Potential gain from including major gene information in breeding value estimation

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Potential gain from including major gene information in

breeding value estimation

C Larzul, E Manfredi, Jm Elsen

To cite this version:

Original

article

Potential

_gain

from

_including

major

gene

information

in

breeding

value estimation

C Larzul

E

Manfredi

JM Elsen

2

1

Station de

génétique quantitative

et

appliquée,

Institut national de la recherche

_agronomique,

78352

_{Jouy-en-Josas cedex;}

2

Institut national de la recherche

_agronomique,

Station d’amélioration

_genetique

des

_animaux,

31320

_{Castanet-Tolosan,}

Prance

(Received

18 March

1996; accepted

11 December

₁₉₉₆₎

Summary - Two indexes were

_compared

for the selection of a

_quantitative

trait in the case

of a mixed inheritance. The first index did not consider the

major

genotype information

(standard

method)

whereas the second index took this information into account

_(modified

method).

Two types of selection scheme were considered: individual selection and selection based on a _progeny test. The model for the estimation of

_genetic

_progress and evolution of allele

_frequencies

takes

_{overlapping generations}

into account. All of the effects studied

suggested

a

_large

number of interactions.

_However,

it can be concluded that information

about the

_major

gene should be put into the selection indexes when the

_heritability

is

low,

the

_major

gene effect

high

and its initial

_{frequency small,}

in

_particular

for a recessive

major

gene. The selection pressure has little influence on the results. In the short term,

the modified method is of more value in the case of individual selection than in the case

of selection based on a _progeny test. On the

whole,

the extra

genetic gain

of the modified method is limited and

_considering

the

major

genotypes in the selection indexes without

any

change

of the selection scheme is

probably

not the best way to use this information.

selection

/ genetic gain

/ major

gene

Résumé - Intérêt de l’inclusion de

l’information

au locus majeur dans l’indice de

sélection. Le but de l’étude est de comparer

l’application

de deux indices dans le cas d’une

sélection sur un caractère

quantitatif

soumis à

_l’effet

d’un

gène

majeur. Dans le _premier

cas, l’indice ne

_prend

_pas en _compte

_{l’information}

sur le

génotype

au locus

majeur

(méthode

standard)

alors que le deuxième indice

prend

en _compte cette

_information

_(méthode

modifiée).

Deux types de schémas sont considërés : sélection individuelle et sélection sur

descendance. Le calcul du

progrès génétique

et de l’évolution des

fréquences alléliques

est

réalisé pas à pas en considérant des

_{générations}

chevauchantes. Tous les

_effets

étudiés sur

la

_{supériorité}

de la méthode

_modifiée

sur la méthode standard

suggèrent

de nombreuses

interactions.

_Cependant,

il ressort que la prise en _compte de

l’information

sur le

gène

majeur

dans l’indexation est _avantageuse dans les cas de

_{faible héritabilité,}

de

_{fort effet}

est

_récessif.

Le taux de sélection n’a que peu

d’influence

sur les résultats.

Enfin,

l’intérêt

de la méthode

_modifiée

est

plus

visible et

_{plus rapide}

dans la sélection individuelle que

dans la sélection sur descendance. Il n’en demeure _{pas moins}

qu’en

dehors des conditions

extrêmes

précédemment citées,

l’intérêt de la méthode

modifiée

sur la méthode standard

reste pour le moins limité et la

prise

en _compte de

_{l’information}

sur les

génotypes

au locus

majeur

dans l’indice de

sélection,

sans

_modification

du schéma de

_sélection,

ne constitue

sûrement pas le meilleur outil de valorisation de cette

information

pour la sélection. sélection

_/

gain génétique

/

gène majeur

INTRODUCTION

Most of

quantitative genetics theory

and its

_application

to animal

breeding

is

based on the

_assumption

that a trait is controlled

by

a _very

_large

number of

small

_independent

_genes.

_{Nevertheless,}

evidence of genes with a

_large

effect on

quantitative

traits is

_increasingly

_being

found in livestock: double

_muscling

in

_pigs

(Ollivier, 1980),

cattle

_(Hanset

and

Michaux,

1985),

Callipyge

in

_sheep

_(Cockett

et

al,

1994),

dwarfism in

_poultry

_(M6rat

and

_Ricard,

_1974),

_{hyperovulation}

in

_sheep

(Booroola

gene:

Piper

and

Bindon,

1982;

Inverdale gene: Davis et

al,

1991),

high

milk

_protein

content in

_goats

_(Grosclaude

et

_al,

_1987),

low

_{technological yield}

for the

_cooking

of ham in

_pigs

_(Le

_Roy

et

_al,

_1990),

_high

milk flow in

_goats

_(Ricordeau

et

_al,

_1990).

In order to take

_greater

advantage

of this

_{genetic variability}

for animal

improvement, specific genetic

evaluation methods and selection schemes should be

applied

(Smith,

1967; Soller, 1978;

Smith and

Webb, 1981; Smith, 1982; Hoeschele,

1990;

Gibson,

1994).

Alternatively,

organisation

of

_matings

_including

genotypic

information may be

proposed

for a more efficient fixation of recessive favourable

alleles

_(eg,

Caballero et

_al,

_1991).

In this _paper,

_genotypes

at the

_major

locus were

perfectly

identified,

an

infre-quent

situation at the

_present

time

_(eg,

milk

_protein

content in

_goats,

halothane in

pigs)

but which should become more

frequent

in the future thanks to _progress made

in molecular

genetics.

The usefulness of

_including

the

_major

_genotype

information

in

_breeding

value estimation was evaluated

by

comparing

it with the standard

sit-uation where this information is not considered. This

_comparison

was

performed

in the framework of selection schemes for a trait measured on _young animals from

both sexes, eg,

growth

rate

_{(scheme I)}

and for a trait measured on females

_only

with

a _{progeny test} of

_sires,

_eg, milk

production,

(scheme

II).

Various

populations

with

different

_genetic

contexts

_{(heritability,}

major

gene

effect,

initial allele

frequencies)

and

_organisation

_(selection

pressure, number of

generations

selected)

were studied.

Standard and modified situations were

_compared

based on the

_genetic

_progress

they

were

expected

to

produce.

The selection schemes considered were _very

_simplified,

only

the main features of the situations studied were

kept.

This _paper

considers,

as

did Gibson

_(1994),

a

dynamic

model where the evolution of allele

frequencies

and

genetic

means are described

_step

_by

_step,

_using

a model

matching

the

_proposition

made

_by

Hill

₍₁₉₇₄₎

and Elsen and

_Mocquot

_(1974).

This is a

_{generalization}

of the

METHODS

Description

of the selection schemes

The

_generations

were

_overlapping

and in

_demographic

_equilibrium

within an infinite

population.

The _{age structure} of the

_population

was constant for both sexes.

A constant selection _pressure of

80%

was assumed for the

_dam-daughter

_path.

The three other

_paths

_(sire-son,

_{sire-daughter,}

_dam-son)

were selected with the

same selection pressure q. The situations

studied,

even if somewhat

_arbitrary,

were

expected

to reflect an _average situation for

_performance

test and _progeny test selection schemes.

Scheme I is a model of a selection

plan

_organized

for instance in a meat

_sheep

or

cattle

breed,

with the trait measured in both sexes at the same

_time,

when animals are between 0 and 1 year old. The

_generation

interval is about 2 years.

Only

one

selection

step

was considered before the first

_reproduction

for each of the two sexes.

The

_proportions

of available

_breeding

animals per age class are

_given

in table I.

Scheme II is a model of a selection

_plan

_organized

in a

_dairy

_species.

The

generation

interval is about 3 _years in the

_present

_study.

The trait was measured

only

in females. Males were selected after a _progeny test on 40

_daughters

whereas

females were selected on their own

_performance

after their first

_{reproduction.}

In this

_scheme,

a constant

30%

of the

_daughters

was

_supposed

to be born from

young progeny tested males. The result of the progeny test was available when

the young males were 2 years old. The first

_reproduction

of females was not used for

_replacement.

The

_proportions

available _{per age} class are

_given

in table I.

Genetic model

The

_principles

of the model were those of Smith

_(1982).

The whole

_population

was divided into classes defined

_by

the

_major

_genotype

i at a

_{single major}

locus

(i

=

AA,

AB or

_BB,

A

_being

the favourable

_allele),

the

_{age j}

and the sex k.

At a

_given

time

_t,

the

_components

of the classes were their relative size _a2!!t,

their

_major

locus

_genotypic

mean value

_C

_i

and their

_polygenic

mean _pzjkt. Time

0

_(t

=

0)

determined the situation before the selection

process

began,

thus the whole

_population

was considered

_homogeneous

for allele

_frequencies

and

_polygenic

a.

jxt

= E

aijxt have been

given

above.

They

were constrained to

_E

_a,jxt = 1. The

i _j

evolution of the

_population

was described

_through

the evolution of the

_components

¡..tijkt and aijxt,

assuming

the within class variances to be constant

during

the whole selection process.

The model included three

_types

of relations as described below.

Ageing

without selection

Between two successive classes of

_{ages j -}

1

_{and j}

_at

time t and t + 1 without

selection,

two

_equalities

occurred

Ageing

with selection

When selection was carried out between the

_{ages j -}

_{1 and j,}

the

_previous

relations became

where

_A

_zj

_-

_ikt

is the mean

polygenic

superiority

of selected individuals in the

class

_{ij -}

lk at time t. In

_practice,

there is

_only

one selection

_step

for

_reproducers,

so that

_only

one _age class was considered for

_ageing

with

_{selection: j =}

1 for both sexes in scheme

_{I; j}

= 2 for females

and j

₌

3 for males in scheme II

where _qijkt is the selection pressure for class

ijk

at time t and _q!k is the selection

pressure, which is

supposed

to be

constant,

for the set of individuals of

_{age j}

and sex k.

Replacement

The

components

of the newborn individuals

depended

on the

_components

of their

parents

(k

= _s for

_sire,

k = d for

dam)

with Tisidi

being

the

probability

that an individual has

_genotype

i

_given

its

_parents

Estimation of the selection pressures and selection differentials

Since the

_algebra

used is similar for male and female selection and since the selection is

_performed

in

_only

one

_step,

neither the index k nor the

_{index j}

_are

specified.

In

order to

_simplify

the

_algebra,

the index t is also

_suppressed.

A

_reproducer

r is characterized

_by

its

_{global genetic}

value

_h

_r

which includes its

_polygenic

value gr and its

major

locus

genotypic

value

G

r

.

The

parental

value

H

r

of a

reproducer

was defined as the

_expected

_progeny

_performance

_Xp,

_ie,

half

the

_breeding

value defined

_by

Falconer

_(1989).

It was estimated

by

the selection

index I =

H

r

corresponding

to the

expectation

of

Xp

dependent

on various

_types

of information

_according

to the case: own

_performance

_X

_r

_(scheme

I and females in scheme

_II)

or

offspring

performances

_X

_o

(males

in scheme

II)

and with the

genotypic

information at the

_{major locus, G}

_r

and

_Go.

In the standard

_method,

the selection is made on an index

supposed

to be an

_expectation

of the

parental

value

when

_ignoring

the existence of the

_major

locus: the index I is defined as a

_simple

regression

on the own

performance

value

_X

_r

(scheme

I)

or

offspring performances

X

o

(males

in scheme

_II).

The evolution of

_genetic

value of selected

_reproducers,

applying

either

_index,

has to be calculated as well as

_changes

of allele

frequencies

and

_polygenic

mean of each

_genotype.

The

_joint

_{probability density}

of the

_genetic

value

1

r

of the

_reproducer

r and of

its index I is

_{f (I’,., I).}

This

_density

is a mixture of subdensities

_O

_i

_,

_{corresponding}

to

genotypes i,.:

with Cti,

being

the

i

r

class

_frequency

_{within the considered group of}

_reproducers.

In

practice:

in

_{scheme I,}

_Cti, = aiost

for _{males and aj}=

aioat

for females

and,

!

§l &dquo;zost

!

£ CYiodt

z z

in scheme

II,

air = L Ct i2st

for males and air =

ailat

for females. The within !

£ °

12s

t

!

2-!!idt

i i

subclass

_{distributions,}

_<!(rr,7),

were assumed to be multi-normal distributed with the moments

_E

_i

_,

and

_V

_i

_,

_depending

on the

particular

case considered. The

components

of these moments are

Cj! :

2

r

h

genotypic

mean value

/

-li,

polygenic

mean of the

i!h

_major

_genotype

class

<7! :

within

_genotype

additive

_polygenic

variance

Q

p

:

within

_genotype

_phenotypic

variance

0&dquo;2

h

2

:

within

_major

_genotype

_{polygenic heritability}

h

2

₌

₂

O

&dquo;p

The within

_genotype

_variances,

_a

_g

and

_QP

_,

were

_independent

of both

_genotype

i

The within

_genotype

_polygenic

mean

_superiority

of the selected individuals is

given by

where T is the selection threshold

_(the

I value above which the candidates are

selected)

and _q the selection pressure

corresponding

to T:

Application

of these

principles

to the different cases studied is described in the

Appendix.

In all cases

_studied,

the threshold is found

iteratively,

as described

_by

Ducrocq

and

Quaas

(1988).

However, contrary

to the standard

situation,

the

_breeding

value evaluation

_taking

the

major

locus

_genotype

into account was obtained after a

two level _{iterative process: since} the

_parental

value

_H

_r

has been defined as the

progeny mean, it

depends

on the

_genotypic

structure of the selected mate

_(ms)

population

(the

aims and

/

-li

mJ

which itself

depends

on the airs and /_{-lirs of the}

selected

_reproducers

_(rs).

_Taking

as a

_{starting point}

the

genotypic

structure of the

mate

_population

before

selection,

the solution was obtained

iteratively

with a

_given

selection pressure q. In order to

simplify

the

algebra

of the young male indexes

I,

it

was assumed that the characteristics

(mean

polygenic

values and

major

genotype

frequencies)

of the female

_population

_(when

selecting

males)

could

_replace

those of their future mates.

Comparison

criteria

The value of

_including

the

_genotype

information in the

_parental

value estimation

was measured

by

the extra

genetic gain

as

compared

with the standard method.

Starting

from an initial

point

where all within

major

_genotype

classes were assumed to have

_equal

_polygenic

means

-lij

kO

/

(

_{= p}

Hi, j,

k),

the nonlinear

change

of the _aijkt

and l’ijkt over time differed between the two

parental

value estimation methods.

The evolution of the

_0-1-year

old females

_(yt

=

Z!c!odt(!t0dt

+

_{Ci) /a.Odt)}

was

used as a measure of

_genetic

_progress, but our

_primary

criterion was:

with

t

f

being

the number of years considered and

by

t

the difference between both

methods for _{year t.}

This criterion was

preferred

to the final deviation

_6y

_tf

which

_gives

_only

a

partial

a

discounting

factor in the

_{t-summations,}

and the

_comparisons

were

_finally

limited to a nondiscounted criterion. The methods were also

_{compared according}

to the evolution of the allele

_frequencies.

Cases studied

The selection methods were

_compared

for various combinations of the

_following

parameters:

Genetic

_parameters:

the within

_major

_genotype

_heritability

coefficient

_(h

₂

₎

was

given

values between 0.1 and 0.5 and the

_’major

_gene effect’ defined here as

AC =

C,9

A

-

C

BB

between 1 and 3 within

_genotype

phenotypic

standard

deviations. Allele A was dominant

(AA

= AB

= AC,

BB =

0),

additive

(AA

= 2AB =

AC,

BB =

0)

or recessive

_(AA

_{= AC,}

AB = BB =

0)

_over

the allele B. Initial

_frequency

p for allele A was tested between 0.1 and 0.9.

The

_{global heritability}

i

- o-&dquo;r -r-&dquo;r

with

_{f rq(G,.)}

the

_frequency

of

genotype G

r

),

which includes both

_polygenes

and

major

genes,

depends

on

_{polygenic heritability,}

_major

_gene effect

(both

constant)

and allele

_frequencies

_(variable

with

_time).

Initial

H

2

is

between 0.11 and 0.81

(table

II).

RESULTS AND DISCUSSION

Evolution of mean

_genetic

and

_polygenic

values

The evolution of the mean

_genetic

values of _young females is illustrated in

_figure

1

for the case of A

dominant,

additive and recessive

with h

2

=

_0.3,

_p =

_0.1,

q = 0.1 I

and AC = 2. In scheme I

(fig la),

when A is dominant or

_additive,

the difference is nil at the

_beginning

of the process. In the medium

term,

the modified method shows

a

higher

increase of mean

_{genetic value, essentially owing}

to the faster fixation of the favourable allele. In the

_long

_term,

the standard method _appears more efficient when

comparing

the final mean

_genetic

value. When allele A is

_recessive,

the modified

method is

_slightly

less efficient in the short term

_{(&mdash;0.02op),}

but from _year

_3,

this method becomes and remains more efficient than the standard selection

_(+0.08!P).

The reduced

_efficiency

of the modified method within the very first years is observed

for the

_large

_major

gene effect

(AC

= 2 or OC =

3),

but _not for OC = 1. In scheme

II

_{(fig lb),}

with the same

_parameters,

the maximal difference between both methods is lower than that observed in scheme I. When A is

_dominant,

mean

_genetic

value

is

_{always higher}

when

_applying

the modified

_method,

with a nil difference at the

beginning

that vanishes in the

_long

run

(+0.06(

7

p).

For A

_additive,

the modified

method becomes less efficient than the standard method within the first 25 _years of selection

_{(year 17).}

In the

_long

term

_{(not shown),}

the modified method becomes less efficient for A recessive but not for A dominant. Lower mean

_genetic

values are

observed for the case of A recessive in the first five

_generations

for the modified

selection

_(-0.05o-p)

_’

The lower

_efficiency

in the

_long

term of marker assisted selection or combined

selection when

_taking

into account a

_major

_gene, when effects of alleles are

_additive,

is now established

(Gibson,

1994;

Woolliams and

_Pong-Wong,

1995).

The recessive

case is not mentioned in these studies. The relative

_superiority

of one method

compared

to the other is

_dependent

on the rate of fixation of the favourable

_allele,

but also on

_polygenic

value evolution till fixation. An

_example

is

_given

in

_figure

2a and b in the case of A recessive and additive with AC =

2, h

2

=

0.3,

p = 0.1 and q = 0.1. The

_polygenic

_mean increases _more

_rapidly

when the standard indexes _are

applied.

This

phenomenon

is observed for both selection

_schemes,

with a

_stronger

effect in the case of scheme II

_during

the

_early

_years. In the case of individual

selection and A

_recessive,

this

_{tendency changes}

after fixation of the favourable effect in the modified method

_{(year 15)}

_giving

a faster increase of

_polygenic

values in this modified method as

compared

to the standard one. When the favourable

allele is fixed in the standard

_scheme,

the evolution

_patterns

become

_parallel.

In the case of scheme

II,

these

_phenomena

do _{not appear}

_during

the first 25 years of

selection.

Choice

_{of period length}

t

f

Our criterion is a measure of the

_weighted

surface between both mean

_genetic

value _curves, truncated at the final time

_t

_f

_.

The criterion

_C(t

_f

₎

reaches its maximum value for intermediate

t

f

,

as illustrated in

_figure

3 for

h

2

=

_0.3,

AC =

2,

p = 0.1

and _q = 0.10 for A recessive. In this

situation,

the maximum is achieved _at

in the case of scheme

I,

and _{at year} 22 in the case of scheme II. For A dominant

and

additive,

the maximum is lower and achieved earlier.

Figure

3 indicates that

_including

the

_major

gene information in the selection

criterion

_gives

a

_slightly

_negative

result in the very first few years,

only

in the

case of a recessive favourable allele. This is

_probably

due to the

_{nonoptimality}

of

our criterion when

_considering,

in the evaluation of the

_breeding

value I of the future

_reproducer,

the

_genotypic

structure of the

_contemporary

mate

_population

before selection as

_{fully representative}

of the whole

_genotypic

structure of the dams. An

_optimal

index should take into account the whole future mate

_population

structure. In

_fact,

this

_negative

result in the _very first few _{years appears} when the initial

_frequency

of allele A is lower than or

_equal

to 0.1

_{(not shown)}

and when allele A is recessive. In this _case, the modified method

permits

selection of AB

genotypes

instead of BB

_genotypes,

even if their

_polygenic

values are lower. The

proportion

of AB in mates is not

_{high enough}

to increase the

proportion

of AA in the _progeny

_greatly,

thus the lower

polygenic gain

is

_probably

not counterbalanced

by

the increase of AA

_genotypes.

In the

_{following discussion,}

unless otherwise

_mentioned,

the results are

_given

for

t

Major

gene and

polygenic

effects

The influence of

_heritability

and

_major

gene effect

parameters

on

_genetic

_progress

is described in

_figure

4a and

_b,

_considering

an initial allele A

_frequency

_p = 0.10

and a selection _{pressure q} = 0.10.

The

_gain

_C(t

_f

₎

decreases when the

_heritability

increases: the

greater

the extent

to which the

genetic

variation _may be

_{explained by}

the

_major

_gene, the more

it becomes worthwhile to include the

_{corresponding}

information in the

breeding

evaluation. This result was

_already

observed

_by

Smith

(1967)

who

compared

selection based on

₍₁₎

individual

_performance,

₍₂₎

known

genetic

loci and

₍₃₎

a

selection index of

₍₁₎

and

₍₂₎

on the basis of their short term _responses. Marker assisted selection is also most useful when the

_heritability

of the trait is low

_(Lande

and

Thompson, 1990;

Ruane and

_Colleau,

1995;

Meuwissen and

_Goddard,

_1996),

at least in the short term. _

The effect of the deviation between AA and BB

_depends

on the

_degree

of

dominance: the

_gain

_G(t

_f

₎

is

_higher

with

increasing major

gene effect when A is

recessive,

and lower in other situations. The main value of

_including

the

_genotypic

information in the

parental

value estimation is the

possibility

of

_selecting

carriers which do not show their

_superiority

when

_only

their

_phenotypes

are considered:

this is the case when A is recessive or when A is codominant or dominant but with a small effect.

This

_gain

_C(t

_f

₎

may be

quite important

when the favourable allele A is recessive

(up

to

200%

in scheme

_I)

but decreases when its dominance over B increases. It becomes

_nearly

nil for full dominance in scheme II. These

results,

which confirm the

_previous

_hypothesis,

could be

_{explained by}

the

_following

_arguments.

When A is recessive and

_infrequent,

the standard selection has poor

efficiency

for increase of

allele A

_frequency,

for AB and BB have the same value.

Thus,

they

have

nearly

the same chance of

being

selected if the number of

reproducers

to be retained is

higher

than the number of AA in the candidates. On the

contrary,

the modified selection

distinguishes

AB and BB

_candidates,

and thus is more efficient to increase A allele

frequency

in the short term. That is not the case when allele A is dominant or when

its

_frequency

is

_high

_enough.

This difference is also reduced in scheme II because AB and BB

_genotypes

of the

_reproducers

are more distinct with _progeny

_testing.

Allele

_frequencies

An illustration of the influence of the initial allele A

_frequency

on the difference

in

_genetic

_progress between methods is

_given

in

_figure

5 for scheme

_I,

A

_recessive,

considering

an

heritability

h

2

= 0.3 and a

_major

_gene effect OC =

_2,

reflecting

the

general findings.

In scheme

_II,

the

_gain

_C(t

_f

₎

is _very low and the differences

_owing

to the initial

frequency

p are

_negligible.

In scheme

_I,

the

_gain

reaches a maximum for small

p

values,

with the

exception

of the recessive allele A case where a maximum is obtained for intermediate values

_(0.10),

while no

_gain

is obtained with a _very small

initial p. This result is due to the

curvilinearity

of allele A

frequency

evolution with

selection. This is illustrated in

_figure

6a and b where A is recessive and q = 0.10: for

and modified methods is maximum when _p = 0.10. This is _{not true} for _a

longer

period,

when the allele A

_frequencies

_may differ between the two methods. These results

_clearly

show that the value of

_{putting genotypic}

information in the

_parental

values is

_directly

related to the acceleration of allele A fixation that it

_permits,

which in turn

_depends

on the

_{starting point}

_p.

Selection scheme and selection _pressure

Figures

3 and 4b were drawn for schemes I and II. In all the cases

_studied,

the

maximum

_gain

_C(t

_f

₎

was much

_higher

for scheme I. There

_might

be two reasons

for this difference:

₍₁₎

more

complete

information about the whole

_genetic

value of

reproducers

was available from the _{progeny test} than from the

performance

test,

thus

_diminishing

the value of

_including

_major

_gene data and

₍₂₎

the

_longer

time taken

_by

scheme II to take into account the extra information

_(ie,

to increase allele

A

_frequency)

on the

_major

_{gene in}

_parental

value evaluation. A

_comparison

based

on a

_{longer length}

_period

_tf should

_give

a

_higher

_C(t

_f

₎

in scheme II and a lower one

in scheme I

_{(cf fig 3).}

The effect of selection _{pressure q}

_depends

on the

_degree

of

_dominance,

scheme

(fig 7)

and initial allele

frequencies

(fig 5)

but in

_general,

it seems to have a _very

GENERAL DISCUSSION

We found

_that,

in

_comparison

with the traditional

_breeding

value

_estimation,

which

assumes

_polygenic

_inheritance,

the inclusion of information about the

_genotype

at a

major

locus is valuable in limited

circumstances,

which could

_roughly

be.defined as

those cases in which the standard methods are less effective at

_fixing

the favourable allele

_(very

low A initial

_frequency,

_recessivity

of

_A)

or when most of the

_gain

comes from the

_major

_gene itself

(low

heritability,

short term

_results).

The value of

including

the

_major

_gene information in the selection indexes may be very

high

in

the most favourable cases

(200%

increase of the

genetic

gain),

but it is more often

low or

slightly

_negative.

The situation of additive

_QTL

was studied

_by

others with

_divergent

results.

Negative long

term results were obtained

_by

Gibson

(1994)

and Woolliams and

Pong Wong

(1995).

On the

_contrary,

_Zhang

and Smith

_(1992),

Gimelfarb and Lande

(1994)

found

_positive

extra rates of

_genetic

_responses with marker-assisted selection based on the use of

_{linkage disequilibrium,}

a situation much less favourable than ours

_owing

to the

progressive disappearance

of

_marker-C!TL

associations.

_However,

in all these

_studies,

a diminution of the

_superiority

of the modified methods when

considering

more

_generations

is constant. The

_divergences

between results _may come

from the characteristics of the genes

studied,

number of

generations

simulated as

well as

_type

of

_modelling

used. The

_{higher efficiency}

of methods

_accounting

for

higher

initial favourable _gene

_frequency

was

_already

shown

_by

Smith

₍₁₉₆₇₎

for an

additive

_major

gene and

by

many others for additive marker

QTL

(eg,

Lande and

Thompson,

1990;

Gimelfarb and

_{Lande, 1994;}

Edwards and

_{Page, 1994;}

Ruane and

Colleau,

1995,

1996).

Contrary

to

_others,

our criterion for

_evaluating

the

_efficiency

of alternative methods did not consider

_only

the mean

_genetic

level or _gene

_frequency

at a

_given

time but included the

_dynamics

of the evolution due to selection. We

_emphasized

that most of the selection schemes are able to fix favourable alleles and the differences between schemes are to be

_appreciated

in the way

they

reach this state.

This

_modelling

is classical for the

_comparison

of selection

_plans

and needed for their economic evaluation.

Our model assumed an infinite number of loci and

_population

size and considered

only

the evolution of

_major

_genotype

_frequencies

and mean

_polygenic

values with selection.

_{Linkage disequilibrium}

between

_major

_{gene and the}

_polygenes

was

automatically

accounted for in the

_model,

but not the Bulmer effect within

_major

genotype.

The

_{corresponding}

reduction in

_polygenic

variance should occur in both standard and modified selection schemes. Whether this reduction is

_higher

in the modified or standard forms is far from obvious for three reasons.

_First,

as

_compared

to the standard

_situation,

the modified method induced a weaker selection pressure

on

_polygenes

within favourable

_genotypes,

and a

_stronger

one within unfavourable

genotypes.

Second,

the individuals of a

_given

_genotype

_may have _progeny of different

genotypes

(BB

giving

for instance AB

_offspring,

and even AA

grand-offspring)

with a

_{corresponding}

redistribution of

_polygenic

variation.

_Third,

the evolutions of allele

frequencies

at a

_polygene

on the one

_hand,

and of

_linkage

_{disequilibrium}

between

polygene

loci on the other

_depend

on their location relative to the

_major

locus. Thus a full model should describe not

_only

this

_possible

variance reduction but also should deal with the

_linkage

between the

_major

locus and some of the minor loci

controlling

the trait. In a simulation of standard and modified selection schemes of

type

I

_describing

the

_polygenic

value as the sum of identified

_QTL

_(defined

_by

their location on the _genome and allele

_effect),

Fournet et al

_(1995,

₁₉₉₇₎

did not find

any

significant

difference in

polygenic

variance reduction between selection schemes.

Finally,

the Bulmer effect is most

_important

at the

_beginning

of a selection scheme

while modification of a selection scheme to account for the

_segregation

of a

_major

gene should occur in an

_already

_{running scheme, minimizing}

this effect.

This

_study

_only

dealt with a

_possible

_change

in

_breeding

value estimations

without any modification of the selection

plan.

The information

_given

_by

_genotypes

at a

_major

locus _may be used to

_change

the

_organization

of the selection scheme itself. The most effective for schemes

_type

II would

_probably

be a

_preselection

of

young males based on their own

_genotype

before

(or

_by

_replacing)

their progeny

test: Smith

_(1967),

Soller

_(1978),

_Gomez-Raya

and Gibson

_(1993).

This kind of

preselection

was studied when

_QTLs,

_indirectly

detected

_through

the use of marker

information,

were known

(eg,

Soller and

_Beckmann,

_1983;

Kashi et

_al,

_1990;

Meuwissen and Van

_Arendonk,

_1992;

_Brascamp

et

_al,

_1993).

A

_dynamic

model similar to the model used in this _paper could

_yield

more information on the

efficiency

REFERENCES

Brascamp EW,

Van Arendonk

JAM,

Groen AF

₍₁₉₉₃₎

Economic

appraisal

of the

utiliza-tion of

_genetic

markers in

_dairy

cattle

_breeding.

J

_Dairy

Sci

_76,

1204-1213

Caballero

_{A, Keightley PD,}

Hill WG

₍₁₉₉₁₎

_Strategies

for

_increasing

fixation

_{probabilities}

of recessive mutations. Genet Res Camb

_58,

129-138

Cockett

_NE,

Jackson

_{SP, Shay T,}

Nielsen

_D,

Moore

SS,

Steele

_MR,

Barendse

_W,

Green

RD,

Georges

M

₍₁₉₉₄₎

Chromosomal localisation of the

callipyge

gene in

sheep

(Ovis

aries)

using

bovine DNA markers. Proc Natl Acad

Sci, USA,

91

Davis

GH,

McEwan

_{JC, Fenessy PF,}

Dodds

KG, Farquhar

PA

₍₁₉₉₁₎

Evidence for the

presence of a

_major

_gene

_influencing

ovulation rate on the X chromosome of

_sheep.

Biol.

_{Reprod. 44,}

620-624

Ducrocq

V, Quaas

RL

₍₁₉₈₈₎

Prediction of

_genetic

response to truncation across

genera-tions. J

_Dairy

Sci

_71,

2543-2553

Edwards

_{MD, Page}

NJ

₍₁₉₉₄₎

Evaluation of marker-assisted selection

through

computer

simulation. Theor

_Appl

Genet

88,

676-382

Elsen

JM, Mocquot

JC

₍₁₉₇₄₎

Recherches _pour une rationalisation

technique

des schemas de selection des bovins et des ovins. Bulletin

_Technique

du

Département

de

Genetique

Animale 17,

INRA,

Paris

Falconer DS

₍₁₉₈₉₎

Introduction to

_Quantitative

Genetics.

_{Longman, London,}

3rd ed Fournet

F, Hospital F,

Elsen JM

₍₁₉₉₅₎

A FORTRAN program to simulate the evolution

of

_{genetic variability}

in a small

_{population. Comput}

Applic

Biosci _11, 469-475

Fournet

_F,

Elsen

JM,

Barbieri

ME,

Manfredi E

₍₁₉₉₇₎

Effect of

_{including major}

gene

information in mass selection: a stochastic simulation in a small

population.

Genet Sel

Evol,

29, 35-56

Gibson JP

₍₁₉₉₄₎

Short term

_gain

at the expense of

long

term response with selection on

identified loci. In: Proc 5th World

_Gong

Genet

_Appl

Livest Prod

_{21, 201-204}

Gimelfarb

A,

Lande R

₍₁₉₉₄₎

Simulation of marker assisted selection in

_hybrid

popula-tions. Genet Res Camb

63,

39-47

Gomez-Raya L,

Gibson JP

₍₁₉₉₃₎

_{Within-family}

selection at an otherwise unselected locus

in

_dairy

cattle. Genome 36, 433-439

Grosclaude F, Mahe

_{MF, Brignon G,}

Distasio

_L,

Jeunet R

₍₁₉₈₇₎

A Mendelian

poly-morphism underlying

quantitative variations of _goat a-Sl casein. Genet Sel Evol 19,

399-412

Hanset

R,

Michaux C

₍₁₉₈₅₎

On the

_genetic

determinism of muscular

_hypertrophy

in the

Belgian

White and Blue cattle breed. I.

_Experimental

data. Genet Sel

Evol 17,

359-368

Hill WG

₍₁₉₇₄₎

Prediction and evaluation of response to selection with

overlapping

generations. Anim

Prod

18,

117-140

Hoeschele I

₍₁₉₉₀₎

Potential

gain

from the insertion of

_major

_genes into

dairy

cattle. J

_Dairy

Sci 73, 2601-2618

Kashi

_Y,

Hallerman E, Soller M

₍₁₉₉₀₎

Marker-assisted selection of candidate bulls for

progeny

testing

programmes. Anim Prod

51,

63-74

Lande

R, Thompson

R

₍₁₉₉₀₎

Efficiency

of marker assisted selection in the

_improvement

of

quantitative

traits. Genetics

124,

743-756

Le

_{Roy P,}

Naveau

_J,

Elsen

JM,

Sellier P

₍₁₉₉₀₎

Evidence for a new

_major

_gene

_influencing

meat

_quality

in

_pigs.

Genet Res Camb 55, 33-40

Meuwissen

_THE,

Van Arendonk JAM

₍₁₉₉₂₎

Potential

_improvements

in rate of

_genetic

gain

from marker-assisted selection in

_dairy

cattle

_breeding

schemes. J

_Dairy

Sci

_75,

1651-1659

Meuwissen _THE, Goddard ME

₍₁₉₉₆₎

The use of marker

_haplotypes

in animal

_breeding

M6rat

_P,

Ricard FH

₍₁₉₇₄₎

Etude d’un

_gene

de nanisme lie au sexe chez la

_poule:

importance

de 1’6tat

_{d’engraissement}

et

_gain

de

_poids

chez 1’adulte. Ann Genet Sel Anim

_{6, 211-217}

Ollivier L

₍₁₉₈₀₎

Le d6terminisme

_g6n6tique

de

_{l’hypertrophie}

musculaire chez le Pore. Ann Genet Sel Anim _12, 383-394

Piper LR,

Bindon BM

₍₁₉₈₂₎

The Booroola Merino and the

_performance

of medium

non-peppin

crosses at Armidale. In: The Booroola Merino

_(LR

_Piper,

BM

Bindon,

RD

Nethery,

eds),

CSIRO, Melbourne,

9-20

Ricordeau

_G,

Bouillon

_J,

Le

_{Roy P,}

Elsen JM

₍₁₉₉₀₎

D6terminisme

g6n6tique

du debit de lait au cours _{de la traite des ch6vres. INRA Prod Anim 3, 121-126}

Ruane

J,

Colleau JJ

₍₁₉₉₅₎

Marker assisted selection for

_{genetic improvement}

of animal

populations

when a

_{single QTL}

is marked. Genet Res Camb

_{66, 71-83}

Ruane

J,

Colleau JJ

₍₁₉₉₆₎

Marker assisted selection for a sex-limited character in a

nucleas

_{breeding population.}

J

_Dairy

Sci 79, 1666-1678

Smith C

₍₁₉₆₇₎

Improvement

of metric traits

_{through specific genetic}

loci. Anim Prod _9,

349-358

Smith C

₍₁₉₈₂₎

Estimates of trends in the Halothane _{gene in}

_pig

stocks with selection.

Z

_{Tierziichtg Zuchtgsbiol}

_99, 232-240

Smith

C,

Webb AJ

₍₁₉₈₁₎

Effects of

_major

_genes on animal

_{breeding strategies.}

Z

Tier-ziichtg Zuchtgsbiol 98,

161-169

Soller M

₍₁₉₇₈₎

The use of loci associated with

_quantitative

effects in

_dairy

cattle

improvement.

Anim Prod

_27,

133-139

Soller

M,

Beckmann JS

₍₁₉₈₃₎

Genetic

_polymorphism

in varietal identification and

_genetic

improvement.

Theor

Appl

Genet

_67,

25-33

Woolliams

_{JA, Pong-Wong}

R

₍₁₉₉₅₎

Short-term versus

long-term

_{responses in}

_breeding

schemes. In:

_46th

Annual

_{Meeting of}

the

_{EAAP, Prague, 4-7 September}

1995

Zhang W,

Smith C

₍₁₉₉₂₎

Simulation of marker-assisted selection

_{utilizing linkage}

dise-quilibrium.

Theor

_Appl

Genet 83, 813-820

APPENDIX

Individual selection

Without

_genotypic

information The selection index I is

with _u, the

_general

mean and

h

2

,

the

_polygenic

_heritability

_(note

that the ranks of the candidates are not affected

_by

the value of this coefficient which could be

replaced

by

the

_global

_heritability

with no effect on the

_genetic

_progress).

The

_joint

distribution of the

_genetic

value

r

r

of the

_reproducer

r and its index I

is

_{f (]F}

_r

_{, 1),}

a mixture of subdensities

_!2r

_{corresponding}

to

_{genotypes i}

_r

_:

The moments

_E

_i

_,,

the within

genotype

expected

means of

r

r

and

I,

and

_Vir,

the variance-covariance matrix of

₁

_r

and

_I,

are

Thus the

_{marginal density}

_Ø

_ir

_(I)

of I is the normal variate

N

of

_expectation

(&mdash;(C!

+ _{/-lir -}

_/

_-t))

and variance

(&mdash;0’!),

and the

_density

_ø

_dr

_{r II)}

of

_F

_r

_given

I is the normal

_jV(Ci,

+ _lti, + 2

₍₁

-h

2(Ci,

+ _{Ai, -}

_It)),

_{a2(l - h2)).}

the normal N(Cir + /-lir

+2(7-

2 (Ci!

_{+! -!)),!(1-!)).}

Following Ducrocq

and

_Quaas

_(1988),

from

_[A2]

and

_[A3],

the

_global

selection

pressure is

given by:

where 4J is a cumulative normal function.

From

_[A2]

and

_!A4!,

the deviation

_A

_i

_,

between selected and candidate

reproduc-ers of the

irh

subclass is

_given

by:

With

_genotypic

information

The selection index I must consider the

_possible

mates with

_genotypes

_(G&dquo;,)

and

ages

(am)

The

_probability

_p(Gn,

=

im, am

=

j

m

)

will be noted

,Cj2m,!m.

The conditional

_expectation

E(XpIGp, X., G

r

, G

m

, a

m

)

is

_given

_by

( It follows that:

The first term

_{(2: p( Gp}

=

iP!Gr

=

i

r

)C

i

,,),

mean

_major

locus value of future _progeny

ip

of the sires with

_genotype

_G

_r

=

_i

_r

_depends

_on the

_genotypic

frequencies

p(G

m

)

of

their mates. It will be noted

_{Cip li}

_r’

The second term

(2 I pi,)

is half the

polygenic

value of the sires with

_genotype

Gr

=

i

r-The third term

_{(2: 2:}

_{(3im,jmMimjm)’}

the

_polygenic

value of their

mates,

depends

jm im

on their

_{genotypic frequencies.}

It will be noted _Mm.

The moments

_E

_ir

and

_Vi

_r

are:

The selection pressure

q is given

in this case

_by:

Progeny

test selection

Without

_genotypic

information The selection index I is

with _it, the

_general

mean of

_offspring,

N the number of tested

_offsprings

and

... J A 1BT J_?

The

_equation

_[Al]

becomes in this situation:

where _q is a combination

_giving

for each

_offspring

_n, the

_genotypes

and ages of the

individual and its dam and

_p(

₇

₎

its

_probability.

The moments

_Ei!.y

and

_Vi

_.

_,

are

The

_density

_</Ji

_r

_-y(I¡f

_r

₎

of I

_given

_F

_r

is the normal variate

_N(Mi

_r

_,y,

_Q2

_y),

with

It is assumed that

_{!p(!y)!i!!(I!r,.)}

is

_{approximately}

normal

_{N(Mir,QZ ),}

with

Wlth T2 = !!, p(’Y)M2!. - M2

·

Thus the

_marginal

_density

_{<! (7)}

of I is the normal variate

and the

_density

_c

_Pd

_r

_rl

_I)

of

_r

_r

_given

I is the normal

This

gives:

2

With Pir =

&mdash;&mdash;

s-

&mdash;&mdash;5-,

the

deviation

D

ir

between selected and candidate

1/47-!+7-!

reproducers

of the

_i!h

subclass is

_given

_by:

With

_genotypic

information

The selection index I is defined

_similarly

to the individual selection index with

genotype

informations:

It follows that:

As in the

_previous

case,

The moments

_E

_ir’Y

and

_Vi,-,

are in this case:

Contrary

to the

_{previous situation,}

_E

_Vr

does not

_depend

on _-y. Thus

f(f&dquo; 1)

=

¿ &OElig;

i

,ød

fr

,!)

is

_normally

distributed

_{(without approximation).}

i r