STRUCTURE Riccardo Negrini [email protected].

STRUCTUREhttp://pritch.bsd.uchicago.edu

Riccardo [email protected]

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

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

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Marchigiana

Italian Limousine

Romagnola

Dice similarity and multivariate analysis

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Distribution Dice similarity between (dotted line) and within breeds

ROM/FRI

ROM/CHI

ROM/MCG

ROM/LMI

ROM/ROM

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

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

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)

FORMAT OF THE DATA FILE:

Label Pop Flag Locus 1 Locus 2 Locus 3 Locus n

Chi1 1 1 145 92 113 Size

Chi1 1 1 145 98 115 Size

Chi2 1 1 143 90 115 …

Chi2 1 1 -9 90 119 …

Chi3 1 0 151 155 117 …

Chi3 1 0 145 92 119

Rom1 2 0 145 98 121

Rom1 2 0 143 90 125

Rom2 2 0 -9 90 125

Rom2 2 0 -9 94 123

Indicate learning samplesAlleles 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)

BUILDING A PROJECT:

Step 1 Step 2

Step 3Step 4

…….if everything goes well:

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

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.

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)

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)

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

The output file

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

Q output without using prior information

Estimated membership in the clusters (k=3) and 90% probability interval (ANCENDIST turned on)

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

PLOT THE RESULTS

• color = cluster

• more colors/line:genetic components of individual

• one vertical line/individual

INFERRING POPULATION STRUCTURE

RESGEN PROJECT: Towards a strategy for the conservation of the genetic diversity

of European cattle

THE DATASETMore that 60 cattle breeds from Europe5 African bos indicus breeds20 individuals per breed30 microsatellites

Structure parameters:Admixture modelsAllele frequencies correlateNo prior information

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 P

eul

Hungaria

n Gre

y

Istri

an

Podolica

Romag

nola

Chianin

a

N’Dam

a

Somba

Lagunai

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Borgou

Zebu influence in Podolian breeds

Model-based clusteringEuropean cattle

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

PodolianIberianAlpineBrown

AlpineIntermediates

AlpineSpotted

FrenchBrown

BritishLowlandPiedBaltic

Red

Nordic

North-WestIntermediates

k=2

k=5

k=7

k=9

Model-based clusteringEuropean cattle

9 homogeneous clusters + 2 intermediate zones.

Courtesy of dr. J. A. Lenstra, dr I. Nijman and Resgen Consortium

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

Phylogeography of Geum reptans

• 59 localities• 177 samples• ≈80 polymorphic

AFLP markers

Phylogeography of Geum reptans

High diversity

Low diversity

Phylogeography of Geum reptans

High diversity

Low diversity

Phylogeography of Ligusticum

mutellinoides

• 127 localities• 381 samples• 123 polymorphic AFLP

markers

Phylogeography of Ligusticum mutellinoides

High diversity

Low diversity

Courtesy of dr. P.Taberlet and Intrabiodiv Consortium

PERFORM ASSIGNEMENT TEST

THE REFERENCE DATASET

CARTINAPiemontese

CabanninaChianina

Calvana

Mucca Pisana

Maremmana

Romagnola

Limousine

Marchigiana

FrisonaRendena

Pezzata Rossa It.

Podolica

BrunaGrigio AlpinaValdostana Pezzata Rossa

16 breeds reared in Italy 416 individuals 3 AFLP primer combinations

132 polymorphisms Information on origins

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 runs0

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LMI BRUMCG MMAFRI CHI MUPROM

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CAL VPRGAL PIMPRI POD CAB REN

90% threshold

90% threshold

THE BLIND TEST

44 Romagnola individuals randomly selected 3 AFLP primer combination ; 132 polymorphism No prior information

THE RESULTS

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ROMAGNOLA

BRUMCG

LIM

GAL VPR

MUPCAL

FRICHIMMA

PRI PIMPOD

CABREN

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

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•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