Article

Investigating Population History Using Temporal GeneticDifferentiationPontus Skoglund1 Per Sjodin1 Tobias Skoglund12 Martin Lascoux34 and Mattias Jakobsson14

1Department of Evolutionary Biology Uppsala University Uppsala Sweden2Department of Information Technology Uppsala University Uppsala Sweden3Department of Ecology and Genetics Program in Plant Ecology and Evolution Uppsala University Uppsala Sweden4Science for Life Laboratory Uppsala Sweden

Corresponding author E-mail skoglundgeneticsmedharvardedu mattiasjakobssonebcuuse

Associate editor Hideki Innan

Abstract

The rapid advance of sequencing technology coupled with improvements in molecular methods for obtaining geneticdata from ancient sources holds the promise of producing a wealth of genomic data from time-separated individualsHowever the population-genetic properties of time-structured samples have not been extensively explored Here weconsider the implications of temporal sampling for analyses of genetic differentiation and use a temporal coalescentframework to show that complex historical events such as size reductions population replacements and transientgenetic barriers between populations leave a footprint of genetic differentiation that can be traced through historyusing temporal samples Our results emphasize explicit consideration of the temporal structure when making inferencesand indicate that genomic data from ancient individuals will greatly increase our ability to reconstruct populationhistory

Key words genetic differentiation FST population structure time-serial sampling ancient DNA

IntroductionRecent advances in molecular genetics have opened up thepossibility of using temporal genetic samples to answer bio-logical questions including studies focusing on viruses(Rodrigo and Felsenstein 1999) and studies of animal andhuman remains (Shapiro and Hofreiter 2014) DNA extractionfrom fossils or ancient material was pioneered some 3 decadesago (Higuchi et al 1984 Paabo 1985) but the field of ancientDNA has been plagued by problems such as contaminationfrom modern-day DNA postmortem DNA damage and lowlevels of endogenous DNA However many problems havebeen resolved in the last few years For example the highfrequency of postmortem damage in ancient DNA sequences(Briggs et al 2007) can be difficult to distinguish from biolog-ical polymorphisms but experimental solutions have beendeveloped such as using enzymes to repair damaged nucleo-tides (Briggs et al 2010) Likewise problems arising from con-tamination from present-day individuals can becircumvented using these same postmortem damage pat-terns (Krause et al 2010 Meyer et al 2014 Skoglund et al2014) coupled with an assessment of whether the DNA orig-inates from a single individual (Green et al 2010 Krause et al2010) These advances have resulted in a remarkable devel-opment exemplified by the explosion in genomic studies ofancient hominid remains such as the sequencing of theNeandertal genome (Green et al 2010 Prufer et al 2014)the Denisova genome (Reich et al 2010 Meyer et al 2012)and genomic investigations of several prehistoric humans(Rasmussen et al 2010 Keller et al 2012 Sanchez-Quinto

et al 2012 Skoglund et al 2012 Raghavan et al 2014)There are even isolated examples of DNA preservation infossils that are hundreds of thousands years old (Orlandoet al 2013 Meyer et al 2014) The new sequencing technol-ogies have been instrumental for this development simplybecause they work with massive amounts of short-frag-mented DNA which is the state in which we find postmor-tem DNA

Theoretical aspects of temporal genetic differentiationhave not been extensively investigated even though manyof the classical population-genetic parameters such asWrightrsquos F-statistics (Wright 1949) stem from temporalmodels For example temporal differences between ancientsamples as well as between ancient samples and modern-dayones complicate interpretations of population-genetic struc-ture Even in the absence of population structure genetic driftis expected to produce genetic differences between geneticdata from different points in time (Krimbas and Tsakas 1971Waples 1989 Nordborg 1998 Anderson et al 2000 Wang2001 Berthier et al 2002 Beaumont 2003 Depaulis et al2009 Nystrom et al 2012) which in practice makes separatinghistorical scenarios of replacement and genetic drift difficult(Nordborg 1998 Serre et al 2004 Haak et al 2005 Castroviejo-Fisher et al 2011 Sjodin et al 2014) However it may be de-sirable to use the temporal structure within a sample to makeinferences because time-structured data offer a new dimen-sion of information for learning about the demographic his-tory That important information can be extracted fromtemporal samples is illustrated by the long tradition of using

The Author 2014 Published by Oxford University Press on behalf of the Society for Molecular Biology and EvolutionThis is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (httpcreativecommonsorglicensesby-nc30) which permits non-commercial re-use distribution and reproduction in any mediumprovided the original work is properly cited For commercial re-use please contact journalspermissionsoupcom Open Access2516 Mol Biol Evol 31(9)2516ndash2527 doi101093molbevmsu192 Advance Access publication June 17 2014

at Uppsala U

niversitetsbibliotek on March 4 2016

httpmbeoxfordjournalsorg

Dow

nloaded from

variance in allele frequencies between multi-individual sam-ples from discrete time points to infer effective population size(Krimbas and Tsakas 1971 Waples 1989 Anderson et al 2000Wang 2001 Berthier et al 2002 Beaumont 2003) and methodsfor using single-locus nonrecombining markers such as mito-chondrial DNA to infer population size changes (Drummondet al 2005 Ramakrishnan et al 2005 Chan et al 2006Drummond and Rambaut 2007 Ramakrishnan and Hadly2009 Navascues et al 2010 Ho and Shapiro 2011)Furthermore the coalescent model (Kingman 1982) is readilyadapted to accommodate time-serial samples (Rodrigo andFelsenstein 1999) and several simulation tools that handletemporal samples have been developed (Anderson et al2005 Jakobsson 2009 Excoffier and Foll 2011) However theuse of genomic data from temporal samples for inferring morecomplex population histories remains largely unexplored Asthe quality and quantity of ancient genomic data is increasingwe need a better understanding of how temporal structureaffects genetic differentiation and diversity In this article wefirst illustrate how temporal structure relates to classicalmodels of population structure by calculating Wrightrsquos fixa-tion index FST in simple demographic models which providesan intuitive understanding of the problem at hand Secondwe demonstrate that genetic data from temporal samples cangreatly aid inferences of population history by highlightingseveral instances where wide temporal sampling can provideinsights that would be hard to obtain otherwise

Fundamental Properties of Temporal GeneticStructure

Genetic drift results in differentiation between structuredpopulations (Wright 1940 1951) In a coalescent framework(Kingman 1982 Hudson 1990 Slatkin 1991) genetic differen-tiation between populations can be viewed as the effect of ashorter expected time of coalescence for lineages from thesame population E[TW] compared with the expected time ofcoalescence for lineages from different populations E[TB] Afundamental metric of genetic differentiation in structuredpopulations is Wrightrsquos fixation index FST which in coalescentterms corresponds to 1[E[TW]((E[TW] + E[TB])2)] whereE[TW] and E[TB] are averaged across populations and com-parisons (Slatkin 1991) Taking mutations into account thiscan be expressed in terms of probabilities of identity by de-scent (IBD) such as FST = (fw fb)(1 fb) Here fb is the prob-ability of IBD for lineages picked from different populationsand fw is the probability of IBD for lineages picked from thesame population (averaged over the different populations)For instance if f1 and f2 are the probabilities of IBD in twodifferent groups 1 and 2

FST frac1405 f1 thorn f2eth THORN fb

1 fb eth1THORN

In this article we consider FST for models where samples aredrawn from two time points and compare this situation to amodel where the two samples are drawn from different pop-ulations that diverged at some point in the past (fig 1)

If the population size N is constant the probability of IBDin both the temporal model and the divergence model forlineages picked from the same population is

f1 frac14 f2 frac142Neth THORN1

2Neth THORN1thorn 2m

frac141

1thorn y eth2THORN

where m is the mutation rate per site per generation and = 4Nm This is simply the probability that two lineages co-alesce before a mutation occurs (2m is the mutation rate inthe two lineages [ignoring m2 terms] and (2N)1 is the coa-lescence rate) As for the probability of IBD between popula-tions in the divergence model (fig 1A) it is

fb frac14 eth1 mTHORNt1eth1 mTHORNt22Neth THORN1

2Neth THORN1thorn 2m

ampexpethyethT1 thorn T2THORN=2THORN

1thorn y

eth3THORN

where T1 = t12N and T2 = t22N and t1 and t2 are the times (ingenerations) to the split of the two populations This expres-sion is derived from considering that neither lineage can havea mutation before they reach the ancestral population andonce in the ancestral population they must coalesce before amutation occurs (as above) Applying the same argument forthe temporal model (fig 1C) two lineages sampled t gener-ations apart will be IBD if there is no mutation in the youngerlineage during t generations and once in the ancestral pop-ulation the two lineages coalesce before any of them mutateHence

fb frac14 eth1 mTHORNt2Neth THORN1

2Neth THORN1thorn 2m

ampexpethyT=2THORN

1thorn y eth4THORN

where T = t2N If T = T1 + T2 then FST in the temporal anddivergence model is the same and

FST frac14 1y

ythorn 1 exp yT=2eth THORN eth5THORN

A B C

FIG 1 Additivity of genetic drift can result in equivalent genetic differ-entiation (FST) under temporal structure and population divergence (Aand B) Thirty individuals are sampled from two populations (15 individ-uals from each population) that diverged at a given time in the past In(A) both samples are taken at the present and in (B) one of the samplesis taken at 05 2Ne generations before present and the other sample istaken at present (C) Thirty individuals are sampled from two discretetime points (15 individuals from each time point) in the history of acontinuous population In all three scenarios the total time that passesbetween each sample is T = 2Ne generations The 15 individuals in eachsample are illustrated as a series of red circles or a series of blue circles

2517

Temporal Population-Genetic Structure doi101093molbevmsu192 MBE at U

ppsala Universitetsbibliotek on M

arch 4 2016httpm

beoxfordjournalsorgD

ownloaded from

Note that this extends naturally also for models withboth divergence and temporal samples such as the modelin figure 1B However this simple relationship betweentemporal structure and divergence models only holdswhen the population size is constant When the populationsize is not constant FST in the temporal and divergencemodels is expected to be equal only under very specific con-ditions (see supplementary fig S1 Supplementary Materialonline)

Neirsquos Estimator of Divergence Time betweenPopulations

Based on a result from Nei (1973) it is commonly stated thatexpected FST in a divergence model with constant size equals1eT2 (letting T denote the total time in coalescent unitsthat separates two populations as above) This result wasderived under a very specific model assumptionmdashnamelythat all polymorphisms were present in the ancestral popu-lation Furthermore this only applies when sampling timesare equal because for a temporal model where polymor-phisms were present in the ancestral population we findinstead that FST = (1eT)2 (supplementary materialSupplementary Material online) Curiously simulations high-light the generality with which FST responds to genetic driftunder constant-size scenarios because Neirsquos case with ascer-tainment of polymorphic loci in the ancestral population ofthe divergence model (FST = 1eT2) corresponds to thetemporal case if ascertainment of polymorphisms is per-formed at the midpoint between the two temporalsamples (fig 2) Likewise the expectation when polymor-phisms are ascertained in the ancestral population of thetemporal model (FST = (1eT)2) corresponds to ascertain-ing in one of the two populations of the divergence model(fig 2)

FST and the Combined Effect of Migration andTemporal Structure

We study the effect of migration by considering a simpleislandstepping-stone model with two populationsdemesof equal size N and a symmetric migration rate m betweenthem and with the two populations being sampled t gener-ations apart In this case FST can be shown to be

FST frac14 12y

2ythorn 1 expethyT=2THORN

thorny

ythorn 4Mfrac121thorn expethethythorn 4MTHORNT=2THORN

8lt

9=

eth6THORN

where = 4Nm M = 2Nm and T = t2N (see supplementarymaterial Supplementary Material online) As M increases thisexpression converges to the formula for FST in a pure tempo-ral model with a population of constant but twice as largeeffective population size (so that the scaled mutation rate islarger by a factor 2 whereas the scaled time is half as largecompare to eq 5 above) Intuitively increasing the migrationrate lowers FST whereas an increase in time between thesampled time points increases FST (fig 3) Importantly for afixed value of FST (and ) there is no definite solution in termsof M because this will depend on T so that FST is not a directmeasure of migration rate under this model unless T is known(which requires that N and t are known) This is similar to thedifficulty associated with differentiating between populationsplit time and migration in spatial divergence models (Nielsenand Wakeley 2001)

ResultsThe simple theoretical models considered above indicate thatboth temporal structure and spatial structure affect FST in arather similar manner but that their effects are sufficiently

0 1 2 3 4

T total

FST

1 - e minus (Nei 1973)Split model ascertainmentTemporal model ascertainment

E(F | θ = 01)Split model minus θ = 01Temporal model minus θ = 01

(1 - e )2Split model ascertainmentTemporal model ascertainment

Present

Past

Temporal modelSplit model

Ascertainment

Present

Past

Temporal modelSplit model

Ascertainment

02

04

10

08

06

00

A B

FIG 2 Dependence of FST in temporal and divergence models conditioning on the allele being polymorphic (A) FST as a function of T the total timethat separates two populations (two times the population divergence time) or the time that separates two samples in model of samples taken at twodifferent time points The gray line shows the function FST = 1eT2 (Nei 1973) (B) The models used for simulating population-genetic data andcomputing FST The split model illustrates a population split T2 time units in the past and the temporal model that illustrates a single population (ofconstant size) from which samples have been taken at two time points Arrows point to where in time sites have been ascertained for variation (seemain text for a full description of the procedure)

2518

Skoglund et al doi101093molbevmsu192 MBE at U

ppsala Universitetsbibliotek on M

arch 4 2016httpm

beoxfordjournalsorgD

ownloaded from

different to prompt caution in interpretations of FST in par-ticular for cases where temporal samples are involved Toinvestigate more complex scenarios of continuous samplingover time we now turn to a simulation-based approach

Stepping-Stone Migration Model with TemporalSamples

In contrast to isolation models stepping-stone migrationmodelsmdashwhere populations (demes) are connected in one-or two-dimensional landscapesmdashtypically result in continu-ous differentiation between individuals rather than discretegenetic clusters of individuals (Novembre and Stephens 2008Engelhardt and Stephens 2010) Given that temporal geneticstructure also affects expected coalescence times betweenlineages it can be expected that temporal differentiationwould display similar behavior To demonstrate this phenom-enon we designed a temporal simulation algorithm (seeMaterials and Methods) based on Hudsonrsquos ldquomsrdquo coalescencesimulation software (Hudson 2002) and simulated a modelwith 100 demes in a two-dimensional habitat (10 10 lattice)with stepping-stone migration We used 4Nem = 2 where m isthe fraction of each subpopulation made up of new migrantseach generation (note that scaling in ms is slightly different tothe theory above) and sampled one haploid individual fromeach deme at ten time points separated by t = 4Ne genera-tions creating a three-dimensional model comprising the two

spatial dimensions and the temporal dimension (fig 4A)Because of the increased complexity of the data pairwisecomparisons such as FST are poorly suited to analyze theresults Instead we used principal component analysis(PCA) to summarize and visualize the resulting population-genetic data (see Materials and Methods) PCA and FST havestrong conceptual connections with principal components(PCs) being closely related to the average coalescent timesbetween pairs of haploid genomes (McVean 2009) We findthat the first three PCs mirror the three dimensions of themodel (three-dimensional Procrustes correlation 0984Plt 105) (fig 4B) Specifically PC1 and PC2 represented iso-lation-by-distance in the two-dimensional habitat whereasPC3 represented temporal differentiation (supplementaryfig S2 Supplementary Material online) but this order ofPCs will depend on the relative magnitudes of the scaledmigration rate and genetic drift between time points(McVean 2009)

Temporal Genetic Differentiation Can Be Informativeabout Complex Population Histories

As illustrated in figure 1C genetic differentiation can alsooccur in the absence of any spatial structure that is in sam-ples taken at different time points from a single continuous(unstructured) population To investigate temporal differen-tiation more closely we simulated a single continuous pop-ulation with an effective population size of 5000 diploidindividuals and a generation time of 25 years sampling 20diploid individuals from the present and an additional 20diploid individuals evenly distributed over the period 500ndash10000 years ago with a 500-year interval between each sam-pled individual (fig 5A) In a PCA we see that PC1 capturesthe temporal genetic differentiation separating the samplesfrom the most recent to the most ancient as a monotonic(but not linear) cline where individuals close in time are alsomore genetically similar (fig 5D and supplementary fig S3Supplementary Material online) To investigate the effect ofpopulation size fluctuations (ie fluctuations in the magni-tude of genetic drift) we reduced the population to a tenth ofits original size between 5000 and 5500 years before presentUnder this sampling scheme the bottleneck is easily detectedas a discontinuation in the monotonic cline (fig 5B and E andsupplementary fig S3 Supplementary Material online)

We also simulated population-genetic data under a diver-gence model of two populations that diverged 10000 yearsago (fig 5C) Ten ancient individuals were sampled at differenttime points between 10000 and 5500 years from one popu-lation and 30 individuals were sampled from the other pop-ulation between 5000 years ago and the present (ten ancientindividuals spread out in time and 20 present-day individuals)This simulation could correspond to a scenario where theolder population was replaced with new colonizers from an-other population In the simulated data individuals sampledbefore the replacement event show a trajectory along PC1through time that is angled away from the individuals in thepopulation that replaced the previous population (fig 5F andsupplementary fig S3 Supplementary Material online) In

0 2 4 6 8 10

T (in generations2Ne)

F ST

000

025

050

075

100 M=0

log(M)=minus2log(M)=minus18log(M)=minus16log(M)=minus14log(M)=minus12log(M)=minus1log(M)=minus08log(M)=minus06log(M)=minus04log(M)=minus02log(M)=0log(M)=02log(M)=04log(M)=06log(M)=08log(M)=1log(M)=12log(M)=14log(M)=16log(M)=18log(M)=2limittemporal

FIG 3 Dependence of FST in a simple temporal island model Themodel consists of two equally sized populations with symmetric migra-tion rate The X axis shows the separation in (scaled) time between thesamples (the scaled mutation rate) is set to 01 The continuous linesshow how FST for models with different (scaled) migration rates dependson time separation The dotted lines show FST if the samples are notseparated in time or equivalently if the effective population size isinfinitely large The red line is the limit when migration is infinitelyfast In this case the model is identical to a purely temporal modelwith a doubled (and constant) population size (the larger populationsize implies that is twice as large) The dark blue line is the limit whenthere is no migration while the light blue line at log(M)=0 is included forreference

2519

Temporal Population-Genetic Structure doi101093molbevmsu192 MBE at U

ppsala Universitetsbibliotek on M

arch 4 2016httpm

beoxfordjournalsorgD

ownloaded from

contrast in the bottleneck scenario the sampled individualsfrom before the bottleneck event show a trajectory along PC1as a function of time that is angled toward the individuals inthe descendant population (fig 5E and supplementary fig S3Supplementary Material online) However FST between theancient individuals from before and after the event was in-distinguishable under the bottleneck model and the replace-ment model (00154 00003 and 00153 00003respectively fig 6) To complement the PCA approach we

reconstructed maximum-likelihood trees (supplementary figS4 Supplementary Material online) using the covariance inallele frequencies between individuals (Pickrell and Pritchard2012) and other pairwise FST comparisons (fig 6) This analysisgave different results depending on the way the samples wereobtained The two scenarios were (again) indistinguishable ifthe samples were grouped into three separate temporal sam-ples In contrast if the full temporal structure was accountedfor so that each sample was treated independently the

A B C

D E F

FIG 5 Temporal sampling distinguishes genetic drift from population structure (A) Constant population size model (B) Bottleneck model (C)Replacement model (D) PC1 stratified by sample time under the constant population size model (E) PC1 stratified by sample time under thebottleneck model (F) PC1 stratified by sample time under the replacement model Each colored circle corresponds to a single-sampled individualexcept for the large circles at time zero which corresponds to 20 sampled individuals in A B and C (in D E and F the 20 individuals sampled at time zeroend up on top of each other) FST between samples from before and after the bottleneckreplacement events at 5500 years ago fails to distinguishbetween the models (FST = 00154 00003 and 00153 00003 respectively see fig 6)

00 02 04 06 08 10

00

02

04

06

08

10

0002

0406

0810

Spatial dimension 1Spatial dimensio

n 2Tem

pora

l dim

ensi

on

minus20 minus10 0 10 20minus15

minus10

minus50

510

15

minus20minus10

010

20

PC1

PC2

PC

3

A B

FIG 4 Genetic differentiation mirrors the sampling scheme in a model with both temporal and spatial structure (A) Two-dimensional stepping-stonemigration model from which ten haploid individuals were sampled at different historical time points (B) PCA of data generated under the model Largesymbols correspond to high PC1 and PC3 values but low PC2 values

2520

Skoglund et al doi101093molbevmsu192 MBE at U

ppsala Universitetsbibliotek on M

arch 4 2016httpm

beoxfordjournalsorgD

ownloaded from

maximum-likelihood trees revealed a difference between thebottleneck model and the replacement model These obser-vations illustrates that many inference tools can lead to in-correct conclusions for temporally sampled data and theyemphasize the importance of considering detailed temporalsampling structure for distinguishing between bottleneck andreplacement models It also illustrates that the considerablepower to distinguish different models that we report is notdirectly linked to the use of PCA methods but is mainly due tothe temporal sampling schemes

Transient Genetic Barriers

To study more complex population models we simulated apopulation split model which involved two populations (Aand B) that diverged 8000 years ago We kept the same sim-ulation parameters and temporal sampling scheme as abovebut assigned the 4 ancient individuals from 3500 4500 5500and 6500 years ago to population B and the remaining 16ancient individuals to population A (fig 7A) Strikingly thepopulation split event is readily identifiable when PC1 is strat-ified by sampling time (fig 7C and supplementary fig S3Supplementary Material online) In a further modificationof the model we simulated secondary admixture betweenthe two populations 3000 years before present and where75 of the genetic material of the recent population wascontributed by population A and 25 was contributed bypopulation B (fig 7B) A plot of PC1 versus sampling timeshows the two series of individuals represented by samplesfrom the two populations becoming more similar as timeapproaches the time of admixture (fig 7D and supplementaryfig S3 Supplementary Material online) suggesting that tran-sient genetic barriers can be investigated using continuoustemporal genetic data

Approximate Bayesian Computation Using TemporalGenetic Differentiation

The observation that some statistics of temporal genetic dif-ferentiation can recapitulate population history suggests that

those statistics can be used to infer population history inmore formal settings We used approximate Bayesian com-putation (Tavare et al 1997 Pritchard et al 1999 Beaumontet al 2002) to exemplify that temporal genetic data can beused to infer parameters of a demographic model based solelyon PC1 loadings of sampled individuals as summary statisticsWe applied this approach to a data set consisting of 44Siberian Woolly Mammoth samples spanning 50000 yearsand genotyped at four microsatellites (Nystrom et al 2012)The original study used conventional summary statistics andaggregated temporal groups to show that a population sizereduction during the Holocene transition could explain thefact that two temporal groups were genetically differentiatedHere we expand the inference to a three-parameter model(fig 8) The time of change the effective population sizebefore the change and the effective population size afterthe change allowing for either a reduction or expansion inpopulation size (see Materials and Methods) The estimatedposterior distribution indicates a size reduction at around11200 years ago with the effective population size in themore recent time period being approximately ten times smal-ler than before the change (table 1 and fig 8) The inferredtiming of this population size reduction coincides with theisolation of Wrangel Island from the Siberian mainland(Vartanyan et al 1993) and thus corroborates the hypothesisthat this restriction of the habitat triggered a founder event inthe resident mammoth population (Nystrom et al 20102012)

Pitfalls When Comparing Ancient Genomes toModern Populations

A common situation is that a single ancient genome is avail-able from a certain time point and the goal is to investigatethe historical relationship between the ancient individual andpresent-day populations To investigate the differentiationbetween a single ancient genome and more recent popula-tions we simulated ten individuals from each of two popu-lations (A and B) which diverged 20000 years ago

Modern vs young Young vs old Modern vs old

Differentiation between temporal groups

F ST

F ST

F ST

000

00

005

001

00

015

002

00

025

constantbottleneckreplacement

A B C

0 2000 4000 6000 8000 10000minus00

050

000

000

50

010

001

5

Differentiation between pairs adjacent in time

Time (years ago)

Event

minusminus

minusminus

minus minusminus minus minus minus minus

minusminus minus

minusminus minus

minus

minus minusminusminus

minusminus

minus minus

minusminus

minus minus

minus

minusminus minus

minus

minusminus

minusminus

minusminus

minus

minus

minus

minus minus

minus

minusminus

minus

minus

minusminus

minusminus

minus

minus minus

minus minus

constantbottleneckreplacement

0 2000 4000 6000 8000 10000

000

001

002

003

004

Differentiation to modern population

Time (years ago)

Event

constantbottleneckreplacement

FIG 6 Genetic differentiation between temporal sample groups (A) FST computed on aggregated sample groups is unable to differentiate thebottleneck and replacement models ldquoModernsrdquo 20 samples from time 0 ldquoYoungrdquo 10 samples from time 0ndash5000 years ago ldquoOldrdquo 10 samplesfrom 5500 to 10000 years ago (B) FST between individuals adjacent in time is able to detect a sudden increase in FST between the pair of individuals thatflank the demographic event (both bottleneck and replacement) but we are unable to separate the replacement and bottleneck scenarios Standarderrors are not shown but ranged between 0002 and 0003 (C) FST between 20 modern individuals and each ancient individual Standard errors are notshown but ranged between 00010 and 00014

2521

Temporal Population-Genetic Structure doi101093molbevmsu192 MBE at U

ppsala Universitetsbibliotek on M

arch 4 2016httpm

beoxfordjournalsorgD

ownloaded from

A B

C D

FIG 8 Approximate Bayesian Computation of Woolly Mammoth demographic history using PC1 loadings as summary statistics (A) Plot of PC1 versusthe age of the mammoth individuals (B) Illustration of the three-parameter model of instantaneous size change (C) Estimated posterior distribution forthe time of size change (D) Estimated posterior distributions of effective population size before and after the size change Prior distributions in (C) and(D) are shown by the gray lines

0 2000 4000 6000 8000

minus200

minus100

010

0

Age (years bp)

PC

1

Age (years bp)

D

B

0 2000 6000 10000

minus400

minus200

010

0

PC1

A

C

FIG 7 Temporal sampling can be used to detect transient genetic barriers (A) Split model (B) Split-admixture model (C) PC1 stratified by time fordata simulated under the split model (D) PC1 stratified by time for data simulated under the split-admixture model Each colored circle corresponds toa single sampled individual except for the large circles at time zero which corresponds to 20 sampled individuals in A and B (in C and D the 20individuals sampled at time zero overlap) The 4 ancient individuals from 3500 4500 5500 and 6500 years ago (marked circles) were sampled frompopulation B (bottom population in the model illustrations) and the remaining ancient 16 individuals were sampled from population A (top populationin the model illustrations)

2522

Skoglund et al doi101093molbevmsu192 MBE at U

ppsala Universitetsbibliotek on M

arch 4 2016httpm

beoxfordjournalsorgD

ownloaded from

(Ne = 10000) and a single 18000-year-old individual from thelineage leading to population B (fig 9) Using PCA we foundthat PC1 captures the spatial differentiation between popu-lations A and B whereas PC2 captures the temporal differen-tiation between the ancient sample and the modern sample(fig 9C) The ancient sample appears closer to population Brecapitulating the population history However when wemodified the model to include a 10-fold population size re-duction in population B after the time of sampling of the

A B

C D

E F

FIG 9 Comparing a single ancient genome to modern populations (A) Population divergence model with constant effective population size (B)Population divergence with a 10-fold population size reduction postdating the ancient individual (C) PCA of 100000 SNPs simulated under the modelin (A) (D) PCA of 100000 SNPs simulated under the model in (B) (E) Population topology inferred using C tests and D tests based on 100000independent SNPs simulated under the model in (A) and (F) population topology inferred using C tests and D tests based on 100000 independentSNPs simulated under the model in (B) Values for the C-statistic are only positive for the correct topology and absolute values of the D-statistic arelowest for the correct topology The tree topologies displayed in (E) and (F) represent the three possible topologies tested and the larger trees representthe true topology (and also the one supported by the statistics) The gray circles in (E) and (F) represent an outgroup individual constructed from theancestral alleles of each simulated locus For details on these tests see Materials and Methods

Table 1 ABC Inference of Northeast Siberian Woolly MammothDemographic History Using PC Loadings as Summary Statistic

Parameter Prior (Uniform) PosteriorMode

Posterior95 CI

Ne before change 200ndash50000 23500 16900ndash29400

Ne after change 200ndash50000 1800 1000ndash8300

Time of change(years ago)

3000ndash40000 11200 5100ndash23100

NOTEmdashABC approximate Bayesian computation Ne is the effective population size

2523

Temporal Population-Genetic Structure doi101093molbevmsu192 MBE at U

ppsala Universitetsbibliotek on M

arch 4 2016httpm

beoxfordjournalsorgD

ownloaded from

ancient genome (15000 years ago fig 9B) the ancient sampleinstead clustered closer to population A (fig 9D) despite thefact that the ancient individual was sampled from the popu-lation that is ancestral to the extant sample from populationB This pattern is due to the fact that less time (on the coa-lescent scale) has passed between the ancient sample and theextant sample from population A and the genetic differenti-ation between the ancient individual and the extant samplefrom population A (FST = 0030 0001) was also smaller thanthe genetic differentiation between the ancient sample andthe extant sample from population B (FST = 0055 0001)Thus if the demographic history was unknown one couldpossibly mistakenly conclude that the ancient sample shares amore recent genetic history with population A solely due tothe different magnitudes of genetic drift Indeed the param-eter of historical interest is often the degree of shared historythat is the amount of shared genetic drift and not the relativedegrees of differentiation Accordingly we were able to iden-tify the correct topology (fig 9E and F) using concordancetests (Schlebusch et al 2012 Skoglund et al 2012) and Dstatistics (Reich et al 2009 Durand et al 2011 Pattersonet al 2012) that are less sensitive to lineage-specific geneticdrift

DiscussionThe main insight that arises from our analyses is that widetemporal sampling provides information that can be hard toattain using modern-day data alone or more clustered tem-poral groups The importance of wide temporal samplingcould also explain previous results suggesting that notmuch statistical power is gained solely by adding one or afew temporal sample groups (Mourier et al 2012) Spatialsampling structure can also have a substantial impact oninferences of population history using modern-day data(Serre and Paabo 2004 Rosenberg et al 2005 Chikhi et al2010 DeGiorgio and Rosenberg 2013) in which case differen-tiating between the relative contributions of migration andgenetic drift because population divergence is a serious chal-lenge (Nielsen and Wakeley 2001) In contrast to the manysimilarities between spatial and temporal structure that wehave highlighted the possibility of migration in the differentdimensions represents a fundamental difference because mi-gration of lineages is not possible in the temporal dimension(except in the case of overlapping generations or seed bankmodels see Kaj et al [2001]) resulting in a more constrainedset of models that may be consistent with a particular patternof genetic variation

One of the enduring challenges in population-genetic anal-ysis of ancient DNA is whether some observed level of geneticdifferentiation between temporal sample groups is the resultof genetic drift (possibly enhanced by a bottleneck) or theresult of a replacement of the older population with newcolonizers from another population (Nordborg 1998) Weshow that this question can be addressed by consideringthe trajectory of genetic relatedness within a temporalsample that spans the time of the putative eventAdditional hypotheses about population history that are dif-ficult to address with genetic data from one or a few time

points but that can be addressed with wide temporal samplesinclude the timing of bottlenecks and transient genetic bar-riers Conventional inference of the timing of population sizereductions usually requires assumptions about mutation rateandor recombination rate (Ramakrishnan et al 2005 Voightet al 2005 Li and Durbin 2011 Mourier et al 2012 Sheehanet al 2013) As illustrated for example in figure 5E the use ofcontinuously distributed temporal data allows accurate iden-tification of the time of population size reduction that isrobust to assumptions about mutation and recombinationrates For these reasons ancient genomic data promise toadvance our understanding of the recent evolutionary historyof many species

Materials and MethodsTo investigate temporal structure under an infinitely many-sites mutation model and population structure (see alsoExcoffier and Foll 2011 Skoglund et al 2011) we developeda temporal coalescent simulation algorithm based onHudsonrsquos (2002) ms The idea here is to use the versatilityof ms to simulate a genealogy but use in-house custom codefor the mutation process to accommodate different branchlengths due to temporal structure The algorithm proceededas follows For a sample of size L ancient diploid individualswe instruct the program ms to create 2L isolated subpopu-lations and sample a single lineage from each At the desiredtime th of each historical sample each of the 2L subpopula-tion is joined (command ldquo-ejrdquo) with the appropriate popula-tion to which they belong From the gene tree output of ms(command ldquo-Trdquo) we subtract th from the external branch ofeach ancient sample and add a single mutation on the result-ing genealogy with probability equal to branch length(Hudson 1990) using custom code For example if there isone individual to be sampled at time 03 and five additionalindividuals at time 04 two lineages are joined to the popu-lation at time 03 and the remaining ten lineages join thepopulation at time 04 To increase precision we modifiedthe source code of ms to produce 12 decimal digits for eachbranch in the gene tree output The custom code is availableupon request We validated the algorithm by comparisonwith COMPASS (Jakobsson 2009) which allows temporalsamples but not from multiple populations Under themodel in figure 1A we obtained identical estimates ofFST = 0337 0001 for both algorithms as well as highly sim-ilar site frequency spectra (supplementary fig S5Supplementary Material online) For all simulations aboveexcept the two-dimensional spatial lattice and the WoollyMammoth analysis (see below) we simulated 2 100000independent (unlinked) SNPs for each individual and com-bined pairs of lineages to create a diploid genotype for eachindividual When time is given in years we assumed a 25-yeargeneration time except in the case of the Woolly Mammothwhere we assumed 15 years as in Nystrom et al (2012)

FST was estimated using equation (53) in Weir (1996) withstandard errors estimated using a block jackknife droppingblocks of 1000 loci in turn PCA was performed using theprcomp function in R 2111 (R Development Core Team2010) Except in the case of microsatellites and the three-

2524

Skoglund et al doi101093molbevmsu192 MBE at U

ppsala Universitetsbibliotek on M

arch 4 2016httpm

beoxfordjournalsorgD

ownloaded from

dimensional stepping-stone model with temporal sampleswe used the normalization suggested by Patterson et al(2006) For the 44 mammoth individuals in Nystrom et al(2012) that had no missing data for the four microsatelliteswe considered each unique microsatellite allele to be a sep-arate marker which were given a count of 0 1 or 2 copies ineach individual Maximum-likelihood trees were inferredusing TreeMix version 111 (Pickrell and Pritchard 2012) as-suming no migration and using a block size of 1000 SNPs forestimating standard errors

To confirm the relationship between temporal structureand divergence models we estimated FST between two sam-ples of 15 diploid individuals each for three simulated demo-graphic models with a constant effective population size (Ne)(fig 1) In the first model (A) both samples were from thesame time point but from two populations that had divergedT = 05 time units into the past (fig 1A) The second model(B) assumed that one sample was T = 05 time units olderthan the other and that the two samples were from differentpopulations that diverged T = 075 time units into the past(fig 1B) The third model assumed a single continuous pop-ulation but with one sample T = 10 coalescent time units(2Ne generations) older than the other (fig 1C) Most impor-tantly in all three models the total coalescent time thatpasses as one follows the history from one sample to theother is T = 10 In all three models we also estimate FST toapproximately 033 (0337 0001 [1 standard error]0334 0001 and 0335 0001 respectively)

To simulate microsatellite data we implemented a step-wise mutation model with = 103 for COMPASS(Jakobsson 2009) as in Nystrom et al (2012) where eachmutation event either (with equal probability) adds or sub-tracts one unit from an arbitrarily chosen starting length(100) After this simulation we considered each simulated(unique) microsatellite allele as its own marker which wascounted as above and used that information as input for thePCA We used the PC1 loading of each individual as summarystatistic (in total a vector of 44 summary statistics) We sim-ulated 100000 replicates from which 02 of the replicateswith the smallest Euclidian distance to the empirical PC1loadings were used to obtain posterior distributions usinglocal linear regression (Beaumont et al 2002) after log trans-formation as implemented in the abc R package (Csillery et al2012)

To investigate the population topology inferred fromsingle individuals we applied tests that utilize sharing of de-rived alleles D-statistics were computed using a strategy ofsampling a single haploid gene copy from each population(Reich et al 2009 Durand et al 2011 Patterson et al 2012)We tested all three possible topologies that could be con-structed using four taxa Population A population B the an-cient individual and an outgroup individual (gray symbol infig 9E and F) that was taken to carry the ancestral allele(which is given in the ms simulations) Specifically the topol-ogies tested were (Outgroup (Ancient (population A pop-ulation B))) (Outgroup (population A (Ancient populationB))) and (Outgroup (population B (Ancient populationA))) For a proposed topology of the form (Outgroup (J (Y

Z))) we denote the count of all observations of a sharedderived allele (ldquoBrdquo) for J and Y that is absent fromOutgroup and Z by ldquoABBArdquo (here ldquoBrdquo symbolizes the derivedstate and ldquoArdquo the ancestral state) and the count of all obser-vations of a shared derived allele for J and Z that is absentfrom Outgroup and Y by ldquoBABArdquo The D-statistic is given by

D frac14BABA ABBA

BABAthorn ABBA eth7THORN

and a deviation from zero suggest a violation of the proposedtopology We computed concordance statistics (Schlebuschet al 2012 Skoglund et al 2012) using the same data andtesting the same topologies but these tests also use the con-figuration where Z and Y share a derived allele that is absentfrom Outgroup and J which we denote ldquoAABBrdquo The concor-dance statistic is given by

C frac14AABBmaxethABBA BABATHORN

AABBthornmaxethABBA BABATHORN eth8THORN

and positive values of C indicate concordance with the pro-posed topology

Supplementary MaterialSupplementary material is available at Molecular Biology andEvolution online (httpwwwmbeoxfordjournalsorg)

Acknowledgments

The authors thank Lucie Gattepaille for comments on a pre-vious version of the article This work was supported by grantsfrom the Sven and Lilly Lawski foundation and the HelgeAxson foundation to PSk from Trygger foundation to PSjand MJ and from the European Research Council to MJ

ReferencesAnderson CNK Ramakrishnan U Chan YL Hadly EA 2005 Serial

SimCoal a population genetics model for data from multiple pop-ulations and points in time Bioinformatics 211733ndash1734

Anderson EC Williamson EG Thompson EA 2000 Monte Carlo eval-uation of the likelihood for N(e) from temporally spaced samplesGenetics 1562109ndash2118

Beaumont MA 2003 Estimation of population growth or decline ingenetically monitored populations Genetics 1641139ndash1160

Beaumont MA Zhang WY Balding DJ 2002 Approximate Bayesiancomputation in population genetics Genetics 1622025ndash2035

Berthier P Beaumont MA Cornuet J-M Luikart G 2002 Likelihood-based estimation of the effective population size using temporalchanges in allele frequencies a genealogical approach Genetics160741ndash751

Briggs AW Stenzel U Johnson PLF Green RE Kelso J Prufer K Meyer MKrause J Ronan MT Lachmann M et al 2007 Patterns of damage ingenomic DNA sequences from a Neandertal Proc Natl Acad SciU S A 10414616ndash14621

Briggs AW Stenzel U Meyer M Krause J Kircher M Paabo S 2010Removal of deaminated cytosines and detection of in vivo methyl-ation in ancient DNA Nucleic Acids Res 38e87

Castroviejo-Fisher S Skoglund P Valadez R Vila C Leonard J 2011Vanishing native American dog lineages BMC Evol Biol 1173

Chan YL Anderson CNK Hadly EA 2006 Bayesian estimation of thetiming and severity of a population bottleneck from ancient DNAPLoS Genet 2451ndash460

Chikhi L Sousa VC Luisi P Goossens B Beaumont MA 2010 Theconfounding effects of population structure genetic diversity and

2525

Temporal Population-Genetic Structure doi101093molbevmsu192 MBE at U

ppsala Universitetsbibliotek on M

arch 4 2016httpm

beoxfordjournalsorgD

ownloaded from

the sampling scheme on the detection and quantification of pop-ulation size changes Genetics 186983ndash995

Csillery K Francois O Blum MGB 2012 abc an R package forapproximate Bayesian computation (ABC) Methods Ecol Evol 25410ndash418

DeGiorgio M Rosenberg NA 2013 Geographic sampling scheme as adeterminant of the major axis of genetic variation in principal com-ponents analysis Mol Biol Evol 30480ndash488

Depaulis F Orlando L Hanni C 2009 Using classical population genet-ics tools with heterochroneous data time matters PLoS One 4e5541

Drummond A Rambaut A 2007 BEAST Bayesian evolutionary analysisby sampling trees BMC Evol Biol 7214

Drummond AJ Rambaut A Shapiro B Pybus OG 2005 Bayesian coa-lescent inference of past population dynamics from molecular se-quences Mol Biol Evol 221185ndash1192

Durand EY Patterson N Reich D Slatkin M 2011 Testing for ancientadmixture between closely related populations Mol Biol Evol 282239ndash2252

Engelhardt BE Stephens M 2010 Analysis of population structure aunifying framework and novel methods based on sparse factor anal-ysis PLoS Genet 6e1001117

Excoffier L Foll M 2011 Fastsimcoal a continuous-time coalescentsimulator of genomic diversity under arbitrarily complex evolution-ary scenarios Bioinformatics 271332ndash1334

Green RE Krause J Briggs AW Maricic T Stenzel U Kircher M PattersonN Li H Zhai WW Fritz MHY et al 2010 A draft sequence of theneandertal genome Science 328710ndash722

Haak W Forster P Bramanti B Matsumura S Brandt G Tanzer MVillems R Renfrew C Gronenborn D Alt KW et al 2005 AncientDNA from the first European farmers in 7500-year-old Neolithicsites Science 3101016ndash1018

Higuchi R Bowman B Freiberg M Ryder OA Wilson AC 1984 DNAsequence from the quagga an extinct member of the horse familyNature 312282ndash284

Ho SY Shapiro B 2011 Skyline-plot methods for estimating demo-graphic history from nucleotide sequences Mol Ecol Resour 11423ndash434

Hudson R 1990 Gene genealogies and the coalescent process NewYork Oxford University Press

Hudson RR 2002 Generating samples under a WrightndashFisher neutralmodel of genetic variation Bioinformatics 18337ndash338

Jakobsson M 2009 COMPASS a program for generating serial samplesunder an infinite sites model Bioinformatics 252845ndash2847

Kaj I Krone SM Lascoux M 2001 Coalescent theory for seed bankmodels J Appl Probab 38285ndash300

Keller A Graefen A Ball M Matzas M Boisguerin V Maixner F LeidingerP Backes C Khairat R Forster M et al 2012 New insights into theTyrolean Icemanrsquos origin and phenotype as inferred by whole-genome sequencing Nat Commun 3698

Kingman JFC 1982 The coalescent Stochastic Process Appl 13235ndash248Krause J Briggs AW Kircher M Maricic T Zwyns N Derevianko A

Paabo S 2010 A complete mtDNA genome of an early modernhuman from Kostenki Russia Curr Biol 20231ndash236

Krimbas CB Tsakas S 1971 The genetics of Dacus oleae V Changes ofesterase polymorphism in a natural population following insecticidecontrol-selection or drift Evolution 25454ndash460

Li H Durbin R 2011 Inference of human population history from indi-vidual whole-genome sequences Nature 475493ndash496

McVean G 2009 A genealogical interpretation of principal componentsanalysis PLoS Genet 5e1000686

Meyer M Fu Q Aximu-Petri A Glocke I Nickel B Arsuaga J-L MartınezI Gracia A de Castro JMB Carbonell E et al 2014 A mitochondrialgenome sequence of a hominin from Sima de los Huesos Nature505403ndash406

Meyer M Kircher M Gansauge M-T Li H Racimo F Mallick S SchraiberJG Jay F Prufer K de Filippo C et al 2012 A high-coverage genomesequence from an archaic Denisovan individual Science 338222ndash226

Mourier T Ho SY Gilbert MTP Willerslev E Orlando L 2012 Statisticalguidelines for detecting past population shifts using ancient DNAMol Biol Evol 292241ndash2251

Navascues M Depaulis F Emerson BC 2010 Combining contemporaryand ancient DNA in population genetic and phylogeographicalstudies Mol Ecol Resour 10760ndash772

Nei M 1973 Analysis of gene diversity in subdivided populations ProcNatl Acad Sci U S A 703321ndash3323

Nielsen R Wakeley J 2001 Distinguishing migration from isolation aMarkov chain Monte Carlo approach Genetics 158885ndash896

Nordborg M 1998 On the probability of Neanderthal ancestry Am JHum Genet 631237

Novembre J Stephens M 2008 Interpreting principal component anal-yses of spatial population genetic variation Nat Genet 40646ndash649

Nystrom V Dalen L Vartanyan S Liden K Ryman N Angerbjorn A2010 Temporal genetic change in the last remaining population ofwoolly mammoth Proc R Soc B Biol Sci 2772331ndash2337

Nystrom V Humphrey J Skoglund P Mc Keown NJ Vartanyan S ShawPW Liden K Jakobsson M Barnes I Angerbjorn A et al 2012Microsatellite genotyping reveals end-Pleistocene decline in mam-moth autosomal genetic variation Mol Ecol 213391ndash3402

Orlando L Ginolhac A Zhang G Froese D Albrechtsen A Stiller MSchubert M Cappellini E Petersen B Moltke I et al 2013Recalibrating Equus evolution using the genome sequence of anearly Middle Pleistocene horse Nature 49974ndash78

Paabo S 1985 Molecular cloning of ancient Egyptian mummy DNANature 314644ndash645

Patterson N Moorjani P Luo Y Mallick S Rohland N Zhan YGenschoreck T Webster T Reich D 2012 Ancient admixture inhuman history Genetics 1921065ndash1093

Patterson N Price AL Reich D 2006 Population structure and eigen-analysis PLoS Genet 2e190

Pickrell JK Pritchard JK 2012 Inference of population splits and mixturesfrom genome-wide allele frequency data PLoS Genet 8e1002967

Pritchard JK Seielstad MT Perez-Lezaun A Feldman MW 1999Population growth of human Y chromosomes a study of Y chro-mosome microsatellites Mol Biol Evol 161791ndash1798

Prufer K Racimo F Patterson N Jay F Sankararaman S Sawyer S HeinzeA Renaud G Sudmant PH de Filippo C et al 2014 The completegenome sequence of a Neanderthal from the Altai MountainsNature 50543ndash49

R Development Core Team 2010 R A language and environment forstatistical computing Vienna (Austria) the R foundation for statis-tical computing Available from httpwwwR-projectorg

Raghavan M Skoglund P Graf KE Metspalu M Albrechtsen A Moltke IRasmussen S Stafford TW Jr Orlando L Metspalu E et al 2014Upper Palaeolithic Siberian genome reveals dual ancestry of NativeAmericans Nature 50587ndash91

Ramakrishnan U Hadly EA Mountain JL 2005 Detecting past popula-tion bottlenecks using temporal genetic data Mol Ecol 142915ndash2922

Ramakrishnan UMA Hadly EA 2009 Using phylochronology to revealcryptic population histories review and synthesis of 29 ancient DNAstudies Mol Ecol 181310ndash1330

Rasmussen M Li Y Lindgreen S Pedersen JS Albrechtsen A Moltke IMetspalu M Metspalu E Kivisild T Gupta R et al 2010 Ancienthuman genome sequence of an extinct Palaeo-Eskimo Nature 463757ndash762

Reich D Green RE Kircher M Krause J Patterson N Durand EY Viola BBriggs AW Stenzel U Johnson PLF et al 2010 Genetic history of anarchaic hominin group from Denisova Cave in Siberia Nature 4681053ndash1060

Reich D Thangaraj K Patterson N Price AL Singh L 2009Reconstructing Indian population history Nature 461489ndash494

Rodrigo AG Felsenstein J 1999 Coalescent approaches to HIV popula-tion genetics Baltimore (MD) Johns Hopkins University Press

Rosenberg NA Mahajan S Ramachandran S Zhao C Pritchard JKFeldman MW 2005 Clines clusters and the effect of study designon the inference of human population structure PLoS Genet 1e70

2526

Skoglund et al doi101093molbevmsu192 MBE at U

ppsala Universitetsbibliotek on M

arch 4 2016httpm

beoxfordjournalsorgD

ownloaded from

Sanchez-Quinto F Schroeder H Ramirez O Avila-Arcos Marıa C PybusM Olalde I Velazquez Amhed MV Marcos Marıa Encina PEncinas Julio Manuel V Bertranpetit J et al 2012 Genomic affinitiesof two 7000-year-old Iberian hunter-gatherers Curr Biol 221494ndash1499

Schlebusch CM Skoglund P Sjodin P Gattepaille LM Hernandez D JayF Li S De Jongh M Singleton A Blum MGB et al 2012 Genomicvariation in seven Khoe-San groups reveals adaptation and complexAfrican history Science 338374ndash379

Serre D Langaney A Chech M Teschler-Nicola M Paunovic MMennecier P Hofreiter M Possnert G Paabo S 2004 No evidenceof Neandertal mtDNA contribution to early modern humans PLoSBiol 2e57

Serre D Paabo S 2004 Evidence for gradients of human genetic diversitywithin and among continents Genome Res 141679ndash1685

Shapiro B Hofreiter M 2014 A Paleogenomic perspective on evolutionand gene function new insights from ancient DNA Science 3431236573

Sheehan S Harris K Song YS 2013 Estimating variable effective popu-lation sizes from multiple genomes a sequentially Markov condi-tional sampling distribution approach Genetics 194647ndash662

Sjodin P Skoglund P Jakobsson M 2014 Assessing the maximum con-tribution from ancient populations Mol Biol Evol 311248ndash1260

Skoglund P Gotherstrom A Jakobsson M 2011 Estimation of popula-tion divergence times from non-overlapping genomic sequencesexamples from dogs and wolves Mol Biol Evol 281505ndash1517

Skoglund P Malmstrom H Raghavan M Stora J Hall P Willerslev EGilbert MTP Gotherstrom A Jakobsson M 2012 Origins and

genetic legacy of Neolithic farmers and hunterndashgatherers inEurope Science 336466ndash469

Skoglund P Northoff BH Shunkov MV Derevianko AP Paabo S KrauseJ Jakobsson M 2014 Separating endogenous ancient DNA frommodern day contamination in a Siberian Neandertal Proc NatlAcad Sci U S A 1112229ndash2234

Slatkin M 1991 Inbreeding coefficients and coalescence times GenetRes 58167ndash175

Tavare S Balding DJ Griffiths R Donnelly P 1997 Inferring coalescencetimes from DNA sequence data Genetics 145505ndash518

Vartanyan SL Garutt VE Sher AV 1993 Holocene dwarf mammothsfrom Wrangel Island in the Siberian Arctic Nature 362337ndash340

Voight BF Adams AM Frisse LA Qian Y Hudson RR Di Rienzo A 2005Interrogating multiple aspects of variation in a full resequencingdata set to infer human population size changes Proc Natl AcadSci U S A 10218508ndash18513

Wang J 2001 A pseudo-likelihood method for estimating effective pop-ulation size from temporally spaced samples Genet Res 78243ndash258

Waples RS 1989 Temporal variation in allele frequencies testing theright hypothesis Evolution 431236ndash1251

Weir BS 1996 Genetic data analysis II Sunderland (MA) SinauerAssociates Inc

Wright S 1940 Breeding structure of populations in relation to speci-ation Am Nat 74232ndash248

Wright S 1949 Population structure in evolution Proc Am Philos Soc93471ndash478

Wright S 1951 The genetical structure of populations Ann Eugen 15323ndash354

2527

Temporal Population-Genetic Structure doi101093molbevmsu192 MBE at U

ppsala Universitetsbibliotek on M

arch 4 2016httpm

beoxfordjournalsorgD

ownloaded from