QTL 作图标记密度及群体大小(Li 2010英)

Heredity (2010) 105, 257

–

267

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ORIGINAL ARTICLE

/hdy

Statistical properties of QTL linkage mapping

in biparental genetic populations

1,2

H Li

, S Hearne

3

, M Ba¨

nziger

4

, Z Li

2

and J Wang

1

1

Institute of Crop Science, The National Key Facility for Crop Gene Resources and Genetic Improvement and CIMMYT China, Chinese

Academy of Agricultural Sciences, Beijing, PR China;

2

School of Mathematical Sciences, Beijing Normal University, Beijing, PR China;

3

International

Institute

of

Tropical

Agriculture

(IITA),

Ibadan,

Oyo

State,

Nigeria

and

4

International

Maize

and

Wheat

Improvement

Center (CIMMYT), Mexico, DF, Mexico

Quantitative

trait

gene

or

locus

(QTL)

mapping is

routinely

used

in

genetic

analysis

of

complex

traits.

Especially

in

practical breeding programs, questions remain such as how

large

a

population

and

what

level

of

marker

density

are

needed to detect QTLs that are useful to breeders, and how

likely it is that the target QTL will be detected with the data

set

in

hand.

Some

answers

can

be

found

in

studies

on

conventional interval mapping (IM). However, it is not clear

whether the conclusions obtained from IM are the same as

those

obtained

using

other

methods.

Inclusive

composite

interval

mapping

(ICIM)

is

a

useful

step

forward

that

highlights

the

importance

of

model

selection

and

interval

testing

in

QTL

linkage

mapping.

In

this

study,

we

investigate the statistical properties of ICIM compared with

IM through simulation. Results indicate that IM is less

responsive to marker density and population size (PS). The

increase in marker density helps ICIM identify indepen-dent

QTLs

explaining

4

5%

of

phenotypic

variance. When

PS

is

4

200, ICIM achieves unbiased estimations of QTL position

and effect. For smaller PS, there is a tendency for the QTL

to be located toward the center of the chromosome, with its

effect

overestimated.

The

use

of

dense

markers

makes

linked

QTL

isolated

by

empty

marker

intervals

and

thus

improves

mapping

efficiency.

However,

only

large-sized

populations

can

take

advantage

of

densely

distributed

markers. These findings are different from those previously

found in IM, indicating great improvements with ICIM.

Heredity

(2010)

105,

257

–

267;

doi:10.1038/hdy.2010.56;

published online 12 May 2010

Keywords: confidence interval; false discovery rate; inclusive composite interval mapping; population size; statistical power

Introduction

Quantitative trait gene or locus (QTL) mapping has become a

routine approach for genetic studies of complex traits in plants,

animals

and

humans

because

of

the

availability

of

high-

throughput molecular markers. In comparison with association

mapping,

QTL

linkage

mapping

in

animals

and

humans

is

normally based on pedigree data, but in plants it is more often

based

on

biparental

genetic

populations.

Statistical

methods

for

QTL

linkage

mapping

have

been

extensively

studied

(Lander and Botstein, 1989; Darvasi et al., 1993; Zeng, 1994;

Whittaker et al., 1996; Piepho, 2000; Sen and Churchill, 2001;

Xu, 2003; Bogdan and Doerge, 2005; Li et al., 2007; Wang,

2009),

and

composite

interval

mapping

(CIM)

proposed

by

Zeng

(1994)

represents

one

of

the

most

commonly

used

methods.

Recently, Li et al. (2007) found that CIM resulted in biased

mapping

results

because

of

the

simultaneous

estimation

of

QTL and background effects in the implementation algorithm.

Inclusive

composite

interval

mapping

(ICIM)

was

then

proposed (Li et al., 2007;

Correspondence: Dr J Wang, Institute of Crop Science, Chinese Academy

of

Agricultural

Sciences,

No.

12

Zhongguancun

South

Street,

Beijing

100081, PR China.

E-mail: wangjk@

Received 4 December 2009; revised 19 March 2010; accepted 30 March

2010; published online 12 May 2010

Wang,

2009)

to

deal

with

this

problem

while

retaining

other

advantages

related

to

CIM.

Major

advantages

of

ICIM

were

summarized

as

follows:

(1)

ICIM

controls

the

sampling

variance better; (2) it makes the background marker selection

process easier and simpler; (3) it gives clearly high logarithm

of the odds (LOD) scores at chromosomal regions with QTL

but

rather

low

LOD

scores

(that

is,

close

to

0)

in

which

no

QTLs

are

located,

thereby

increasing

mapping

power

and

decreasing the false discovery rate (FDR); (4) it is robust for

mapping

parameters;

(5)

it

can

be

extended

to

map

digenic

epistatic QTLs regardless of whether the two interacting QTLs

have significant additive effects or not; and (6) the expectation

and

maximization

(EM)

algorithm

used

in

ICIM

has

a

high

convergence

speed

and

is

therefore

less

computing

intensive

(Li et al., 2007, 2008; Zhang et al., 2008).

Available

mapping

methods

have

their

own

statistical

properties and power for detecting QTL. Factors influen-cing

the

statistical

power

of

each

method

include

mapping

population

size

(PS),

marker

density,

signifi-cance

level

in

declaring

the

existence

of

QTL,

contribu-tion

of

the

segregating

QTL

to

the

observed

phenotypic

variance

and

genetic

distances

of

QTL

to

markers.

There

are

several

simulation

studies

on

how

these

factors

affect

the

detection

power

of

interval

mapping

(IM).

Darvasi

et

al.

(1993)

investigated

the

effect

of

marker

density

in

a

backcross

population, and concluded that reducing marker spacing below

10 or 20 cM does not provide

Statistical properties of QTL linkage mapping

H Li et al

258

additional gains, regardless of PS and gene effect. At 20 cM

marker density and assuming QTLs have equal effects with all

positive

alleles

from

one

parent,

Beavis

(1994)

showed

that

the

estimated

effects

with

correctly

identified

QTLs

were

greatly

overestimated

if

only

100

progeny

were

evaluated,

slightly

overestimated

if

500

progeny

were

evaluated

and

fairly close to the actual magnitude when 1000 progeny were

evaluated; this was statistically explained by Xu (2003). Using

an analytical method, Piepho (2000) showed that the power of

QTL detection and the standard errors of effect estimates are

little affected by an increase in marker density beyond 10 cM.

The bias of estimators of QTL effects and locations from IM

was discussed by Bogdan and Doerge (2005). On the basis of

multiple

interval

mapping,

Mayer

et

al.

(2004)

studied

the

accuracy of position and effect estimates of linked QTLs in F

2

populations

by

simula-tion.

Some

theoretical

and

simulation

studies have also been conducted on the confidence interval of

IM

(Visscher

et

al.,

1996;

Dupuis

and

Siegmund,

1999).

Recently,

Bogdan

et

al.

(2008)

showed

the

influence

of

marker density on the detection power of small- or medium-

sized QTLs by a modified version of the Bayesian information

criterion.

ICIM has superior genetic and statistical properties, which

may

represent

an

important

improvement

in

QTL

linkage

mapping. It may be misleading to assume that the influence on

ICIM of experimental parameters such as PS, QTL effect and

marker

density

is

the

same

as

has

been

found

in

IM.

Our

objectives

in

this

study

were

(1)

to

investigate

the

effect

of

genetic

effect,

PS

and

marker

density

on

statistical

power,

position

and

effect

estima-tions

of

ICIM

and

(2)

to

provide

practical and statistical tables of probabilities and confidence

intervals

so

that

a

QTL

can

be

identified

in

mapping

populations of various sizes.

160 cM in length, similar to the maize genome. Four marker

densities (MD) were used (that is, MD

?

40, 20, 10 and 5 cM)

from sparse to dense, which corresponded to 5, 9, 17 and 33

evenly distributed markers on each chromosome. Two genetic

models (Tables 1 and 2) were simulated.

In

the

first

genetic

model

(Table

1),

there

were

eight

independent

QTLs,

that

is,

IQ1

–

IQ8,

with

different

levels

of

additive

effects

on

a

quantitative

trait

of

interest

(Table

1).

IQ1

had

the

smallest

genetic

effect,

explaining

only

1%

of

phenotypic

variation,

that

is,

phenotypic

variance

explained

(PVE)

?

1%, whereas

IQ8 had the largest effect, explaining

30% of phenotypic variation, that is, PVE

?

30%

(Table

1).

The

eight

QTLs

were

distributed

on

different

chromosomes,

and no interac-tions between QTLs were considered. The error

variance

was

set

at

0.25,

for

a

total

of

phenotypic

variance

equal to one. Thus, the additive effect of a QTL was equal to

the

square

root

of

the

corresponding

PVE

(Table

1).

Broad-

sense heritability of this quantitative trait was therefore 0.75,

which is the sum of PVE as all QTLs were not linked.

Table 1 One genetic model consisting of eight independent QTLs

QTL

Chromosome

Position (cM)

Additive effect

PVE (%)

1

2

3

4

5

10

20

30

IQ1

IQ2

IQ3

IQ4

IQ5

IQ6

IQ7

IQ8

1

2

3

4

5

6

7

8

25

32

39

46

53

60

67

74

0.1000

0.1414

0.1732

0.2000

0.2236

0.3162

0.4472

0.5477

Materials and methods

Genetic models used in simulation

In this paper, we considered a hypothetical genome consisting

of 10 chromosomes. Each chromosome was

Table 2 One genetic model of two linked QTLs

Abbreviations:

PVE,

phenotypic

variance

explained;

QTL,

quanti-tative

trait locus.

The

genome

consists

of

10

chromosomes,

each

160

cM

in

length.

The

eight QTLs were represented by IQ1

–

IQ8. Each QTL was represented by

chromosome

number,

position

(cM),

additive

genetic

effect

and

proportion of PVE by the QTL. The phenotypic variance was fixed at 1.0,

and

the

additive

effect

of

a

QTL

was

equal

to

the

square

root

of

the

corresponding PVE. Broad-sense heritability was set at 0.75, which is the

sum of PVE, as all QTLs are not linked. Therefore, the error variance was

0.25.

Linkage phase

Position (cM)

Additive effect

LQ1

LQ2

32

42

52

32

42

LQ1

LQ2

0.3162

0.3162

0.3162

0.3162

0.3162

Genetic

a

variance (V

G

)

0.3637

0.3340

0.3097

0.0362

0.0659

Error

variance (V

e

)

0.8

0.8

0.8

0.8

0.8

Heritability

2

b

(H

)

PVE (%) of

c

each QTL

Coupling

22

22

22

22

22

0.3162

0.3162

0.3162

0.3162

0.3162

0.3125

0.2945

0.2791

0.0433

0.0761

8.59

8.82

9.01

11.96

11.55

Repulsive

22

52

0.3162

0.3162

0.0902

0.8

0.1013

11.23

Abbreviations: PVE, phenotypic variance explained; QTL, quantitative trait locus.

The genome consists of 10 chromosomes, each 160 cM in length. The two QTLs

were represented by

LQ1 and LQ2. They

were represented by their

positions (cM) on chromosome 1, additive genetic effects, total genetic variance, error variance, broad-sense heritability and proportions of the PVE.

a

c

V

G

?

a

1

+a

2

+2(1< /p>

–

2r)a

1

a

2

where a

1

and a

2

are the additive effects of LQ1 and LQ2, respectively, and r is the recombination frequency between LQ1

and LQ2. Haldane mapping function is used to convert genetic distance to recombination frequency.

2

2

Broad- sense heritability was calculated as H

?

V

G

/( V

G

+V

e

) .

2

2

PVE of LQ1 was calculated as a

1

/(V

+V

e

), and PVE of LQ2 was calculated as a

2

< br>/(V

G

+V

e

). As a

1

?

a

2

in the linkage model, LQ1 and LQ2 have

the same PVE. Error variance was fixed at 0.8. If LQ1 and LQ2 were not linked, each would explain 10% of the phenotypic variance, and the heritability

would be 0.2.

2

2

2

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