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PSMIX: an R package for population structure inference via maximum likelihood method



Inference of population stratification and individual admixture from genetic markers is an integrative part of a study in diverse situations, such as association mapping and evolutionary studies. Bayesian methods have been proposed for population stratification and admixture inference using multilocus genotypes and widely used in practice. However, these Bayesian methods demand intensive computation resources and may run into convergence problem in Markov Chain Monte Carlo based posterior samplings.


We have developed PSMIX, an R package based on maximum likelihood method using expectation-maximization algorithm, for inference of population stratification and individual admixture.


Compared with software based on Bayesian methods (e.g., STRUCTURE), PSMIX has similar accuracy, but more efficient computations.

PSMIX and its supplemental documents are freely available at


Information about population structure, namely population stratification and admixture, is useful in a variety of situations, such as association studies of genes underlying complex traits, subspecies classification, genetic barrier detection, and evolutionary study [110]. For example, it is very important to identify genetic ancestry and admixture in admixture mapping [7, 8]. The presence of population stratification or admixture may pose a practical nuisance as well. In association studies, case-control design is often used to identify genetic variants underlying complex traits by comparing allele frequencies between unrelated individuals that are affected and those unaffected. However, the presence of population stratification or admixture in the sample can lead to spurious associations between a candidate marker and a phenotype [5, 10, 11]. In forensic studies, the identification of reference groups is central but becomes difficult when there exists population stratification [12, 13]. In the estimation of the magnitude of inbreeding, it is useful to distinguish between the causes for the excess homozygosity which might be consanguineous mating or population substructure, or an artifact due to factors like null alleles [14]. In all these situations, identifying population stratification or admixture has been an important component.

Population structure can be identified based on visible characters such as language, culture, physical appearance, and geographic region. But this can be subjective and may bear no relevance to genetics. Evanno et al. [15] gave a good example by mentioning migratory bats which can be found thousands of kilometers apart but from the same breeding roost in winter [16]. Statistical methods have been proposed to infer population stratification and individual admixture using multilocus genotype data [1, 2, 1731]. Different methods use different statistical tools and population genetic assumptions. Pritchard et al. [2] introduced a model-based clustering method to infer population structure and assign individuals to populations using multilocus genotype data. They used Bayesian formulation and generated the posterior distributions using a Markov Chain Monte Carlo (MCMC) method based on Gibbs sampling. Their main modeling assumptions are Hardy-Weinberg equilibrium (HWE) within populations and linkage equilibrium (LE) between markers within each population. Falush et al. [21] extended the method to allow for loose linkage between loci. The method of Corander et al. [17, 18] uses multilocus molecular markers and geographical information provided by the sampling design. Unlike the methods of Pritchard et al. [2] and Falush et al. [21], the methods of both Dawson and Belkhir [19] and Corander et al. [17, 18] can directly estimate the number of (sub)populations and assign individuals to the (sub)populations. The main difference between the two approaches is the parametric assumption of the number of populations [1719, 32]. Corander et al. [18] considered the geographical sampling design of the individuals and set the maximum number of populations allowed to be the number of locations sampled, whereas for Dawson and Belkhir [19], it is the total number of individuals. Corander et al. [17] generalized the approach of Corander et al. [18] and it became more similar to the approach of Dawson and Belkhir [19] in terms of model assumptions and some technical details, especially when the data is specified for individual level analysis. Guillot et al. [23, 24] used spatial statistical models employing both landscape ecology and population genetics information, which is especially useful in situations of young populations exhibiting low genetic differentiation [23, 33]. Excoffier et al. [20] applied approximate Bayesian computation method to the estimation of all the parameters of an explicit admixture model. Their method can easily deal with complex mutation models and partially linked loci and is superior when the admixture is more ancient [20]. The majority of the methods for population structure inference are Bayesian approaches [1, 2, 1726] with few exceptions such as Tang et al. [30], Satten et al. [29], Wang [31], and Purcell and Sham [28]. Meanwhile, several methods have been proposed for the assignment of individuals to populations [3436]. As for computer programs available based on existing methods, the majority are also based on Bayesian MCMC methods, such as STRUCTURE [2, 21], GENELAND [24], BAPS/BAPS 2 [17, 18], and ADMIXMAP [25, 37, 38], with the exception of L-POP[28] which is based on latent class analysis. Table 1 summarizes some of the commonly used software for population structure inference. STRUCTURE is the most commonly used program for population structure inference which has been used both on humans [4, 13, 39] and other species [3, 4042] (at the time this article is written, the paper of Pritchard et al. [2], where the method of STRUCTURE was originally proposed, has been cited about 760 times). We choose to compare the performance of our package with STRUCTURE and L-POP (the representative of the frequentist methods).

Table 1 Commonly used software for population structure inference


We have developed an efficient R package, named PSMIX (Population Structure inference via MIXture model), for population stratification and individual admixture inference. Since R can be slow when computation is intensive, we implemented the expectation-maximization (EM) algorithm [43] using C programming language. PSMIX is mainly based on the methods proposed in Tang et al. [30] and Liu et al. [27]. Three models (described in section 2.2, 2.3, and 2.4, respectively) are discussed in full detail in [27]. The second one is equivalent to the model proposed in Tang et al. [30]. The first model is a special case of the second one. In Tang et al. the method itself has been fully assessed by simulation studies [30].


We used two real datasets from Rosenberg et al. [4] and one simulated dataset from Tang et al. [30] to demonstrate the functionality of PSMIX. One real dataset contains two American populations, Pima and Surui with 25 and 21 individuals, respectively; the other contains two European populations, Sardinian and Russian with 28 and 25 individuals, respectively. The simulated data set contains 50 individuals from each of the two ancestral populations, and 200 individuals from the admixed population. The true individual admixture values of the admixed individuals are also available.

To evaluate the efficiency of PSMIX, we randomly selected 100 markers from the Pima-Surui dataset with no missing values and tried the four models available in STRUCTURE2.0. Burnin length and number of MCMC replications after burnin were both set to be 10,000 in the analyses. The time needed for each run of STRUCTURE2.0 increased almost linearly with the increase of number of clusters. On our PC with Pentium III 500 MHZ CPU and 384 MB SDRAM, when K = 2, about two and a half minutes were needed for each run of STRUCTURE2.0. For all PSMIX runs, we set the stopping criterion to be that the parameter difference <10-6 between consecutive iterations, or 10,000 steps, whichever was reached first. For the same Pima-Surui data with 100 markers, each run of PSMIX needed about 6 seconds.

To evaluate the accuracy of PSMIX, we compared the results of PSMIX with those of STRUCTURE. Figure 1 gives a sample run for the Pima-Surui dataset using only the first 50 markers. For the Pima-Surui dataset using the first 50 markers from the original data, the correlation coefficient between the results of PSMIX and STRUCTURE was greater than 0.999. For the Sardinian-Russian dataset, when all 377 markers were used, both STRUCTURE 2.0 (use independent allele frequencies among populations with admixture model) and PSMIX had one individual misclustered. The correlation coefficient between the results was 0.906. The two methods produced very similar results. This is consistent with the findings in Tang et al. [30]. Figure 2 shows the results of STRUCTURE, L-POP, and PSMIX. We can see that the results of PSMIX are much closer to those of STRUCTURE.

Figure 1
figure 1

Comparison of estimates of individual admixture of STRUCTURE (x-axis) and PSMIX (y-axis) for the data of Pima and Surui from Rosenberg et al. (2002). Only the first 50 markers were used.

Figure 2
figure 2

Estimates of STRUCTURE, PSMIX and L-POP for the data of Pima and Surui (the first 21 samples are Surui) from Rosenberg et al. (2002). Only the first 50 markers were used.

To evaluate the performance of PSMIX, we also used a simulated data set exhibiting population admixture. From Figure 3 we can see the PSMIX performs pretty well and the results are almost identical to those from STRUCTURE.

Figure 3
figure 3

Estimates of STRUCTURE and PSMIX for the simulated data.


We have implemented a likelihood based method of population structure inference into an efficient R package, PSMIX. PSMIX can be used in population genetics and disease gene mapping, wherever population stratification or individual admixture is needed to be estimated from genetic markers. Compared with other available similar programs, PSMIX has several advantages. First, it is computationally efficient and provides similar accuracy under realistic situations (Tang, et al. [30] and Liu et al., Technical Report [27]). And thus the confidence intervals of the estimates can be constructed via resampling methods, e.g., the bootstrap method [30]. Second, as shown in Tang et al. [30], it performs a little better (compared with STRUCTURE) under some conditions involving a small number of ancestors and markers. We note that L-POP is also computationally efficient. However, it is not clear if L-POP can perform better under such conditions. Third, it is very flexible. It is likelihood based and can be easily incorporated into study designs, such as marker choice [30]. The program is implemented as a public R package and can be easily extended and incorporated into other packages. This is an advantage of PSMIX over STRUCTURE and L-POP, which has only executable programs.

We would like to note that the examples used in this work are mainly for the purpose of demonstrating the R package, not for the purpose of the assessing the underlying method. Please refer to Tang et al. [30] for a detailed assessment of the methodology.

In our simulation and application to real data, PSMIX and STRUCTURE gave very similar results. This is not surprising because estimating parameters via maximum likelihood and maximum a posterior with flat prior is formally strictly similar, where PSMIX belongs to the former and STRUCTURE belongs to the latter.

Many studies have been performed to assess the ability of STRUCTURE in assigning individuals to their populations of origin using either real data or simulated data [3, 4447]. However, very limited studies have been performed to assess the ability of STRUCTURE in detecting the number of populations. Recently, Evanno et al. [15] performed a systematic study on this issue using simulations. They simulated amplified fragment length polymorphism (AFLP) and microsatellite genetic data under three population structure models: the island model, a contact zone, and a hierarchical island model [15]. Their major finding is that the "log probability of data", an ad hoc criterion suggested by Pritchard et al. [2] for detecting the number of populations, does not provide a correct estimation of the number of populations most of the time [15]. However, they found that another ad hoc statistic, which is based on the rate of change in the log probability of the data between successive numbers of populations, can accurately detect the uppermost hierarchical level of structure [15]. They also found some other factors that can affect the detection of the number of populations [15]. These findings are important and useful in that with the increasing usage of STRUCTURE, they provide guidance on how to use STRUCTURE to detect the number of populations. However, PSMIX does not directly detect the number of populations in this version. Due to its computation efficiency, model selection methods such as Akaike information criterion (AIC) [28, 48], Bayesian information criterion (BIC) [49], and even more general, penalized likelihood based methods [50, 51] can be used for this purpose. The findings of Evanno et al. [15] may be incorporated into PSMIX as well. This is one of our future works.

EM approach and Bayesian MCMC approach have their own advantages and disadvantages. They both can trap in local modes, although theoretically speaking, Bayesian MCMC approach can converge to the true value eventually, maybe after an unrealistic long time. However, the Bayesian MCMC approach, in addition, has the label switching problem. Two authors (Stephens and Donnelly) of the paper where the method of STRUCTURE was proposed [2] mentioned in other papers [52, 53] on methods to deal with this problem. Although this issue is believed to be well addressed by STRUCTURE, it does make the Bayesian MCMC approach more complicated. However, this topic is beyond the scope of this work. From the users' point of view, they only see the computation efficiency and stability of the methods.

We think that it may be necessary to explicitly explain some details about the models mentioned in this work. First, the orientation of Tang et al. [30] is different from that of STRUCTURE, L-POP, and Liu et al. [27]. The goal of the former was to estimate individual admixture for the admixed individuals. The original focus of the latter was to "identify discrete clusters roughly corresponding to subpopulations" [30]. STRUCTURE, L-POP, and Liu et al. [27] use methods for clustering, although they "can also be applied to an admixture model" [30]. So initially, Tang et al. [30] faced a population (the "admixed group" in their paper) that is currently in Hardy-Weinberg equilibrium, but was created as the result of admixture at some point in the past. However, as emphasized in Tang et al. [30], the problem may not be identifiable without the inclusion of pseudo-ancestors who are proxies of the true pure ancestry [25]. Here the nonidentifiablity issue is related to the problem, and by no means pertains to the method. In other words, the nonidentifiablity issue exists and has nothing to do with the statistical methods to be used, if pseudo-ancestors are not included. Therefore, the actual data Tang et al. [30] dealt with consist of "I0 individuals from the admixed group, as well as IK subjects from each of the K ancestral populations" [30], that is, a stratified "pooled" population. So the actual data all these methods deal with are the same in the sense that the data consist of stratified populations within which Hardy-Weinberg equilibrium holds. One major difference is that Tang et al. [30] only focus on the individual admixture of the people in the admixed population (their original population). Facing the same data, the method in Tang et al. [30] is for clustering as well, in spirit. They included pseudo-ancestors and used clustering method in order to estimate individual admixture. In other words, all the aforementioned methods are for population stratification, and can be applied to estimate individual admixture. Thus the comparisons made in this work are appropriate. We also want to emphasize here the importance of inclusion of ancestral populations or their surrogates when individual admixture is needed; otherwise the problem may not be identifiable no matter what method to use.


In summary, we have implemented a new, likelihood based method for inference of population stratification and individual admixture which is available as a public R package. Although the package has several advantages over its peers, we strongly suggest that the users use different software in their analysis. If the results from these software are consistent; this may provide more support for the results; if the results are not consistent, further investigation is needed. A potential limitation is the assumption of independence among markers behind PSMIX, which will be addressed in future versions of PSMIX.

Availability and requirements

Project name: PSMIX

Project home page:

Operating system(s): MS Windows, Linux, Mac

Programming language: C, R

Other requirements: R 2.0 or higher

License: GPL

Any restrictions to use by non-academics: none


  1. 1.

    Patterson N, Hattangadi N, Lane B, Lohmueller KE, Hafler DA, Oksenberg JR, Hauser SL, Smith MW, O'Brien SJ, Altshuler D, Daly M, Reich D: Methods for high-density admixture mapping of disease genes. Am J Hum Genet 2004,74(5):979–1000. 10.1086/420871

    PubMed Central  CAS  Article  PubMed  Google Scholar 

  2. 2.

    Pritchard JK, Stephens M, Donnelly P: Inference of population structure using multilocus genotype data. Genetics 2000,155(2):945–959.

    PubMed Central  CAS  PubMed  Google Scholar 

  3. 3.

    Rosenberg NA, Burke T, Elo K, Feldman MW, Freidlin PJ, Groenen MA, Hillel J, Maki-Tanila A, Tixier-Boichard M, Vignal A, Wimmersh K, Weigend S: Empirical evaluation of genetic clustering methods using multilocus genotypes from 20 chicken breeds. Genetics 2001,159(2):699–713.

    PubMed Central  CAS  PubMed  Google Scholar 

  4. 4.

    Rosenberg NA, Pritchard JK, Weber JL, Cann HM, Kidd KK, Zhivotovsky LA, Feldman MW: Genetic structure of human populations. Science 2002,298(5602):2381–2385. 10.1126/science.1078311

    CAS  Article  PubMed  Google Scholar 

  5. 5.

    Cardon LR, Palmer LJ: Population stratification and spurious allelic association. Lancet 2003,361(9357):598–604. 10.1016/S0140-6736(03)12520-2

    Article  PubMed  Google Scholar 

  6. 6.

    Freedman ML, Reich D, Penney KL, McDonald GJ, Mignault AA, Patterson N, Gabriel SB, Topol EJ, Smoller JW, Pato CN, Pato MT, Petryshen TL, Kolonel LN, Lander ES, Sklar P, Henderson B, Hirschhorn JN, Altshuler D: Assessing the impact of population stratification on genetic association studies. Nat Genet 2004,36(4):388–393. 10.1038/ng1333

    CAS  Article  PubMed  Google Scholar 

  7. 7.

    Montana G, Pritchard JK: Statistical tests for admixture mapping with case-control and cases-only data. Am J Hum Genet 2004,75(5):771–789. 10.1086/425281

    PubMed Central  CAS  Article  PubMed  Google Scholar 

  8. 8.

    Reich D, Patterson N: Will admixture mapping work to find disease genes? Philos Trans R Soc Lond B Biol Sci 2005,360(1460):1605–1607. 10.1098/rstb.2005.1691

    PubMed Central  CAS  Article  PubMed  Google Scholar 

  9. 9.

    Marchini J, Cardon LR, Phillips MS, Donnelly P: The effects of human population structure on large genetic association studies. Nat Genet 2004,36(5):512–517. 10.1038/ng1337

    CAS  Article  PubMed  Google Scholar 

  10. 10.

    Chen HS, Zhu X, Zhao H, Zhang S: Qualitative semi-parametric test for genetic associations in case-control designs under structured populations. Ann Hum Genet 2003,67(Pt 3):250–264. 10.1046/j.1469-1809.2003.00036.x

    CAS  Article  PubMed  Google Scholar 

  11. 11.

    Risch NJ: Searching for genetic determinants in the new millennium. Nature 2000,405(6788):847–856. 10.1038/35015718

    CAS  Article  PubMed  Google Scholar 

  12. 12.

    National research council: The Evaluation of Forensic DNA Evidence. 1996.

    Google Scholar 

  13. 13.

    Kim JJ, Verdu P, Pakstis AJ, Speed WC, Kidd JR, Kidd KK: Use of autosomal loci for clustering individuals and populations of East Asian origin. Hum Genet 2005,117(6):511–519. 10.1007/s00439-005-1334-8

    Article  PubMed  Google Scholar 

  14. 14.

    Overall AD, Nichols RA: A method for distinguishing consanguinity and population substructure using multilocus genotype data. Mol Biol Evol 2001,18(11):2048–2056.

    CAS  Article  PubMed  Google Scholar 

  15. 15.

    Evanno G, Regnaut S, Goudet J: Detecting the number of clusters of individuals using the software STRUCTURE: a simulation study. Mol Ecol 2005,14(8):2611–2620. 10.1111/j.1365-294X.2005.02553.x

    CAS  Article  PubMed  Google Scholar 

  16. 16.

    Petit E, Balloux F, Goudet J: Sex-biased dispersal in a migratory bat: a characterization using sex-specific demographic parameters. Evolution Int J Org Evolution 2001,55(3):635–640.

    CAS  Article  Google Scholar 

  17. 17.

    Corander J, Waldmann P, Marttinen P, Sillanpaa MJ: BAPS 2: enhanced possibilities for the analysis of genetic population structure. Bioinformatics 2004,20(15):2363–2369. 10.1093/bioinformatics/bth250

    CAS  Article  PubMed  Google Scholar 

  18. 18.

    Corander J, Waldmann P, Sillanpaa MJ: Bayesian analysis of genetic differentiation between populations. Genetics 2003,163(1):367–374.

    PubMed Central  CAS  PubMed  Google Scholar 

  19. 19.

    Dawson KJ, Belkhir K: A Bayesian approach to the identification of panmictic populations and the assignment of individuals. Genet Res 2001,78(1):59–77. 10.1017/S001667230100502X

    CAS  Article  PubMed  Google Scholar 

  20. 20.

    Excoffier L, Estoup A, Cornuet JM: Bayesian analysis of an admixture model with mutations and arbitrarily linked markers. Genetics 2005,169(3):1727–1738. 10.1534/genetics.104.036236

    PubMed Central  CAS  Article  PubMed  Google Scholar 

  21. 21.

    Falush D, Stephens M, Pritchard JK: Inference of population structure using multilocus genotype data:linked loci and correlated allele frequencies. Genetics 2003,164(4):1567–1587.

    PubMed Central  CAS  PubMed  Google Scholar 

  22. 22.

    Fu R, Dey DK, Holsinger KE: Bayesian models for the analysis of genetic structure when populations are correlated. Bioinformatics 2005,21(8):1516–1529. 10.1093/bioinformatics/bti178

    CAS  Article  PubMed  Google Scholar 

  23. 23.

    Guillot G, Estoup A, Mortier F, Cosson JF: A spatial statistical model for landscape genetics. Genetics 2005,170(3):1261–1280. 10.1534/genetics.104.033803

    PubMed Central  CAS  Article  PubMed  Google Scholar 

  24. 24.

    Guillot G, Mortier F, Estoup A: Geneland: A computer package for landscape genetics. Molecular Ecology Notes 2005,5(3):708–711.

    Article  Google Scholar 

  25. 25.

    Hoggart CJ, Parra EJ, Shriver MD, Bonilla C, Kittles RA, Clayton DG, McKeigue PM: Control of confounding of genetic associations in stratified populations. Am J Hum Genet 2003,72(6):1492–1504. 10.1086/375613

    PubMed Central  CAS  Article  PubMed  Google Scholar 

  26. 26.

    Holsinger KE, Wallace LE: Bayesian approaches for the analysis of population genetic structure: an example from Platanthera leucophaea (Orchidaceae). Mol Ecol 2004,13(4):887–894. 10.1111/j.1365-294X.2004.02052.x

    Article  PubMed  Google Scholar 

  27. 27.

    Liu N, Wu B, Zhao H: Inference of population structure using mixture model. Technical report 2005. []

    Google Scholar 

  28. 28.

    Purcell S, Sham P: Properties of structured association approaches to detecting population stratification. Hum Hered 2004,58(2):93–107. 10.1159/000083030

    Article  PubMed  Google Scholar 

  29. 29.

    Satten GA, Flanders WD, Yang Q: Accounting for unmeasured population substructure in case-control studies of genetic association using a novel latent-class model. Am J Hum Genet 2001,68(2):466–477. 10.1086/318195

    PubMed Central  CAS  Article  PubMed  Google Scholar 

  30. 30.

    Tang H, Peng J, Wang P, Risch NJ: Estimation of individual admixture: analytical and study design considerations. Genet Epidemiol 2005,28(4):289–301. [] 10.1002/gepi.20064

    Article  PubMed  Google Scholar 

  31. 31.

    Wang J: Maximum-likelihood estimation of admixture proportions from genetic data. Genetics 2003,164(2):747–765.

    PubMed Central  PubMed  Google Scholar 

  32. 32.

    Manel S, Gaggiotti OE, Waples RS: Assignment methods: matching biological questions with appropriate techniques. TRENDS in Ecology and Evolution 2005,20(3):136–142. 10.1016/j.tree.2004.12.004

    Article  PubMed  Google Scholar 

  33. 33.

    Coulon A, Guillot G, Cosson J-F, Angibault JMA, Aulagnier S, Cargnelutti B, Galan M, Hewison AJM: Genetics structure is influenced by lansdcape features. Empirical evidence from a roe deer population. Molecular Ecology Notes, in press.

  34. 34.

    Banks MA, Eichert W: WHICHRUN (version 3.2): a computer program for population assignment of individuals based on multilocus genotype data. J Hered 2000,91(1):87–89. 10.1093/jhered/91.1.87

    CAS  Article  PubMed  Google Scholar 

  35. 35.

    Cornuet JM, Piry S, Luikart G, Estoup A, Solignac M: New methods employing multilocus genotypes to select or exclude populations as origins of individuals. Genetics 1999,153(4):1989–2000.

    PubMed Central  CAS  PubMed  Google Scholar 

  36. 36.

    Rannala B, Mountain JL: Detecting immigration by using multilocus genotypes. Proc Natl Acad Sci USA 1997,94(17):9197–9201. 10.1073/pnas.94.17.9197

    PubMed Central  CAS  Article  PubMed  Google Scholar 

  37. 37.

    McKeigue PM, Carpenter JR, Parra EJ, Shriver MD: Estimation of admixture and detection of linkage in admixed populations by a Bayesian approach: application to African-American populations. Ann Hum Genet 2000,64(Pt 2):171–186. 10.1046/j.1469-1809.2000.6420171.x

    CAS  Article  PubMed  Google Scholar 

  38. 38.

    Hoggart CJ, Shriver MD, Kittles RA, Clayton DG, McKeigue PM: Design and analysis of admixture mapping studies. AmJ Hum Genet 2004,74(5):965–978. 10.1086/420855

    CAS  Article  Google Scholar 

  39. 39.

    Li SL, Yamamoto T, Yoshimoto T, Uchihi R, Mizutani M, Kurimoto Y, Tokunaga K, Jin F, Katsumata Y, Saitou N: Phylogenetic relationship of the populations within and around Japan using 105 short tandem repeat polymorphic loci. Hum Genet 2006,118(6):695–707. 10.1007/s00439-005-0106-9

    CAS  Article  PubMed  Google Scholar 

  40. 40.

    Kuroda Y, Kaga A, Tomooka N, Vaughan DA: Population genetic structure of Japanese wild soybean (Glycine soja) based on microsatellite variation. Mol Ecol 2006,15(4):959–974.

    CAS  Article  PubMed  Google Scholar 

  41. 41.

    Manel S, Bellemain E, Swenson JE, Francois O: Assumed and inferred spatial structure of populations: the Scandinavian brown bears revisited. Mol Ecol 2004,13(5):1327–1331. 10.1111/j.1365-294X.2004.02074.x

    CAS  Article  PubMed  Google Scholar 

  42. 42.

    Pearse DE, Arndt AD, Valenzuela N, Miller BA, Cantarelli V, Sites JW Jr: Estimating population structure under nonequilibrium conditions in a conservation context: continent-wide population genetics of the giant Amazon river turtle, Podocnemis expansa (Chelonia; Podocnemididae). Mol Ecol 2006,15(4):985–1006.

    CAS  Article  PubMed  Google Scholar 

  43. 43.

    Dempster AP, Laird NM, Rubin DB: Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society Series B 1977, 34: 1–38.

    Google Scholar 

  44. 44.

    Yang BZ, Zhao H, Kranzler HR, Gelernter J: Practical population group assignment with selected informative markers: characteristics and properties of Bayesian clustering via STRUCTURE. Genet Epidemiol 2005,28(4):302–312. 10.1002/gepi.20070

    Article  PubMed  Google Scholar 

  45. 45.

    Pritchard JK, Donnelly P: Case-control studies ofassociation in structured or admixed populations. Theor Popul Biol 2001,60(3):227–237. 10.1006/tpbi.2001.1543

    CAS  Article  PubMed  Google Scholar 

  46. 46.

    Turakulov R, Easteal S: Number of SNPS loci needed to detect population structure. Hum Hered 2003,55(1):37–45. 10.1159/000071808

    Article  PubMed  Google Scholar 

  47. 47.

    Manel S, Berthier P, Luikart G: Detecting Wildlife Poaching: Identifying the Origin of Individuals with Bayesian Assignment Tests and Multilocus Genotypes. Conservation Biology 2002,16(3):650–659. 10.1046/j.1523-1739.2002.00576.x

    Article  Google Scholar 

  48. 48.

    Akaike H: A new look at the statistical identification model. IEEE Trans Automatic Control 1974, 19: 716–723. 10.1109/TAC.1974.1100705

    Article  Google Scholar 

  49. 49.

    Zhu X, Zhang S, Zhao H, Cooper RS: Association mapping, using a mixture model for complex traits. Genet Epidemiol 2002,23(2):181–196. 10.1002/gepi.210

    Article  PubMed  Google Scholar 

  50. 50.

    Chen H, Chen J, Kalbfleisch JD: A modied likelihood ratio test for homogeneity in finite mixture models. Journal of Royal Statistical Society B 2001, 63: 19–29. 10.1111/1467-9868.00273

    Article  Google Scholar 

  51. 51.

    Chen H, Chen J, Kalbfleisch JD: Testing for a finite mixture model with two components. Journal of Royal Statistical Society B 2004, 66: 95–115. 10.1111/j.1467-9868.2004.00434.x

    Article  Google Scholar 

  52. 52.

    Stephens M: Dealing with label-switching in mixture models. Journal of Royal Statistical Society B 2000, 62: 795–809. 10.1111/1467-9868.00265

    Article  Google Scholar 

  53. 53.

    Stephens M, Smith NJ, Donnelly P: A new statistical method for haplotype reconstruction from population data. Am J Hum Genet 2001,68(4):978–989. 10.1086/319501

    PubMed Central  CAS  Article  PubMed  Google Scholar 

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We thank the two anonymous reviewers for their insightful and constructive comments which have greatly improved the presentation of our work. We thank Dr. Hua Tang for sending us her presentation slides. This work was supported in part by NIH grants GM59507 and GM57672.

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Correspondence to Hongyu Zhao.

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Authors' contributions

BW participated in the design of the study, implemented PSMIX, and helped to draft the manuscript; NL participated in the design of the study, performed the analysis, and drafted the manuscript; HZ conceived the study, participated in its design and helped to draft the manuscript. All authors read and approved the final manuscript.

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Wu, B., Liu, N. & Zhao, H. PSMIX: an R package for population structure inference via maximum likelihood method. BMC Bioinformatics 7, 317 (2006).

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  • Markov Chain Monte Carlo
  • Latent Class Analysis
  • Population Stratification
  • Approximate Bayesian Computation
  • Admix Population