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STRUCTURE Riccardo Negrini

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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 Classify individuals of unknown origins Detecting “cryptic” populations structure Identify immigrant Identify mixed individuals Demonstrating the presence of a populations structure

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 Marchigiana Italian Limousine Romagnola Dice similarity and multivariate analysis

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

6 STRUCTURE main assumption: H-W equilibrium within populations Linkage equilibrium between loci within populations  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  STRUCTURE does 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

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 POSTERIOR distribution of the parameters (The conditional distribution of the parameters given the data)

9 FORMAT OF THE DATA FILE: LabelPopFlagLocus 1Locus 2Locus 3Locus n Chi11114592113Size Chi11114598115Size Chi21114390115… Chi211-990119… Chi310151155117… Chi31014592119 Rom12014598121 Rom12014390125 Rom220-990125 Rom220-994123 Indicate learning samples Alleles in rowsMissing 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 1Step 2 Step 3Step 4

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 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 Allele frequencies independent : it assumes that allele frequencies in each populations are independent drown from a distribution specified by a parameters. The prior says that we expect the allele frequencies in each population to be reasonably different from each others.

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 (10 6 )

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. 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. 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)

16 INTERPRETING THE OUTPUT: The screen during run Number of MCMC iteration Divergence between populations calculated as Fst Log of data given the current values of P and Q 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 Posterior probability of belonging to the presumed population Estimated probability of belonging to the second populations or have parent and grandparent that belong to the second population

20 PLOT THE RESULTS color = cluster more colors/line: genetic components of individual one vertical line/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 Swedish Red Polled Bohemian Red Polish Red Red Danish Angeln MRY Red HF dual Red HF dairy Groningen WH Swiss HF British HF Jutland 1950 Dutch Belted German BP-W Friesian-Holland Belgian Blue Germ. Shorthorn Maine-Anjou Normande 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. Germ. Simmental Simmental Hinterwaelder German Yellow Evolene Eringer Piemontese Grigio Alpina Rendena Cabannina 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 Podolica Romagnola Chianina N'Dama Somba Lagunaire Borgou Zebu Peul k=2  EUR AFR  k=2  Europe – Africa Zebu Peul Hungarian GreyIstrian Podolica Romagnola Chianina N’Dama SombaLagunaireBorgou  Zebu influence in Podolian breeds Model-based clustering European cattle

23 Swedish Red Polled Bohemian Red Polish Red Red Danish Angeln MRY Red HF dual Red HF dairy Groningen WH Swiss HF British HF Jutland 1950 Dutch Belted German BP-W Friesian-Holland Belgian Blue Germ. Shorthorn Maine-Anjou Normande 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. Germ. Simmental Simmental Hinterwaelder German Yellow Evolene Eringer Piemontese Grigio Alpina Rendena Cabannina 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 Podolica Romagnola Chianina N'Dama Somba Lagunaire Borgou Zebu Peul Podolian Iberian Alpine Brown Alpine Intermediates Alpine Spotted French Brown BritishLowland Pied Baltic Red Nordic North-West Intermediates k=2 k=5 k=7 k=9 Model-based clustering European 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 Phylogeography of Geum reptans High diversity Low diversity

27 Phylogeography of Geum reptans High diversity Low diversity

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

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

30 PERFORM ASSIGNEMENT TEST

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

32 Checking the reference dataset 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% 20000 burn-in + 50000 routine MCMC; 8 independent runs 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Probabilità LMIBRUMCGMMAFRICHIMUPROM 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Probabilità CALVPRGALPIMPRIPODCABREN 90% threshold

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

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

35 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 May;28(4):302-12. Sullivan PF, Walsh D, O'Neill FA, Kendler KS. Evaluation of genetic substructure in the Irish Study of High-Density Schizophrenia Families. Psychiatr Genet. 2004 Dec;14(4):187-9. Lucchini V, Galov A, Randi E. Evidence of genetic distinction and long-term population decline in wolves (Canis lupus) in the Italian Apennines. Mol Ecol. 2004 Mar;13(3):523-36 Peever TL, Salimath SS, Su G, Kaiser WJ, Muehlbauer FJ. Historical and contemporary multilocus population structure of Ascochyta rabiei (teleomorph: Didymella rabiei) in the Pacific Northwest of the United States. Mol Ecol. 2004 Feb;13(2):291-309. Falush D, Stephens M, Pritchard JK. Inference of population structure using multilocus genotype data: linked loci and correlated allele frequencies. Genetics. 2003 Aug;164(4):1567-87. Bamshad MJ, Wooding S, Watkins WS, Ostler CT, Batzer MA, Jorde LB. Human population genetic structure and inference of group membership. Am J Hum Genet. 2003 Mar;72(3):578-89. Epub 2003 Jan 28. Koskinen MT. Individual assignment using microsatellite DNA reveals unambiguous breed identification in the domestic dog. Anim Genet. 2003 Aug;34(4):297-301. Rosenberg NA, Pritchard JK, Weber JL, Cann HM, Kidd KK, Zhivotovsky LA, Feldman MW. Genetic structure of human populations. Science. 2002 Dec 20;298(5602):2381-5. Rosenberg NA, Burke T, Elo K, Feldman MW, Freidlin PJ, Groenen MA, Hillel J, Maki-Tanila A, Tixier- Boichard M, Vignal A, Wimmers K, Weigend S. Empirical evaluation of genetic clustering methods using multilocus genotypes from 20 chicken breeds. Genetics. 2001 Oct;159(2):699-713 Randi E, Pierpaoli M, Beaumont M, Ragni B, Sforzi A. Genetic identification of wild and domestic cats (Felis silvestris) and their hybrids using Bayesian clustering methods. Mol Biol Evol. 2001 Sep;18(9):1679-93 for who are very interested


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