ASSOCIATION MAPPING. L unica scienza che permette a esperti diversi di utilizzare informazioni uguali per trarre conclusioni diverse.

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1 ASSOCIATION MAPPING Statistica: L unica scienza che permette a esperti diversi di utilizzare informazioni uguali per trarre conclusioni diverse. Evan Esar

2 Analisi QTL 1. Disporre di popolazioni idonee Da specifico incrocio Individui diversi 2. Misurare il carattere (fenotipo) 3. Descrivere il genotipo 4. Trovare una associazione statistica tra marcatori e fenotipo

3 Linkage Il linkage è un concetto fisico: r!!! gameti Non ricombinanti Ricombinanti

4 Popolazioni di mappa (RILs, DH, F2..) 1. Pochi fenotipi 2. Richiedono molto tempo 3. Hanno «solo» 2 alleli per locus 4. «pochi» eventi possibili di ricombinazione 5. Spesso basso potere di risoluzione

5 Association mapping in germplasm collections. Objectives: - Mapping by GWAS the loci underlying the natural variation - Characterizing the allelic variation (molecular and functional) at loci / genes of interest (candidate genes/chromosomal regions) Meyer and Purugganan Nature Reviews Genetics 2013

6 Association mapping 1. Popolazioni potenzialmente molto più numerose 2. Materiale già pronto 3. Hanno molti alleli per locus 4. Molti eventi di ricombinazione 5. Potenzialmente alto potere di risoluzione

7 Mapping of genetic factors controlling Mendelian and quantitative traits: 2) Mapping methods: a) Linkage analysis in plants maps genes using gametic phase disequilibrium created in a single- or multiplegeneration cross "ad Hock" Segregating populations are created, maintained, genotyped and phenotyped Populations: F2 individuals, BC individuals, F3 progenies, RI lines, intermated lines, multiparental populations b) Association mapping Relies on segregating variation in natural populations. multiparental populations with complex pedigrees crop germplasm collections with various degrees of relatedness between accessions natural populations

8 5 Research time 1 positional cloning association mapping intermated RILs near isogenic lines recombinant inbred pedigree F2/BC > Gene/allele number 5 Alleles evaluated Resolution (bp) association mapping in diverse germplasm positional cloning association in narrow germplasm NIL pedigree F2 - RIL Resolution (bp)

9 ~ LINKAGE DISEQUILIBRIUM

10 2 loci biallelici p A1 p A2 A1 A2 B1 B2 p B1 p B2 B1 B2 A1 P A1B1 P A1B2 A2 P A2B1 P A2B2

11 Linkage Equilibrium p A1 p A2 A1 A2 B1 B2 p B1 p B2 Expected frequencies P A1B1 = p A1 p B1 P A1B2 = p A1 p B2 P A2B1 = p A2 p B1 P A2B2 = p A2 p B2 B1 B2 A1 P A1B1 P A1B2 A2 P A2B1 P A2B2

12 Linkage Disequilibrium p A1 p A2 A1 A2 Non random associaton of alleles X B1 B2 p B1 p B2 Expected frequencies P A1B1 = p A1 p B1 P A1B2 = p A1 p B2 P A2B1 = p A2 p B1 P A2B2 = p A2 p B2 B1 D AiBj = P AiBj B2 - p Ai p Bj A1 PA1B1 PA1B2 A2 PA2B1 PA2B2

13 Linkage Disequilibrium Decay of linkage disequilibrium (LD) with time for four different recombination fractions (θ). For unlinked loci (θ = 0.5), LD decays rapidly within a small number of generations. For closely linked loci (θ < 0.05), the decay in LD is extremely slow. Abbreviation: D = coefficient of LD (Mackay and Powell, 2007).

!!! D normalizzato D D < 0 D > 0 D min = -min (p A1 p B2, p

14 Linkage Disequilibrium D AiBj = P AiBj - p Ai p Bj D dipende dalla frequenza allelica caratteristica rischiosa!!!! D normalizzato D D < 0 D > 0 D min = -min (p A1 p B2, p A2 p B1 ) D = D /D min D max = min (p A1 p B1, p A2 p B2 ) D = D/D max

15 Linkage Disequilibrium Quadrato del coefficiente di correlazione tra due marcatori Riflette il potere statistico di calcolare LD r 2 = D AiBj2 / (p A1 p A2 p B1 p B2 ) Basso r 2 campione GRANDE (N) per trovare LD tra i marcatori

16 D = ( * 0.45) = D max = min (0.70 * 0.55, 0.30 * 0.45) = D = / = r 2 = (0.115) 2 / 0.70 * 0.30 * 0.55 * 0.45 =

17 LD: scenari diversi (1) Total LD completa correlazione tra due polimorfismi due mutazioni nessuna ricombinazione Flint-Garcia, Thornsberry and Buckler, Ann Rev Plant Biol 54,

18 LD: scenari diversi (2) assenza di completa correlazione dei polimorfismi diversa storia mutazione assenza di ricombinazione r <<<< D r sensibile alla storia mutazionale Flint-Garcia, Thornsberry and Buckler, Ann Rev Plant Biol 54,

19 LD: scenari diversi(3) Total LE equilibrio di linkage Flint-Garcia, Thornsberry and Buckler, Ann Rev Plant Biol 54,

20 Inter-sect at 2.16 cm

22 Marker-phenotype association probability LD high and wide marker gene medium to high LD extent LD low 10 cm Conventional artificial mapping populations F2, BC1, DH, RIL (100 lines) low number of recombination events per genotype Gene/QTL discovery whole genome scan no fine validation Two alleles only Population isolates Germplasm of selfing species Elite germplasm medium to low number of recombinations cumulated through several generations (100 linee) Gene/QTL discovery and validation a few genes/alleles Germplasm of outbred species or highly diversified germplasm (100 lines) high number of recombinations cumulated through several generations Candidate gene approach Fine gene/allele validation Several genes/alleles large artificial mapping populations several thousands of individual

23 Species Mating system, germplasm and LD range (average distance where r2 = 0.10) Human Outcrossing - Nigerian: 5 kb - European: 80 kb Cattle Outcrossing: 10 cm Drosophila Outcrossing: <1 kb Maize Outcrossing - Diverse maize: 1 kb or less - Diverse inbred lines: 1.5 kb - Elite (cultivated) lines: > 100 kb Arabidopsis Selfing: 250 kb Sugarcane Outcrossing/vegetative: 10 cm propagation Wheat and Barley selfing - Diverse barley: less than 1 cm - Elite (cultivated) germplasm up to 1-20 cm up to 60 cm Haplotype blocks: extensive regions showing no recombinations and inherited from a know "foundation genotype"

25 Phenotyping Dati raccolti con un adeguato numero di repliche entro ambienti, tra ambienti e anni diversi Disegni sperimentali adeguati (e.g., α-lattice) Metodi statistici di analisi appropriati

26 AM statistical approaches Marcata struttura di popolazione e famigliarità Struttura di popolazione Struttura diu popolazione e famigliarità Campione ideale senza struttura di popolazione o parentela Campione con famigliarità Yu and Buckler, Curr Opin Biotechnology 17,

27 AM statistical approaches Yu and Buckler, Curr Opin Biotechnology 17,

28 Linkage disequilibrium and population structure When population subdivision is present, it ispossible to find statistical associations between a disease phenotype and arbitrary markers that have no physical linkage to causative loci Such associations occur because population subdivision (or any other form of nonrandom mating) permits marker-allele frequencies to vary among segments of the population, as the result of genetic drift or founder effects (Slatkin 1991). Pop structure causes: - natural selection (e.g. main adaptation traits: vernalization and photoperiod sensitivity) - breeder's selection (based on ideotypes, particularly in inbred crops, founders are successfull cultivars)

29 Spurious association due to population structure Cases Controls

30 Spurious association due to population structure Cases Controls Subpop 1 Subpop 2

31 Random - mated population - no selection / drift No pop structure Chr. xx experimental population F2 RIL BC DH Hardy-Weinberg population equilibrium Destructured germplasm collections Spike colour gene Mol marker M1or M2 Trait: spike colour Marker M: tightly linked to the trait

32 Chr. 2 or whole genome Chr. 1 Structured populations Trait: spike colour marker N Marker M: tightly linked to the trait Marker N: show LD with the marker M and spurious association with the trait N2N2 marker M Founder 2 Founder 1 N2N2 N2N2 N2N2 N2N2 N2N2 N2N2 N2N2 N2N2 N2N2 N2N2 N2N2 N2N2 N2N2 Subpop 2 enriched of founder 2' alleles at many Subpop 1 enriched of founder 1' alleles at many loci in the genome

34 Kinship (coancestry, relatedness) known or unknown population history

36 Mixed Linear Model Uses a random effect to estimate the fraction of phenotypic variation that can be explained by genome-wide marker data The phenotypic covariance between individuals is proportional to their relatedness (K) Composite approach Q+K I: identity matrix u: random deviates due to to genome-wide relatedness Observations vector y = Xα + Qβ + Iu + ε Residual X: genotypes a: allele effects to be estimated Q: population structure B: vector of subpopulation effects

38 Trait Analysis by association, Evolution and Linkage

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