofabetterterm,wewillrefertosimswhohave tions,themaximumpopulationwas25million,reachedin
nolivingdescendantsasextinct.Inotherwords,theseare theyear2000B.C,andthenmaintainedthereafter. Other
sims whose lineage has died out. Clearly, anyone who simulationscontinuedtoamaximumlevelof50million.
producesnochildrenisextinctupontheirdeath.Buteven The migration rates between towns and countries are
thosewhoproducesomechildrenmaybecomeextinctif expressedasapercentageofbirths.Therefore,asthepop-
5
ROHDE COMMONANCESTORSOF ALLLIVING HUMANS
ulationincreases, the total numberofmigrantsincreases ingthedescendantswouldbefairlysimple,exceptthatit
proportionally. In Models A andB, the rate of theports requiresmemoryproportionaltothesquareofthenumber
was(cid:2)xedtoachieveaparticularnumberofmigrantsper of living sims. With a maximum population of 50 mil-
generation once the population had reached maximum lion, this would involve the computation and storage of
size. However,priorto that point, proportionatelyfewer over300terabytesofinformation.
migrantswouldbeusingtheports. Therefore, (cid:2)nding the common ancestors is not
tractable using a straightforward approach. However, a
methodwas developedtozeroin on thecommonances-
2.1.5 Initialization
tors using an initial approximation followed by a series
There is one remaining aspect of the model to be de- of re(cid:2)nements. This process begins by tracking the an-
scribed, which is the method of initialization. Although cestrynotofalllivingsims,butofasmall,randomlyse-
somesimulationswerestartedintheyear20000BC,oth- lected subset of them. Dependingon the availablecom-
ers werestartedas recentlyas 5000BC ifa morerecent putermemory,therearetypicallybetween192and512of
start date would not interfere with the results. In order theseindividuals,whoareknownastracers. Byworking
to get things going, we need some initial sims. A sim- backwardsthroughtherecords,theancestryofthesetrac-
ple approachmight be to create all of the initial sims in ers is determined. This is done by computing,for every
thesameyear.However,inthatcase,theirchildrenwould othersim,abitvectorinwhichtheithbitisturnedonif
formababyboomanditwouldtakesometimefortheage thatsimisanancestoroftheithtracer.Asidefromthefact
distributionwithinthepopulationtostabilize.Unlessthat thattheithtracerautomaticallyhastheithbitturnedon,
stableagedistributionisknowninadvance,therewillal- aparent’sbitvectorwillbethebit-wisedisjunctionofhis
waysbesomeinstabilityintroducedbythecreationofthe or her children’s vectors. These bit vectors still present
initialpeople. a heavy memory burden, but can be handled more ef(cid:2)-
Therefore,thesimulationactuallybegins100yearsbe- cientlybystoringonlytheuniquevectors.
fore the desired start date. An initial set of sims is gen- Ifa sim is notan ancestorof everyoneofthe tracers,
erated,eachinarandomtownandeachbornatarandom thatsimcouldnotpossiblybea commonancestor(CA).
timewithina40-yearwindow. Themodelisthenrunas However,ifasimisacommonancestorofallofthetrac-
usual, with the initial sims startingto produceoffspring. ers,thereisahighprobabilitythatthesimisanancestor
Althoughthepopulationdoesnothaveanaturalagepro- ofalargeproportionofthelivingsims.Suchancestorsare
(cid:2)le initially,as therearenooldpeople,itquicklysettles referredtoaspotentialcommonancestors(PCAs).Unfor-
intoanear-normaldistributionwithinthe(cid:2)rst100years. tunately,itisgenerallythecasethatthemostrecentPCAs
Thepopulationwillroughlydoubleduringthese(cid:2)rst100 that are found in this (cid:2)rst backward phase are not actu-
yearsasfewerpeopledieofoldagethanareborn. Thus, ally true CAs. Therefore, this superset of the CAs must
thesizeoftheinitialpopulationisadjustedtoachievethe bere(cid:2)ned.
desiredlevelattheendofthe100-yearperiod. The next step is to start with a set of the most re-
cent PCAs and trace their lineage forwardthroughtime.
Thisisdoneinmuchthesamewaythatdescendancywas
2.2 Findingcommonancestors
traced in the backwardphase(cid:151)a sim’s ancestors are the
A simulation with a maximum population of 50 million disjunctionof hisorherparents’ancestors. Inthis case,
simswillinvolveatotalofapproximately1.2billionsims weeventuallydeterminewhichofthe mostrecentPCAs
overitscourse. Asthemodelruns,itgenerates(cid:2)lescon- is an ancestor of each of the living sims. If one of the
tainingthevitalstatisticsofeachsim,includinghisorher PCAs was an ancestor of all of the living sims, then we
parents,sex,birthanddeathyears,andplaceofbirth,typ- areguaranteedtohavefoundthetrueMRCA.Otherwise,
icallytotalingabout60gigabytesofcompresseddataper anewsetoftracersischosenandasecondbackwardpass
trial. Althoughrunningthe simulationis relativelyeasy, isperformedtore(cid:2)nethesetofPCAs.
analyzingthis genealogicaldata to identify the common Selecting the new set of tracers randomly would help
ancestorspresentsasigni(cid:2)cantcomputationalproblem. a little bit, but not much. A more effective approach is
Let us refer to all of the sims alive in the year 2000, totryto(cid:2)ndthesimswhoaredif(cid:2)culttoreach,meaning
when the simulations end, as living sims. A true com- that they descend from the fewest number of the PCAs.
monancestor(CA)is someonewhois anancestorofall Wealsoneedto(cid:2)ndadiversesetoftracers. Iftheyareall
livingsims. Astraightforwardsearchforcommonances- dif(cid:2)culttoreachbecausetheyliveinthesameplace, the
torswouldstartwiththelivingsimsandworkbackwards useofmorethanoneas atracer wouldberedundant. In
intime,trackingforeveryothersim,whichoftheliving ordertosatisfy these constraints,the tracersare selected
sims are his or her descendants. These descendants are inorder,withthenexttracerchosenbeingthelivingsim
theunionofalldescendantsofhisorherchildren.Track- withthehighestscore,de(cid:2)nedasfollows:
6
ROHDE COMMONANCESTORSOF ALLLIVING HUMANS
consistent,withtheMRCAandACAdateshavingastan-
darddeviationlessthan10%ofthemean,andoftenunder
scorei = 2(cid:0) xp;i+ t2Txp;t 2%. ThevarianceislargerfortheACApointandforthe
pX2P (cid:0) P (cid:1) simulationswithearlierdates.
The(cid:2)rst simulation,referredtoas A1, usedfairlylib-
Inthisequation,iisthesimbeingconsideredasapos-
eral parameters, as shown in the top row of Figure 3.
sibletracer.P isthesetofPCAswhosedescendantswere
Themaximumpopulationwas25million,reachedinthe
tracked.Theindicatorvariablex is1ifsimiisnotade-
p;i
year4000BP.TheChangeTownProbwas20%,meaning
scendantofPCAp,and0otherwise.T isthesetoftracers
that80%ofthe sims marrywithin theirbirth town. The
thathavebeenselectedthusfar. Thismethodessentially
ChangeCountryProbwassetto0.1%,soabout1in1000
balancesthenumberofnewtracersthatarenotdescended
simsleavetheirhomecountry,whichmayseemsomewhat
fromeachofthePCAs,thusincreasingthediversityofthe
high. Buttoputthisinperspective,withapopulationof
newtracers.
25 million, there are about 48,000 people born in each
Oncethesetracershavebeenchosen,theirancestorsare
countryper generation. So, on average, a ChangeCoun-
foundasinthe(cid:2)rststep.Inthiscase,simsareonlyidenti-
tryProbof0.1%willresultin48peopleleavingacountry
(cid:2)edasPCAsiftheyareancestorsofallofthenewtracers
every30years,whichcertainlydoesnotseemexcessive.
andalloftheoriginaltracers. Forthispurpose,theprior
Moreliberalisthefactthat,insimulationA1,thereare
PCA-statusofeverysimisstoredusingacompressedrun-
no locality constraints on inter-country migration or the
length encoding. The most recent PCAs are once again
useofports.Migrantshaveanequalchanceoftravelingto
selectedandtheirlineagestracedforwardthroughtime.It
anycountrywithinthecontinentandcanuseaportfrom
isusuallythecasethatoneofthesenewPCAsisactually
anywherewithinthecontinent.ThePortRatewassetto10
aCA, whichmeanswe havefoundthe trueMRCA. Oc-
migrantspergeneration,ineachdirection,whichisabout
casionally,anadditionalsetofdif(cid:2)culttracersisrequired,
1migranteverythreeyears.
withonemorebackwardandforwardphase.
Working backwards in time from the date of the ThebarsontherighthalfofFigure3depictthecom-
MRCA,theproportionofCAsinthepopulationincreases mon ancestry timelines. The dates are in years before
graduallyuntil,eventually,everyoneiseitheraCAofall present,withthepresentlocatedontheright.Inthewhite
ofthelivingsimsoristheancestorofnoneofthem,and region,therearenotyetanycommonancestors. Moving
isthereforeextinct.Thus,apointwillbereachedatwhich backwardsintime,theMRCAisfoundattheborderbe-
100% of the non-extinct sims are CAs. This will be re- tweenthewhiteandgraybars,in1720BPinthiscase.In
ferred to as the all common ancestors, or ACA, point. thegrayregionthereisanincreasingnumberofcommon
Although this successive re(cid:2)nement approach does (cid:2)nd ancestorsuntilwereachtheACApoint,at2880BP.Inthe
thetrueMRCA,itdoesnotnecessarily(cid:2)ndthetrueACA blackregion,allofthesimsareeitherextinctorcommon
point,onlythepointatwhicheveryoneisapotentialCA. ancestorsofthelivingsims. Thus,inthiscase,thereisa
However, the ACA point that appears in the same back- fairlyrapidtransitionbetweentheappearanceofthe(cid:2)rst
wardphasethattheMRCAisfoundisnearlyalwaysthe CAandthepointatwhicheveryonealivetodaysharesthe
correctone,orquiteclosetoit. Thiscanbeveri(cid:2)edwith samesetofancestors.
additional re(cid:2)nement steps, which generally lead to no TheactualrateofthistransitionforoneoftheA1sim-
furtherchange. ulations is shown in the red line in Figure 4. The small
redmarkeratthebottomrightofthe(cid:2)guredenoteswhere
theMRCAoccurred,at1800BP.Fromthatpointon,the
2.3 Results
percentageofCAsinthepopulationgrowsslowlyat(cid:2)rst,
A numberof simulations were conductedwith Model A reaching1%in1940BP,andthenveryrapidly,reaching
undervariousparametersettings. Ofprincipalinterestis 50%in2160BPand99%in2400BP.Thenthereisarel-
the date of appearance, working backwards, of the most ativelylongperiodduringwhichmost,butnotall,ofthe
recent common ancestor (MRCA date) and the date at simsareeitherCAsorextinct. Ittakesanother570years
which all of the non-extinct sims are common ancestors toreachthetrueACApoint,denotedbytheredmarkerat
(ACAdate).Thesedateswillbemeasuredinyearsbefore thetopofthe(cid:2)gure.
present (BP), wherethe present is takento be2000AD. It is likely that the notion of a relatively recent ACA
WhenwerefertotheMRCAtime,itisthelengthoftime pointmayleadtosomeconfusion.Ifweconsideronlyan-
betweenthepresentandwhentheMRCAwaslastliving. cestorswholivedpriortotheACApoint,aJapaneseanda
Therefore, a longer MRCA time means that the MRCA Norwegiantodaysharetheexactsamesetofancestors.At
livedlessrecently. (cid:2)rst glance this seems patently ridiculous. Certainly the
Foreachsimulation,atleastthreetrialswereperformed Japanese and Norwegian have quite different genotypes
andtheresultsaveraged. Ingeneral,thetrialswerequite duetoverydifferentancestry. Theconfusingfactisthat
7
ROHDE COMMONANCESTORSOF ALLLIVING HUMANS
b
Simulation Max Population (mil)ChangeTownProbChangeCountryProb NonLocalCountryProPortRate NonLocalPortProb All CommSoomn eAC CnocmoNemmsotmoo Crnoso nAm Anmcnecosentsr tAyo nrTsciemsetolirnse
A1) 25 20% 0.1% 100% 10 100%
A1b) 12.5 20% 0.1% 100% 10 100%
A1c) 50 20% 0.1% 100% 10 100%
A2) 25 20% 0.1% 100% 10 5%
A3) 25 20% 0.1% 100% 1 100%
A4) 25 20% 0.1% 5% 10 100%
A5) 25 2% 0.1% 100% 10 100%
A6) 25 20% 0.01% 100% 10 100%
A7) 25 2% 0.01% 5% 1 5%
A8) 25 2% 0.01% 5% 1 100%
A9) 25 2% 0.01% 5% 10 5%
A10) 25 2% 0.01% 100% 1 5%
A11) 25 20% 0.01% 5% 1 5%
A12) 25 2% 0.1% 5% 1 5%
12K 10K 8K 6K 4K 2K 0
Years Before Present
Figure 3: Results of the Model A simulations with various parameter settings. The timelines are in years before
present,withthepresentlocatedontheright.Inthewhiteregiontherearenotyetanycommonancestors.Theborder
betweenthewhiteandgrayregionsistheMRCApoint,whentheMRCAdied.Theborderbetweenthegrayandblack
regionsistheACApoint.
100%
s
r
o
t
es 80%
c
n
A
n
o 60%
m
m
o
C
f 40%
o
e
g Simulation A1
a
nt Simulation B7
e 20%
c Simulation C1
r
e
P
0%
18000 16000 14000 12000 10000 8000 6000 4000 2000 0
Years Before Present
Figure 4: Percentage of non-extinct sims who are commonancestors of everyoneliving in the year 2000for three
representativetrials. Theverticalmarkersshowthedatesatwhichthecurvesreach0%and100%.
8
ROHDE COMMONANCESTORSOF ALLLIVING HUMANS
bothofthesestatementsaretrue. AlthoughtheJapanese
and Norwegian have the same set of ancient ancestors,
theydidnotreceiveanequalhereditarycontributionfrom
eachofthoseancestors. TheJapaneseowesasmallpro-
portionofhisgeneticmakeuptopeoplelivinginnorthern
EtouproepoeplseevlievrianlgthionuasnanddayroeuarnsdaJgaop,aann,dwahlialregtehperoopppoortsiiotne meter Change1089000%%% AABB1818 - ---11>>22 BA-->>22 --BA6677
iecsxoatnSrmsuimiedinueoerlfdaatbtfihlouyenr,tNshbeouArrtw1ionbengSlayienacindnt.ioAdTni1hs5ctur.s3imb,.utahtnieoiipnru.alnaTctheeisstthrpyeodimnoteasxwidimlilfufbemer A Date due to Para 567000%%%
C
population size, keeping the (cid:2)nal port rate the same in MR 40%
t(eArm1bs)ocfamusiegsraanlmtsopsetrngoencehraantgioen,.wHhaillevidnogutbhleinpgopitu(lAat1iocn) Change in 2300%%
McauRsCeAsaavnedryAsCliAghtti,mpeo.ssAibslywneo’lnl-sseigeniin(cid:2)csaimntu,liantciorenasBe7icn, Percent 10%
0%
alargerpopulationcanactuallyleadtomorerecentdates NonLocalPortProb PortRate NonLocalCountryProb ChangeTownProb ChangeCountryProb
Parameter
underdifferentconditions. Thelargerpopulationhaslit-
tledirecteffectontheancestrycoalescencetimebecause Figure5:ThepercentchangeintheMRCAdateresulting
it occursaftertheMRCA lived. Themostimportantde- fromvariousparameterchangesforModelsAandB.The
termineroftherateofspreadofalineageisnottheabso- redbarsindicatethepercentchangefromSimulationA1
lutenumberofpeoplewiththelineagebutthepercentage toeithersimulationA2,A3,A4,A5,orA6,dependingon
ofpeople. Asthepopulationuniformlygrowsorshrinks thevariableinquestion.Thebluebarsindicatethepercent
overtime,thispercentageisnotaffected. Theonlypoint changefromthelessconservativesimulationsA8(cid:150)A12to
atwhichthetotalpopulationplaysaroleisatthetimeof themoreconservativeA7.
theoriginalancestor. Atthatpoint,thepercentageofthe
populationrepresentedbythatancestorisindeedafunc-
tion of the populationsize. Thus, a larger population at
the time that an ancestor lived would result in a longer
delay for that person to become a CA. But a population
thatgrowsuniformlyoncetheancestorhasdieddoesnot
resultinasimilardelay. Largerpopulationsdo,however,
tendtohavemoremigrantsacrossthemostdif(cid:2)cultbar-
riers,resultinginafasterspreadoflineage.Inthecaseof
simulations A1(cid:150)A1c, these effects are either minimal or 100%
counteracting. Change 90% AAB118 ---1>>2 BA->22 --A667
Simulations A2(cid:150)A6 were similar to A1, but each ma- meter 80% B8-12 -> B7
nipulated a single parameter, applying a more conserva- Para 70%
triavmeevtearl.ueStiomtuelsattitohneAse2nsliotwiveitryedofthteheNmonoLdoeclatolPtohratPtrpoab- Date due to 5600%%
from100%to 5%, so most users of a portmust be born A
tcsiinmrmeiaaetlss.le.siToRnuhetrehlcaseeetiMvcpeoeRurtCconetArsnyitmt.icmuThleahantaeingoedenfsfaAei6cn1t.2,Mo%tfhRetiCrhneicAsrwecadahssaaetnaeign1aet1nhi.d4se%AAquCCiintAAe- Percent Change in AC 12340000%%%%
date are shown in the left-most bars in Figures 5 and 6, 0%
respectively. NonLocalPortProb PortRate NonLPoacaralCmouentetrryProb ChangeTownProb ChangeCountryProb
SimulationA3loweredthePortRatefrom10simsper
generationto just one per generation. This resulted in a Figure6: The percentchangein the ACA date resulting
17.2%increaseintheMRCAtimeanda12.9%increase fromvariousparameterchangesforModelsAandB.
in the ACA time. Thus, the model is not tremendously
sensitive to migration rate by itself. Once a lineage has
spreadthroughoutmostorallofacontinent,itonlytakes
asinglenon-extinctmigranttospreadthatlineagetoan-
9
ROHDE COMMONANCESTORSOF ALLLIVING HUMANS
other continent and even very low migration rates may
resultinonlyshort-termdelays.
Simulation A4 lowered the NonLocalCountryProb
from100%to5%causingmostmigrationbetweencoun-
triestobelocal.Thisreducestherateofadmixturewithin
continents, resultingin a 24.4%increasein MRCA time
and an 18.1% increase in ACA time. Simulation A5 re-
ducedtheadmixtureratewithincountriesbyloweringthe
ChangeTownProbparameter from 20% to 2%. This has
a similar effect on the overall dates, also increasing the
MRCA time by 24.4% and increasing the ACA time by
19.8%. Finally,simulationA6reducedtheChangeCoun-
tryProb from 0.1% (1 in 1,000)to 0.01% (1 in 10,000).
Thishasthegreatesteffectofthesingle-parametermanip-
ulations,increasingtheMRCAandACAtimesby30.5%
and28.0%,respectively.
If these (cid:2)ve parameter changes have independent ef-
Figure7: ModelB.Ahighlysimpli(cid:2)edworldmap.
fects, we mightexpecttheneteffectofcombiningallof
themtobeeitherthesumoftheirindependentadditiveef-
fects orthe productoftheirmultiplicativeeffects. Ifthe rate at which lineage can spread long distances across
effectswereadditive,itwouldresultinpredictedMRCA continents. Lineage can spread fairly rapidly if either
andACAdatesof3570BPand5355BP,respectively. If theChangeCountryProbishigh,meaningtherearemore
theeffectsweremultiplicative,thepredicteddateswould inter-country migrants or the NonLocalCountryProb is
be 4533BP and6241BP, respectively. Theactual dates high, meaning that there may be only a few migrants
ofthe combinedparameterchangesfromSimulationA7 but they are more likely to travel long distances. When
are 4910 BP and 9790 BP. Thus, the effects of the pa- thereare bothfew migrantsandtheytend to moveshort
rametersappeartobegreaterthantheirindependentaddi- distances, there is a much greater resulting effect on the
tiveormultiplicativecombinationandwemightconclude MRCAdate.
thatthereisinteractionbetweenthem.Thisisparticularly Interestingly,thesamedoesnotholdtruefortheACA
truefortheACAdate,whichexperiencesagreaterchange date,showninFigure6.Infact,alloftheparametersseem
(240% relative to simulation A1) than does the MRCA to interact in determining it. As a result, the ACA date
date(186%). However,wedonotyetknowthenatureof becomes increasingly sensitive and the ratio between it
thisinteraction. andtheMRCAdateincreaseswhenalloftheparameters
SimulationsA8(cid:150)A12startwiththesameparameterval- areassignedmoreconservativevalues.
ues as A7, but change each of the variables back to its
less-conservativesetting. Thepointistotestthesensitiv-
3 Model B: Coarse real-world
ityofthemodeltoeachparameterinthisnewpartofthe
space. Thesensitivityismeasuredasthepercentchange topology
inMRCAorACAfromthelessconservativesimulation,
A8forexample,tothemoreconservativeA7.Ifaparam- Thefully-connectedworldofModelAwasaninteresting
eterisactingindependentlyanditseffectsaremultiplica- forumtoexperimentwiththeparametersofthemodelbe-
tive,weshouldexpecttoseethesamepercentagechange causeofitsresemblancetomoretraditionalstructuredco-
in the blue bars in Figures 5 and 6 as we saw in the red alescencemodels. However,itclearlybearslittleresem-
bars.Ifthebluebarsarehigher,itindicatesthatthemodel blancetotherealworld.ModelB,therefore,takesasmall
ismoresensitivetotheparameterwhentheotherparame- steptowardsamorerealisticmodeloftheworld,usingthe
tersaremoreconservative,suggestingthattheparameters map shown in Figure 7. The continents are intended to
areinteracting. resemble,clockwisefromthelowerleft,Africa,Eurasia,
In terms of MRCA, the PortRate, and the Change- North America, South America, and Australia/Oceania.
TownProbappeartobeactingindependentlyoftheother ThecontinentsareinternallythesameasinModelA,ex-
parameters. However, the NonLocalCountryProb, the cept that Eurasia is twice as wide as the others. There
ChangeCountryProb, and to some extent the NonLocal- areonlyfourbidirectionalportsinthismodel,withSouth
PortProb have greater effects in simulations A7(cid:150)A12. AmericaconnectedtoNorthAmericaandtheotherconti-
Thisindicatesthattheseparametersareinteracting,prob- nentsconnectedtoEurasia.Weareinterestedprimarilyin
ably with one another. These parameters all affect the theeffectthisstructurewillhaveonthespreadoflineages
10