Effect of including major gene information in mass selection: a stochastic simulation in a small population

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Effect of including major gene information in mass

selection: a stochastic simulation in a small population

F Fournet, Jm Elsen, Me Barbieri, E Manfredi

To cite this version:

Original

article

Effect of

_including

_major

_gene

information

in

mass

selection:

a

stochastic

simulation

in

a

small

population

F

_Fournet,

JM Elsen

ME

Barbieri

E

Manfredi

Station d’amélioration

9

6n6tique

des

_animaux,

Institut national

de la recherche

_agronomique,

31,!20

Castanet-Tolosan,

France

(Received

5 December 1995;

accepted

18 November

₁₉₉₆₎

Summary - A

_quantitative

trait under the control of a

_major

_gene

_plus

a finite number of _genes with small effects was described

_using

a stochastic model where

_number,

size

and

_linkage

between

_QTL

may vary. Selection schemes defined

by

the selection criteria

(individual

phenotype, major

genotype and combination of both sources of

information),

the

_population

size and the selection intensities in male and female

_paths

were considered.

Different

_{genetic hypotheses}

were studied

_concerning

the

_major

_gene

effect,

the number

of small

quantitative

loci and the

linkage

between genes. The

ranking

of the selection

schemes over 30

_generations

was

performed

with the

following

criteria: time taken for the

fixation of the favourable A allele at the

major

locus and differences between the cumulated discounted

gains

obtained with each scheme. The interactions between the

major

gene and

the

_{flanking (aTLs}

were also studied. The main result was that the inclusion of

_major

_gene information in selection schemes was

_mostly

efficient in the medium and

_long

term when the gene was rare and recessive and in the medium term when it was rare and

_additive,

essentially

due to a

_rapid

fixation of the favourable A allele and to a limited risk of

_losing

it

_{by genetic}

drift for a rare recessive gene. major gene

/

QTL

/

selection

_/

Monte-Carlo

Résumé - Inclusion de l’information à un locus majeur en sélection massale : un

modèle stochastique dans une _{petite population.} Un caractère

quantitatif

sous le contrôle d’un

_{gène majeur}

et d’un nombre

_fini

de

_gènes

à

_{effets faibles}

est décrit à l’aide d’un modèle

stochastique

où le nombre de

QTL

et leur liaison peuvent varier. Plusieurs schémas de

_{sélection, dé,finis}

par leurs critères de sélection

(performance

individuelle,

génotype

au

_{gène majeur}

ou combinaison des deux _types

_{d’information),}

la taille de la

_population

et l’intensité de sélection pour les voies mâle et

femelle,

sont considérés.

Différentes hypothèses génétiques

sont

_envisagées,

concernant

_l’effet

du

gène

majeur, le nombre de

_QTL

et la liaison entre locus

_adjacents.

Le classement des schémas de sélection

à moyen et

long

terme

quand

le

gène

est rare et

_récessif,

et à moyen terme

quand

il est

rare et

_additif.

Cela est essentiellement dû à une

_{fixation rapide}

de l’allèle

_favorable

A et à

un

_risque

limité de _perte du

gène

par dérive

génétique

dans le cas d’un

_gène

_récessif

rare.

gène majeur

/

QTL

/

sélection

_/

Monte-Carlo

INTRODUCTION

Many

models

_describing

the evolution of

_genetic

_variability

in _response to selection

are based on the

_assumption

that a trait is controlled

by

an infinite number of small

independent

genes.

Nevertheless,

the evidence for a small number of

_QTL

with medium to

_large

effects on

_quantitative

traits is

_increasing

in livestock

_(M6rat

and

Ricard,

1974;

Ollivier,

1980; Piper

and

_Bindon,

_1982;

Le

_Roy

et

_al,

_1990;

_Tanksley,

1993).

To take more

_advantage

of this

_genetic

_variability

for animal

_improvement,

specific

evaluation methods and selection schemes should be

_applied

_(Smith,

_1967;

Soller, 1978;

Smith and

_{Webb, 1981; Smith, 1982; Stam, 1986; Hoeschele, 1990;}

Kennedy

et

_{al, 1990;}

McLaren et

al, 1990;

Sehested and

Mao, 1992;

Gibson,

1994;

Ruane and

_Colleau,

_1995;

Whittaker et

_{al, 1995;}

Larzul et

_al,

_1997).

These

papers

pointed

out the value of

considering

the

major

gene

characteristics,

ie,

the

favourable allele initial

_frequency,

and the

type

of

_genetic

determinism

_(dominance

or

additivity,

allele

effects).

_They

also showed that the evolution of the

_polygenic

distribution

_depends

on the _way in which

_major

_gene information is taken into

account,

with the extreme case where maximal

_{extra-response}

due to a

_segregating

locus

_(in

_proportion

of fixable locus

_effect)

is obtained when

_{counter-selecting}

the

major

gene

(Gibson,

1994).

This

_study

_attempted

to achieve a more

_precise

_description

of the

_coevolution,

due to

_selection,

of the distribution of a

_major

gene and of the other

QTLs

controlling

the selected trait. In the

_simulation,

the _genome of the individuals was described

_using

a stochastic model in which the

polygenic

inheritance was described

by

a finite number of linked _{genes with} additive effects. In

_particular,

this model

allowed a

_precise

_study

of the evolution of the

genetic

variance and the influence of the

_major

gene on its

flanking

QTLs.

The effects of three selection

methods,

for a trait measurable in the two sexes, were described. To

_simplify

the

_genetic

interpretation

of the

results,

these selection methods were all based on individuals’

phenotypes

and differed

_by

the _way in which the

_major

gene information was

included

_{(or not)}

in the selection criterion. When it was

_included,

the individual

genotypes

at the

_major

_gene and the effects of each

_possible

_genotype

on the trait were

suppposed

to be known without error.

METHODS

Description

of the model

The

_algorithm

_used,

introduced

_{by Hospital}

₍₁₉₉₂₎

and further

_{developed by}

Fournet et al

_(1995),

was based on a model which describes each individual of

are

_pooled

in sets of

_equal

size

_(the

_major

_gene

_being

located in the middle of the first

_set),

_independent

from each other but with

_linkage

within-set. Two sizes of genome were simulated in order to

_study

the critical influence of this

_parameter:

5 chromosomes with 2

_(aTLs

on each

_(total

= 10

QTLs)

and 10 chromosomes with 10

_(aTLs

on each

_(total

= 100

(aTLs).

The recombination _rates between

any

adjacent QTLs, including

the

_major

_gene

_(except

when the distance between the

major

locus and the two

_{neighbouring QTLs}

was

varied),

were

kept

identical

(0.09)

in the two situations. No interference was assumed. In this

_work,

the _genes were

biallelic and the allele effects were

_given

the values a or -a at _any

_QTL

_except

the

_major

locus.

_Genotypes

in the first

_generation

were

_given

initial

frequencies

_pi

of the favourable allele at each

_locus,

these

_{frequencies being}

drawn from a

(0,1)

uniform distribution. Once these first

_generation

_genotypes

had been

_simulated,

the

polygenic genetic

variance was calculated from:

where L is the number of

_QTLs,

and a the _{gene effect. The environmental}

variance was

_adjusted

in order to obtain a

_given

_within-major

_genotype

_heritability

h

2

=

_{or 2p. , / (oa 2P.!}

₊

₀

_{,2) e in}

the first

_generation

of selection and added to the

_polygenic

variance

_or2p.,

to obtain the

_within-major

_genotype

residual

_phenotypic

variance. This

_{approach implies}

that initial

_heritability

is constant for all cases studied

while the evolution of

_{heritability along}

_generations

varies

_according

to each case. Various

_hypotheses

were made on the

_major

_gene contribution

_(initial

_frequency

of the favourable allele

_A,

level of dominance and difference

_(G

_AA

_-G

_BS

₎

between

homozygous

genotypes).

These are detailed below. The values of the three

_possible

genotypes

were

expressed

in residual

phenotypic

standard deviation units and added

to the

_polygenic

effects to

_give

the

_genetic

values of the individuals. Environmental

effects were

_randomly

drawn from a Gaussian distribution

_!V(0,

_0’

_{e 2)}

and added to

genetic

values to

_generate

_phenotypic

values.

The

_generations

did not

_overlap.

As described

_below,

the males and females

underwent

_steps

of evaluation and directional selection. The selected individuals

were

_{randomly mated,}

their

_gametes

were formed

_by

the

_parental

chromosomes

going

through

meiosis and

_{recombination,}

and the

_offspring

_genotypes

were gen-erated

_{by pairing}

of the

_paternal

and maternal

_gametes

_(see

Fournet et

_{al, 1995,}

for technical

_details).

The new-born individuals then

_replaced

their

_parents

and

went

_through

the same

_steps,

with the same

_{cycle being performed}

until the 30th

generation

of selection was reached. An entire run of 30

_generations

of selection was

performed

100 times for each case studied. The mean values for total

_genetic

mean

and variance

_(ie,

_accounting

for the

_major

gene and the

(aTLs),

total

phenotypic

mean and

_{variance, major}

gene

frequency, (aTL’s genetic

mean and variance on the chromosome

_carrying

the

_major

gene and on the non-carrier ones, were calculated

per

generation

over the 100

_repetitions

and screened out. This

_{oligogenic model,}

Selection methods

Three different selection

_methods,

_depending

on the _{way in which} the

_major

_gene information was included in the selection

criteria,

were considered.

_They

were chosen to be as

_simple

as

_possible,

in order to avoid _any

_confusing

_parameter

that would make the results difficult to

_interpret.

In

_particular,

’Animal Model-BLUP’

techniques

were not considered

here;

this

_point

will be discussed in the Discussion and conclusion.

Phenotypic

selection: the male and female candidates were evaluated on the

basis of their own

_{performances,}

with the best ones

_being

selected as breeders. This method was considered as the standard selection

_method,

in which the

_major

_gene

information is

_ignored.

Genotypic

selection: the candidates were selected first on their

_major

_genotypes

(AA

first,

then AB and

_possibly

_BB)

and

then,

for the last

_genotype

retained,

on

their

_phenotype.

Combined selection:

_following

Larzul et al

_(1997),

the candidates were evaluated on the

expected genetic

values of their

_offspring,

calculated as the sum of the

offspring

expected

additive

_polygenic

value and their

_expected

value at the

_major

locus,

accounting

for the known

_major

_genotype

of the candidate and for the

genotype

distribution in the

_population

of mates.

These selection methods _were,

_{respectively,}

called

_{Sp, S}

_G

and

_Sc.

Comparison

criteria

Three criteria were chosen to compare the

_efficiency

of the three selection methods.

- The time taken for the fixation of the favourable allele

at the

_major

locus

described

_by

₍₁₎

the

_generation

number when the A allele

_frequency

reached

_0.95,

and

₍₂₎

the

_generation

number upon

complete

fixation.

- The differences between the cumulative discounted

gains

obtained with combined and

_phenotypic,

combined and

genotypic, genotypic

and

_phenotypic

selection methods

_(expressed

as a

_percentage

of the cumulated discounted

_gain

for the

standard

_phenotypic

selection

_method).

The cumulated discounted

_gain

for a selection method was

_{given by:}

with t the

_{generation number,}

0 the

_discounting

rate

_(assumed

to be

5%

per

year),

t

the

length

of the

_{discounting period}

and

P

t

the

_phenotypic

response from

generation

t - 1 to t for the

_given

selection method. The choice of this

_comparison

criterion was

_supported

_by

the fact

_that,

whatever the selection method

_considered,

the favourable alleles would be fixed in the

_long

_term,

but the

_dynamics

of this

fixation and of the

phenotypic

means would differ from one scheme to another.

Discounting

is a classical tool used

_{by geneticists}

(Poutous

and

_{Vissac, 1962; Hill,}

applied

to numerous selection schemes

(Soller

et

_{al, 1966; Hinks, 1970;}

Danell et

al,

1976).

Two situations were considered: in both cases 30 _years of

_selection,

but

repre-sented

_by

either six

_generations

of

_5-year

olds

_(cattle)

or 30

_generations

of

1-year

olds

_{(rabbit, poultry).}

- The differences between total

genetic

response obtained after 30 years with each

selection method were also

_given.

The statistical

_significance

of all the

_{comparisons presented}

between methods

(except

time to

_fixation)

was evaluated with a Student’s

_t-test,

using

the standard

deviations for each

_parameter

over the 100

_repetitions

of the simulation.

Cases studied

In the first

_part

of the

_study,

a

_population

of 192 individuals

_(half

_males,

half

females)

was simulated.

Twenty

five

_percent

of the males and

50%

of the females

(24

males and 48

_females)

were selected as

_parents

for the next

_generation.

A

’within-major

genotype’ heritability

of 0.25 was assumed for the selected trait. The

ranking

of selection methods was studied for various values of the

_parameters

_defining

the

major

gene, and for the two numbers of

QTLs,

in order to test the

sensitivity

of this

_ranking

to the characteristics of the genome.

Initial

_frequency

of the favourable allele

The initial

_frequency

of the favourable allele A

_fq(A)

at the

_major

locus was

_given

the values

0.1,

0.5 or 0.9.

Mode of inheritance

Three kinds of

_genetic

determinism at the

_major

_gene were tested:

_additivity

of the

two alleles A and

B,

dominance of the A

_allele,

dominance of the B allele.

Effect of the

_major

gene

The difference between the mean values of the two

_homozygotes

_(G

_AA

_-G

_BS

₎

was assumed to be

_1,

2 or 3

_within-major

genotype

phenotypic

standard deviations.

In the second

_part

of the

_study,

the evolution of the

_ranking

of the three selection methods with

_parameters

_defining

the

_population

_management

_(size

of

the

_population

and selection

_intensity)

was

_studied,

for three cases

_only,

chosen as the most informative after the

_{previous comparison:}

a recessive favourable

_allele,

with initial

_frequencies

of 0.1 or

_0.5,

and a rare additive favourable allele at the

major

locus. For all cases, a medium effect

(2

QP

)

was

_given

to the

_major

gene. Two

population

sizes N

₍₁₉₂

and 480

_individuals)

and for each

_size,

two

_proportions

_p

of selected males

₍₂₅

and

_6.25%),

were

tested,

with a small and a

large polygenic

RESULTS

Characteristics of the _genome

100

_QTLs

and a

_major

_gene

The results differed

_{widely depending}

on the

_major

_gene

effect,

_genetic

determinism or initial

_frequency

of the favourable

_allele,

as illustrated in

_figure

la and b

_showing

the evolution of the

_phenotypic

response in the three selection

methods,

with an

initial A allele

_frequency

of

_0.1,

_{respectively,}

for a _{gene of}

large

effect

(G

AA

-G

BB

=

3

QP

)

with A recessive

(fig la)

and for _a

gene of moderate effect

(G

AA

-G

BB

=

1

QP

)

with A dominant

(fig lb).

The

ranking

of the selection methods varied with the

_type

of

_major

gene, with

S

G

being

the better method and

Sp

the

worst in the first

_situation,

and the

_contrary

in the second case. As

_Sc

was

_always

intermediate between the other two

_methods,

results

_presented

in the

_following

tables will focuse on

_S

_P

and

_S

_G

_.

For a

_higher

initial

_frequency,

the differences between methods were less

_striking,

and vanished when

_fq(A)

was 0.9. Thus the discussion will focus more on results obtained with an initial

frequency

of 0.1.

Table I shows the time taken for the fixation of the favourable allele in all the situations studied. For

_{phenotypic selection,}

fixation

_speed

increased with the initial

frequency

and the

_major

_gene effect. When

_considering

an initial A allele

_frequency

of medium to

_high,

whatever the effect of _{the gene,} a recessive favourable allele was easier to select than an additive one, itself easier to select than a dominant one: if A is

_dominant,

AB animals are eliminated in the

genotypic method,

they

are ranked as AA and

kept

in the

phenotypic

method and have a

good

chance of

being

chosen in the combined

_method,

while

_maintaining

a

_high

_percentage

of the

B allele in the

_population

as

compared

with the

_genotypic

selection. The time taken

to reach fixation was thus _very

_long

when A was

_dominant,

due to the fact that

only

individual information was

used,

a well known result in

population

_genetics

(Falconer,

1981;

Larzul et

al,

1997).

When

_considering

a low initial A allele

_frequency,

the fixation of the A allele was

easier for an additive allele than a dominant _one, itself easier than a recessive one,

as

expected.

The recessive A allele was difficult to select due to the risk of

_losing

it.

Indeed,

the

_proportion

of AA

_genotypes

was almost zero and AB was rare in the

first

_generations

and if the

_polygenic

values of the few

_{heterozygotic}

animals were

low,

these animals could be eliminated at the

_beginning

of _{the selection process in}

the

_phenotypic

selection method. This

_phenomenon

was observed in the case of a

large

major

gene, where the mean A allele

frequency

reached a

plateau

at 0.91:

9%

of the runs showed a loss of the favourable

_major

allele. The

_dynamic

_aspect

of this fixation _process can be outlined. In the first

_generations,

the favourable A allele had a random risk of

being

lost due to its low

_frequency.

If and when the A allele was not

_lost,

its

_frequency

followed the evolution described

_previously

for medium

In

_{genotypic selection,}

the time taken to reach fixation

depended

only

on the

initial

_frequency

of the A allele. The fixation was

always

very fast

(in

generation

4 for a low initial

frequency

and in

generation

1 for

f q(A)

=

0.9).

Generally,

the

_ranking

of the selection methods

_concerning

time to fixation was

S

G

striking

point

on these two

_figures

was the

_{genetic lag}

in

_polygenic

_response

_during

the first

_generations

when

_selecting

first on the

_major

_gene

(S

G

):

selection _pressure was

_put

_only

on the

_major

_gene, and

_hardly

_any

_{genetic gain}

was obtained on the

QTLs.

This

_{polygenic lag}

was recovered in the case of a rare recessive favourable

allele

_{(fig 2a)}

but not in the situation of a rare dominant A allele

_(fig

_2b).

The values of the cumulated differences of discounted

_gains

between selection methods are

_presented

in tables II and III.

For the

_long

run

(table II),

rather small differences were observed between

_S

_G

and

_Sp,

_except

for a favourable A allele rare and recessive

_where,

as

_explained

before, including

the

major

gene information meant

_avoiding

the risk of

_losing

the favourable allele. In this

_situation,

the selection methods ranked from

_S

_G

to

S

P

,

with a

_superiority

of the

_genotypic

selection method over standard

_phenotypic

found between

_phenotypic

and

_{genotypic methods,}

the combined method

_being

intermediate. This

suggests

that the effort made for the fixation of the favourable

allele at the

_{major locus,}

_resulting

in a

_{polygenic lag}

in the

_genotypic

selection

The contrasts between

S

G

and

Sp

were enhanced when

considering

the short run

(table III)

and were

_generally

in favour of the

_genotypic

_method,

but with a

lower

_significance

level: the

_superiority

over the

_phenotypic

method was

_168,

105 and

34%

for a rare recessive

_major

_gene with

decreasing

effect

(3,

2 or 1

ap).

For a low initial

_frequency,

whatever the effect of the

_major

gene, the value of

S

G

versus

S

P

was

_high

for the recessive _case, medium for the additive case and low to

_negative

for the dominant case

(table III).

This was

_directly

linked to the fixation rate of the A allele

_(see

_fig

_2b).

When the initial

_frequency

was

_0.9,

the

superiority

of

S

G

over

Sp

was medium to low when A was

additive,

almost zero for A recessive and

medium to

_weakly

_negative

for A dominant. The relative

_superiority

of combined selection over

_phenotypic

selection was less

_striking

than the relative

_superiority

of

genotypic

selection over

_phenotypic

_selection,

but the trend was the same.

In

_conclusion,

the results obtained in the medium and

_long

term showed the

same

tendency,

with

S

G

being

valuable not

_only

for the recessive case but also

for the additive one in the medium term. The differences in total

genetic

response

Sp.

As it will be shown

_later,

this can be attributed to smaller loss of

_polygenic

variance in the

S

G

method. No

_significant

differences were

_observed,

neither in the

QTLs

nor in the total

genetic

response. This result was obtained

_{probably because,}

whatever the selection method

_used,

the favourable allele at the

_major

_gene would be fixed in the

_long

term. But the fixation process differs in

timing

(as

shown in

fig

2a),

leading

to a

higher phenotypic

_{response in} the first

_generations

in

S

G

,

and the

_comparison

of discounted cumulative

_{genetic gains}

enables this difference to be

demonstrated.

Generally,

as shown in

figures

la and

b,

2a and

b, S

G

provided,

in the first

generations,

a

_higher

_phenotypic

_response than

Sp

and

_S

_c

_,

due to a faster fixation of the favourable allele. This was obtained without loss of

_{polygenic variance,}

these

variances

_remaining

_very close in the three methods over the 30 _years

(fig

3a and

_b),

but at the _expense of a

polygenic

lag

which was not

_always

recovered

_(fig

_2b).

Moreover,

polygenic

variance

_might

be

_higher

in

_S

_G

_,

due to the lack of selection

in the first

generations,

individuals with poor

polygenic

values

being

retained: in

table

V,

the

_polygenic

variance

_remaining

in

_S

_G

at

_generation

5

_(this

_generation

allele in

_S

_G

₎

was 1.4 and

4.4%

higher

than the

genetic

variance obtained with

Sp

at the same

_generation,

for the cases

_{corresponding, respectively,}

to

_figure

2a

and b. This

_{might explain}

the faster evolution of

_polygenic

_response observed in

S

G

after fixation of the

_major

gene

(fig

2a and

b),

although

these differences were

not

_significant.

The influence of the

_major

_gene on the

_{flanking (aTLs}

was studied more

_precisely

with the deviation between

_{polygenic genetic}

_gain

on the chromosome

_carrying

the

_major

_gene and on the

_non-carrying

_ones,

_expressed

as a

_percentage

of the total

_polygenic

_gain.

The differences observed

_(table

_VI)

between the two kinds of

chromosomes were

_globally

_very weak

(no

_{statistically significant}

differences were

found).

For the

genotypic

selection

_method,

the

positive

difference of

gains

obtained on

the non-carrier chromosomes relative to the chromosome

_carrying

the

_major

gene

depended

only

on the initial

_frequency

of

_A,

_increasing

when

_fg(A)

was

_lower,

due

to a

longer

time taken for fixation and a

higher polygenic

lag

on the chromosome

carrying

the

_major

_gene.

_Indeed,

this selection method first concentrated on the

the

_{flanking QTLs.}

Since the

_(aTLs

were not selected

_during

these first

_generations,

the fixation of unfavourable alleles at the

(aTLs

on the chromosome

carrying

the

major

gene was not due to the Bulmer’s effect but was

produced

by

the

_genetic

linkage

between the

_major

_gene and the

_{flanking (aTLs}

_{(hitch-hiking).}

For

_phenotypic

and combined selection

methods,

interactions

_appeared

between

the effect and the allelic dominance of the

_major

gene. When the gene effect was

large,

the maximal difference was observed for A

_recessive,

then A dominant and

finally

A

_additive,

the

_opposite

_being

found for a smaller

QTL.

The difference

decreased when the initial

_frequency

increased. This was due to an earlier fixation

of the A allele when

_fg(A)

was

_higher,

with the chromosome

_carrying

the

_major

gene and the non-carrier ones

_{behaving identically}

after the fixation.

Ten

_QTLs

and a

_major

_gene

The same

study

was

performed

for a small

_polygenic

_genome

_{(10 (aTLs).}

In

_general,

the trend was the same for 100 and 10

_QTLs,

whatever the

_comparison

criteria

considered.

Therefore,

results

_presented

here for 10

_QTLs

are not as detailed as for

the 100

_(aTLs

situation.

The time taken for the fixation of the favourable allele at the

_major

_gene was

nearly

the same between the two genomes. The chance of

losing

the favourable allele

at the

_major

_gene when rare and recessive was

_{only slightly higher}

with 10

_(aTLs

as

compared

to the 100

_(aTLs

case.

_Indeed,

the risk for AB animals to be eliminated due to a

possible

low

polygenic

value,

as

explained

for 100

QTLs,

was

higher

with

10

_QTLs

as the

_polygenic

_part

of the _genome was smaller. The difference however

The cumulated differences of discounted

_gains

between the selection

methods,

for a

_long

term

_objective,

showed a

_higher

_superiority

of the

_genotypic

method over the

_phenotypic

method with 10

_QTLs

than for 100

_QTLs

_(26.6,

19.8 and

13.6%

for

10

_QTLs

versus

_24.0,

17.1 and

8.1%

for 100

_QTLs,

_{respectively,}

for a

_major

_gene of

3,

2 and 1 up with a rare recessive A

_allele).

This is consistent with the

_preceding

remark about the time taken for fixation: if the risk for the favourable allele at

the

_major

locus to be lost is

_higher

with a small

_polygenic

_genome, then a

rapid

fixation with the

genotypic

method is more valuable.

When considered in the medium

term,

the

superiority

of the

genotypic

method

followed the same trend as with 100

QTLs:

the

_superiority

of this method over the

phenotypic

method was

essentially

found for a rare recessive allele at

_{major locus,}

but in the case of 10

_QTLs,

was extended to the case of a recessive

_major

_gene

with intermediate initial

_frequency

_(C

_GP

is

6.9%

for 10

_QTLs

_against

-0.5%

for 100

_QTLs,

see table

III).

Results

_concerning

the differences in

_polygenic

variance between methods and the behaviour of the

_{QTLs flanking}

the

_{major locus,}

with 10

_QTLs,

were _very

Population

management

The main conclusion of the first

_part

of this

study

was that

taking

account of the

_major

_gene information was

_mostly

efficient for a rare recessive

_{major allele,}

whatever the size of the

_polygenic

genome.

Indeed,

the

genotypic

selection method

allowed for a

_rapid

fixation of the favourable allele at the

_{major locus,}

whereas selection based on the

phenotype

could lead to this allele

_being

lost.

The second

_part

of the

_study,

aimed at

_testing

the effect of the

_population

management

parameters,

such as

_population

size and selection

_intensity,

was then

based on this case of a rare recessive

major allele,

with a medium _gene effect

(2 ap).

Two other situations were

_{investigated:}

a recessive favourable allele at a

major

locus with intermediate initial

_frequency,

because the simulation of a small

genome

pointed

out the value of the

genotypic

method in this case

_also,

and a rare

additive A allele at a

_{major locus,}

in order to enable a

_comparison

with results in

the

_literature,

in which

additivity

was the most

_{frequent assumption.}

The

_following

results are

presented

and discussed for the case of a small

polygenic

_genome

(10

CaTLs),

because the results for 100

_(aTLs

were less

_{pronounced, although}

very

similar.

The results on the time taken for the fixation of the favourable allele showed that the risk of

losing

a rare recessive favourable allele with the

_phenotypic

selection

method was lower when

decreasing

the selection

intensity

and

increasing

the

population

size. This risk also

_appeared

in the combined selection method for a rare

additive favourable allele when the selection pressure was

_strong

and the

population

size small. The risk of

_losing

the favourable allele at the

_major

_gene then

_depended

on a combination between the

quantity

of favourable alleles in the

population

and

the

_capacity

of the selection method used to

_pick

_up the available alleles.

The differences between methods in cumulated discounted

gains,

when

consid-ered for 30

_generations,

were

_{appreciable only}

for a rare recessive favourable allele

at the

_major

gene. The

superiority

of the

genotypic

method over the

phenotypic

method was the same

(around 19%)

for _any value of N and p

except

for a

large

population strongly selected,

where this

_superiority

was

_only

12.6%.

In

_fact,

the

genetic variability

in this case seemed to be

_{large enough}

and used with sufficient

intensity

to achieve

_good

_progress with the

_phenotypic

selection

_method,

thus

re-ducing

the value of the

_genotypic

method. This

hypothesis

was

_supported

_by

the

fact that the

_highest

_{phenotypic gain}

was observed for this combination of N and _p.

The same

_phenomenon

was

pointed

out when

_considering

this

comparison

criterion for 6

_generations,

with an extension to the case of a small

_population

strongly

selected. The

_superiority

of

S

G

over

_Sp,

whatever the

population size,

was found to be

_lower,

_although

_{widely positive,}

when the selection

_intensity

was

higher

(around

60%

for p =

6.25%

against

100%

for

p =

25%).

This _was not

surprising

as the

_strong

selection

_intensity

_{provided high}

_genetic

progress in the

first

_generations,

the loss of

genetic variability

due to the selection

_(and

even more

in the small

_population)

_being

not sensitive

_enough,

at the 6th

_generation,

to reduce this progress.

observed. In the case of a rare recessive favourable allele at the

_{major locus,}

where the method

_S

_G

_appeared

to be the most

_appropriate,

the

_polygenic

variance at

generation

5 was

_higher

when the selection

_intensity

was lower. This

phenomenon

may be

explained by observing

the way in which

CaTLs

are selected

_during

the

early

generations.

With a

25%

selection

_rate,

all the AA

(1%)

and AB

(18%)

animals

_belonging

to the first

_generation

are

retained,

with

polygenic

selection

occurring

only

for the BB animals

_(with

a

6/81

selection

rate).

This lack of selection

in carrier

_genotypes

_preserves the

_{polygenic variability.}

On the

contrary,

with a

6.25%

selection rate even the AB are selected with a selection rate of 5.25 over 18

applied

to a small AB

_{subpopulation,}

_while,

in the

_phenotypic

selection

_method,

the candidate

population

(the

whole

_population)

is much

larger,

thus

leading

to

a smaller decrease in the

_{polygenic variability.}

The

_polygenic

variance in method

S

G

was

_then,

_{respectively, only}

0.9%

_higher

and

2.8%

lower than in method

_Sp

for N = 192 and N = 480

when p

=

6.25%,

_against

11.1 and

13.3%

higher

when

p =

25%.

The last

parameter

studied was the deviation between

_{polygenic genetic gains}

on the chromosome

_carrying

the

_major

_gene and the non-carrier ones. In the three cases

of

_genetic

determinism

studied,

and whatever the selection

method,

the observed deviation

_ranged

from the situation where the selected individuals were _very few

(N

=

192,

p =

6.25%),

with a

_polygenic

_gain

lower on the chromosome

carrying

the

_major

gene, to the situation where

they

were the most numerous

(N

=

_480,

p =

25%),

with a

_polygenic

_gain

_higher

on the chromosome

_carrying

the

_major

_gene

(see

table

_VII).

The first

part

of the

study

had concluded that there was a

_slight

negative

influence of the

_major

_gene on the

_flanking

_QTLs,

due to

_hitch-hiking

phenomena

during

the fixation of the

_major

_gene. This effect seems to be more

pronounced

when selection

_intensity

is

_higher

and

_population

size is smaller. On the

contrary,

in a

_large

_population

rather

_weakly

_selected,

the selection _pressure

_applied

to the chromosome

_carrying

the

_major

_{gene is} lower with

_respect

to non-carrier

ones. The

_{genetic variability}

conserved on this chromosome

during

the

_generations

taken for the fixation of the

_major

_gene is

_higher

and leads to a

_higher

_gain

on this

chromosome between the fixation and

_generation

30. But once

_again,

the observed differences were not

_significant.

This

phenomenon

should vary with the recombination rate

_(r).

To test this

hypothesis,

the

_change

of the observed deviation in

_{polygenic gain}

between the chromosome

_carrying

the

_major

_gene and the non-carrier chromosomes with the recombination rate was studied

(see

fig

4).

The behaviour of the difference was

clearly sigmoid,

with

_positive

values

_(higher

_polygenic

_gain

on the chromosome

carrying

the

_major

_gene)

for intermediate recombination rates

_(0.01-0.2),

and

negative

values elsewhere.

_During

the first

_generations

before A

_fixation,

very

little selection _pressure was

_put

on the

_(aTLs

linked to the

major locus,

with all chromosomes

_carrying

the A allele

_being

selected. For _very small recombination

rates,

the

_hitch-hiking

effect

_explains

the loss of favourable

_(aTLs

linked to the B

allele. For intermediate

distances,

recombinations occur and all the alleles at these

(aTLs

are

_kept,

without selection. When the recombination rate is

_higher

than

20-30%,

selection is

possible

on these

QTLs but,

due to residual

_linkage

with the

_major

locus,

itself submitted to a

_strong

selection _pressure, this selection affects

_only

a

for r =

_0.5,

the

(aTLs

and the

major

gene were

independent

and no difference in

polygenic gain

was found between the chromosome

carrying

the

major

gene and

DISCUSSION AND CONCLUSION

Our

_objective

was to

_study

the value of a new

_type

of

modelling

in the evaluation of selection methods

_{including major}

gene information and to describe in which conditions the information on a

_major

_gene was useful and how it could

bring

a

higher

response. The use of a stochastic model

_describing

polygenic

inheritance

by

a finite number of

QTLs,

and

locating

the

major

_gene on a distinct

_chromosome,

allowed an

_{original approach}

to the

subject.

To achieve this

_{study, hypotheses}

were

made

concerning

the selected trait

_(measured

in both

_sexes),

the _accuracy of the

knowledge

on the

_major

_genotype

(supposed

known without

error)

and the selection

method used

_(one-stage

selection based on individual

performances).

The results

presented

above are valid under these

_assumptions,

and

_{possible changes}

of the

main conclusions when

_departing

from these

_hypotheses

are then to be discussed. The first conclusion of this

_study

is that the value of

_including

information on the individual

_genotypes

at a

_major

locus in a

_one-stage

selection

scheme,

when the selected trait is measured in both _sexes, remains _very small in

95%

of the cases

studied.

_However,

and that is the second conclusion to be underlined in this

work,

the inclusion of

_major

_gene information can

_provide

_extra-gain

in the medium and

long

term when the favourable allele at the

_major

locus is rare and recessive and in

the medium term when it is rare and additive. This is in

good

_agreement

with the

results of Larzul et al

_(1997).

_They

also found a

higher

_superiority

of the combined

method over

phenotypic

selection for the recessive case with

fq(A)

of

_0.1,

with values of

_120,

80 and

20%

for a

_decreasing

effect of

_major

_gene and

h

2

0.25.

These

values are to be

_compared

with

_71,

28 and

5%

in our model

(results

not

_presented),

where the size of the

_population

is reduced

_(thus

_diminishing

the initial available

genetic

variability)

and the selection

_intensity

is lower

_(the

_variability

is thus less

intensively

exploited).

In the two

_models,

the differences were

clearly

found to be lower for A additive and even more for A dominant.

Taking

account of the

major

gene information

essentially

leads to a faster fixation of the favourable

allele,

at

the expense of a

_{genetic lag}

in the selection of

flanking

QTLs

but without loss of

polygenic

variance. These results

_partially

_agree with Gibson

₍₁₉₉₄₎

for the additive case in the

long

term

_situation,

where the

_phenotypic

selection method is

_always

superior

to other selection methods.

Our

_study

also shows

_that,

_although

the number of loci used to simulate

polygenic

inheritance is below the threshold

required

to

_represent

the infinitesimal model

₍₁₆₀₀

_(aTLs

for De Boer and Van

Arendonk, 1995,

or 1000

(aTLs

for Fournet

and

_Elsen,

_1996),

no

_large

differences are found between the results of the two

simulated genomes

(10

and 100

_C!TLs).

For a rare recessive favourable allele at the

_{major locus,}

the value of the

_genotypic

selection method is also to diminish the risk of

_losing

the favourable A allele

_by

genetic

drift. The second

part

of the

_study

_provided

evidence of this risk in a small

population

strongly

selected,

and the

_rapid

fixation of the A allele enabled

_by

the

genotypic

method

_prevented

this risk.

As a

_{general conclusion,}

_excluding

this case of a recessive favourable

allele,

the

value of

including major

gene information is small. This result was obtained in the case of individual selection on a trait

_expressed

and measurable on the male and

(1)

The

_efficiency

of the methods

studied,

as an alternative to a standard selection

programme,

might

be

higher

when selected traits are not

_expressed

in both sexes

(milk

yield

for

_dairy

_bulls)

or not measurable in the live animals

_(carcass

_quality

in

pigs),

as shown in recent studies

_concerning

marker-assisted selection

_(Kashi

et

_al,

1990;

Meuwissen and Van

Arendonk, 1992; Brascamp

et

_{al, 1993;}

Meuwissen and

Goddard, 1996;

Ruane and

Colleau,

1996).

(2)

The _accuracy of the information on

_major

_genotypes

might

also

_temperate

the conclusions of this

_study.

Here we have assumed the

_major

_genotype

to be known without error. If the

_major

_genotype

had been estimated

given

marker

information,

the

_extra-gain

due to the inclusion of this information would have been less

_important,

due to the risk of error in the estimation.

(3)

The nature of the selection schemes used for the

comparison

may

modify

the

_strength

of our conclusions. Gibson

(1994)

and Larzul et al

₍₁₉₉₇₎

show that the effect of

_including

major

gene information is lower in the case of _progeny test

than in individual

_phenotypic

selection. This may be due to a better

knowledge

of

genetic

value when

_including

information on relatives. Larzul et al

₍₁₉₉₇₎

_proposed

this

_explanation

when

_comparing

the responses obtained with selection on own

performance

(scheme I)

and with selection on _progeny test

_{(scheme II):}

the

extra-gain

due to the inclusion of

_major

_gene information is

_higher

in scheme I than in

scheme II.

Gibson

₍₁₉₉₄₎

also

_compared

these two

schemes,

and the

_{differences, although}

in disfavour of the inclusion of

_major

_gene, were less

_important

when

_selecting

on _progeny test than on individual

performance.

These two

_examples

allow us to

conclude that the

_advantage

obtained in our work in favour of the inclusion of

major

gene information would have been less

striking

if information on relatives

had been included in the selection

criterion,

in the case of a _{progeny test} scheme

for

_example,

or when

_increasing

the

_quantity

of information used for the estimation

of the

_breeding

values,

as in the schemes

_{suggested by Kinghorn}

et al

₍₁₉₉₃₎

and Janss et

_{al (1995).}

To

_complete

these

conclusions,

and in order to evaluate how the cumulated discounted

gain

obtained in the

_genotypic

selection

_method,

for the most favourable

case

(ie,

a rare and recessive favourable allele at the

major locus,

considered

for six

_generations

of

_selection),

would

_change

when

compared

to a more

_precise

evaluation method

_(eg,

animal model

_BLUP),

the simulation of a selection method

based on true

_genetic

values was

performed. So,

a new selection method was

constructed on the basis of the combined selection method

(described

in Selection

methods),

but in which the

expected genetic

values in the

_offspring

were now

calculated from the true

_{polygenic genetic}

value of the

_parents

and from the

expected genetic

value at the

major

locus

depending

on the

_parents’

_genotypes.

The

_comparison

between the

_genotypic

and the new combined selection

methods,

when based on the true

genetic

values in the favourable case of a rare and recessive

allele of

_large

effect at the

_{major locus,}

showed an

_extra-gain

of

48.0%

in favour

of the

_genotypic

method relative to the new combined

_{method, against}

56.4%

in the

previous comparison

with the combined method based on the individual

method

S

G

obtained when

_using

an animal model. We can then consider that our

results would still hold in this situation of

_genetic

evaluation.

Finally,

the intermediate

_ranking

of the combined selection may be

surprising.

This

_ranking

was

_probably

due to the fact that in this method the candidates

were not selected on the _presence of the

_major

_gene but on its effects. A

dynamic

selection

_{method, ie,}

the choice of a

_varying

selection

_strategy,

_depending

on the

frequency

of the

_major

gene

throughout

the

generations

of

selection, might

be the

optimal

solution. REFERENCES

Brascamp

EW,

Van Arendonk

_JAM,

Groen AF

₍₁₉₉₃₎

Economic

_appraisal

of the utilisa-tion of

_genetic

markers in

_dairy

cattle

_breeding.

J

Dairy

Sci

_76,

1204-1213

De Boer

_IJM,

Van Arendonk JAM

₍₁₉₉₂₎

Prediction of addditive and dominance effects

in selected or unselected

populations

with

inbreeding.

Theor

Appl

Genet

84,

451-459

Cunningham EP, Ryan

J

₍₁₉₇₅₎

A note on the effect of the

discounting

rate and

_length

of the

_{accounting period}

on the economic value of

_{genetic improvement}

in cattle

populations.

Anim Prod

_21,

77-80

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