Mapping genes for quantitative traits using linkage disequilibrium

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Mapping genes for quantitative traits using linkage

disequilibrium

Me Goddard

To cite this version:

Mapping

genes

for

quantitative

traits

using linkage disequilibrium

ME

Goddard

Centre

_for

Genetic

_{Improvement of Livestock,}

Animal and

_{Poultry Science,}

University of Guelph, Guelph, Ontario,

Canada NIG 2W1

(Proceedings

of the 9th

_{European Colloquium}

on

_Cytogenetics

of Domestic

_Animals;

Toulouse-Auzeville,

10-13

July

1990)

quantitative trait loci

_/

marker-assisted selection

_/

_{linkage disequilibrium} INTRODUCTION

Many economically important

traits of livestock are

_quantitative

in nature and controlled

_by

many genes

(quantitative

trait loci or

QTLs)

and environmental factors. If we could find

_genetic

markers linked to

_QTLs,

this information would be

useful for marker-assisted selection

_(MAS)

and

_{eventually might help}

us to

_identify

and clone the

_QTL

itself. Markers can be shown to be linked to a

QTL

for the trait

under

_{study by}

within

_{family linkage}

studies.

_{However, large}

numbers of

_offspring

per

family

are

_required

and the

_{linkage phase}

must be determined for each

_family.

This reduces the value of the information for MAS. The presence of other loci and

environmental factors

_influencing

the trait also makes it difficult to _map the

_QTLs

with _any

_precision.

Linkage disequilibrium

can cause associations between alleles at marker and

QTL

which are consistent across the

population,

rather than

being

restricted to

a

_family.

Such associations would be very useful for MAS as discussed

by

Lande

and

Thompson

(1990).

Because

_{linkage disequilibrium usually}

occurs

_only

with close

_linkage,

it _may be useful for more

_{precise mapping}

of

QTLs.

The

_proportion

of the

_genetic

variance controlled

_by

the

_{QTL which,}

due

to

_{linkage disequilibrium,}

can be

_{explained by genetic}

markers is an

_important

parameter.

It influences both the value of the marker for MAS and the size of the

_experiment

_necessary to detect the effect

_(Lande

and

_Thompson,

_1990).

The

proportion

of variance

_explained

_might

be increased

_{by using}

marker

_haplotypes

at

a number of

_closely

linked markers instead of a

_single

marker locus.

This paper describes the factors

_controlling

the

proportion

of

_QTL

variance

explained by markers,

including

marker

_haplotypes,

and the use of this information

for

_mapping

the

_{QTL. Linkage disequilibrium}

can occur

through crossbreeding,

*

Currently

on leave

_{from Department of}

_Agriculture

and Rural

_Affairs,

Victoria,

epistasis

or finite

_population

size. Here I will consider

_mainly

the effect of finite

population

size and

_briefly

mention

_{crossbreeding.}

MATERIALS AND METHODS

The

_following

model was

_{investigated by}

simulation. Four linked loci were

_equally

spaced

on the chromosome with a recombination rate between the outside loci of ’c’. The second locus was a

QTL

and the other 3 were

_genetic

markers. There were 2 alleles _per locus and

_initially

all _gene

_frequencies

were 0.5 and there was

linkage equilibrium.

Finite

_population

size

_(n)

caused some

_inbreeding

and

_linkage

disequilibrium

to accumulate. Each

_generation,

2n

_gametes

were

_sampled

after

allowing

for recombination in the

_parents.

The

_proportion

of

_QTL

variance

_{explained by}

the markers

_(P)

was calculated

in 3 _ways

_according

to the marker information used:

₁₎

for individual marker loci

(P

i

);

2)

using

a

_{multiple regression}

based on the 3 loci

(P

2

);

and

3)

_using

the 8

marker

_haplotypes

defined

_by

the 3 loci

_(P

₃

_).

_(This

is

_equivalent

to

_including

the

interactions between marker loci in the

multiple

regression.)

The number of

_replicates

of each simulation was 400

_(n

=

32)

or 200

_(n

=

128)

or 100

_{(n = 512),}

so that the mean P values

presented

in tables I and II have

standard errors of

_{approximately}

0.01.

RESULTS AND DISCUSSION

The results of the simulation

_depend

_upon 3

_parameters:

the

_population

size

_(n),

the recombination rate

_(c)

and the number of

_generations

_(t).

_However,

Hill and Robertson

₍₁₉₆₈₎

found for

_{disequilibrium}

between two loci that if nc was held

constant and t was scaled in

_proportion

_{to n,} the results were

_{approximately}

constant. This

proposition

was

_investigated

for the current 4 locus model and the results are

presented

in table I. The results show that if nc and

t/n

were

held _constant,

_P

₃

was

_{approximately}

the same. Similar results

_apply

to

_{Hand P}

₂

provided n

is not too low.

_{Consequently,}

the 3

parameters

can be reduced to 2.

Constant

_t/n

_implies

almost

_{equal inbreeding}

coefficient

_(F)

and this is also

_given

The effect of nc and F on

_proportion

of variance

_explained

are shown in table

II. P increased with F but reached a maximum

and, although

not shown in table

II,

declined at _very

_high

F values. The maximum for

P

I

was much lower than the

equilibrium expression

(1/(4 nc/3

+

₁₎₎

_{given by}

Sved

₍₁₉₇₁₎

because

_replicates

were included where the marker locus became fixed for one allele. Marker

haplotypes

explain

a much

_{higher proportion}

of variance than

_{single markers, especially}

at low F values. A linear combination of the markers

_(P

₂

₎

was intermediate between

_P

_l

and

P

3

.

The third marker added

_{significantly}

to

_{both P}

₂

and

P

3

showing

that

markers,

other than those

_bracketing

the

QTL,

are useful.

Decreasing

nc

(ie,

closer

linkage)

had little effect on P at _very low F

_values,

but caused P to

_approach

a

higher

maximum as F increased.

At levels of F accumulated over time in livestock breeds

_(0.10-0.30),

the amount

of variance

_{explained by}

marker

_haplotypes

would make them very valuable for

MAS. Intense selection of males within some breeds causes the effective

_population

size to be

_quite

low.

_Young

et al

₍₁₉₈₈₎

found the rate of

_inbreeding

in the

USA Holstein

_population

to be

_0.2%/yr

_{corresponding}

to a

_generation

effective

population

size of about 50. If n = 100 and _c =

_0.032,

_so that _nc =

_3.2,

the

average

distance between markers is 1.6 cM. To cover the whole _genome with markers at

this

_density

would

_require

about 2 000 markers. A more

practical approach

would

be to _map an

important QTL

to a 10-20 cM

region using family linkage

studies

and then to find additional markers within this

_region

for the

_study

of

_linkage

disequilibrium.

Lande and

_{Thompson (1990)}

conclude that past

crossbreeding

will be a more

important

source of

_{linkage disequilibrium}

than finite

_population

size.

_However,

they

appear to be

_thinking

of crosses between

_highly

inbred lines. For lines which

diverge

due to

_{genetic drift,}

the

_expectation

of

_P

_I

can be shown to be

_proportional

to

_FS.1,,

where

F

ST

is

_Wright’s

coefficient of

_divergence

between

populations.

Consequently,

at low

_F

_ST

values

_typical

of livestock

_breeds,

_P

_I

is _very small. In the simulations

_{reported above, crossbreeding}

could be simulated

_{by crossing}

two

On the _average, markers more

_tightly

linked to a

QTL

show

_higher

P values than

less

_tightly

linked

_{markers, implying}

that P values would be useful in

_establishing

the _map

_position

of the

_QTL.

_However,

the variation in P between

_replicates

is _very

large.

The coefficient of variation is

_{approximately}

50%

for

_,

_P

₃

70%

for

_P

₂

and over

100%

for

_P

_l

_.

_{Consequently,}

differences in P values between markers will seldom be

_significant.

Hill and Weir

₍₁₉₈₈₎

_{previously pointed}

out the

_{high variability}

of

disequilibrium

coefficients.

_Perhaps

the

_only

conclusion that can be drawn is

that,

if a

_high

P value is found in a

_{large population,}

the marker and

QTL

must be

closely

linked.

The effect of initial _gene

_frequencies

other than

_0.5,

multiallelic

_loci,

selection and mutation on these results need further

_{investigation.}

CONCLUSIONS

Linkage disequilibrium

between

_genetic

markers and

_(aTLs

should cause

relation-ships

between the markers and

_quantitative

traits which

_apply

to an entire

popula-tion or breed. The use of

_haplotypes

based on several

_closely

linked markers would

make these

_relationship

useful for marker-assisted selection.

ACKNOWLEDGMENTS

This research was

_{supported by}

funds from the Natural Sciences and

_Engineering

Research

Council, Semex, Canada,

and the Victorian

_Department

of

_Agriculture

and Rural Affairs.

REFERENCES

Hill

_WG,

Robertson A

_{(1968) Linkage disequilibrium}

in finite

_populations.

Theor

_A!PI

Genet 38, 226-231

Hill

WG,

Weir BS

₍₁₉₈₈₎

Variances and covariances of

_{squared linkage disequilibria}

in

finite

populations.

Theor

_Popul

Biol _33, 54-78

Lande

_{R, Thompson}

R

_{(1990) Efficiency}

of marker-assisted selection in the

_improvement

of

_quantitative

traits. Genetics 124, 743-756

Sved JA

₍₁₉₇₁₎

_{Linkage disequilibrium}

and

_homozygosity

of chromosome segments in

finite

_populations.

Theor

_Popul

Biol 2, 125-141