© 2003 Nature PublishingGroupREVIEWSNATURE REVIEWS | GENETICS VOLUME 4 | JULY 2003 | 535sequences,whereas the second relies on mathematicalmodels of population structure.This review does not cover all aspects of popula-tion structure; instead, we focus on models andmethods for the study of population structure thatuse DNA sequence data, which we illustrate withexamples from the literature on human populations.Our species has had a complex DEMOGRAPHIC HISTORYand provides examples of many kinds of populationstructure.Also, a considerable part of modern med-ical genetics relies on an understanding of humandemographic history, so there is a strong demand forhigh-quality human population-genetic research.Starting simplyTo gain a starting purchase, we need a simple populationmodel that does not have structure. Sewall Wright andRonald A.Fisher independently described what has cometo be the standard simple population model for most cir-cumstances2,3.The main feature of the Wright–Fishermodel(BOX 1) is the persistence of a single populationof constant size,with random mating among individ-uals (panmixia). For most purposes it is assumed thatthe population has persisted for a long period (literally aninfinite length of time, for mathematical purposes).In the early twentieth century,when the new scienceof genetics was picking up steam,the big questionwas whether Mendel’s rules of inheritance could bereconciled with a Darwinian theory of evolution. Inthe course of finding out that they were compatible,the new science of population genetics was born1.To day,as at the beginning, population genetics is thestudy of how evolution works as a genetic process innatural populations. It is a difficult science,which isoften highly mathematical in theory and approximatein application.Real populations are rarely simple,soit is difficult to research and develop theories aboutthem.Natural populations are also dynamic in manydimensions: over time they change in size,densityand location,and over space they can fragment intoseveral populations and join with others.An aware-ness of those complexities,and a desire to have evolu-tionary models that are as realistic as possible, has ledmany population geneticists to focus their efforts onwhat has come to be called the ‘structure’of naturalpopulations.This field has grown with the availabilityof comparative DNA sequence data from naturalpopulations.However, growth has proceeded in twodifferent directions:the first relies on graphical depic-tions of the branching evolutionary history of DNATHE STUDY OF STRUCTUREDPOPULATIONS — NEW HOPE FOR ADIFFICULT AND DIVIDED SCIENCEJody Hey* and Carlos A.Machado‡Natural populations, including those of humans, have complex geographies and histories.Studying how they evolve is difficult, but it is possible with population-based DNA sequence data.However, the study of structured populations is divided by two distinct schools of thought andanalysis. The phylogeographic approach is fundamentally graphical and begins with a gene-treeestimate. By contrast, the more traditional approach of using summary statistics is fundamentallymathematical. Both approaches have limitations, but there is promise in newer probabilisticmethods that offer the flexibility and data exploitation of the phylogeographic approach in anexplicitly model-based mathematical framework.*Department of Genetics,Rutgers the State Universityof New Jersey, 604 AllisonRoad, Piscataway,New Jersey 08854, USA.‡Department of Ecology andEvolutionary Biology,University of Arizona,1041 East Lowell Street,BSW 308, Tucson,Arizona 85721, USA.Correspondence to: J.H.e-mail:[email protected]:10.1038/nrg1112DEMOGRAPHIC HISTORYThe reproductive history of apopulation or group ofpopulations. This can includepopulation sizes,sex ratios,migration rates, population-splitting events,variation inreproductive rates and timesamong organisms, as well asvariation over time in all of thesequantities.© 2003 Nature PublishingGroupPOISSON DISTRIBUTIONA probability distribution that iscommonly used to describe thefrequency at which similar butindependent events can beexpected to occur over a givenperiod of time.GENE EXCHANGEThe process by which geneticmaterial is shared amongorganisms, which can occurthrough sexual reproduction orlateral genetic transfer.GENETIC DRIFTRandom changes in genefrequency in a population thatoccur when a finite number ofprogeny are formed by therandom sampling of gametesfrom the parents.HARDY-WEINBERGA classical mathematicalprinciple in population genetics that describes theexpected frequencies ofgenotypes for one locus afterone generation of randommating if the allele frequenciesin the parents are known.EVOLUTIONARY TREEA graph or branching diagramthat describes the pattern ofevolutionary ancestry (historicalrelationships) among a group oforganisms.GENE TREEA graph or branching diagramthat describes the pattern ofancestry among homologousDNA sequences from differentindividuals of a population orspecies.PHYLOGENETIC TREEA graph or branching diagramthat describes the pattern ofancestry among different speciesor other taxa.536 | JULY 2003 | VOLUME 4 www.nature.com/reviews/geneticsREVIEWSfrequencies and,in the case of diploid populations,departures from HARDY-WEINBERG expectations. Thesemeasurements lend themselves well to the fitting of equi-librium models, but generally do not have the informa-tion content that is needed to assess whether modelparameters have changed over time. By contrast,a set ofDNA sequences from one gene often shows a large num-ber of polymorphic sites with high information contentthat will provide greater scope for the interpretation ofchanging population-model parameters.A divided science — to tree or not to tree?When population geneticists began collecting DNAsequence data from natural populations in the late1970s,the field underwent a notable shift,and a splitdeveloped between two main schools of thought.Unlikeallelic data,DNA sequence data can be readily applied tothe calculation ofEVOLUTIONARY TREES,and some investiga-tors quickly realized that these kinds of trees could be abasis for the study of population history. Such GENE TREES are different from traditional PHYLOGENETIC TREES(the former describe the pattern of DNA ancestry in apopulation,the latter a pattern of taxon ancestry), but thetools that SYSTEMATICS uses for building evolutionary treescould be used to build population gene trees.Using DNA sequence data