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Sessão Temática 2
Análise Bayesiana
Utilizando a abordagem Bayesiana no
mapeamento de QTL´s
Roseli Aparecida Leandro
SEAGRO / 50ª RBRAS Londrina, Paraná 04 a 08 de Julho de 2005
Prof. Dr. Cláudio Lopes Souza Jr.
 Prof. Dr. Antônio Augusto Franco Garcia
 (Departamento de Genética ESALQ/USP)
Elisabeth Regina de Toledo
 (PPG Estatística e Experimentação
Agronômica, ESALQ/USP)
Qualitative trait
Mendelian gene
Quantitative trait
Bayesian mapping of QTL
Geneticists are often interested in
locating regions in the chromosome
contributing to phenotypic variation of a
quantitative trait.
Effects :
Additive, dominance
Genetics Markers
Escala dos Valores
Se d = 0
Se d/a = 1
Se d /a < 1
Se d/a > 1
Efeito Aditivo
em que: d/a é o grau de dominância
Chromosomal regions of known location
Do not have a physiological causal
association to the trait under study
Genetics Markers
studying the joint pattern of inheritance of
the markers and trait
can be made about the number,
location and effects of the QTL affecting trait.
Experimental Design
Offspring data: Divergent inbred lines
Backcross ( code 0=aa, 1=Aa )
(code –1=aa, 0=Aa, 1=AA)
Reason: maximize linkage desiquilibrium
F2 Design
Data set
QTL phenotype model
 One
Multiple QTL phenotype
 Our
aim is to make joint inference about
the number of QTL, their positions (loci)
and the sizes of their effects.
 Assume
that a linkage map has been
developed for the genome.
Genetic Map
0 < r = fração de recombinação < 0.5
Classic approach
 Interval
mapping (Lander &
 Least squares method (Haley &
 Composite interval mapping
(Jansen, 1993; Jansen and Stam, 1994;
Zeng 1993, 1994)
Bayesian approach
 Satagopan
et al. (1996)
 Satagopan
& Yandell (1998)
 Sillanpää
& Arjas (1998)
 The
joint posterior distribution of all
unknowns (s, , Q, ) is proportional to
 In
practice, we observe the phenotypic trait
and the marker genotypes
NOT the QTL genotypes
 For
convenience consider only one linkage
group with ordered markers {1,2,...,m}.
Assume that genotypes:
 The
markers are assumed to be at known
The conditional distribution
assuming the loci segregate independently
** under Haldane assumption of independent
The marginal likelihood of the parameters s, 
and  for the ith individual may be obtained
from the joint distribution of traits and QTL
by summing over the set of all possible QTL
genotypes for the ith individual,
When the data Y are n independent
observations, the marginal likelihood for the
trait data is the product over individuals, a
familiar misture model likelihood,
 The
joint likelihood is a mixture of
densities, and hence, is difficult to
evaluate when there are multiple QTL.
 The
joint posterior distribution of all
unknowns (s, , Q, ) is proportional to
 A Bayesian
approach combined with
reversible jump MCMC is well suited for
QTL studies
Random-sweep Metropolis-Hastings
algorithm for general state spaces
(Richardson and Green, 1997)
current state of the chain indexed by s.
The chain can
move to a “birth” step
(number of loci s  s+1 )
move to a “death” step
(number of loci s  s-1 )
continue with “current” number (s) of loci
 Simulated
F2 intercross
 n=250
 2 QTL
Satagopan, J. M.; Yandell, B. S. (1998)
 Bayesian model determination for
quantitative trait