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Sessão Temática 2
Análise Bayesiana
Utilizando a abordagem Bayesiana no
mapeamento de QTL´s
Roseli Aparecida Leandro
ESALQ/USP
11o
SEAGRO / 50ª RBRAS Londrina, Paraná 04 a 08 de Julho de 2005
Colaboradores

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.
Location
Effects :
Additive, dominance
QTL
Genetics Markers
Escala dos Valores
Genotípicos
Se d = 0
Se d/a = 1
Se d /a < 1
Se d/a > 1
Efeito Aditivo
Codominância
Dominância
Completa
Dominância
Parcial
Sobredominânci
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
By
studying the joint pattern of inheritance of
the markers and trait
Inferences
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 )
(Recessive)
(code –1=aa, 0=Aa, 1=AA)
F2

Reason: maximize linkage desiquilibrium
F2 Design
Data set
QTL phenotype model
 One
QTL
Multiple QTL phenotype
Model
 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 &
Botstein,1989)
 Least squares method (Haley &
Knott,1992)
 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
but
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
distances

*
The conditional distribution
assuming the loci segregate independently
** under Haldane assumption of independent
recombination
The marginal likelihood of the parameters s, 
and  for the ith individual may be obtained
from the joint distribution of traits and QTL
genotypes.
by summing over the set of all possible QTL
genotypes for the ith individual,

Therefore,

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)

Suppose
current state of the chain indexed by s.

The chain can
(1)
move to a “birth” step
(number of loci s  s+1 )
(2)
move to a “death” step
(number of loci s  s-1 )
(3)
continue with “current” number (s) of loci
Simulation
 Simulated
F2 intercross
 n=250
1
cromossome
 2 QTL
Referências

Satagopan, J. M.; Yandell, B. S. (1998)
 Bayesian model determination for
quantitative trait