STRUCTURE

1. STRUCTURE http://pritch.bsd.uchicago.edu Riccardo Negrini riccardo.negrini@unicatt.it

2. A model-based clustering methods that use molecular markers to: • Infer the properties of populations starting from single individuals • Demonstrating the presence of a populations structure • Detecting “cryptic” populations structure • Classify individuals of unknown origins • Identify immigrant • Identify mixed individuals

3. Distance-based methods Easy to apply and visually appealing but • The cluster identify are heavily dependant to the distance measures and to the graphical representation chosen • Difficult to asses the level of confidence of the cluster obtained • Difficult to incorporate additional information • More suited to exploratory data analysis than to fine statistical inference

4. Dice similarity and multivariate analysis Italian Limousine Marchigiana Romagnola

5. Distribution Dice similarity between (dotted line) and within breeds ROM/FRI ROM/LMI ROM/ROM ROM/MCG ROM/CHI

6. STRUCTURE main assumption: H-W equilibrium within populations Linkage equilibrium between loci within populations • STRUCTUREdoes not assume a particular mutation process so it can be use with the most common molecular markers (STR, RFLP, SNP, AFLP). Sequence data, Y chromosome or mtDNA haplotypes have to be recoded as a single locus with many alleles • STRUCTURE accounts for the presence of H-W and LD by introducing population structure and attempts to find populations grouping that (as far as possible) are not in disequilibrium

7. STRUCTURE adopt a BAYESIAN approach: Let X denote the genotype of the sampled individuals Let Z denote the unknown population of origin of the individuals Let P denote the unknown allele frequencies in all populations Under H-W and LE each allele at each locus in each genotype in an independent drown from the appropriate frequency distributions Having observed X, the knowledge on Z and P is given by the posterior probability of Bayes theorem: Pr (Z, P|X) = Pr(Z) Pr(P) Pr(X|Z, P) It is not possible to compute the distribution exactly but it is possible to obtain approximate samples of Z and P using MCMC and than make inference based on summary statistics of this samples

8. Bayesian inferences: basic principles • No logic distinction between parameters and data. Both are random variables: data “observed” and parameters “unobserved” • PRIOR encapsulates information about the values of a parameters before observing the data • LIKELIHOOD is a conditional distribution that specified the probability of the data at any particular values of the parameters • Aims of Bayesian inference is to calculate the POSTERIORdistribution of the parameters (The conditional distribution of the parameters given the data)

9. FORMAT OF THE DATA FILE: Indicate learning samples Alleles in rows Missing data File in txt format with tabs Dominant data: code 1 the band presence (AA or Aa) and 2 the absence (aa) second alleles as missing data (-9)

10. BUILDING A PROJECT: Step 1 Step 2 Step 4 Step 3

11. …….if everything goes well:

12. MODELLING DECISION: Ancestry model: No admixture model: each ind comes purely from one of the k populations. The output is the posterior prob that individual i comes from the pop k. The prior prob for each populations is 1/k. appropriate for discrete populations and for dominat data Admixture model: ind may have mixed ancestry i.e have inherited some fractions of its genome from ancestors in population k. The output is the posterior mean estimates of this proportions Linkage model: If t generation in the past there was an admixture event that mixed the k populations, any individual chromosome resulted composed of “chunks” inherited as discrete units from ancestors at the time of admixture. Using prior population information: this is the default option in structure. Not recommended in the exploratory preliminary analysis of the data. Popflag allow to specify which samples had to be used as learning samples to assist clustering

13. Frequency mode: Allele frequencies independent: it assumes that allele frequencies in each populations are independent drown from a distribution specified by a parameters l. The prior says that we expect the allele frequencies in each population to be reasonably different from each others. Allele frequencies correlate: it assumes that allele frequencies in the different populations are likely to be correlate probably due to migrations or shared ancestry. The K populations represented in the dataset have each undergone an independent drift away from the ancestral allele fequencies

14. How long run the program? Length of burn-in period: number of MCMC iteration necessary to reach a “stationary distribution”: the state it visit will tend to the probability distribution of interest (e.g. Pr(Z, P|X)) that no longer depend on the number of iteration or the initial state of the variables. Number of MCMC after burn-in: number of iteration after burn-in to get accurate parameters estimate Loosely speaking: usually burn-in from 10,000 to 100,000 iteration are adequate. Good estimate of the parameters P and Q can be obtained with fairly short run (100,000). Accurate estimation of Pr(X|K) need quite long run (106)

15. How to choose k (number of populations)? No rules, but only iterative method: i.e. try different k and different Length of burn-in period and number of MCMC iteration after burn-in. • Fully resolving all the groups in your dataset testing all the values until highest values likelihood values are reached • Determining the rough relation (low K) Be careful to: • Run several independent run for each K in order to verify the consistency of the estimates across run • Population structure leads to LD among unlinked loci and departures from H-W. These are the signals used by STRUCTURE. But also inbreeding, genotyping errors or null alleles can lead to the same effect.

16. INTERPRETING THE OUTPUT: The screen during run Number of MCMC iteration Log of data given the current values of P and Q Divergence between populations calculated as Fst Current estimates of ln(P|K) averaged over all the iteration since the end of burn-in period

17. The output file Current estimates of Prln(P|K) averaged over all the iteration since the end of burn-in period

18. Q output without using prior information Estimated membership in the clusters (k=3) and 90% probability interval (ANCENDIST turned on)

19. Q output using prior information Estimated probability of belonging to the second populations or have parent and grandparent that belong to the second population Posterior probability of belonging to the presumed population

20. PLOT THE RESULTS • one vertical line/individual • color = cluster • more colors/line: genetic components of individual

21. INFERRING POPULATION STRUCTURE RESGEN PROJECT: Towards a strategy for the conservation of the genetic diversity of European cattle THE DATASET More that 60 cattle breeds from Europe 5 African bos indicus breeds 20 individuals per breed 30 microsatellites Structure parameters: Admixture models Allele frequencies correlate No prior information

22. Germ. Simmental Simmental Hinterwaelder German Yellow Evolene Eringer Piemontese Grigio Alpina Rendena Cabannina Swiss HF British HF Jutland 1950 Dutch Belted German BP-W Friesian-Holland Belgian Blue Germ. Shorthorn Maine-Anjou Normande Podolica Romagnola Chianina N'Dama Somba Lagunaire Borgou Zebu Peul Bretonne BP Charolais Ayrshire Highland Hereford Dexter Aberdeen Angus Jersey Guernsey Betizu A Betizu B Pirenaica Blonde d'Aquitaine Limousin Bazadais Gasconne Aubrac Salers Montbéliard Pezzata Rossa Ital. Swiss Brown Germ. Br. Württemberg Germ. Br. Bavaria Germ. Br. Orig Bruna Pirineds Menorquina Mallorquina Retinta Morucha Avilena Sayaguesa Alistano Rubia Gallega Asturiana Valles Asturiana Montana Tudanca Tora de Lidia Casta Navarra Hungarian Grey Istrian Swedish Red Polled Bohemian Red Polish Red Red Danish AngelnMRY Red HF dual Red HF dairy Groningen WH k=2 • EUR AFR Podolica Hungarian Grey Istrian Romagnola N’Dama Chianina Zebu Peul Somba Lagunaire Borgou • k=2 • Europe – Africa Model-based clusteringEuropean cattle • Zebu influence in Podolian breeds

23. Germ. Simmental Simmental Hinterwaelder German Yellow Evolene Eringer Piemontese Grigio Alpina Rendena Cabannina Swiss HF British HF Jutland 1950 Dutch Belted German BP-W Friesian-Holland Belgian Blue Germ. Shorthorn Maine-Anjou Normande Podolica Romagnola Chianina N'Dama Somba Lagunaire Borgou Zebu Peul Bretonne BP Charolais Ayrshire Highland Hereford Dexter Aberdeen Angus Jersey Guernsey Betizu A Betizu B Pirenaica Blonde d'Aquitaine Limousin Bazadais Gasconne Aubrac Salers Montbéliard Pezzata Rossa Ital. Swiss Brown Germ. Br. Württemberg Germ. Br. Bavaria Germ. Br. Orig Bruna Pirineds Menorquina Mallorquina Retinta Morucha Avilena Sayaguesa Alistano Rubia Gallega Asturiana Valles Asturiana Montana Tudanca Tora de Lidia Casta Navarra Hungarian Grey Istrian Swedish Red Polled Bohemian Red Polish Red Red Danish AngelnMRY Red HF dual Red HF dairy Groningen WH k=2 k=5 k=7 k=9 Nordic LowlandPied British FrenchBrown AlpineSpotted Iberian Podolian AlpineBrown BalticRed North-WestIntermediates AlpineIntermediates Model-based clusteringEuropean cattle • 9 homogeneous clusters + 2 intermediate zones. Courtesy of dr. J. A. Lenstra, dr I. Nijman and Resgen Consortium

24. INTRABIODIV: Tracking surrogates f. intraspecific biodiversity: towards efficient selection strategies f. the conservation of natural genetic resources using comparative mapping & modelling approaches

25. Phylogeography of Geum reptans • 59 localities • 177 samples • ≈80 polymorphic AFLP markers

26. High diversity Low diversity Phylogeography of Geum reptans

27. High diversity Low diversity Phylogeography of Geum reptans

28. Phylogeography of Ligusticum mutellinoides • 127 localities • 381 samples • 123 polymorphic AFLP markers

29. High diversity Low diversity Phylogeography of Ligusticum mutellinoides Courtesy of dr. P.Taberlet and Intrabiodiv Consortium

30. PERFORM ASSIGNEMENT TEST

31. Bruna Grigio Alpina Rendena Valdostana Pezzata Rossa Frisona CARTINA Pezzata Rossa It. Piemontese Romagnola Limousine Cabannina Marchigiana Chianina Calvana Podolica Mucca Pisana Maremmana • 16 breeds reared in Italy • 416 individuals • 3 AFLP primer combinations 132 polymorphisms • Information on origins THE REFERENCE DATASET

32. LMI MCG BRU FRI MMA CHI ROM MUP 1 0.9 0.8 0.7 0.6 Probabilità 0.5 0.4 0.3 0.2 0.1 0 CAL GAL VPR PRI PIM POD CAB REN 1 0.9 0.8 0.7 Probabilità 0.6 0.5 0.4 0.3 0.2 0.1 0 Checking the reference dataset 90% threshold 20000 burn-in + 50000 routine MCMC; 8 independent runs 90% threshold 98% of individuals correctly assigned with a p>90% (91% con p>99%) 100% of Romagnola individuals from the genetic center assigned with p>99%

33. THE BLIND TEST • 44 Romagnola individuals randomly selected • 3 AFLP primer combination ; 132 polymorphism • No prior information

34. Assignement probability to the different breeds of the reference dataset ROMAGNOLA REN CAB POD PIM PRI VPR GAL CAL MUP CHI MMA FRI 36 Romagnola cattle assigned with p>99% BRU MCG LIM 4 Romagnola cattle assigned with 90%>p>99% 4 Romagnola cattle not assigned THE RESULTS

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